Abt Associates Inc. ¦ 4800 Montgomery Lane ¦
Bethesda, MD 20814 ¦ www.abtassociates.com
Abt Associates Inc.
Environmental Benefits Mapping and Analysis Program
Technical Appendices
May 2005
Prepared for
Office of Air Quality Planning and Standards
U.S. Environmental Protection Agency
Research Triangle Park, NC
Bryan Hubbell, Project Manager
Prepared by
Abt Associates Inc.
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Appendix A: Function Editor A-l
Appendix B: Monitor Rollback B-l
B .1 Monitor Rollbacks B-l
B .1.1 Percentage Rollback B-l
B .1.2 Incremental Rollback B-2
B .1.3 Rollback to a Standard B-2
Appendix C: Air Pollution Exposure Estimation Algorithms C-l
C . 1 Direct Modeling C-2
C .2 Closest Monitor C-2
C .2.1 Closest Monitor - Temporal Scaling C-3
C .2.2 Closest Monitor - Spatial Scaling C-4
C .2.3 Closest Monitor - Temporal and Spatial Scaling C-5
C .3 Voronoi Neighbor Averaging (VNA) C-6
C .3.1 Voronoi Neighbor Averaging (VNA) - Temporal Scaling C-9
C .3.2 Voronoi Neighbor Averaging (VNA) - Spatial Scaling C-10
C .3.3 Voronoi Neighbor Averaging (VNA) - Temporal & Spatial Scaling C-l 1
C .4 Temporal and Spatial Scaling Adjustment Factors C-l 1
C .4.1 Calculation of Scaling Factors C-12
C .4.2 How BenMAP Scales Daily and Hourly Data C-12
C .5 Binned Metrics C-14
Appendix D: Types of Concentration-Response Functions & Issues in the Estimation of Adverse
Health Effects D-l
D.l Overview D-l
D . 1.1 Review Relative Risk and Odds Ratio D-l
D .2 The Estimation of Health Effect Incidence Change D-3
D.2.1 Linear Model D-3
D .2.2 Log-linear Model D-4
D .2.3 Logistic Model D-5
D .2.4 Cox proportional Hazards Model D-ll
D .3 General Issues in Estimating Health & Welfare Benefits D-l2
D .3.1 Choosing Epidemiological Studies and Developing Concentration-Response
Functions D-l2
D .4 Issues in Using Concentration-Response Functions D-l9
D.4.1 S-Plus Issue D-19
D .4.2 Thresholds D-20
D .4.3 Degree of Prematurity of Mortality D-21
D .4.4 Estimating Effects for Multiple Age Groups D-21
Appendix E: Sources of Prevalence and Incidence Data E-l
E.l Mortality E-l
E .2 Hospitalizations E-l
E .3 Emergency Room Visits for Asthma E-3
E .4 Nonfatal Heart Attacks E-4
E .5 School Loss Days E-5
E.5.1 All-Cause School Loss Rates E-5
E .5.2 Illness-Related School Loss Rates E-5
E .6 Other Acute and Chronic Effects E-6
E.6.1 Acute Bronchitis E-7
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E .6.2 Chronic Bronchitis Incidence Rate E-7
E .6.3 Chronic Bronchitis Prevalence Rate E-8
E .6.4 Lower Respiratory Symptoms E-8
E .6.5 Minor Restricted Activity Days (MRAD) E-8
E .6.6 Work Loss Days E-8
E .7 Asthma-Related Health Effects E-8
E.7.1 Asthma Attacks E-9
E .7.2 Asthma Exacerbation E-9
E .7.3 Shortness of Breath E-9
E .7.4 Wheeze E-10
E .7.5 Cough E-10
E .7.6 One or More Symptoms E-10
E .7.7 Chronic Asthma E-10
E .7.8 Upper Respiratory Symptoms E-10
E .7.9 Asthma Population Estimates E-10
Appendix F: Particulate Matter Concentration-Response Functions F-l
F .1 Long-term Mortality F-3
F . 1.1 Mortality - Mean, All Cause (Krewski et al., 2000) - Reanalysis of Pope et al.
(1995) F-3
F .1.2 Mortality - Median, All Cause (Krewski et al., 2000) - Reanalysis of Pope et al.
(1995) F-4
F . 1.3 Mortality - Median, Random Effects with Regional Adjustment (Krewski et al.,
2000) - Reanalysis of Pope et al. (1995) F-4
F . 1.4 Mortality - Median, Random Effects with Independent Cities (Krewski et al.,
2000) - Reanalysis of Pope et al. (1995) F-5
F .1.5 Mortality (Krewski et al., 2000) - Reanalysis of Dockery et al. (1993) F-5
F .1.6 Mortality, All Cause (Pope et al., 1995) F-6
F .1.7 Mortality, All Cause (Dockery et al., 1993) F-7
F .1.8 Mortality, All Cause (Pope et al., 2002) - Based on ACS Cohort F-7
F .1.9 Mortality, Cardiopulmonary (Pope et al., 2002) - Based on ACS Cohort .... F-9
F .1.10 Mortality, Lung Cancer (Pope et al., 2002) - Based on ACS Cohort F-10
F .1.11 Infant Mortality (Woodruff et al., 1997) F-12
F .2 Short-term Mortality F-14
F.2.1 Short-Term Mortality, Non-Accidental (Fairley, 2003) F-14
F .2.2 Short-Term Mortality, Non-Accidental (Ito, 2003) F-14
F .2.3 Short-Term Mortality, Non-Accidental (Klemm and Mason, 2003) F-15
F .2.4 Short-Term Mortality, Non-Accidental (Moolgavkar, 2003) F-15
F .2.5 Short-Term Mortality, Non-Accidental (Schwartz et al., 1996) F-16
F .2.6 Short-Term Mortality, Non-Accidental (Schwartz, 2003) F-17
F .2.7 Short-Term Mortality, Chronic Lung Disease - Lag Adjusted (Schwartz et al.,
1996) F-18
F .3 Chronic Illness F-20
F .3.1 Chronic Bronchitis (Abbey et al., 1995c, California) F-20
F .3.2 Chronic Bronchitis (Schwartz, 1993) F-21
F .4 Hospitalizations F-29
F .4.1 Hospital Admissions for All Respiratory (Burnett et al., 1997, Toronto) .... F-29
F .4.2 Hospital Admissions for All Respiratory (Burnett et al., 2001, Toronto) .... F-31
F .4.3 Hospital Admissions for All Respiratory (Schwartz, 1995, New Haven) . . . F-33
F .4.4 Hospital Admissions for All Respiratory (Schwartz, 1995, Tacoma) F-34
F .4.5 Hospital Admissions for All Respiratory (Thurston et al., 1994, Toronto) . . F-34
F .4.6 Hospital Admissions for Asthma (Burnett et al., 1999, Toronto) F-36
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F .4.7 Hospital Admissions for Asthma (Lin et al., 2002, Toronto) F-38
F .4.8 Hospital Admissions for Asthma (Sheppard et al., 1999; Sheppard, 2003) . . F-42
F .4.9 Hospital Admissions for Asthma (Thurston et al., 1994, Toronto) F-44
F .4.10 Hospital Admissions for Chronic Lung Disease (Lippmann et al., 2000; Ito,
2003) 1-45
F .4.11 Hospital Admissions for Chronic Lung Disease (Moolgavkar, 2000c;
Moolgavkar, 2003) F-46
F .4.12 Hospital Admissions for Chronic Lung Disease (Moolgavkar et al., 1997,
Minneapolis) F-49
F .4.13 Hospital Admissions for Chronic Lung Disease (Schwartz, 1994a, Minneapolis)
F-49
F .4.14 Hospital Admissions for Chronic Lung Disease (less Asthma) (Burnett et al.,
1999, Toronto) F-50
F .4.15 Hospital Admissions for Chronic Lung Disease (less Asthma) (Moolgavkar,
2000c) F-51
F .4.16 Hospital Admissions for Chronic Lung Disease (less Asthma) (Samet et al.,
2000, 14 Cities) F-52
F .4.17 Hospital Admissions for Chronic Lung Disease (less Asthma) (Schwartz, 1994b,
Detroit) F-53
F.4.18 Hospital Admissions for Pneumonia (Burnett et al., 1999, Toronto) F-54
F .4.19 Hospital Admissions for Pneumonia (Lippmann et al., 2000; Ito, 2003) .... F-55
F .4.20 Hospital Admissions for Pneumonia (Moolgavkar et al., 1997, Minneapolis)
F-56
F .4.21 Hospital Admissions for Pneumonia (Samet et al., 2000, 14 Cities) F-57
F .4.22 Hospital Admissions for Pneumonia (Schwartz, 1994a, Minneapolis) F-58
F .4.23 Hospital Admissions for Pneumonia (Schwartz, 1994b, Detroit) F-59
F .4.24 Hospital Admissions for All Cardiovascular (Burnett et al., 1997, Toronto)
F-59
F .4.25 Hospital Admissions for All Cardiovascular (Moolgavkar, 2000b; Moolgavkar,
2003) F-62
F .4.26 Hospital Admissions for All Cardiovascular (Samet et al., 2000, 14
Cities) F-65
F .4.27 Hospital Admissions for Dysrhythmias (Burnett et al., 1999, Toronto) F-66
F .4.28 Hospital Admissions for Dysrhythmia (Lippmann et al., 2000; Ito, 2003) . . F-67
F .4.29 Hospital Admissions for Congestive Heart Failure (Lippmann et al., 2000; Ito,
2003) F-68
F .4.30 Hospital Admissions for Ischemic Heart Disease (Lippmann et al., 2000; Ito,
2003) 1-69
F .5 Emergency Room Visits F-72
F .5.1 Emergency Room Visits for Asthma (Norris et al., 1999) F-72
F .5.2 Emergency Room Visits for Asthma (Schwartz et al., 1993, Seattle) F-73
F .6 Acute Effects F-75
F .6.1 Acute Bronchitis (Dockery et al., 1996) F-75
F .6.2 Acute Myocardial Infarction (Heart Attacks), Nonfatal (Peters et al., 2001)
F-75
F .6.3 Any of 19 Respiratory Symptoms (Krupnick et al., 1990) F-77
F .6.4 Lower Respiratory Symptoms (Schwartz and Neas, 2000) F-80
F .6.5 Lower Respiratory Symptoms (Schwartz et al., 1994) F-81
F .6.6 Minor Restricted Activity Days: Ostro and Rothschild (1989) F-82
F .6.7 School Loss Days, All Cause (Chen et al., 2000) F-83
F .6.8 School Loss Days, All Cause (Gilliland et al., 2001) F-84
F .6.9 School Loss Days, All Cause (Ransom and Pope, 1992, Provo) F-85
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F .6.10 School Loss Days, All Cause (Ransom and Pope, 1992, Orem) F-86
F .6.11 School Loss Days, Illness-Related (Gilliland et al., 2001) F-88
F .6.12 School Loss Days, Respiratory Illness-Related (Gilliland et al., 2001) F-89
F .6.13 Work Loss Days (Ostro, 1987) F-90
F .7 Asthma-Related Effects F-95
F .7.1 Acute Bronchitis (McConnell et al., 1999) F-95
F .7.2 Asthma Attacks (Whittemore and Korn, 1980) F-96
F .7.3 Asthma Exacerbation, Cough (Ostro et al., 2001) F-97
F .7.4 Asthma Exacerbation, Cough (Vedal et al., 1998) F-99
F .7.5 Asthma Exacerbation, Moderate or Worse (Ostro et al., 1991) F-100
F .7.6 Asthma Exacerbation, One or More Symptoms (Yu et al., 2000) F-100
F .7.7 Asthma Exacerbation, Shortness of Breath (Ostro et al., 1995) F-101
F .7.8 Asthma Exacerbation, Shortness of Breath (Ostro et al., 2001) F-102
F .7.9 Asthma Exacerbation, Wheeze (Ostro et al., 2001) F-104
F .7.10 Chronic Phlegm (McConnell et al., 1999) F-106
F .7.11 Upper Respiratory Symptoms (Pope et al., 1991) F-108
F .8 Welfare Effects F-110
F .8.1 Household Soiling Damage (ESEERCO, 1994) F-110
Appendix G: Ozone Concentration-Response Functions G-l
G . 1 Short-term Mortality G-3
G.l.l Short-Term Mortality, Non-Accidental (Fairley, 2003) G-3
G .1.2 Short-Term Mortality, Non-Accidental (Ito and Thurston, 1996, Chicago) . . G-4
G.1.3 Short-Term Mortality, Non-Accidental (Kinney et al., 1995, Los Angeles) . G-4
G .1.4 Short-Term Mortality, Non-Accidental (Moolgavkar et al., 1995, Philadelphia)
G-5
G.1.5 Short-Term Mortality, Non-Accidental (Samet et al., 1997, Philadelphia) .. G-5
G . 1.6 Short-Term Mortality, Non-Accidental (World Health Organization (WHO)
Working Group, 2003, Europe) G-6
G .2 Chronic Illness G-9
G.2.1 Chronic Asthma (McDonnell et al., 1999) G-9
G .3 Hospital Admissions G-l2
G .3.1 Hospital Admissions for All Respiratory (Burnett et al., 1997, Toronto) . . . G-12
G .3.2 Hospital Admissions for All Respiratory (Burnett et al., 2001, Toronto) . . . G-13
G .3.3 Hospital Admissions for All Respiratory (Schwartz, 1995, New Haven) .. G-14
G .3.4 Hospital Admissions for All Respiratory (Schwartz, 1995, Tacoma) G-15
G .3.5 Hospital Admissions for All Respiratory (Thurston et al., 1994, Toronto) . G-16
G .3.6 Hospital Admissions for Asthma (Burnett et al., 1999, Toronto) G-17
G .3.7 Hospital Admissions for Asthma (Sheppard et al., 1999, Seattle) G-18
G .3.8 Hospital Admissions for Asthma (Thurston et al., 1994, Toronto) G-19
G .3.9 Hospital Admissions for Chronic Lung Disease (Moolgavkar et al., 1997,
Minneapolis) G-19
G .3.10 Hospital Admissions for Chronic Lung Disease (less Asthma) (Burnett et al.,
1999, Toronto) G-20
G .3.11 Hospital Admissions for Chronic Lung Disease (less Asthma) (Schwartz, 1994b,
Detroit) G-21
G .3.12 Hospital Admissions for Pneumonia (Burnett et al., 1999, Toronto) G-21
G .3.13 Hospital Admissions for Pneumonia (Moolgavkar et al., 1997, Minneapolis)
G-22
G .3.14 Hospital Admissions for Pneumonia (Schwartz, 1994b, Detroit) G-23
G .3.15 Hospital Admissions for Pneumonia (Schwartz, 1994a, Minneapolis) .... G-23
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G .3.16 Hospital Admissions for All Cardiovascular (Burnett et al., 1997, Toronto)
G-24
G .3.17 Hospital Admissions for Dysrhythmia (Burnett et al., 1999, Toronto) .... G-25
G .4 Emergency Room Visits G-28
G .4.1 Emergency Room Visits for Asthma (Cody et al., 1992, Northern NJ) .... G-28
G .4.2 Emergency Room Visits for Asthma (Jaffe et al., 2003) G-28
G .4.3 Emergency Room Visits for Asthma (Norris et al., 1999) G-29
G .4.4 Emergency Room Visits for Asthma (Schwartz et al., 1993, Seattle) G-29
G .4.5 Emergency Room Visits for Asthma (Stieb et al., 1996, New Brunswick) . G-30
G .4.6 Emergency Room Visits for Asthma (Weisel et al., 1995, Northern NJ) . . . G-31
G .5 Acute Morbidity G-33
G .5.1 Any of 19 Respiratory Symptoms: Krupnick (1990) G-33
G .5.2 Minor Restricted Activity Days: Ostro and Rothschild (1989) G-35
G .5.3 School Loss Days, All Cause (Chen et al., 2000) G-37
G .5.4 School Loss Days, All Cause (Gilliland et al., 2001) G-38
G .5.5 School Loss Days, Illness-Related (Gilliland et al., 2001) G-39
G .5.6 School Loss Days, Respiratory Illness-Related (Gilliland et al., 2001) .... G-41
G .5.7 Worker Productivity: Crocker and Horst (1981) G-42
G .6 Asthma-Related Effects G-45
G.6.1 Asthma Attacks (Whittemore and Korn, 1980) G-45
G .6.2 Asthma Exacerbation, Cough (Ostro et al., 2001) G-45
G .6.3 Asthma Exacerbation, Shortness of Breath (Ostro et al., 1995) G-47
G .6.4 Asthma Exacerbation, Shortness of Breath (Ostro et al., 2001) G-47
G .6.5 Asthma Exacerbation, Wheeze (Ostro et al., 2001) G-49
Appendix H: Economic Value of Health Effects H-l
H.l Overview of Valuation H-l
H.2 Mortality H-3
H.2.1 Value of a Statistical Life Based on 26 Studies H-3
H.2.2 Value of a Statistical Life Based on Selected Studies H-3
H.3 Chronic Illness H-4
H.3.1 Chronic Bronchitis H-4
H.3.2 Chronic Bronchitis Reversals H-7
H.3.3 Chronic Asthma H-7
H.3.4 Non-Fatal Myocardial Infarctions (Heart Attacks) H-8
H.4 Hospital Admissions & Emergency Room Visits H-10
H.4.1 Hospital Admissions H-ll
H.4.2 Emergency Room Visits for Asthma H-12
H.5 Acute Symptoms and Illness Not Requiring Hospitalization H-13
H.5.1 Acute Bronchitis in Children H-l4
H.5.2 Upper Respiratory Symptoms (URS) in Children H-l5
H.5.3 Lower Respiratory Symptoms (LRS) in Children H-16
H.5.4 "Any of 19 Respiratory Symptoms" H-16
11.5.5 Work Loss Days (WLDs) 11-17
H.5.6 Minor Restricted Activity Days (MRADs) H-17
H.5.7 Asthma Exacerbation H-l8
H.5.8 School Loss Days H-18
Appendix I: Uncertainty & Pooling 1-1
I.1 Uncertainty 1-1
I.1.1 Characterization of Uncertainty Surrounding Incidence Changes 1-1
1.1.2 Characterization of Uncertainty Surrounding Dollar Benefits 1-2
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1.2 Pooling 1-3
1.2.1 Weights Used for Pooling 1-3
1.2.2 The Mechanics of Pooling in BenMAP 1-8
1.2.3 Summing Distributions 1-9
1.2.4 Subtracting Distributions 1-9
References J-l
vi
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Appendix A: Function Editor
The function editor is used to develop both health impact functions and valuation functions. This
appendix describes the syntax of this editor.
A.l User Defined Variables
In addition to pre-defined variables that you can select from the Available Variables list, you can create
your own variables in the C-R Function Editor.
A variable is an identifier whose value can change at runtime. Put differently, a variable is a name for a
location in memory; you can use the name to read or write to the memory location. Variables are like
containers for data, and, because they are typed, they tell the compiler how to interpret the data they hold.
The basic syntax for a variable declaration is
var identifierList: type;
where identifierList is a comma-delimited list of valid identifiers and type is any valid type. For example,
var I: Integer;
declares a variable I of type Integer, while
var X, Y: Real;
declares two variables~X and Y—of type Real.
Consecutive variable declarations do not have to repeat the reserved word var:
var
X, Y, Z: Double;
I, J, K: Integer;
Digit: 0..9;
IndicatorName: String;
Okay: Boolean;
Variables can be initialized at the same time they are declared, using the syntax
var identifier: type = constantExpression;
where constantExpression is any constant expression representing a value of type type. Thus the
declaration
var I: Integer = 7;
is equivalent to the declaration and statement
var I: Integer;
A-l
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Appendix A. Data Setup
I:=7;
Multiple variable declarations (such as var X, Y, Z: Real;) cannot include initializations, nor can
declarations of variant and file-type variables.
A.2 The Script Language
In the C-R Function Editor, you can evaluate complex block of statements.
You can use constructions like:
If...then...else;
for I:= ... to .. do ;
while... do ;
repeat.... until...;
break;
assignment
try...finally...end;
try...except...end;
Each function you create can be a single statement or a block of statements.
When you specify it as a block of statements, your script must conform to the rules of the script language,
as follows:
1. Each single statement must end with a semicolon (;)
2. You can use the following statements:
variable := expression;
If logical expression then statement(s) [else statements)];
for variable :=from expression to/downto to expression do statement(s);
while logical expression do statement(s);
repeat statement(s) until logical expression;
try statement(s) finally statement(s) end;
try statement(s) except statement(s) end;
inline comments: // comment... until the end of the line
nested comments: { nested comment}
Statement(s) in the above declarations states that you can specify either a single statement or a block of
statements. The block of statements must be enclosed in begin ... end keywords. It is not necessary to
enclose the body of the function in begin .. end. Cycle statements can use break keyword to break the
cycle (break must also end with semicolon.)
A.3 Operands
A-2
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Appendix A. Data Setup
Expressions may contain following constant and variable types:
Integer numbers;
Floating point numbers;
Scientific numbers;
Decimal separator for all floating point and scientific-format numbers in expressions, is independent of
the Regional Settings of Windows and always is a decimal point
Boolean values - TRUE or FALSE;
Date type values - values of that type must be put in quotes (''and also date separator character is
independent of the Regional Settings of Windows and always is a slash - /, i.e. - '01/01/2005'
Sstring values - values of that type must be put in double quotes (" "); If a string contains double quotes,
you should double them(i.e., "this is a ""string );
A.4 Operations
Arithmetical
+ - * /•
div - integer division;
mod - modulo;
A - power of;
- - negate;
<<=>=> <> =•
? ? ? ? ? ?
Logical
and, or, xor, not;
Bitwise
and, or, xor;
~ - negate;
A.5 Arithmetic Functions
ABS(X) absolute value
SQR(X) square = XA2 = X*X
SQRT(X) square root
SIGN(X) sign of X; = 1 for X>0, =0 for X=0, =-1 for X<0
ZERO(X) =0 for X=0, = 1 for X<>0
TRUNC(X)=INT(X) integer part
FRAC(X) fractional part
ROUND(X) rounds X to the nearest integer value
CEIL(X) always returns "ceil" integer value
A-3
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Appendix A. Data Setup
FLOOR(X) always returns "floor" integer value
DEC(X) decrements a value X by 1 and returns a new value
INC(X) increments a value X by 1 and returns a new value
ARG(X,Y) argument(phase) of X and Y
RADIUS(X,Y) = sqrt(sqr(X)+sqr(Y))
POWER(X,Y) raises X to a power of Y (Y is a floating point value)
IPOWER(X,Y) raises X to a power of Y (Y is a integer value)
X A Y raises X to a power of Y (same as above two functions)
EXP(X) exponent
LN(X) natural logarithm
LG(X) decimal logarithm
LOG(X) base 2 logarithm
SIN(X) sine
COS(X) cosine
TAN(X) tangent
COTAN(X) cotangent
ASIN(X) arcsine
ACOS(X) arccosine
ATAN(X) arctangent
SINH(X) hyperbolic sine
COSH(X) hyperbolic cosine
TANH(X) hyperbolic tangent
A.6 Aggregate Functions
AVG(Xl,X2,...)returns average value of (unlimited number of) arguments.
MAX(X1,X2,...) maximum of (unlimited number of) arguments.
MIN(X1,X2,...) minimum of (unlimited number of) arguments.
SUM(Xl,X2,...)sum of (unlimited number of) arguments.
PROD(X 1 ,X2,..) product of (unlimited number of) arguments.
A-4
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Appendix B: Monitor Rollback
This Appendix details the rollback procedures that you can perform on monitor data. The
rollback procedure is a quick way to determine the monitor levels that would exist under various kinds of
changes that you can specify. This includes three basic types of rollbacks: Percentage, Increment, and
Rollback to Standard.
B .1 Monitor Rollbacks
Once a set of monitors has been selected, the user may define one or more non-overlapping
rollback regions. A region is simply a set of states with an associated set of rollback parameter values.
Three rollback types are available - Percentage Rollback, Incremental Rollback, and Rollback to a
Standard. Each of these rollback types has different rollback parameters associated with it.
B .1.1 Percentage Rollback
Percentage Rollback involves setting only two parameters - a percentage and a background
level. The rollback procedure is similarly straightforward - each observation at each monitor in the region
has the portion of its value which is above background level reduced by percentage.
Example: Background Level: 35; Percentage: 25
Initial Observations at a monitor in rollback region:
20 20 25 59 35 51 83 35 30 67 87 79 63 35 35
If we select the background level of 35, we first calculate the portion of each observation that is
above background level, that is, we subtract the background level from the initial observation level.
Observations below background level are given a value of 0.
Observation portions above background level:
0 0 0 24 0 16 48 0 0 32 52 44 28 0 0
When we apply the rollback percentage, each observation portion gets reduced by 25%.
Reduced portions above background level:
0 0 0 18 0 12 36 0 0 24 39 33 21 0 0
Then, each reduced portion is added to the background level of 35. Zero values are replaced by
the initial observations.
Reduced Observations:
20 20 25 53 35 47 71 35 30 59 74 68 56 35 35
B-l
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Appendix B. Monitor Rollback
B .1.2 Incremental Rollback
Incremental Rollback similarly involves setting only two parameters - an increment and a
background level. The rollback procedure is quite similar to the percentage rollback procedure - each
observation at each monitor in the region has the portion of its value which is above background level
reduced by increment. The reduced values are not allowed to become negative, however - that is, they
are truncated at zero.
Example: Background Level: 35; Increment: 25
Initial Observations:
20 20 25 59 35 51 83 35 30 67 87 79 63 35 35
Observation portions above background level:
0 0 0 24 0 16 48 0 0 32 52 44 28 0 0
Reduced portions above background level:
000000 23 007 27 19 30 0
Reduced Observations:
20 20 25 35 35 35 58 35 30 42 62 54 38 35 35
B .1.3 Rollback to a Standard
Rollback to a Standard has two groups of parameters - those associated with the Attainment
Test, which determines whether a monitor is in attainment (meets the standard), and those associated with
the Rollback Methods, which are used to bring out of attainment monitors into attainment.
The Attainment Test parameters are Metric, Ordinality, and Standard. A monitor is
considered in attainment if the nth highest value of the metric specified by Metric is at or below the value
specified by Standard, where n is the value specified by Ordinality. For example, if Metric is
TwentyFourHourDailyAverage, Ordinality is two, and Standard is eighty five, a monitor will be
considered in attainment if the second highest value of TwentyFourHourDaily Average is at or below
eighty five.
Supported metrics for pollutants with hourly observations (Ozone) include
FiveHourDailyAverage, EightHourDailyAverage, TwelveHourDailyAverage,
TwentyFourHourDaily Average, OneHourDailyMax, and EightHourDailyMax. Supported metrics for
pollutants with daily observations (PM10, PM2.5) include TwentyFourHourDaily Average and
Annual Average. For Annual Average, Ordinality does not apply, since there is only a single metric
value to work with.
The Rollback Method parameters are Interday Rollback Method, Interday Background
Level, Intraday Rollback Method, and Interday Background Level. These four parameters determine
B-2
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Appendix B. Monitor Rollback
the rollback procedures used to bring out of attainment monitors into attainment. The Interday Rollback
Method and Background Level are used to generate target values for the metric specified by the
Attainment Test. The Intraday Rollback Method and Background Level are used to adjust hourly
observations to meet the target metric values generated in the previous step. As such, the Intraday
Rollback Method and Background Level are used only for pollutants with hourly observations (ozone).
Interday Rollback - Generating Target Metric Values
Because standards are defined on metrics, not directly on observations, the first step in rolling
back out of attainment monitors is generating target metric values. There are four supported rollback
methods for Interday Rollbacks - Percentage, Incremental, Peak Shaving, and Quadratic. Each of these
rollback methods requires some preprocessing of the initial monitor metric values. We will discuss this
preprocessing first, and then go through Percentage, Incremental, and Peak Shaving rollbacks in turn.
Quadratic rollback is more complicated than these first three, and has its own section.
The Interday Background Level specifies the portion of each metric value which cannot be
affected by human intervention - we call this portion the non-anthropogenic portion. Whatever portion is
left over after subtracting out the background level is referred to as the anthropogenic portion. The
anthropogenic portion of the initial monitor metric values is the only part which will be affected by the
Interday Rollback Method.
BenMAP calculates an out of attainment value by determining the particular monitor metric value
which caused the monitor to be out of attainment - this value is the nth highest value of the metric
specified by the Attainment Test metric, where n is the Attainment Test ordinality. BenMAP then
calculates an anthropogenic out of attainment value by subtracting the Interday Background Level from
the out of attainment value. BenMAP also calculates an anthropogenic standard by subtracting the
Interday Background Level from the Attainment Test standard. Finally, BenMAP calculates a set of
anthropogenic metric values and a set of non-anthropogenic metric values using the following procedure
on each initial monitor metric value:
IF the metric value is less than or equal to the Interday Background Level,
non-anthropogenic metric value = metric value
anthropogenic metric value = 0
ELSE
non-anthropogenic metric value = Interday Background Level
anthropogenic metric value = metric value - Interday Background Level
Interday Rollback - Percentage
To generate target metric values using Percentage rollback, BenMAP calculates the percentage
required to reduce the anthropogenic out of attainment value to exactly the anthropogenic standard. This
percentage reduction is then applied to all of the anthropogenic metric values. Finally, these reduced
anthropogenic metric values are added to the non-anthropogenic metric values to give the final target
metric values.
B-3
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Appendix B. Monitor Rollback
Example:
Initial Metric Values:
30 35 50 100 80 44 67 88 90 70 50 30 55 90 80 85
Attainment Test: Highest value of metric <= 70
Interday Background Level: 40
Out of Attainment Value: 100
Anthropogenic Out of Attainment Value: 60 (= 100 - 40)
Anthropogenic Standard: 30 (= 70 - 40)
Percentage Reduction Required: 50% (=(60-30)/60)
Non-Anthropogenic Metric Values:
30 35 40 40 40 40 40 40 40 40 40 30 40 40 40 40
Anthropogenic Metric Values:
0 0 10 60 40 4 27 48 50 30 10 0 15 50 40 45
Reduced Anthropogenic Metric Values:
0 0 5 30 20 2 14 24 25 15 5 0 8 25 20 23
Target Metric Values:
30 35 45 70 60 42 54 64 65 55 45 30 48 65 60 63
Interday Rollback - Incremental
To generate target metric values using Incremental Rollback, BenMAP calculates the increment
required to reduce the anthropogenic out of attainment value to exactly the anthropogenic standard. This
incremental reduction is then applied to all of the anthropogenic metric values (but - they are not allowed
to fall below zero). Finally, these reduced anthropogenic metric values are added to the non-
anthropogenic metric values to give the final target metric values.
Example:
Initial Metric Values:
30 35 50 100 80 44 67 88 90 70 50 30 55 90 80 85
Attainment Test: Highest value of metric <= 70
Interday Background Level: 40
Interday Rollback Method: Incremental
Out of Attainment Value: 100
Anthropogenic Out of Attainment Value: 60
Anthropogenic Standard: 30 (=70 - 30)
B-4
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Appendix B. Monitor Rollback
Incremental Reduction Required: 30
Non-Anthropogenic Metric Values:
30 35 40 40 40 40 40 40 40 40 40 30 40 40 40 40
Anthropogenic Metric Values:
0 0 10 60 40 4 27 48 50 30 10 0 15 50 40 45
Reduced Anthropogenic Metric Values:
0 0 5 30 20 2 14 24 25 15 5 0 8 25 20 23
Target Metric Values:
30 35 45 70 60 42 54 64 65 55 45 30 48 65 60 63
Interday Rollback - Peak Shaving
To generate target metric values using Peak Shaving rollback, BenMAP simply truncates all
anthropogenic metric values at the anthropogenic standard. These reduced anthropogenic metric values
are added to the non-anthropogenic metric values to give the final target metric values.
Example:
Initial Metric Values:
30 35 50 100 80 44 67 88 90 70 50 30 55 90 80 85
Attainment Test: Highest value of metric <= 70
Interday Background Level: 40
Interday Rollback Method: Peak Shaving
Anthropogenic Standard: 30
Non-Anthropogenic Metric Values:
30 35 40 40 40 40 40 40 40 40 40 30 40 40 40 40
Anthropogenic Metric Values:
0 0 10 60 40 4 27 48 50 30 10 0 15 50 40 45
Reduced Anthropogenic Metric Values:
0 0 10 30 30 4 27 30 30 30 10 0 15 30 30 30
Target Metric Values:
B-5
-------
Appendix B. Monitor Rollback
30 35 50 70 70 44 67 70 70 70 50 30 55 70 70 70
Intraday Rollback - Adjusting Hourly Observations
Once a set of target metric values has been calculated for a pollutant with hourly observations
(e.g., Ozone), BenMAP must adjust the hourly observations so that they produce the target metric values.
There are three supported rollback methods for Intraday Rollback - Percentage, Incremental, and
Quadratic. Each of these rollback methods requires some preprocessing of the initial monitor
observations, and each can require multiple iterations to hit the target metric values. We will discuss this
preprocessing and iteration first, and then go through Percentage and Incremental rollbacks in turn.
Quadratic rollback is more complicated than these first two, and has its own section.
For various reasons, each of the Intraday Rollback methods can fail to hit the target metric
values during a single pass through the rollback procedure (these will be discussed in detail below). As
such, each of the rollback methods uses an iterative approach to get within a threshold of each of the
target metric values - currently this threshold is 0.05. The iterative approach works as follows:
For each target metric value, BenMAP calculates the current value of the Attainment Test
metric. For the first iteration, the metric value will be calculated using unadjusted hourly observations.
For subsequent iterations, the metric value will be calculated using the current values of the adjusted
hourly observations.
If the difference between the metric value and the target metric value is less than or equal to 0.05,
the rollback procedure is finished. Otherwise, another iteration is required.
The Intraday Background Level specifies the portion of each observation which cannot be
affected by human intervention - we call this portion the non-anthropogenic portion. Whatever portion is
left over after subtracting out the background level is referred to as the anthropogenic portion. The
anthropogenic portion of the initial monitor observations is the only part which will be affected by the
Intraday Rollback Method.
In a way analogous to the Interday Rollback procedure, BenMAP calculates the twenty-four
hourly anthropogenic observations and the twenty-four hourly non-anthropogenic observations using the
following procedure for each hourly observation:
IF the current value of the observation is less than or equal to the Intraday Background Level,
non-anthropogenic observation = observation
anthropogenic observation = 0
ELSE
non-anthropogenic observation = Intraday Background Level
anthropogenic observation = observation - Intraday Background Level
Given (i) an Attainment Test Metric (e.g., EightHourDailyMax), (ii) an Intraday Background
Level, and (iii) a target metric value for the day, BenMAP proceeds to adjust hourly observations in the
following steps:
1. Calculate the Attainment Test metric (e.g., the 8-hour daily maximum);
2. Identify the "window" - i.e., the set of hours used to calculate the metric (e.g., if the 8-hour daily
maximum is achieved in the first 8 hours, then the window is comprised of the first 8 hours);
B-6
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Appendix B. Monitor Rollback
3. Calculate the non-anthropogenic hourly observations (=min(hourly observation, Intraday
Background Level));
4. Calculate the anthropogenic hourly observations (=hourly observation - Intraday Background
Level);
5. Calculate the non-anthropogenic metric value (= the metric using the non-anthropogenic hourly
observations in the "window");
6. Calculate the anthropogenic metric value (= the metric using the anthropogenic hourly
observations in the "window");
7. Calculate the anthropogenic target metric value (= the target metric value minus the non-
anthropogenic metric value);
8. Calculate the reduction required to get the anthropogenic metric value down to the anthropogenic
target metric value;
9. Adjust all anthropogenic hourly observations by the reduction calculated on the previous step;
10. Calculate the adjusted hourly observations (= the adjusted anthropogenic hourly observation +
the non-anthropogenic hourly observation).
Intraday Rollback - Percentage
Below, we present two examples of a percentage-based Intraday Rollback. In one example, a
single iteration is needed, and in the second example, two iterations are required because a number of the
monitor values fall below the assumed background level.
Example: All Hourly Observations Exceed the Intraday Background (Single
Iteration)
If all of the hourly observations in a day are greater than the Intraday Background Level, then the
above procedure is straightforward and can be accomplished in a single iteration. We illustrate with the
following example. Suppose that:
Metric = EightHourDailyMax,
Target metric value for a given day = 85
Intraday Background Level = 40.
And that the hourly observations on that day are:
530 45 50 60 45 45 45 60 70 100 100 100 100 100 100 100 100 60 45 50 45 45 47 47
Based on these observations, we see that the 8-hour daily maximum =110.
Assuming a background level of 40, then the Anthropogenic hourly observations are:
490 5 10 20 5 5 5 20 30 60 60 60 60 60 60 60 60 20 5 10 5 5 7 7
B-7
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Appendix B. Monitor Rollback
Then, we know:
Anthropogenic metric value = 70.
Non-anthropogenic metric value = 40.
Anthropogenic target metric value = 45.
Percentage reduction required = ((70-45)/70) = 35.7%
All of the hourly anthropogenic observations are reduced by 35.7%. The average of the first 8
values (the window on which the Test metric is based) will be exactly 45, the anthropogenic target metric
value. Finally, the adjusted hourly observations are calculated by adding the non-anthropogenic hourly
observation to the adjusted hourly anthropogenic observations.
Example: Some Hourly Observations are Below the Intraday Background (Multiple
Iterations Required)
In the above example, the anthropogenic target metric value was met on a single iteration because
all of the hourly observations were greater than the Intraday Background Level. In this case, a simple
percent reduction of all hourly values will produce an average in the window that is equal to the
anthropogenic target metric value. If some of the hourly observations in a day are less than or equal to
the Intraday Background Level, however, then BenMAP uses an iterative procedure. On each iteration,
it adjusts hourly observations using the 10-step method given above. It then compares the new metric
value to the target metric value. If the difference is less than or equal to 0.05 ppb, the rollback procedure
is finished. Otherwise, another iteration is required. The iterative procedure is illustrated in the following
example.
Note that we are presenting an example below with an intraday background of 40 ppb. We only
use a non-zero intraday background as a sensitivity analysis in Exhibit 4-5, where we use intraday
backgrounds of 10, 20, 30, and 40. For the rest of our results we use an intraday background of 0 ppb.
Suppose that:
Metric = EightHourDailyMax,
Target metric value for a given day = 85
Intraday Background Level = 40.
Suppose also that the hourly observations on that day are:
530 20 25 60 35 35 40 60 70 100 100 100 100 100 100 100 100 60 33 40 30 30 25 20
Then, we know that the 8-hour daily maximum = 100.6.
Non-Anthropogenic Hourly Observations, Iteration One:
40 20 25 40 35 35 40 40 40 40 40 40 40 40 40 40 40 40 33 40 30 30 25 20
Anthropogenic Hourly Observations, Iteration One:
490 0 0 20 0 0 0 20 30 60 60 60 60 60 60 60 60 20 0 0 0 0 0 0
B-8
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Appendix B. Monitor Rollback
Non-Anthropogenic Metric Value: 34.4 (EightHourDailyMax - calculated over the same eight
hour window as the initial metric value was calculated
over)
Anthropogenic Metric Value: 66.3
Anthropogenic Target Metric Value: 50.6
Percentage Reduction Required: 23.6%
Reduced Anthropogenic Hourly Observations, Iteration One:
374 0 0 15 0 0 0 15 23 46 46 46 46 46 46 46 46 15 0 0 0 0 0 0
Reduced Hourly Observations, Iteration One:
414 20 25 55 35 35 40 55 63 86 86 86 86 86 86 86 86 55 33 40 30 30 25 20
Reduced Metric Value (EightHourDailyMax): 85.8
Target Metric Value (EightHourDailyMax): 85
Non-Anthropogenic Hourly Observations, Iteration Two:
40 20 25 40 35 35 40 40 40 40 40 40 40 40 40 40 40 40 33 40 30 30 25 20
Anthropogenic Hourly Observations, Iteration Two:
374 0 0 15 0 0 0 15 23 46 46 46 46 46 46 46 46 15 0 0 0 0 0 0
Non-Anthropogenic Metric Value: 40 (EightHourDailyMax - calculated over the same eight
hour window the initial metric value was calculated
over)
Anthropogenic Metric Value: 45.8
Anthropogenic Target Metric Value: 45
Percentage Reduction Required: 1.9%
Reduced Anthropogenic Hourly Observations, Iteration Two:
368 0 0 15 0 0 0 15 23 45 45 45 45 45 45 45 45 15 0 0 0 0 0 0
Reduced Hourly Observations, Iteration Two:
408 20 25 55 35 35 40 55 63 85 85 85 85 85 85 85 85 55 33 40 30 30 25 20
Reduced Metric Value (EightHourDailyMax): 85
The above example, in addition to illustrating the Intraday Percentage Rollback, also illustrates
one reason why the iterative procedure can be necessary. When using the EightHourDailyMax metric in
the Attainment Test, it is possible for the window over which the maximum eight hour average occurs to
move after a single pass through the rollback procedure. When this happens, it becomes necessary to go
through additional iterations to hit the target metric value.
B-9
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Appendix B. Monitor Rollback
Intraday Rollback - Incremental
To adjust hourly observations using Incremental rollback, BenMAP calculates the increment
required to reduce the anthropogenic metric value to exactly the anthropogenic target metric value. This
incremental reduction is then applied to all of the anthropogenic observations (but - they are not allowed
to fall below zero). Finally, these reduced anthropogenic observations are added to the non-
anthropogenic observations to give the final reduced observations.
Example:
Initial Hourly Observations:
20 20 25 60 35 35 40 70 35 30 65 90 76 65 35 35 54 60 33 40 30 30 25 20
Initial Metric Value (EightHourDailyMax): 60
Target Metric Value (EightHourDailyMax): 55
Intraday Background Level: 40
Intraday Rollback Method: Incremental
Non-Anthropogenic Hourly Observations, Iteration One:
20 20 25 40 35 35 40 40 35 30 40 40 40 40 35 35 40 40 33 40 30 30 25 20
Anthropogenic Hourly Observations, Iteration One:
0 0 0 20 0 0 0 30 0 0 25 50 36 25 0 0 14 20 0 0 0 0 0 0
Non-Anthropogenic Metric Value (EightHourDailyMax): 38.8
Anthropogenic Metric Value (EightHourDailyMax): 21.3
Anthropogenic Target Metric Value (EightHourDailyMax): 16.3
Incremental Reduction Required: 5.0
Reduced Anthropogenic Hourly Observations, Iteration One:
0 0 0 15 0 0 0 25 0 0 20 45 31 20 0 0 9 15 0 0 0 0 0 0
Reduced Hourly Observations, Iteration One:
20 20 25 55 35 35 40 65 35 30 60 85 71 60 35 35 49 55 33 40 30 30 25 20
Reduced Metric Value (EightHourDailyMax): 56.25
Target Metric Value (EightHourDailyMax): 55
Non-Anthropogenic Hourly Observations, Iteration Two:
20 20 25 40 35 35 40 40 35 30 40 40 40 40 35 35 40 40 33 40 30 30 25 20
Anthropogenic Hourly Observations, Iteration Two:
B-10
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Appendix B. Monitor Rollback
0 0 0 15 0 0 0 25 0 0 20 45 31 20 0 0 9 15 0 0 0 0 0 0
Non-Anthropogenic Metric Value (EightHourDailyMax): 38.8
Anthropogenic Metric Value (EightHourDailyMax): 17.5
Anthropogenic Target Metric Value (EightHourDailyMax): 16.3
Incremental Reduction Required: 1.25
Reduced Anthropogenic Hourly Observations, Iteration Two:
0 0 0 14 0 0 0 24 0 0 19 44 30 19 0 0 8 14 0 0 0 0 0 0
Reduced Hourly Observations, Iteration Two:
20 20 25 54 35 35 40 64 35 30 59 84 70 59 35 35 48 54 33 40 30 30 25 20
Reduced Metric Value (EightHourDailyMax): 55.3
Target Metric Value (EightHourDailyMax): 55
This example should actually continue for one further iteration, with a new Incremental
Reduction of 0.3. This illustrates another reason why the iterative procedure can be necessary - for
incremental reductions, the prohibition against values becoming negative can cause target metric values to
not be met. Incremental reductions thus very often require multiple iterations.
Interday and Intraday Rollback - Quadratic
Quadratic rollback is based on an algorithm developed by Horst and Duff (1995). The idea
behind quadratic rollback is to reduce large values proportionally more than small values while just
achieving the standard - that is, the out-of-attainment value should be more or less at the standard after the
rollback (some small amount of error is involved).
The original quadratic rollback algorithm is designed to roll back hourly observations given a
desired peak value. That is, it assumes that the Attainment Test metric is the one-hour average and the
Attainment Test ordinality is one. As such, the algorithm was modified slightly to allow for ordinalities
other than one to be used.
The basic formula for quadratic rollback is:
Reduced Observation = [1-(A + B* Initial Observation ) ] * Initial Observation
where:
i ranges over the days being reduced.
A= 1 - V
V = Min( 1, Vj)
Vj = ( 2 * Maximum Observation Value * Standard) / X;
X; = ( 2 * Maximum Observation Value * Metricsl) - Metrics,2
B = Max( 0, [( V * Out of Attainment Value - Standard) / Out of Attainment Value2])
B-ll
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Appendix B. Monitor Rollback
Quadratic Rollback - Interday
Because Quadratic Rollback was originally designed to adjust hourly observations to meet a daily
metric standard, it is slightly complicated to use it to generate target metric values.
First, Quadratic Rollback calculates the anthropogenic out of attainment value by subtracting the
Intraday Background Level from the out of attainment value. Note that this differs from the other
interday rollback methods, which subtract the Interday Background Level from the out of attainment
value. Similarly, the anthropogenic standard is calculated by subtracting the Intraday Background Level
from the standard.
The anthropogenic observations and non-anthropogenic observations are then calculated. For
pollutants which have daily observations (PM10, PM2.5) the anthropogenic metric values are used (see
above for their calculation). For pollutants which have hourly observations (Ozone), Quadratic Rollback
loops through each metric value and calculates the twenty four corresponding anthropogenic observations
and non-anthropogenic observations as follows:
IF the metric value is at or below the Interday Background Level,
For each observation,
non-anthropogenic observation = observation
anthropogenic observation = 0
ELSE
For each observation,
IF the observation is at or below the Intraday Background Level
non-anthropogenic observation = observation
anthropogenic observation = 0
ELSE
non-anthropogenic observation = Intraday Background Level
anthropogenic observation = observation - Intraday Background
Level
A new set of anthropogenic metric values is then calculated by generating the Attainment Test
metric from the anthropogenic observations. The Quadratic Rollback algorithm is then called, passing in
the anthropogenic metric values as Metrics, anthropogenic observations as Observations, anthropogenic
standard as Standard, and anthropogenic out of attainment value as Out of Attainment Value. The result
is a set of reduced anthropogenic observations. These are then added together with the non-
anthropogenic observations to give a final set of reduced observations.
Then, if Quadratic Rollback was also selected as the Intraday Rollback method, these
observations are used as the final reduced observations for the monitor. Otherwise, metric targets are
generated from these hourly observations, and the observations themselves are discarded.
Quadratic Rollback - Intraday
Quadratic Rollback can also be used to adjust hourly observations to meet metric targets
generated via a different rollback method. In this case, the algorithm is used to adjust each set of twenty
four hourly observations to meet the corresponding metric target. Intraday Quadratic Rollback uses the
normal set of anthropogenic observations as Observations, a single normal anthropogenic metric value as
B-12
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Appendix B. Monitor Rollback
Metrics, and the normal anthropogenic metric target as Standard. Intraday Quadratic Rollback tends to
always slightly miss its metric target, so it is not run in an iterative fashion as the other Intraday Rollback
Methods are (doing so would sometimes result in an infinite loop).
B-13
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Appendix C: Air Pollution Exposure Estimation Algorithms
BenMAP has grouped individuals into what we refer to as "population grid-cells," where the
grid-cells typically conform to some type of grid used in an air quality model, such as the REMSAD air
quality model, or just the counties of the United States. For each type of grid, the population is built in
each grid-cell by aggregating census block data. In the next step, BenMAP estimates the air pollution
exposure for each grid-cell, with the assumption that people living within a particular grid-cell experience
the same air pollution levels.
You have a variety of approaches to estimate the exposure to air pollution for the people living
within a given population grid-cell. Perhaps the simplest approach is to use model data directly, and to
assume that the people living within a particular model grid-cell experience the level estimated by the
model. An alternative approach is to use air pollution monitoring data, where you may choose the closest
monitor data to the center of a grid-cell or take an average of nearby monitors. In a third general
approach, you may combine both modeling and monitoring data to estimate exposure.
When combining modeling and monitoring data, BenMAP scales or adjusts the monitoring data
with modeling data. The advantage of modeling data is that they can provide predictions for years in
which monitoring data are not available, as well as to provide predictions in areas of the country for
which monitoring data are not available. And the advantage of monitor data is that they are based on
actual observations. Combining both sources of information, allows BenMAP to make more informed
predictions.
The goal of estimating exposure is to provide the necessary input for concentration-response
functions, so that BenMAP can estimate the impact of air pollution on adverse health effects. Exhibit C-l
lists the types of metrics commonly used in concentration-response functions. In the case of air pollution
metrics calculated on a daily basis, such as the one-hour maximum and the 24-hour average, it is often the
case that there are missing days of data. Air quality modeling is often conducted on a subset of the days
in the year, and air quality monitors often miss a number of observations through out the year. To
account for missing days, BenMAP represents the distribution of daily metrics with a certain number
points or "bins," where each bin represents a certain range of the distribution, with the underlying
assumption that missing days have the same distribution as the available data. For example, for analyses
of the United States the Environmental Protection Agency has typically used 153 bins to represent the
ozone season from May through September, and for particulate matter they have used 365 bins to
represent the year. In addition to being able to account for incomplete or missing data, and using bins to
represent the distribution provides a uniform approach that allows for easy comparison of different
monitors.
C-l
-------
Appendix C. Air Pollution Exposure Estimation Algorithms
Exhibit C-l. Metrics Typically Used in Concentration-Response Functions for Criteria Air
Pollutants
Measurement
Frequency
Metric Name
Metric Description
Daily
Daily Average
Daily average
(e.g., PM25, PM10)
Annual Average
Average of four quarterly averages. The four quarters are defined as: Jan-Mar,
April-June, Jul-Sep, Oct-Dec.
Annual Median
Median of values through out the year.
Flourly
(e.g., Ozone)
1-hour Daily Max
5-hour Daily Average
8-hour Daily Average
12-hour Daily Average
24-hour Daily Average
Flighest hourly value from 12:00 A.M. through 11:59 P.M.
Average of hourly values from 10:00 A.M. through 2:59 P.M.
Average of hourly values from 9:00 A.M. through 4:59 P.M.
Average of hourly values from 8:00 A.M. through 7:59 P.M.
Average of hours from 12:00 A.M. through 11:59 P.M.
Note that the 8-hour daily average differs from the maximum 8-hour moving average described in the Federal Register (6 FR /
Vol. 62, No. 138 / Friday, July 18, 1997 / Prepublication).
C .1 Direct Modeling
When using direct modeling data to estimate exposure, BenMAP assumes that the people living
within a particular air pollution model grid-cell experience the same air pollution levels. BenMAP then
estimates the air pollution metrics of interest. For pollutants measured hourly, such as ozone, these
include the one-hour maximum and 24-hour average, and for pollutants measured daily, such as
particulate matter, these include the annual mean and annual median.
Generally modeling data providing hourly observations are complete for any given day.
However, both hourly and daily often have missing days of observations. Given the estimated metrics,
BenMAP then represents the distribution of daily metrics with the number of days specified for each
pollutant. By calculating bins with the available days, BenMAP assumes that the distribution of missing
days is similar to the distribution of available monitoring.
C .2 Closest Monitor
When using the closet monitor to represent air pollution levels at a population grid-cell, BenMAP
identifies the center of the population grid-cell, and then chooses the monitor that is closest to the center.
In the simplest case, BenMAP assigns the closest monitor to a population grid-cell, uses the monitoring
data to calculate the annual and daily air pollution metrics, and then calculates the bins that represent the
distribution of the daily metrics. The annual metrics and the binned daily metrics are then used in the
calculation of health effects.
The figure below presents nine population grid-cells and three monitors, with the focus on
identifying the monitor closest to grid-cell "E." In this example, the closest monitor happens to be 10
miles away from the center of grid-cell E, and the data from this monitor would be used to estimate air
pollution levels for the population in this grid-cell. An analogous procedure would be used to estimate air
pollution levels in the other grid-cells (A, B, C, D, F, G, H, and I).
C-2
-------
Appendix C. Air Pollution Exposure Estimation Algorithms
A
B
15 miles
*
25 miles C
*
D
10 miles *
E
~ #
F
* 15 miles
G
*
30 miles
H
*
20 miles
I
*
25 miles
# = Center Grid-Cell "E"
= Air Pollution Monitor
To capture some of the information generated by air pollution models, BenMAP can also scale
the data from the closest monitor with air pollution modeling data. BenMAP includes two types of
scaling - "temporal" and "spatial" scaling. We discuss each below.
C .2.1 Closest Monitor - Temporal Scaling
With temporal scaling, BenMAP scales monitoring data with the ratio of the future-year to base-
year modeling data, where the modeling data is from the modeling grid-cell containing the monitor. In
the case of pollutants typically measured hourly, such as ozone, BenMAP scales the hourly monitor
values, calculates the annual and daily metrics of interest, and then bins the daily metrics. In the case of
pollutants typically measured daily, BenMAP scales the daily values, calculates the annual metrics of
interest, and then bins the daily metric.
Consider the case in the figure below. To forecast air pollution levels for 2030, BenMAP would
multiply the 1995 monitor value (80 ppb) by the ratio of the 2030 model value (70 ppb) to the 1995
model value (95 ppb):
Forecast2030 = Monitor Value 1995 * (Model Value D 2030 / Model Value D 1995)
Forecast2030 = 80 ppb * (70 ppb / 95 ppb) = 58.9 ppb.
C-3
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Appendix C. Air Pollution Exposure Estimation Algorithms
A
B
C
*
*
Model: d
E
F
1995 95 ppb
2030 70 ppb
-#
*
Monitor:
1995 80 ppb
G
H
I
*
*
*
# = Center Grid-Cell "E"
= Air Pollution Monitor
In this example, we have examined the adjustment of a single monitor value with the ratio of
single model values. The approach is essentially the same when there are multiple monitor values and
multiple model values. When there are multiple monitor values,
C .2.2 Closest Monitor - Spatial Scaling
With spatial scaling, we are estimating a monitor value for the center of each population grid-cell.
We start by choosing the closest monitor to the center of each population grid-cell, and then we scale this
closest monitor with modeling data. In particular, BenMAP multiplies the monitoring data with the ratio
of the base-year modeling data for the destination grid-cell to the base-year modeling data for grid-cell
containing the monitor. The spatial scaling occurs in the same fashion as with temporal scaling. In the
case of pollutants typically measured hourly, such as ozone, BenMAP scales the hourly monitor values,
calculates the annual and daily metrics of interest, and then bins the daily metrics. In the case of
pollutants typically measured daily, BenMAP scales the daily values, calculates the annual metrics of
interest, and then bins the daily metric.
To estimate air pollution levels for 1995 in grid-cell "E" below, BenMAP would multiply the
1995 closest monitor value (80 ppb) by the ratio of the 1995 model value for grid-cell "E" (70 ppb) to the
1995 model value for grid-cell "D" (95 ppb):
Forecast1995 = Monitor Value1995 * (Model Value E 1995 / Model Value D 1995)
Forecast1995 = 80 ppb * (85 ppb / 95 ppb) = 71.6 ppb.
C-4
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Appendix C. Air Pollution Exposure Estimation Algorithms
A
B
*
C
*
Model: D
Model: E
F
1995 95 ppb
1995 85 ppb
ic
Monitor:
-#
*
1995 80 ppb
G
H
I
*
*
*
# = Center Grid-Cell "E"
= Air Pollution Monitor
C .2.3 Closest Monitor - Temporal and Spatial Scaling
Combining both temporal and spatial scaling, BenMAP first multiplies monitoring data with both
the ratio of the future-year to base-year modeling data, where the modeling data is from the modeling
grid-cell containing the monitor. This gives a temporary forecast for 2030. BenMAP then multiplies this
temporary forecast with the ratio of the future-year modeling data for the destination grid-cell to the
future-year modeling data for grid-cell containing the monitor. As seen below, this simplifies to
multiplying monitoring data with both the ratio of future-year modeling data from the destination grid-
cell to the base-year modeling data from the grid-cell containing the monitor. Again, as described for
temporal and spatial scaling, BenMAP first scales the hourly and daily values, generates the metrics of
interest and then bins the daily metrics.
To forecast air pollution levels for 2030 in the figure below, BenMAP would multiply the 1995
monitor value (80 ppb) by the ratio of the 2030 model value (70 ppb) to the 1995 model value (95 ppb):
Temporary Forecast 2030 = Monitor Value 1995 * (Model Value D 2030 / Model Value D 1995)
Temporary Forecast2030 = 80 ppb * (70 ppb / 95 ppb) = 58.9 ppb.
Forecast 2030 = Temporary Forecast 2030 * (Model Value E 2030 / Model Value D 2030)
Forecast 2030 = 58.9 ppb * (60 ppb / 70 ppb) = 50.5 ppb.
Note that through cancellation, this equation simplifies to:
Forecast 2030 = Monitor Value 1995 * (Model Value E 2030 / Model Value D 1995)
C-5
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Appendix C. Air Pollution Exposure Estimation Algorithms
A
B
C
*
*
Model: d
Model: £
F
1995 95 ppb
1995 85 ppb
2030 70 ppb
2030 60 ppb
-#
*
Monitor:
1995 80 ppb
G
H
I
*
*
*
# = Center Grid-Cell "E"
*
= Air Pollution Monitor
C .3 Voronoi Neighbor Averaging (VNA)
Like the closest monitor approach, the Voronoi Neighbor Averaging (VNA) algorithm uses
monitor data directly or in combination with modeling data. However, instead of using the single closest
monitor to estimate exposure at a population grid-cell, the VNA algorithm interpolates air quality at every
population grid cell by first identifying the set of monitors that best "surround" the center of the
population grid-cell.
*
*
*
#
*
*
*
*
# = Center Grid-Cell "E"
*
= Air Pollution Monitor
C-6
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Appendix C. Air Pollution Exposure Estimation Algorithms
In particular, BenMAP identifies the nearest monitors, or "neighbors," by drawing a polygon, or
"Voronoi" cell, around the center of each BenMAP grid cell. The polygons have the special property that
the boundaries are the same distance from the two closest points.
# = Center Grid-Cell "E"
*
= Air Pollution Monitor
We then choose those monitors that share a boundary with the center of grid-cell "E." These are
the nearest neighbors, we use these monitors to estimate the air pollution level for this grid-cell.
* 15 miles
10 miles *
*
20 miles
# = Center Grid-Cell "E"
*
= Air Pollution Monitor
C-7
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Appendix C. Air Pollution Exposure Estimation Algorithms
To estimate the air pollution level in each grid-cell, BenMAP calculates the annual and the binned
daily metrics for each of the neighboring monitors, and then calculates an inverse-distance weighted
average of the metrics. The further the monitor is from the BenMAP grid-cell, the smaller the weight.
In the figure below, the weight for the monitor 10 miles from the center of grid-cell E is
calculated as follows:
J_
10
WelghtWm,les = ~T~\ 1 f
+ +
V10 15 15
The weights for the other monitors would be calculated in a similar fashion. BenMAP would
then calculate an inverse-distance weighted average for 1995 air pollution levels in grid-cell E as follows:
Forecast1995 = 0.35*80 ppb + 0.24*90 ppb+ 0.24*60 ppb + 0.18*100 ppb = 81.2 ppb .
A
B
Monitor:
1995 90 ppb ^
15 miles
C
*
D
Monitor: *
1995 80 ppb
10 miles
LD
F
*
Monitor:
1995 60 ppb
15 miles
G
*
/ H
*
Monitor:
1995 100 ppb
20 miles
I
*
# = Center Grid-Cell "E"
*
= Air Pollution Monitor
Note that BenMAP is calculating an inverse-distance weighted average of the annual metrics and
the binned daily metrics. Alternatively, BenMAP could calculate an inverse-distance weighted average of
the hourly and daily observations, calculated the annual and daily metrics, and then binned the daily
metrics.
C .3.1 Voronoi Neighbor Averaging (VNA) - Temporal Scaling
C-8
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Appendix C. Air Pollution Exposure Estimation Algorithms
As with forecasting air pollution levels by temporally scaling the closest monitor, BenMAP can
combine VNA with temporal scaling. BenMAP temporally scales all of the neighboring monitors,
calculates the metrics of interest, and then calculates an inverse distance-weighted average of the metrics.
Consider the example in the figure below. To forecast air pollution levels for 2030, BenMAP
would multiply the 1995 monitor value by the ratio of the 2030 model value to the 1995 model value:
Forecast2030 = ^ Weight. * Monitor:
Model. 2030
i=i Modeli 1995
70^| ( 100^1 { 80^| ( 120^|
Forecast2W0 = [ 0.35*80*— + 0.24*90*—— + 0.24*60*— + 0.18*100*—— = 64.1ppb
95/ V 85 / v 60/ V 100/
A
Model: b
1995 100 ppb
2030 85 ppb
Monitor:
1995 90 ppb ^
15 miles
C
*
Model: d
1995 95 ppb
2030 70 ppb
Monitor: *
1995 80 ppb
10 miles
LD
Model: p
1995 80 ppb
2030 60 ppb
*
Monitor:
1995 60 ppb
15 miles
G
*
Modal: H
199? 120 ppb
2030 100 ppb
Monitor:
1995 100 ppb
20 miles
I
*
# = Center Grid-Cell "E"
*
= Air Pollution Monitor
C .3.2 Voronoi Neighbor Averaging (VNA) - Spatial Scaling
BenMAP can also combine VNA with spatial scaling. For each of the neighbor monitors,
BenMAP multiplies the monitoring data with the ratio of the base-year modeling data for the destination
grid-cell to the base-year modeling data for grid-cell containing the monitor. The spatial scaling occurs in
the same fashion as with temporal scaling. In the case of pollutants typically measured hourly, such as
ozone, BenMAP scales the hourly monitor values, calculates the annual and daily metrics of interest, and
then bins the daily metrics. In the case of pollutants typically measured daily, BenMAP scales the daily
values, calculates the annual metrics of interest, and then bins the daily metric.
Consider the example in the figure below. To forecast air pollution levels for 1995, BenMAP
would multiply the 1995 monitor value by the ratio of the 1995 model value to the 1995 model value:
C-9
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Appendix C. Air Pollution Exposure Estimation Algorithms
ModelE jggj
Forecast,qq, = / Weight, * Monitor * , , , ,"
ti Model, l995
85^ ( 85^ ( 85^| ( 85 ^
Forecastigg5 = [ 0.35*80*—J + ^0.24*90* + ^0.24*60*—J + ^0.18* 100* = ^Q&ppb
A
Model: B
1995 100 ppb
Monitor:
1995 90 ppb ^
15 miles
C
*
Model: D
1995 95 ppb
Monitor: *
1995 80 ppb
10 miles
Model: /e
1995 85/ppb
-#
/
Model: F
1995 80 ppb
*
Monitor:
1995 60 ppb
15 miles
G
*
Mod/l: H
1995 120 ppb
*
Monitor:
1995 100 ppb
20 miles
I
*
# = Center Grid-Cell "E"
*
= Air Pollution Monitor
C .3.3 Voronoi Neighbor Averaging (VNA) - Temporal & Spatial Scaling
Combining both temporal and spatial scaling, BenMAP multiplies monitoring data with the ratio
of the future-year to base-year modeling data, where the future-year modeling data are from the
destination grid-cell and the base-year modeling data are from the grid-cell containing the monitor. One
the hourly and daily monitoring data are scaled, BenMAP generates the metrics of interest, bins the daily
metrics, and then uses the metrics to estimate adverse health effects in the population grid-cell.
The figure below gives an example of combining temporal and spatial scaling.
Model E
Forecast2030 = ^ Weightt * Monitor *
lE, 2030
!oc /el | (l(l^
60^1 ( 60 ^ ( 60^ f 60)
Forecasts = 0.35*80*— + 0.24*90* + 0.24*60*— + 0.18*100* = 50.0
95) \ 100) \ 80J I 120/
C-10
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Appendix C. Air Pollution Exposure Estimation Algorithms
C .4 Temporal and Spatial Scaling Adjustment Factors
As presented in the preceding examples of temporal and spatial scaling, both closest monitor and
VNA use model data to scale monitor observations. In the examples, we scaled single monitor values
with the ratio of single model values. In fact, however, the scaling involves multiple monitor values and
multiple model values.
To proceed with the scaling, BenMAP takes the modeling values and splits them into groups. For
ozone, the United States Environmental Protection Agency has generally used 10 adjustment factors for
the ozone season, where the first group represents the first 10 percent of the model observations; the
second group represents the observations between the 10th and 20th percentile; and so on through the
tenth group, which represents the observations between the 90th and 100th percentiles. BenMAP then
averages the values in each group. For particulate matter, the United States Environmental Protection
Agency has generally used five adjustment factors for each of the four seasons in the year, where the first
group in each season represents the first 20 percent of the model observations; the second group
represents the observations between the 20th and 40th percentiles; and so on. Then, as for ozone model
values, BenMAP averages the particulate matter model values in each group.
BenMAP treats the monitor values in a similar way. It sorts the monitor values from low to high,
and divides them into the same number groups as there are scaling factors.
C .4.1 Calculation of Scaling Factors
In developing scaling factors, BenMAP sorts the modeling data into either 10 groups or 20
groups, depending on the pollutant (e.g., 10 for ozone and for particulate five for each of the four
seasons). Given the number of groups, then BenMAP determines how to assign the model values. In
determining to which group a value belongs, BenMAP assigns a two-digit "percentile" to each value.
With values in a given grid-cell sorted from low to high, the percentile for each value will equal: (the
observation rank number minus 0.5) divided by (the total number of values) multiplied by (100). If there
are 250 hourly values, the first hourly value will have a percentile = (1 -0.5)/(250)*(100) = 0.20%; the
27th value will have a percentile = (27-0.5)/(250)*(100) = 10.60%; and so on.
Each data group is represented by "group-lo" and "group-hi" values. These are the minimum and
the maximum percentiles in each group, where group-lo equals: (group rank minus 1) multiplied by (100)
divided by (the number of groups); and group-hi equals: (group rank) multiplied by (100) divided by (
the number of groups) minus 0.001. If there are ten groups: the first group will have: group-lo =
(1-1)/100* 10 = 0.000%, and group-hi = (1/100* 10)-0.001 = 9.999% ; the second group will have:
group-lo = (2-l)/100* 10 = 10.000%, and group-hi = (2/100* 10)-0.001 = 19.999% ; and so on to the tenth
group, which will have: group-lo = (10-1)/100* 10 = 90.000%, and group-hi = (10/100* 10)-0.001 =
99.999%. BenMAP assigns each observation to a particular group with the following algorithm: if
"group-lo" <"percentile" < "group-hi", then assign the observation to that data group.
C .4.2 How BenMAP Scales Daily and Hourly Data
Below we give the equations that BenMAP uses when scaling daily (e.g., particulate matter) and
hourly (e.g., ozone) monitor values.
C-ll
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Appendix C. Air Pollution Exposure Estimation Algorithms
Scaling Daily (e.g., Particulate Matter) Monitor Values
After preparing the model and monitor data, BenMAP calculates the following:
, , Remsadjkfuture
adjusted monitor . , „ = monitor ., • ——
J i,j,future i,j,base Rffft/fSAD
where:
adjusted monitor = predicted daily PM25 level, after adjustment by model data (|ig/m3)
monitor = observed daily PM2 5 monitor level (|ig/m3)
i = day identifier
j = model season/quintile group (1 to 20)
k = grid cell identifier for population grid cell
1 = grid cell identifier for grid cell containing monitor
base = base-year (e.g., 2000)
future = future-year (e.g., 2020)
REMSAD = representative model season/quintile value (|ig/m3)
After adjusting the monitor values to reflect air quality modeling, BenMAP calculates for each
monitor the PM25 metrics needed to estimate adverse health effects. In the case of Voronoi Neighbor
Averaging, BenMAP then calculates an inverse-distance weighted average of the neighbors identified for
each population grid cell:
n
population grid cell^ = £ adjusted monitorm fiiture ¦ weightm ¦
m= 1
where:
population grid cell
adjusted monitor
m
future
weight
= inverse distance-weighted PM2 5 metric at population grid cell (|ig/m3)
= predicted PM2 5 metric, after adjustment by model data (|ig/m3)
= monitor identifier
= future-year (e.g., 2020)
= inverse-distance weight for monitor
After generating the bins for both the baseline and control scenarios, BenMAP can use these to
calculate the change in air quality needed in most C-R functions to calculate the change in adverse health
effects. To calculate the change in air quality, BenMAP subtracts the baseline value in the first bin from
the control value in the first bin, and so on for each of the bins created for the daily PM2 5 average.
Scaling Hourly (e.g., Ozone) Monitor Values
After preparing the model and monitor data, BenMAP calculates the following:
CAMXjkjuture
adjusted momtorl j future = momtort
J,base / ' AA/fy
CAMX j,1,base
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Appendix C. Air Pollution Exposure Estimation Algorithms
where:
adjusted monitor = predicted hourly ozone level, after adjustment by model data (ppb)
monitor = observed hourly ozone monitor level (ppb)
i = hour identifier
j = model decile group (1 to 10)
k = grid cell identifier for population grid cell
1 = grid cell identifier for grid cell containing monitor
base = base-year (e.g., 1996)
future = future-year (e.g., 2030)
CAMX = representative model decile value (ppb)
After adjusting the monitor values to reflect air quality modeling, BenMAP calculates for each
monitor the ozone metrics needed to estimate adverse health effects. In the case of Voronoi Neighbor
Averaging, BenMAP then calculates an inverse-distance weighted average of the neighbors identified for
each population grid cell:
n
population grid cell= £ adjusted monitorm Juture ¦ weightm ¦
m= 1
where:
population grid cell = inverse distance-weighted ozone metric at population grid cell (ppb)
adjusted monitor = predicted ozone metric, after adjustment by model data (ppb)
m = monitor identifier
future = future-year (2020, 2030)
weight = inverse-distance weight for monitor
After generating the bins for both the baseline and control scenarios, BenMAP can use these to
calculate the change in air quality needed in most C-R functions to calculate the change in adverse health
effects. To calculate the change in air quality, BenMAP subtracts the baseline value in the first bin from
the control value in the first bin, and so on for each of the bins created for the daily ozone metrics.
C .5 Binned Metrics
When estimating air pollution exposure, BenMAP calculates both daily metrics, such as the 24-
hour daily average, and annual metrics, such as the annual mean. Because daily metrics are often not
available for the entire year, BenMAP calculates representative values or bins with the available daily
metrics, under the assumption that the missing days have a similar distribution. Each bin represents a
day. In the case where there are 365 bins, the set of bins represents the entire year.
When combining air pollution metrics from multiple monitors, BenMAP first calculates the bins
for the daily metrics, and then combines the bins, such as with some form of VNA. Once BenMAP has
calculated binned exposure measures for both a baseline and a control scenario, BenMAP then takes the
difference between the two scenarios for each bin - taking the difference between the baseline value in
the first bin and the control value in the first bin, and so on for each of the bins.
C-13
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Appendix C. Air Pollution Exposure Estimation Algorithms
C-14
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Appendix D: Types of Concentration-Response Functions & Issues
in the Estimation of Adverse Health Effects
This Appendix provides of an overview regarding the concentration-response (C-R) functions
that BenMAP uses to estimate the impact of a change in air pollution on adverse health effects. It
provides a description of the particular types of C-R functions that BenMAP uses. And then summarizes
the approach used to choose the C-R functions included in BenMAP, and presents some issues associated
with the use of C-R functions.
D .1 Overview
The relationship between the concentration of a pollutant, x, and the population response, y, is
called the concentration-response (C-R) function. For example, the concentration of the pollutant may be
fine particulate matter (PM2 5) in |ig/m ' per day, and the population response may be the number of
premature deaths per 100,000 population per day. C-R functions are estimated in epidemiological
studies. A functional form is chosen by the researcher, and the parameters of the function are estimated
using data on the pollutant (e.g., daily levels of PM25) and the health response (e.g., daily mortality
counts). There are several different functional forms, discussed below, that have been used for C-R
functions. The one most commonly used is the log-linear form, in which the natural logarithm of the
health response is a linear function of the pollutant concentration.
For the purposes of estimating benefits, we are not interested in the C-R function itself, however,
but the relationship between the change in concentration of the pollutant, Ax, and the corresponding
change in the population health response, Ay. We want to know, for example, if the concentration of
PM2 5 is reduced by 10 |ig/nr'. how many premature deaths will be avoided? The relationship between Ax
and Ay can be derived from the C-R function, as described below.
Many epidemiological studies, however, do not report the C-R function, but instead report some
measure of the change in the population health response associated with a specific change in the pollutant
concentration. The most common measure reported is the relative risk associated with a given change in
the pollutant concentration. A general relationship between Ax and Ay can, however, be derived from the
relative risk. The relative risk and similar measures reported in epidemiological studies are discussed in
the sections below. The derivation of the relationship of interest for BenMAP - the relationship between
Ax and Ay - is discussed in the subsequent sections.
D .1.1 Review Relative Risk and Odds Ratio
The terms relative risk and odds ratio are related but distinct. Exhibit D-l provides the basis for
demonstrating their relationship.
D-l
-------
Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
Exhibit D-l. Relative Risk and Odds Ratio Notation
Exposure
Fraction of Population
Adverse Effect Measure
Affected
Not Affected
Relative Risk
Odds
Baseline Pollutant Exposure
Yo
1-Yo
Y
-------
Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
D .2 The Estimation of Health Effect Incidence Change
The functional form of the relationship between the change in pollutant concentration, Ax, and
the change in population health response (usually an incidence rate), Ay depends on the functional form
of the C-R function from which it is derived, and this depends on the underlying relationship assumed in
the epidemiological study chosen to estimate a given effect. For expository simplicity, the following
subsections refer simply to a generic adverse health effect, "y" and uses particulate matter (PM) as the
pollutant - that is, Ax = APM - to illustrate how the relationship between Ax and Ay is derived from each
of several different C-R functions.
Estimating the relationship between APM and Ay can be thought of as consisting of three steps:
(1) choosing a functional form of the relationship between PM and y (the C-R function),
(2) estimating the values of the parameters in the C-R function assumed, and
(3) deriving the relationship between APM and Ay from the relationship between PM and y (the
C-R function).
Epidemiological studies have used a variety of functional forms for C-R functions. Some studies
have assumed that the relationship between adverse health and pollution is best described by a linear
form, where the relationship between y and PM is estimated by a linear regression in which y is the
dependent variable and PM is one of several independent variables. Log-linear regression1 and logistic
regression are other common forms.
D .2.1 Linear Model
A linear relationship between the rate of adverse health effects (incidence rate) and various
explanatory variables is of the form:
y-a\f3- PM
where a incorporates all the other independent variables in the regression (evaluated at their mean values,
for example) times their respective coefficients. The relationship between the change in the rate of the
adverse health effect from the baseline rate (y0) to the rate after control (yc) associated with a change from
PM0 to PMC is then:
A y= yc-y0=P-{PMC - PM0 )= /zapm.
For example, Ostro et al. (1991, Table 5) reported a PM25 coefficient of 0.0006 (with a standard
error of 0.0003) for a linear relationship between asthma and PM25 exposure.2
'The log-linear form used in the epidemiological literature on ozone- and PM-related health effects is often referred to as
"Poisson regression" because the underlying dependent variable is a count (e.g., number of deaths), believed to be Poisson
distributed. The model may be estimated by regression techniques but is often estimated by maximum likelihood techniques. The
form of the model, however, is still log-linear.
2Ostro et al. (1991) happen to use the natural logarithm of PM25.
D-3
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Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
The lower and upper bound estimates for the PM25 coefficient are calculated as follows:
Plover bound = P~ (1-9&<7p )= 0.0006- (1.96-0.0003)= 1.210 5
Pupper bound = P+ (1-96^ )= 0.0006+ (1.960.0003)= 0.00119
It is then straightforward to calculate lower and upper bound estimates of the change in asthma.
D .2.2 Log-linear Model
The log-linear relationship defines the incidence rate (y) as:
y=B-ep'PM
or, equivalently,
ln( y)= a+ (3- PM,
where the parameter B is the incidence rate of y when the concentration of PM is zero, the parameter p is
the coefficient of PM, ln(y) is the natural logarithm of y, and a = ln(B).3
The relationship between APM and Ay is:
^y=yc-y0 = Be^-Be^PM\
This may be rewritten as:
Ay= e?-pM° (efi<™*-pMo) -1)= y0.{ep-*™-1) ,
where y0 is the baseline incidence rate of the health effect (i.e., the incidence rate before the change in
PM).
The change in the incidence of adverse health effects can then be calculated by multiplying the
change in the incidence rate, Ay, by the relevant population (e.g., if the rate is number per 100,000
population, then the relevant population is the number of 100,000s in the population).
3 Other covariates besides pollution clearly affect mortality. The parameter B might be thought of as containing these
other covariates, for example, evaluated at their means. That is, B = B0exp{plx1 + ... + Pnxn}, where B0 is the incidence of y when
all covariates in the model are zero, and x1;... , xn are the other covariates evaluated at their mean values. The parameter B drops out
of the model, however, when changes in y are calculated, and is therefore not important.
D-4
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Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
When the PM coefficient (P) and its standard error (op) are published (e.g., Ostro et al., 1989),
then the coefficient estimates associated with the lower and upper bound may be calculated easily as
follows:
Plower bound = P~ (1-96" CTg )
PuPPerbound = P+(l-96-°p)-
Epidemiological studies often report a relative risk for a given APM, rather than the coefficient, p
(e.g., Schwartz et al., 1995, Table 4). Recall that the relative risk (RR) is simply the ratio of two risks:
RR=y-Ap*r
yc
Taking the natural log of both sides, the coefficient in the C-R function underlying the relative
risk can be derived as:
InCRR)
APM
The coefficients associated with the lower and upper bounds (e.g., the 2.5 and 97.5 percentiles)
can be calculated by using a published confidence interval for relative risk, and then calculating the
associated coefficients.
Because of rounding of the published RR and its confidence interval, the standard error for the
coefficient implied by the lower bound of the RR will not exactly equal that implied by the upper bound,
so an average of the two estimates is used. The underlying standard error for the coefficient (op) can be
approximated by:
_/?-A .5 percentile
^ P, 2.5 percentile ~
1.96
_ $91.5 percentile ft
®'/?, 97.5 percentile ~
1.96
^ (3,2.5 percentile ^ (3,91.5 percentile
o
D-5
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Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
D .2.3 Logistic Model
In some epidemiological studies, a logistic model is used to estimate the probability of an
occurrence of an adverse health effect. Given a vector of explanatory variables, X, the logistic model
assumes the probability of an occurrence is:
y = prob{occurrence \ X ¦ /?)
e*-P
vl+e^.
where p is a vector of coefficients.4 This may be rewritten as:
ex-P e-x-p j
y = l+ex'p' e-x'p = l+e-x-fi
The odds of an occurrence is:
„ y Kl+e-*-'
odds =
l~y i- 1
l+e-x-e
1
^ A+e-*-") U+e-^J 1 xp
odds -x = ( n-x.p ^ =~T^=g
1-
1+ e
-X-P
e H \ e
1+ e
-x-p
In {odds) = X ¦ p .
The odds ratio for the control scenario (oddsc) versus the baseline (odds0) is then:
,, H odds \l-yc) \e-x^J ex
odds ratio = ¦
odds0 f y0 ) ( 1 ^ ex"'p
i-yj ^
The change in the probability of an occurrence from the baseline to the control (Ay), assuming
that all the other covariates remain constant, may be derived from this odds ratio:
4Greene (1997, Chapter 19) presents models with discrete dependent variables; in particular, page 874 presents the logit
model. See also Judge et al. (1985, p. 763).
D-6
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Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
odds ratio
yc
Jo
.1- JV
6XJ er .ePMj
APM-/3
eXafs ~ er ¦ eFMofs
yc
{ y° )
?APM-p
i-yc u-j0.
Jo
?APM-p
yj
jc + jc •
'^A
vi-yj
jAPM-fi _
U-j0J
jAPM-p
yc
j0
.1" Jo-
APM-P
Jo
.1-Jo.
• e
kPM-p
Jo I . eAPM-P
jc = ¦
-1" Jo^
y0-e
KPM'P
1 +
/ \ A PM'P
Jo capm-p \-yQ + yQ-e
i-yj
Multiplying by:
-APM-p
-&PM-P 5
gives:
Jc =
Jo
(l-Jo)-e_A/5M'/?+Jo
D-7
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Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
ky = yc-y0 =
(l"3;o)-e"A/5M'/?+3;o
yo ¦
The change in the number of cases of the adverse health effect is then obtained by multiplying by
the relevant population:
ts. Incidence = ts.y ¦ pop =
y0
(1 -y0)-e-^ + y0
y o
• pop.
When the coefficient (P) and its standard error (op) are published (e.g., Pope et al., 1991, Table 5),
then the coefficient estimates associated with the lower and upper bound may be calculated easily as
follows:
Plower bound = P ~ (1-96 • Op )
Pupper bound ~ P (1-96 £Xg ) .
Often the logistic regression coefficients are not published, and only the odds ratio corresponding
to a specified change in PM is presented (e.g., Schwartz et al., 1994). It is easy to calculate the
underlying coefficient as follows:
In (odds ratio) = A PM- p
\wipdds ratio)
P =
APM
The coefficients associated with the lower and upper bound estimates of the odds ratios are
calculated analogously.
The underlying standard error for the coefficient (op) can be approximated by:
_P~P2, percentile
^(3, 2.5 percentile
^ j3, 97.5 percentile
1.96
/^97.5 percentile P
1.96
°> =
^P, 2.5 percentile ^p, 97.5 percentile
D-8
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Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
Sometimes, however, the relative risk is presented. The relative risk does not equal the odds
ratio, and a different procedure should be used to estimate the underlying coefficient.5
The relative risk (RR) is simply:
RR = ^-,
yc
where y0 is the risk (i.e., probability of an occurrence) at the baseline PM exposure and yc is the risk at the
control PM exposure.
When the baseline incidence rate (y0) is given, then it is easy to solve for the control incidence
rate (yc):
y = ys.
RR
The odds ratio, may then be calculated:
y0
odds ratio = '
yc
Given the odds ratio, the underlying coefficient (P) may be calculated as before:
ln(odds ratio)
^= APM '
The odds ratio and the coefficient calculated from it are dependent on the baseline and control
incidence rates. Unfortunately, it is not always clear what the baseline and control incidence rates should
be. Abbey et al. (1995b, Table 2) reported that there are 117 new cases of chronic bronchitis out of a
sample of 1,631, or a 7.17 percent rate. In addition, they reported the relative risk (RR = 1.81) for a new
case of chronic bronchitis associated with an annual mean concentration "increment" of 45 ng/m3 of
PM25 exposure.
Assuming that the baseline rate for chronic bronchitis (y0) should be 7.17 percent, the question
becomes whether the "increment" of 45 //g/m3 should be added to or subtracted from the existing PM2 5
concentration. If added the control incidence rate (yc) would be greater than the baseline rate (y0), while
subtraction would give a control rate less than the incidence rate. In effect, one might reasonably derive
two estimates of the odds ratio:
5Note that ESEERCO (1994, p. V-21) calculated (incorrectly) the underlying regression coefficient for Abbey et al. (1993,
Table 5) by taking the logarithm of the relative risk and dividing by the change in TSP.
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y0 1.81-0.0717
,1 - yJ U- (1.81-0.0717).
oddsratiol = — = \ = 1-931
1-yJ VI- 0.0717
y0 I ( 0.0717 1
oddsratio2 = y° = (l \ = 1-873
y c
i -x
1.81
0.0717
V1" 1.81 )
lnO9^ = 0()1462
45
ln(1.873)
/?, = — -= 0.01394.
45
An alternative is to simply assume that the relative risk (1.81) is reasonably close to the odds ratio
and calculate the underlying coefficient. It is easy to show that the relative risk equals:
¦ _ _ /i \ „-hPM-p
RR = ^ = {l-y0)-e-APM?+y0 .
yc
Assuming that:
e-^^(l-y0ye-^+y0
RR=e
- APM- p
It is then possible to calculate the underlying coefficient:
In (RR)
-APM
= P
AJn(181) = 001319
45
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Since this coefficient estimate is based on the assumption that
e-™-' +ya ,
it should be used in a C-R function that maintains this assumption. In effect, it should be applied to a log-
linear C-R function:
Using the formula for the change in the incidence rate and assuming a 10 /ig/nr' decline in PM25,
it is shown that this results in changes within the bounds suggested by the two estimates based on using
the estimated odds ratios:
0717
Av, =7 r— 0.0717 = -0.00914
(1-0.0717)-e10 0 01462 + 0.07 1 7
0717
Ay2 =7 , lnnnnQ4 0.0717 = -0.00874
(l-0.0717)-e10 0 01394 + 0.07 1 7
A>>3 = 0.0717. (e-lcwl 01319-l)
-1 = -0.00886.
In this instance, it seems that simply using the relative risk to estimate the underlying coefficient
results in a good approximation of the change in incidence. Since it is unclear which of the two other
coefficients (P, or p2) should be used ~ as the published work was not explicit - the coefficient based on
the relative risk and the log-linear functional form seems like a reasonable approach.
D .2.4 Cox proportional Hazards Model
Use of a Cox proportional hazards model in an epidemiological study results in a C-R function
that is log-linear in form. It is often used to model survival times, and as a result, this discussion focuses
on mortality impacts.
The Cox proportional hazards model is based on a hazard function, defined as the probability that
an individual dies at time t, conditional on having survived up to time t (Collet, 1994, p. 10). More
formally, the hazard function equals the probability density function for the risk of dying divided by one
minus the cumulative probability density function:
hiX,t)= .
1 -F(X,t)
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The proportional hazards model takes the form:
h(X,t) = h0(t)e
X-l
where X is a vector of explanatory variables, p is a vector of coefficients, and h0(t) is the so-called
"baseline hazard" rate.6 This terminology differs from that used in most of this discussion: this "baseline
hazard" is the risk when all of the covariates (X) are set to zero; this is not the risk in the baseline
scenario.
Taking the ratio of the hazard functions for the baseline and control scenarios gives the relative
risk:
_ h(X0,t) _ h0(t)ex°'p _ p
KXc,t) h0(t)ex^
where it is assumed that the only difference between the baseline and control is the level of PM pollution.
The relative risk is often presented rather than the coefficient p, so it is necessary to estimate p in
order to develop functional relationship between APM and Ay, as described previously for log-linear C-R
functions.
D .3 General Issues in Estimating Health & Welfare Benefits
Changes in air pollution result in changes in a number of health and welfare effects, or
"endpoints," that society values. This chapter discusses key issues in their estimation. The first part of
this section discusses the development of C-R functions, based on the results from epidemiological
studies, and the second part discusses some general issues that arise with C-R functions.
D .3.1 Choosing Epidemiological Studies and Developing Concentration-Response
Functions
This section reviews the steps we performed in selecting and developing C-R functions for
inclusion in BenMAP. The first section of this appendix describes how we chose studies from the
epidemiological literature for use in the present analysis. In any given study, there are often a large
number of estimated relationships between air pollution and adverse health effects, because the estimated
relationship can depend on the number and types of pollutants included in the model, among other
reasons. We then describe how we chose the specific estimated relationships, or models, from among the
potentially large number available in any given study. And then we briefly discuss how we convert the
estimated model into C-R functions, which then allow us to quantify the change in adverse health effects
due to a change in air pollution exposure.
6 The Cox proportional hazards model is sometimes termed a "semi-parametric" model, because the baseline hazard rate is
calculated using a non-parametric method, while the impact of explanatory variables is parameterized. Collet (1994) details the
estimation of Cox proportional hazards models; in particular, see Collet's discussion (pp. 95-97) of nonparametric estimation of the
baseline hazard.
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Study Selection
We relied on an up-to-date assessment of the published scientific literature to ascertain the
relationship between particulate matter and ozone exposure and adverse human health effects. We
evaluated studies using a variety of selection criteria, including: its location and design, the characteristics
of the study population, and whether the study was peer-reviewed (Exhibit D-2).
In selecting studies for use in this analysis, priority was given to studies that focused on PM2 5 and
ozone, given that the emissions reductions from nonroad sources are likely to result primarily in reduced
ambient PM25 and ozone levels. For a given health effect, if sufficient PM25 studies were available, we
selected them rather than PM10 studies in the base analysis. In addition, results from several recent
studies allowed for the inclusion of new health effects, such as myocardial infarction for PM2 5 and school
loss days for ozone.
While a broad range of serious health effects have been associated with exposure to elevated
ozone and PM levels, we include only a subset of health effects in this quantified benefit analysis. Health
effects are excluded from this analysis for three reasons: (i) the possibility of double counting (such as
hospital admissions for specific respiratory diseases); (ii) uncertainties in applying effect relationships
based on clinical studies to the affected population; or (iii) a lack of an established C-R relationship.
A more detailed description of the studies and health effects included in this analysis are
presented in Appendices F and G.
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Exhibit D-2. Summary of Considerations Used in Selecting C-R Functions
Consideration
Comments
Peer reviewed
research
Study type
Study period
Peer reviewed research is preferred to research that has not undergone the peer review process.
Among studies that consider chronic exposure (e.g., over a year or longer) prospective cohort studies are
preferred over cross-sectional studies because they control for important individual-level confounding
variables that cannot be controlled for in cross-sectional studies.
Studies examining a relatively longer period of time (and therefore having more data) are preferred,
because they have greater statistical power to detect effects. More recent studies are also preferred because
of possible changes in pollution mixes, medical care, and life style over time. However, when there are
only a few studies available, studies from all years will be included.
Population attributes The most technically appropriate measures of benefits would be based on C-R functions that cover the
entire sensitive population, but allow for heterogeneity across age or other relevant demographic factors. In
the absence of C-R functions specific to age, sex, preexisting condition status, or other relevant factors, it
may be appropriate to select C-R functions that cover the broadest population, to match with the desired
outcome of the analysis, which is total national-level health impacts.
Study size
Study location
Pollutants included
in model
Measure of PM
Economically
valuable health
effects
Non-overlapping
endpoints
Studies examining a relatively large sample are preferred because they generally have more power to detect
small magnitude effects. A large sample can be obtained in several ways, either through a large population,
or through repeated observations on a smaller population, i.e. through a symptom diary recorded for a panel
of asthmatic children.
U.S. studies are more desirable than non-U.S. studies because of potential differences in pollution
characteristics, exposure patterns, medical care system, population behavior and life style.
When modeling the effects of ozone and PM (or other pollutant combinations) jointly, it is important to use
properly specified C-R functions that include both pollutants. Use of single pollutant models in cases
where both pollutants are expected to affect a health outcome can lead to double-counting when pollutants
are correlated.
For this analysis, C-R functions based on PM25 are preferred to PM10 because reductions in emissions from
diesel engines are expected to reduce fine particles and not have much impact on coarse particles. Where
PM25 functions are not available, PM10 functions are used as surrogates, recognizing that there will be
potential downward (upward) biases if the fine fraction of PM10 is more (less) toxic than the coarse
fraction.
Some health effects, such as forced expiratory volume and other technical measurements of lung function,
are difficult to value in monetary terms. These health effects are not quantified in this analysis.
Although the benefits associated with each individual health endpoint may be analyzed separately, care
must be exercised in selecting health endpoints to include in the overall benefits analysis because of the
possibility of double counting of benefits. Including emergency room visits in a benefits analysis that
already considers hospital admissions, for example, will result in double counting of some benefits if the
category "hospital admissions" includes emergency room visits.
Model Selection
For any given study selected for use in this analysis, there are often multiple models quantifying
the relationship between air pollution exposure and adverse health. For each model, we needed to
identify the specific models that we would use to develop C-R functions.
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Single Pollutant versus Multipollutant Models
Many of the epidemiological studies present results both for the case where only one pollutant is
entered into the health effects model, or single-pollutant models, and where two or more pollutants are
entered into the health effects model, or multi-pollutant models. When attempting to quantify the impact
of a single pollutant, such as PM2 5, on adverse health effects, the use of single-pollutant models may
result in biased estimates. For example, to the extent that any of the co-pollutants present in the ambient
air may have contributed to the health effects attributed to PM2 5 in single pollutant models, risks
attributed to PM25 might be overestimated where C-R functions are based on single-pollutant models.
In multi-pollutant models, it may be difficult to sort out which pollutants are exerting an
independent effect when pollutants in a given location are highly correlated. As discussed in the 2002
draft PM CD (U.S. EPA, 2002a), inclusion of pollutants that are highly correlated with one another can
lead to misleading conclusions in identifying a specific causal pollutant. When collinearity exists, multi-
pollutant models would be expected to produce unstable and statistically insignificant effects estimates
for both PM and the co-pollutants (U.S. EPA, 2002a, p.9-130).
Single- and multi-pollutant models each have potential advantages and disadvantages, with
neither type clearly preferable over the other, however, the regulatory focus of this analysis is on PM and
ozone. For regulatory analyses which consider two pollutants together, adding incidence changes for a
given health endpoint, based on a single-pollutant PM model, to the incidence changes based on a single-
pollutant ozone model could result in an overestimate of incidence change, if both have an effect on the
health endpoint and there is some collinearity between the two pollutants.
As a result, our first choice for this analysis is to use multi-pollutant models with both PM and
ozone, rather than single-pollutant models and multi-pollutant models with other pollutants. If multi-
pollutant models with both PM and ozone were not available, then models with other co-pollutants were
preferred to single-pollutant models. In the absence of multi-pollutant models from a given study, single
pollutant models were selected for use in the analysis.
Model Selection Criteria
In many epidemiological studies of air pollution and health, researchers estimate and present
numerous single pollutant and multi-pollutant models for the same pollutant and health endpoint. These
models may differ from each other in a number of characteristics, including: the functional form of the
model, the covariates included in the model, the pollutant exposure metric, the lag structure, and the study
population.
For the purposes of estimating health benefits associated with pollutant changes, it is neither
realistic nor advantageous to include every model presented in each study. However, it is important that a
relatively objective process be used to select among models. Described below are the criteria that were
used as guidance in the selection of a particular model from among several models presented in a study.
It is not possible in all cases to select a model using a completely objective and mechanical process. In
many cases, professional judgement and an understanding of the study context are necessary as well to
select the most appropriate models. Exhibit D-3 summarizes the selection criteria that we used.
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Exhibit D-3. Description of Selection Criteria
Selection Criteria
Description
Goodness-of-fit statistics
If an appropriate measure for model selection is reported for each of several models in a study,
then this measure may be used as the basis on which to select a model.
Best captures distributed
Select the model that appears to best capture a distributed lag effect: If multiple single-lag models
lag
and/or moving average models are specified, select the model with the largest effect estimate, all
else equal.
Best set of control
Select the model which includes temporal variables (i.e. season, weather patterns, day of the
variables
week) and other known non-pollutant confounders, all else equal. Select the model which uses
the most sophisticated methods of capturing the relationship between these variables and the
dependent variable (e.g., affords the most flexibility in fitting possible nonlinear trends).
Useful for health effects
The model must be in a form that is useful for health effects modeling (e.g., the pollutant variable
modeling
should be a continuous variable rather than a categorical variable).
Biologically plausible
Select only those models that are biologically plausible.
Sample size
Select the model with the larger sample size, all else equal.
Goodness-of-Fit Statistics
Model specification (or mis-specification) is one of the most important issues confronting
researchers - and those who apply the results of their research. The goal is to select the "right model" -
i.e., the model that has included all the variables that should be in the model (i.e., are relevant) and has
not included any variables that should not be in the model (i.e., that are irrelevant). However, is not often
known which model is the "right model." There are several ways of selecting one model from among
several. One way is to use a goodness of fit measure, which provides a measure of how well a model fits
the data. There are a variety of goodness of fit measures available, but use of such measures can at times
be misleading. In order to select models based on a goodness of fit criterion, it is important to understand
the meaning behind typical goodness of fit measures.
One of the most common goodness of fit measures is R2, often called the "explained variance" or
the "coefficient of multiple determination." R2 measures the proportion of the total variability in the
dependent variable (e.g., the daily incidence of a health effect) that is explained by the linear regression.
The closer R2 is to 1.0, the greater this proportion. The problem with R2, however, is that it can be
increased simply by adding more independent variables to the model, regardless of the variables'
relevance to predicting the dependent variable. In the extreme, if there are N observations in the dataset,
a model with N explanatory variables will result in an R2 of 1, but it would be a meaningless model with
respect to predictive value. If several models are reported in a study, all with the same number of
variables, this drawback is avoided. In that case, if R2 is reported for each estimated model, this may be a
reasonable measure of the relative goodness of fit of the models and an acceptable way to select a single
model from among several.
In many cases, however, R2 is a problematic measure of goodness of fit, for the reason stated
above. In view of the drawback of R2, several alternative measures of goodness of fit have been
developed which essentially penalize the model for additional variables - or, equivalently, give "points"
for parsimony. Two of the more commonly used of these measures are the adjusted R2 and Akaike's
Information Criterion (AIC). The selection criterion, using the adjusted R2, is to select the model with the
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largest adjusted R2; the selection criterion, using the AIC, is to select the model with the smallest AIC.
Both of these measures offset the incremental "fit" gained by including variables in the model with a
"penalty" for increasing the number of explanatory (independent) variables. It should be noted, however,
that several such measures have been suggested, and there is no clear way to determine which of these
measures to select the "best" model is itself the "best" measure. Nevertheless, if a measure of goodness
of fit (particularly, one of the measures that consider parsimony) is presented in a paper, this provides a
reasonable means by which to select one model out of several.
Often, however, no goodness of fit measure is presented in a paper. A common approach for
deciding the appropriate set of independent variables to be included in a model is to include a variable if
its t-value exceeds the critical value for testing whether the variable's coefficient is significantly different
from zero at the 5 percent level. Several variables, or an entire model, can similarly be tested with an F-
test. (If all the coefficients are being tested jointly, the null hypothesis being tested is that all the
coefficients are zero, in which case the model has no more predictive value than the mean of the
dependent variable.) In some cases, a comparison of F-statistics (or their corresponding p-values) can be
used to select from among several models - in particular, if the F-test for one model suggests that one
cannot reject the null hypothesis at the five percent level whereas the F-test for another model suggests
that one should reject the null hypothesis.7
For example, Stieb et al. (1996) estimated the association between ozone and ER visit rates using
both a linear model (in which ER visit rate was a linear function of ozone level) and a quadratic model (in
which ER visit rate was a linear function of ozone level squared). No goodness of fit measure was
reported in the paper. However, model p-values were reported. The linear model was not statistically
significant at the 5% level, whereas the quadratic model was highly significant. This suggests that the
linear model does no better in predicting ER visits than the mean of ER visits, whereas the quadratic
model has predictive value. The authors of the study themselves noted that "only ozone appeared to have
a nonlinear relationship with visit rates" (Stieb et al., 1996, p. 1356) and that "quadratic, linear-quadratic,
and indicator models consistently fit the data better than the linear model..." (Stieb et al., 1996, p. 1358).
Based on the relative model p-values presented in the paper, corroborated by the authors' observations,
the quadratic model was selected for inclusion in this analysis.
Best Captures a Distributed Lag Effect.
The question of lags and the problems of correctly specifying the lag structure in a model has
been discussed extensively (U.S. EPA, 2002a, Section 8.4.4). In many time-series studies, after the basic
model is fit (before considering the pollutant of interest), several different lags are typically fit in separate
single-lag models and the most significant lag is chosen. The 2002 draft PM CD notes that "while this
practice may bias the chance of finding a significant association, without a firm biological reason to
establish a fixed pre-determined lag, it appears reasonable" (U.S. EPA, 2002a, p. 8-237).
There is recent evidence (Schwartz, 2000b) that the relationship between PM and health effects
may best be described by a distributed lag (i.e., the incidence of the health effect on day n is influenced by
PM concentrations on day n, day n-1, day n-2 and so on). If this is the case, a model that includes only a
single lag (e.g., a 0-day lag or a 1-day lag) is likely to understate the total impact of PM. The 2002 draft
PM CD makes this point, noting that "if one chooses the most significant single lag day only, and if more
7 If F-statistics are both (or all) greater than the critical value, it is less clear that a comparison of these F-statistics would
be a good way to select a model.
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than one lag day shows positive (significant or otherwise) associations with mortality, then reporting a
RR [relative risk] for only one lag would also underestimate the pollution effects" (U.S. EPA, 2002a, p.
8-241). The same may hold true for other pollutants that have been associated with various health effects.
Several studies report similar models with different lag structures. For example, Moolgavkar
(2000c) studied the relationship between air pollution and respiratory hospital admissions in three U.S.
metropolitan areas. The author reports models with PM lagged from zero to five days. Since the lagging
of PM was the only difference in the models and the relationship is probably best described using a
distributed lag model, any of single-lag effect estimates are likely to underestimate the full effect.
Therefore, we selected the model with the largest effect estimate.
Most Sophisticated Model That Includes Temporal Variables
A correctly specified model for evaluating air pollution and health would include all variables
that are relevant independent predictors of the health outcome and none that are not. If there are variables
that are known from prior literature to be associated with both air pollution and the health endpoint (e.g.
temperature or season), then omitting these variables is likely to result in biased effect estimates - the C-R
function would attribute too much or too little of the health effect to the pollutant. Since temporal and
weather patterns are known to confound the relationship between air pollution and health, we selected the
models which, all else equal, adjusted for these factors over those that did not.
Useful for Health Effects Modeling
In order for a model to be selected for use, the pollutant must be a continuous variable, so that
changes in incidence of the health effect can be predicted to result from any change in pollutant
concentration. Those models which examine the effects of being above or below a pollutant threshold or
those that look at changes in health associated with categories of pollutant levels are not useful for this
purpose.
For example, in a study of the association between air pollution and emergency room (ER) visits,
Stieb et al. (1996) estimated several different models. One of these models relates ER visit rates to being
above or below the 95th percentile value of ozone (that is, it essentially estimates an average ER visit rate
for days above the 95th percentile value of ozone and a different average ER visit rate for days below it).
In another study, Peters et al. (2001) estimated a model using quintiles of PM levels. None of these
models is appropriate for use in CAPMS. Instead, we selected models which associate the incidence
(rate) of a health effect with the pollutant concentration.
Biologically Plausible.
If a model includes a relationship that simply doesn't make biological sense, it is probably mis-
specified and should not be used for predictive purposes. It is sometimes not clear, however, what is
biologically plausible and what is not. For example, Stieb et al. (1996) estimated a linear-quadratic model
- i.e., a model which included both ozone and the square of ozone as independent variables - in a study
of air pollution and ER visits. The coefficient of the linear term in this model was negative, while the
coefficient of the quadratic term was positive. A graph of the model showed a curve which "dips" at low
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levels of ozone - i.e. at low ozone levels, increases in ozone are associated with decreases in risk. Since
ozone is not likely to be beneficial at any levels, this model is not considered to be biologically plausible.
Sample Size
Several studies report the results of an analysis using different population subsets. All else equal,
the model based on the larger population, which results in more statistical power, is selected. For
example, Pope et al. (1991) studied the association between PM and respiratory health in children. The
authors report results for a school-based sample of 34 children and a patient-based sample of 21 residents.
Since there are many more observations in the school-based sample (3,096 versus 1,912) and no other
significant differences between the models, the model estimated from the school-based sample is used.
Chen et al. (2000) examined the association between air pollution and school absenteeism. The
authors reported results by elementary school grade and for all grades combined. With all else equal in
the models, the C-R function with the larger number of observations was selected (i.e., the model based
on all grades combined).
As discussed above, these criteria are used as general guidance when it is not obvious which
model should be chosen from a particular study. The purpose of this process is to provide as objective a
protocol as possible for selecting C-R functions. However, model selection can never be a completely
mechanical and objective process because it often depends on the specific context of the particular study.
In some cases, consideration of several of the aforementioned criteria must be weighed before selecting
C-R functions for use in the analysis. The C-R functions selected for use in this analysis are described
below with study summaries and a description of which model was selected, when multiple models are
available.
D .4 Issues in Using Concentration-Response Functions
This section briefly summarizes some of the issues that arise when using C-R functions.
D .4.1 S-Plus Issue
Recently, the Health Effects Institute (HEI) reported findings by health researchers at Johns
Hopkins University and others that have raised concerns about aspects of the statistical methods used in a
number of recent time-series studies of short-term exposures to air pollution and health effects
(Greenbaum, 2002). The estimates derived from the long-term exposure studies, which typically account
for a major share of the economic benefits, are not affected. Similarly, the time-series studies employing
generalized linear models (GLMs) or other parametric methods, as well as case-crossover studies, are not
affected.
As discussed in HEI materials provided to EPA and to CASAC (Greenbaum, 2002), researchers
working on the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) found problems in
the default "convergence criteria" used in Generalized Additive Models (GAM) and a separate issue first
identified by Canadian investigators about the potential to underestimate standard errors in the same
statistical package. These and other scientists have begun to reanalyze the results of several important
time series studies with alternative approaches that address these issues and have found a downward
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revision of some results. For example, the mortality risk estimates for short-term exposure to PM10 from
NMMAPS were overestimated (this study was not used in this benefits analysis of fine particle effects).
However, both the relative magnitude and the direction of bias introduced by the convergence issue is
case-specific. In the C-R functions described in detail in Appendices F and G, we have included the
available reanalyses of previous studies, such as those collected in a recent document from the Health
Effects Institute (2003).
D .4.2 Thresholds
When conducting clinical (chamber) and epidemiological studies, C-R functions may be
estimated with or without explicit thresholds. Air pollution levels below the threshold are assumed to
have no associated adverse health effects. When a threshold is not assumed, as is often the case in
epidemiological studies, any exposure level is assumed to pose a non-zero risk of response to at least one
segment of the population.
The possible existence of an effect threshold is a very important scientific question and issue for
policy analyses. The EPA Science Advisory Board Advisory Council for Clean Air Compliance, which
provides advice and review of EPA's methods for assessing the benefits and costs of the Clean Air Act
under Section 812 of the Clean Air Act, has advised EPA that there is currently no scientific basis for
selecting a threshold of 15 |ig/m3 or any other specific threshold for the PM-related health effects
considered in typical benefits analyses (U.S. EPA, 1999b). This is supported by the recent literature on
health effects of PM exposure (Rossi et al., 1999; Daniels et al., 2000; Pope, 2000; Schwartz, 2000c)
which finds in most cases no evidence of a non-linear concentration-response relationship and certainly
does not find a distinct threshold for health effects. The most recent draft of the EPA Air Quality Criteria
for Particulate Matter (U.S. EPA, 2002a) reports only one study, analyzing data from Phoenix, AZ, that
reported even limited evidence suggestive of a possible threshold for PM2 5 (Smith et al., 2000).
Recent cohort analyses by the Health Effects Institute (Krewski et al., 2000) and Pope et al. (Pope
et al., 2002) provide additional evidence of a quasi-linear concentration-response relationship between
long-term exposures to PM2 5 and mortality. According to the latest draft PM criteria document, Krewski
et al. "found a visually near-linear relationship between all-cause and cardiopulmonary mortality residuals
and mean sulfate concentrations, near-linear between cardiopulmonary mortality and mean PM2 5, but a
somewhat nonlinear relationship between all-cause mortality residuals and mean PM2 5 concentrations that
flattens above about 20 |ig/m\ The confidence bands around the fitted curves are very wide, however,
neither requiring a linear relationship nor precluding a nonlinear relationship if suggested by reanalyses."
The Pope et al. analysis, which represented an extension to the Krewski et al. analysis, found that the
concentration-response relationships relating PM2 5 and mortality "were not significantly different from
linear associations."
Daniels et al. (2000) examined the presence of threshold in PM10 concentration-response
relationships for daily mortality using the largest 20 U.S. cities for 1987-1994. The results of their
models suggest that the linear model was preferred over spline and threshold models. Thus, these results
suggest that linear models without a threshold may well be appropriate for estimating the effects of PM10
on the types of mortality of main interest. Schwartz and Zanobetti (2000) investigated the presence of
threshold by simulation and actual data analysis of 10 U.S. cities. In the analysis of real data from 10
cities, the combined concentration-response curve did not show evidence of a threshold in the PM10-
mortality associations. Schwartz et al. (2002) investigated thresholds by combining data on the PM25-
mortality relationships for six cities and found an essentially linear relationship down to 2 |ig/m3. which is
D-20
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Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
at or below anthropogenic background in most areas. They also examined just traffic related particles and
again found no evidence of a threshold. The Smith et al. (2000) study of associations between daily total
mortality and PM25 and PM10_2 5 in Phoenix, AZ (during 1995-1997) also investigated the possibility of a
threshold using a piecewise linear model and a cubic spline model. For both the piecewise linear and
cubic spline models, the analysis suggested a threshold of around 20 to 25 |ig/m \ However, the
concentration-response curve for PM2 5 presented in this publication suggests more of a U- or V-shaped
relationship than the usual "hockey stick" threshold relationship.
Finally, in a recent review of methods for estimating the public health benefits of air pollution
regulations, National Research Council (2002) concluded that there is no evidence for any departure from
linearity in the observed range of exposure to PM10 or PM2 5, nor any indication of a threshold. They cite
the weight of evidence available from both short and long term exposure models and the similar effects
found in cities with low and high ambient concentrations of PM.
D .4.3 Degree of Prematurity of Mortality
It is possible that the short-term studies are detecting an association between air pollution and
mortality that is primarily occurring among terminally ill people. Critics of the use of short-term studies
for policy analysis purposes correctly point out that an added risk factor that results in terminally ill
people dying a few days or weeks earlier than they otherwise would have (referred to as "short-term
harvesting") is potentially included in the measured PM mortality "signal" detected in such a study.
While some of the detected excess deaths may have resulted in a substantial reduction in lifespan, others
may have resulted in a relatively small decrease in lifespan. Studies by Spix et al (1993) and Pope et al.
(1992) yield conflicting evidence, suggesting that harvesting may represent anywhere from zero to 50
percent of the deaths estimated in short-term studies. However, recent work by Zeger et al. (1999),
Schwartz (2000a), and Zanobetti et al. (2002) that focused exclusively on this issue, reported that short-
term harvesting does not play a major role in the PM-mortality relationship.8
Moreover, it is not likely that the excess mortality reported in a long-term prospective cohort
study like Pope et al. (1995) contains any significant amount of this short-term harvesting. The Cox
proportional hazard statistical model used in the Pope study examines the question of survivability
throughout the study period (ten years). Deaths that are premature by only a few days or weeks within
the ten-year study period (for example, the deaths of terminally ill patients, triggered by a short duration
PM episode) are likely to have little impact on the calculation of the average probability of surviving the
entire ten-year interval.
D .4.4 Estimating Effects for Multiple Age Groups
For analyses focusing on a year well past the year 2000, you should note that the population age
distribution is expected to change over time, with a greater percentage of the population moving into
older age categories. Because baseline incidence rates for older populations tend to exceed those for
younger populations for several health endpoints (most importantly, for mortality), this demographic shift
has important implications for the estimation of future-year incidence change. If you apply a C-R
8Zeger et al. (1999, p. 171) reported that: "The TSP-mortality association in Philadelphia is inconsistent with the
harvesting-only hypothesis, and the harvesting-resistant estimates of the TSP relative risk are actually larger - not smaller - than the
ordinary estimates."
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Appendix D. Types of C-R Functions & Issues in the
Estimation of Adverse Health Effects
function to an entire population, using one average baseline incidence, this demographic shift would be
missed, and the future-year incidence change would be significantly underestimated.
To take into account projected demographic shifts and the corresponding implications for
predicted incidence change, we have included C-R functions for separate age groups within the entire
population to which a C-R function is applicable, using projected populations in each age group.
Projected baseline incidences (incidence rates times populations) used in the calculation of future-year
pollutant-related incidence change therefore better reflect the expected demographic shifts.
The ideal approach would be have future-year incidence rates. However, these are not available.
Thus to the extent that you use baseline incidence rates (which may decline slightly over time for younger
age groups and increase for the oldest groups), you may be mis-estimating incidence change for particular
age groups to the extent that baseline incidence rates change overtime.
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Appendix E: Sources of Prevalence and Incidence Data
Concentration-Response (C-R) functions developed from log-linear or logistic models estimate
the percent change in an adverse health effect associated with a given pollutant change. In order to
estimate the absolute change in incidence using these functions, we need the baseline incidence rate of the
adverse health effect. This appendix describes the data used to estimate baseline incidence rates for the
health effects considered in this analysis.
E .1 Mortality
Age, cause, and county-specific mortality rates were obtained from the U.S. Centers for Disease
Control (CDC) for the years 1996 through 1998. CDC maintains an online data repository of health
statistics, CDC Wonder, accessible at http://wonder.cdc.gov/. The mortality rates provided are derived
from U.S. death records and U.S. Census Bureau postcensal population estimates. Mortality rates were
averaged across three years (1996 through 1998) to provide more stable estimates. When estimating rates
for age groups that differed from the CDC Wonder groupings, we assumed that rates were uniform across
all ages in the reported age group. For example, to estimate mortality rates for individuals ages 30 and
up, we scaled the 25-34 year old death count and population by one-half and then generated a population-
weighted mortality rate using data for the older age groups. Population-weighted national mortality rates
are presented in Exhibit E-1.
Exhibit E-l. National Mortality Rates for Selected Conditions, by Age Group
Mortality Category Mortality Rate by Age Group (deaths per 100 people per year)
(ICD codes)
0-17 18-24 25-29 30-34 35-44 45-54 55-64 65-74 75-84 85+
All-Cause
0.045
0.093
0.119
0.119
0.211
0.437
1.056
2.518
5.765
15.160
Non-Accidental (ICD <800)
0.025
0.022
0.057
0.057
0.150
0.383
1.006
2.453
5.637
14.859
Chronic Lung Disease (ICD
0.000
0.001
0.001
0.001
0.002
0.009
0.046
0.166
0.367
0.561
490-496)
Cardio-Pulmonary
0.004
0.005
0.013
0.013
0.044
0.143
0.420
1.163
3.179
9.846
Source: We obtained data from 1996-1998 from the CDC Wonder (http://wonder.ede.gov/). County-specific rates are used in the
C-R functions.
E .2 Hospitalizations
Regional hospitalization counts were obtained from the National Center for Health Statistics'
(NCHS) National Hospital Discharge Survey (NHDS). NHDS is a sample-based survey of non-Federal,
short-stay hospitals (<30 days)9, and is the principal source of nationwide hospitalization data. The
survey collects data on patient characteristics, diagnoses, and medical procedures.
9The following hospital types are excluded from the survey: hospitals with an average patient length of stay of greater than
30 days, federal, military, Department of Veterans Affairs hospitals, institutional hospitals (e.g. prisons), and hospitals with fewer
than six beds.
E-l
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Appendix E. Sources of Prevalence and Incidence Data
Public use data files for the year 1999 survey were downloaded10 and processed to estimate
hospitalization counts by region. NCHS groups states into four regions using the following groupings
defined by the U.S. Bureau of the Census:
• Northeast - Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New
York, New Jersey, Pennsylvania
• Midwest - Ohio, Indiana, Illinois, Michigan, Wisconsin, Minnesota, Iowa, Missouri, North
Dakota, South Dakota, Nebraska, Kansas
• South - Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina,
South Carolina, Georgia, Florida, Kentucky, Tennessee, Alabama, Mississippi, Arkansas,
Louisiana, Oklahoma, Texas
• West - Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada,
Washington, Oregon, California, Alaska, Hawaii
We calculated per capita hospitalization rates, by dividing these counts by the estimated regional
population estimates for 1999 that we derived from the U.S. Bureau of the Census and the population
projections used by NHDS to generate the counts. Note that NHDS started with hospital admission
counts, based on a sample of admissions, and then they used population estimates to generate population-
weighted hospital admission counts that are representative of each region. This weighting used forecasts
of 1999 population data. Ideally, we would use these same forecasts to generate our admission rates.
However, while NHDS presented counts of hospital admissions with a high degree of age specificity, it
presented regional population data for only four age groups: 0-14, 15-44, 45-64, and 65+.11 Using only
the NHDS data, we would be limited to calculating regional admission rates for four groups. Because we
are interested in a broader range of age groups, we turned to 2000 Census.
We used the 2000 Census to obtain more age specificity, and then corrected the 2000 Census
figures so that the total population equaled the total for 1999 forecasted by NHDS. That is, we sued the
following procedure: (1) we calculated the count of hospital admissions by region in 1999 for the age
groups of interest, (2) we calculated the 2000 regional populations corresponding to these age groups, (3)
calculated regional correction factors, that equal the regional total population in 1999 divided by the
regional total population in 2000 by region, (4) multiplied the 2000 population estimates by these
correction factors, and (5) divided the 1999 regional count of hospital admissions by the estimated 1999
population.
The endpoints in hospitalization studies are defined using different combinations of ICD codes.
Rather than generating a unique baseline incidence rate for each ICD code combination, for the purposes
of this analysis, we identified a core group of hospitalization rates from the studies and applied the
appropriate combinations of these rates in the C-R functions:
• all respiratory (ICD-9 460-519)
• chronic lung disease (ICD-9 490-496)
• asthma (ICD-9 493)
• pneumonia (ICD-9 480-487)
• acute bronchitis (ICD-9 466)
• acute laryngitis (ICD-9 464)
• all cardiovascular (ICD-9 390-459)
10 Data are available at ftp://ftp.edc.gov/pub/Health_Statistics/NCHS/Datasets/NHDS/
11 See: 1999nhds_summary.pdf (p. 187) for published regional population estimates for 1999.
E-2
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Appendix E. Sources of Prevalence and Incidence Data
• ischemic heart disease (ICD-9 410-414)
• dysrhythmia (ICD-9 427)
• congestive heart failure (ICD-9 428)
For each C-R function, we selected the baseline rate or combination of rates that most closely
matches to the study endpoint definition. For studies that define chronic lung disease as ICD 490-492,
494-496, we subtracted the incidence rate for asthma (ICD 493) from the chronic lung disease rate (ICD
490-496). In some cases, the baseline rate will not match exactly to the endpoint definition in the study.
For example, Burnett et al. (2001) studied the following respiratory conditions in infants <2 years of age:
ICD 464.4, 466, 480-486, 493. For this C-R function we apply an aggregate of the following rates: ICD
464, 466, 480-487, 493. Although they do not match exactly, we assume that relationship observed
between the pollutant and study-defined endpoint is applicable for the additional codes. Exhibit E-2
presents a summary of the national hospitalization rates for 1999 from NHDS.
Exhibit E-2. Hospitalization Rates, by Region and Age Group
Hospitalization Rate by Age Group
Hospitaliz ation Category (admissions per 100 people per year)
0-18
18-24
25-34
35-44
45-54
55-64
65+
Respiratory
all respiratory
460-519
1.066
0.271
0.318
0.446
0.763
1.632
5.200
acute laryngitis
464
0.055
0.002
0.001
0.002
0.008
0.000
0.005
acute bronchitis
466
0.283
0.017
0.014
0.017
0.027
0.040
0.156
pneumonia
480-487
0.308
0.069
0.103
0.155
0.256
0.561
2.355
asthma
493
0.281
0.081
0.110
0.099
0.144
0.161
0.205
chronic lung disease
490-496
0.291
0.089
0.124
0.148
0.301
0.711
1.573
Cardiovascular
all cardiovascular
390-429
0.030
0.052
0.146
0.534
1.551
3.385
8.541
ischemic heart disease
410-414
0.004
0.008
0.031
0.231
0.902
2.021
3.708
dysrhythmia
427
0.011
0.017
0.027
0.076
0.158
0.392
1.387
congestive heart failure
428
0.003
0.005
0.011
0.011
0.160
0.469
2.167
Source: As described in the text, we obtained the regional count of hospital admissions from National Hospital Discharge Survey
(NHDS), and we obtained the population data from the 2000 U.S. Census and NHDS.
E .3 Emergency Room Visits for Asthma
Regional asthma emergency room visit counts were obtained from the National Hospital
Ambulatory Medical Care Survey (NHAMCS). NHAMCS is a sample-based survey, conducted by
NCHS, designed to collect national data on ambulatory care utilization in hospital emergency and
outpatient departments of non-Federal, short-stay hospitals (<30 days).12
12 The target universe of the NHAMCS is in-person visits made in the United States to emergency and outpatient
departments of non-Federal, short-stay hospitals (hospitals with an average stay of less than 30 days) or those whose specialty is
general (medical or surgical) or children's general.
E-3
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Appendix E. Sources of Prevalence and Incidence Data
Public use data files for the year 2000 survey were downloaded13 and processed to estimate
hospitalization counts by region. We obtained population estimates from the 2000 U.S. Census. The
NCHS regional groupings described above were used to estimate regional emergency room visit rates.
Exhibit E-3 presents the estimated asthma emergency room rates by region.
Exhibit E-3. Emergency Room Visit Rates for Asthma, by Region and Age Group
ER Category
ICD-9 Code
Region
0-18
ER Visit Rate
(visits per 100 people per year)
18-64
65+
asthma
493
Northeast
0.761
0.802
0.300
Midwest
1.476
0.877
0.334
South
1.243
0.420
0.192
West
0.381
0.381
0.137
Source: We obtained ER visit counts for the year 2000 from the National Hospital Ambulatory Medical Care Survey (NHAMCS)
and population data were obtained from the 2000 U.S. Census.
E .4 Nonfatal Heart Attacks
The relationship between short-term particulate matter exposure and heart attacks was quantified
in a case-crossover analysis by Peters et al. (2001). The study population was selected from heart attack
survivors in a medical clinic. Therefore, the applicable population to apply to the C-R function is all
individuals surviving a heart attack in a given year. Several data sources are available to estimate the
number of heart attacks per year. For example, several cohort studies have reported estimates of heart
attack incidence rates in the specific populations under study. However, these rates depend on the
specific characteristics of the populations under study and may not be the best data to extrapolate
nationally. The American Heart Association reports approximately 540,000 new heart attacks per year
using data from a multi-center study (Haase, 2002, to be published in the American Heart Association's
2003 Statistical Handbook). Exclusion of heart attack deaths reported by CDC Wonder yields
approximately 330,000 nonfatal cases per year.
An alternative approach to the estimation of heart attack rates is to use data from the National
Hospital Discharge Survey, assuming that all heart attacks that are not instantly fatal will result in a
hospitalization. According to the National Hospital Discharge Survey, in 1999 there were approximately
829,000 hospitalizations due to heart attacks (acute myocardial infarction: ICD-9 410) (Popovic, 2001,
Table 8). We used regional hospitalization rates over estimates extrapolated from cohort studies because
the former is part of a nationally representative survey with a larger sample size, which is intended to
provide reliable national estimates. As additional information is provided regarding the American Heart
Association methodology, we will evaluate the usefulness of this estimate of heart attack incidence.
Rosamond et al. (1999) reported that approximately six percent of male and eight percent of
female hospitalized heart attack patients die within 28 days (either in or outside of the hospital). We,
therefore, applied a factor of 0.93 to the count of hospitalizations to estimate the number of nonfatal heart
attacks per year. To estimate the rate of nonfatal heart attack, we divided the count by the population
13 Data are available at ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Datasets/NHAMCS/
E-4
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Appendix E. Sources of Prevalence and Incidence Data
estimate for 2000 from the U.S. Census. Exhibit E-4 presents the regional nonfatal heart attack incidence
rates.
Exhibit E-4. Nonfatal Heart Attack Rates, by Region and Age Group
Endpoint (ICD codes)
Region
0-18
Nonfatal Heart Attack Rate
(cases per 100 people per year) *
18-64
65+
nonfatal heart attacks (ICD-9 410)
Northeast
0.0000
0.2167
1.6359
Midwest
0.0003
0.1772
1.4898
South
0.0006
0.1620
1.1797
West
0.0000
0.1391
1.1971
" Rates are based on data from the 1999 National Hospital Discharge Survey (NHDS) and an estimate from Rosamond et al.
(1999) that approximately 7% of individuals hospitalized for a heart attack die within 28 days.
E .5 School Loss Days
Epidemiological studies have examined the relationship between air pollution and a variety of
measures of school absence. These measures include: school loss days for all causes, illness-related, and
respiratory illness-related. We have two sources of information. The first is the National Center for
Education Statistics, which provided an estimate of all-cause school loss days, and the other is the
National Health Interview Survey (Adams et al., 1999, Table 47), which has data on different categories
of acute school loss days. Exhibit E-5 presents the illness-related rates used in this analysis.
E .5.1 All-Cause School Loss Rates
Based on data from the U.S. Department of Education (1996, Table 42-1), the National Center for
Education Statistics estimates that for the 1993-1994 school year, 5.5 percent of students are absent from
school on a given day. This estimate is comparable to study-specific estimates from Chen et al. (2000)
and Ransom and Pope (1992), which ranged from 4.5 to 5.1 percent.
We use the total or all-cause school absence rate in C-R functions based on studies by Chen et al.
(2000), Gilliland et al. (2001) and Ransom et al. (1992). We also use the all-cause school absence rate as
a population adjustment in C-R functions derived from Gilliland et al. (2001), for which it is necessary to
estimate the average proportion of children attending school on a given day. This is described in more
detail in the specific C-R function summaries.
E .5.2 Illness-Related School Loss Rates
The National Health Interview Survey (NHIS) has regional estimates of school loss days due to a
variety of acute conditions (Adams et al., 1999). NHIS is a nationwide sample-based survey of the health
of the noninstitutionalized, civilian population, conducted by NCHS. The survey collects data on acute
conditions, prevalence of chronic conditions, episodes of injury, activity limitations, and self-reported
health status. However, it does not provide an estimate of all-cause school loss days.
E-5
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Appendix E. Sources of Prevalence and Incidence Data
In estimating illness-related school loss days, we started with school loss days due to acute
problems (Adams et al., 1999, Table 47) and subtracted lost days due to injuries, in order to match the
definition of the study used in the C-R function to estimate illness-related school absences (Gilliland et
al., 2001). We then divided by 180 school days per to estimate /'//ness-related school absence rates per
school day. Similarly, when estimating respiratory illness-related school loss days, we use data from
Adams et al. (1999, Table 47). Note that we estimated 180 school days in a year to calculate respiratory
illness-related school absence rates per year.
Exhibit E-5. School Loss Day Rates
Type of School Loss Day "
Northeast
Absence Rate by Region
(cases per 100 students per year)
Midwest South
West
Respiratory illness-related absences
131.4
165.6
109.8
223.2
Illness-related absences
244.8
262.8
255.6
370.8
All-cause
990.0
990.0
990.0
990.0
s We based illness-related school loss day rates on data from the 1996 NHIS (Adams et al., 1999, Table 47) and an estimate of
180 school days per year. This excludes school loss days due to injuries. We based the all-cause school loss day rate on data
from the National Center for Education Statistics (U.S. Department of Education, 1996, Table 42-1).
E .6 Other Acute and Chronic Effects
For many of the minor effect studies, baseline rates from a single study are often the only source
of information, and we assume that these rates hold for locations in the U.S. The use of study-specific
estimates are likely to increase the uncertainty around the estimate because they are often estimated from
a single location using a relatively small sample. These endpoints include: acute bronchitis, chronic
bronchitis, upper respiratory symptoms, lower respiratory symptoms. Exhibit E-6 presents a summary of
these baseline rates.
E-6
-------
Appendix E. Sources of Prevalence and Incidence Data
Exhibit E-6.
Selected Acute and Chronic Effects Rates
Endpoint
Age
Parameter"
Rate
Source
Acute Bronchitis
8-12
Incidence
4.300
(American Lung Association, 2002a,
Table 11)
Chronic Bronchitis
27+
Incidence
0.378
(Abbey et al., 1993, Table 3)
Chronic Bronchitis
18+
Prevalence
4.43%
18-44
45-64
3.67%
5.05%
(American Lung Association, 2002b,
Table 4)
65+
5.87%
Lower Respiratory Symptoms
(LRS)
7-14
Incidence
43.8
(Schwartz et al., 1994, Table 2)
Minor Restricted Activity Days
(MRAD)
18-64
Incidence
780.0
(Ostro and Rothschild, 1989, p. 243)
Work Loss Day (WLD)
18-64
Incidence
217.2
18-24
25-44
197.1
247.5
(Adams et al., 1999, Table 41); (U.S.
Bureau of the Census, 1997, No. 22)
45-64
179.6
s The incidence rate is the number of cases per 100 people per year. Prevalence refers to the fraction of people that have a
particular illness during a particular time period.
E .6.1 Acute Bronchitis
The annual rate of acute bronchitis for children ages 5 to 17 was obtained from the American
Lung Association (2002a, Table 11). The authors reported an annual incidence rate per person of 0.043,
derived from the 1996 National Health Interview Survey.
E .6.2 Chronic Bronchitis Incidence Rate
The annual incidence rate for chronic bronchitis is estimated from data reported by Abbey et
al.(1993, Table 3). The rate is calculated by taking the number of new cases (234), dividing by the
number of individuals in the sample (3,310), dividing by the ten years covered in the sample, and then
multiplying by one minus the reversal rate (estimated to be 46.6% based on Abbey et al. (1995a, Table
1)). We then multiplied this result by 100 to calculate an annual incidence rate per 100 people of 0.378.
Age-specific incidence rates are not available. Abbey et al. (1995a, Table 1) did report the
incidences by three age groups (25-54, 55-74, and 75+) for "cough type" and "sputum type" bronchitis.
However, they did not report an overall incidence rate for bronchitis by age-group. Since, the cough and
sputum types of bronchitis overlap to an unknown extent, we did not attempt to generate age-specific
incidence rates for the over-all rate of bronchitis.
E-7
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Appendix E. Sources of Prevalence and Incidence Data
E .6.3 Chronic Bronchitis Prevalence Rate
We obtained the annual prevalence rate for chronic bronchitis from the American Lung
Association (2002b, Table 4). Based on an analysis of 1999 National Health Interview Survey data, they
estimated a rate of 0.0443 for persons 18 and older, they also reported the following prevalence rates for
people in the age groups 18-44, 45-64, and 65+: 0.0367, 0.0505, and 0.0587, respectively.
E .6.4 Lower Respiratory Symptoms
Lower respiratory symptoms (LRS) are defined as two or more of the following: cough, chest
pain, phlegm, wheeze. The proposed yearly incidence rate for 100 people, 43.8, is based on the
percentiles in Schwartz et al. (Schwartz et al., 1994, Table 2). The authors did not report the mean
incidence rate, but rather reported various percentiles from the incidence rate distribution. The percentiles
and associated per person per day values are 10th = 0 percent, 25th = 0 percent, 50th = 0 percent, 75th = 0.29
percent, and 90th = 0.34 percent. The most conservative estimate consistent with the data are to assume
the incidence per person per day is zero up to the 75th percentile, a constant 0.29 percent between the 75th
and 90th percentiles, and a constant 0.34 percent between the 90th and 100th percentiles. Alternatively,
assuming a linear slope between the 50th and 75th, 75th and 90th, and 90th to 100th percentiles, the estimated
mean incidence rate per person per day is 0.12 percent.14 We used the latter approach in this analysis, and
then multiplied by 100 and by 365 to calculate the incidence rate per 100 people per year.
E .6.5 Minor Restricted Activity Days (MRAD)
Ostro and Rothschild (1989, p. 243) provide an estimate of the annual incidence rate of MRADs
(7.8). We multiplied this estimate by 100 to get an annual rate per 100 people.
E .6.6 Work Loss Days
The yearly work-loss-day incidence rate per 100 people is based on estimates from the 1996
National Health Interview Survey (Adams et al., 1999, Table 41). They reported a total annual work loss
days of 352 million for individuals ages 18 to 65. The total population of individuals of this age group in
1996 (162 million) was obtained from (U.S. Bureau of the Census, 1997, No. 22). The average annual
rate of work loss days per individual (2.17) was multiplied by 100 to obtain the average yearly work-loss-
day rate of 217 per 100 people. Using a similar approach, we calculated work-loss-day rates for ages 18-
24, 25-44, and 45-64, respectively.
E .7 Asthma-Related Health Effects
Several studies have examined the impact of air pollution on asthma development or
exacerbation. Many of the baseline incidence rates used in the C-R functions are based on study-specific
estimates. The baseline rates for the various endpoints are described below and summarized in Exhibit E-
7.
14 For example, the 62.5th percentile would have an estimated incidence rate per person per day of 0.145 percent.
E-8
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Appendix E. Sources of Prevalence and Incidence Data
Exhibit E-7. Asthma-Related Health Effects Rates
Endpoint
Age
Parameter °
Rate
Source
Acute Bronchitis
9-15
Incidence
32.6
(McConnell et al., 1999, Table 2)
Asthma Attacks
18+
Incidence
2008
1999 National Health Interview Survey
Asthma Exacerbation, Shortness of
Breath, African American
8-13
8-13
Incidence
Prevalence
1351
7.40%
(Ostro et al., 2001, p.202)
Asthma Exacerbation, Wheeze,
African American
8-13
8-13
Incidence
Prevalence
2774
17.30%
(Ostro et al., 2001, p.202)
Asthma Exacerbation, Cough, African
American
8-13
8-13
Incidence
Prevalence
2446
14.50%
(Ostro et al., 2001, p.202)
Asthma Exacerbation, Cough
6-13
Incidence
3139
(Vedal et al., 1998, Table 1 p. 1038)
Asthma Exacerbation, One or more
symptoms
5-13
Incidence
21900
(Yu et al., 2000, Table 2 p. 1212)
Chronic Asthma, Male
27+
Incidence
0.219
(McDonnell et al., 1999, Table 4)
Phlegm
9-15
Incidence
25.7
(McConnell et al., 1999, Table 2)
Upper Respiratory Symptoms (URS)2
9-11
Incidence
12479
(Pope et al., 1991, Table 2)
* The incidence rate is the number of cases per 100 people per year. Prevalence refers to the fraction of people that have a
particular illness during a particular time period.
E .7.1 Asthma Attacks
The annual rate of asthma attacks among asthmatics is estimated from the 1999 National Health
Interview Survey. Individuals with asthma were asked about the number of wheezing attacks per year.
The average number of wheezing attacks per year was multiplied by 100 to obtain a wheezing attack rate
per year per 100 people for individuals 18 and older. We assume that this rate of wheezing attacks can be
used as a surrogate for asthma attacks.
Note that the same survey examined wheezing attacks for children. However, the number of
wheezing attacks per year were censored at 12 (compared to censoring at 95 for adults). Due to the
potential for underestimation of the number of children's wheezing attacks, we used the adult rate for all
individuals.
E .7.2 Asthma Exacerbation
There are a variety of types of symptoms for asthma exacerbation. We calculated rates for
shortness of breath, wheeze, cough, and other asthma related effects.
E .7.3 Shortness of Breath
To estimate the annual rate of new shortness of breath episodes among African-American
asthmatics, ages 8-13, we used the rate reported by Ostro et al. (2001, p.202). We estimated the daily
prevalence of shortness of breath episodes among African-American asthmatics, ages 8-13, by taking a
weighted average of the reported rates in Ostro et al. (2001, p.202).
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Appendix E. Sources of Prevalence and Incidence Data
E .7.4 Wheeze
The daily rate of new wheeze episodes among African-American asthmatics, ages 8-13, is
reported by Ostro et al. (2001, p.202) as 0.076. We multiplied this value by 100 and by 365 to get the
annual incidence rate per 100 people. The daily rate of prevalent wheeze episodes (0.173) among
African-American asthmatics, ages 8-13, is estimated by taking a weighted average of the reported rates
in Ostro et al. (2001, p.202).
E .7.5 Cough
The daily rate of new cough episodes among African-American asthmatics, ages 8-13, is reported
by Ostro et al. (2001, p.202) as 0.067. We multiplied this value by 100 and by 365 to get the annual
incidence rate per 100 people. The daily rate of prevalent cough episodes (0.145) among African-
American asthmatics, ages 8-13, is estimated by taking a weighted average of the reported rates in Ostro
et al. (2001, p.202).
E .7.6 One or More Symptoms
Yu et al. (2000, Table 2, p. 1212) reported a daily rate of at least one asthma episode per
asthmatic child ages 5-13. An asthma episode is defined as at least one of the following asthma
symptoms: wheezing, coughing, chest tightness, or shortness of breath.
E .7.7 Chronic Asthma
We derived the annual incidence rate per 100 people by taking the number of new cases (32),
dividing by the number of individuals in the sample (972), as reported by (McDonnell et al., 1999, Table
4), and then dividing by the 15 years in the sample. We then multiplied by 100 to get the annual
incidence rate per 100 people.
E .7.8 Upper Respiratory Symptoms
Upper Respiratory Symptoms are defined as one or more of the following: runny or stuffy nose;
wet cough; burning, aching, or red eyes. Using the incidence rates for upper respiratory symptoms
among asthmatics, published in Pope et al. (1991, Table 2), we calculated a sample size-weighted average
incidence rate.
E .7.9 Asthma Population Estimates
In studies examining the association between air pollution and the development or exacerbation
of asthma, often times an estimate of the percent of the population with asthma is required. Asthma
percentages were obtained either directly from the National Health Interview Survey (NHIS) or an
American Lung Association (2002c) report summarizing data from NHIS. Exhibit E-8 presents asthma
prevalence rates used define asthmatic populations in the C-R functions.
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Appendix E. Sources of Prevalence and Incidence Data
Exhibit E-8. Asthma Prevalence Rates Used to Estimate Asthmatic Populations
Population Group
Prevalence
Source
All Ages
3.86%
<18
5.27%
5-17
5.67%
American Lung Association (2002c, Table 7)1
18-44
3.71%
45-64
3.33%
65+
2.21%
African-American, 5 to 17
7.26%
American Lung Association (2002c, Table 9)11
African-American, <18
7.35%
Male, 27+
2.10%
2000 NHIS public use data filesb
1 The work by the American Lung Association is based on the 1999 National Health Interview Survey.
b See ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Datasets/NHIS/2000/
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Appendix F: Particulate Matter Concentration-Response Functions
In this Appendix, we present the concentration-response (C-R) functions used to estimate PM-
related adverse health effects. Each sub-section has an Exhibit with a brief description of the C-R
function and the underlying parameters. Following each Exhibit, we present a brief summary of each of
the studies and any items that are unique to the study.
Note that the main text describes the methods that we used to choose these C-R functions from
the wide range available in the literature. In addition, Appendix D mathematically derives the standard
types of C-R functions that we encountered in the epidemiological literature, such as, log-linear, logistic
and linear, so we simply note here the type of functional form. Finally, Appendix E presents a description
of the sources for the incidence and prevalence data used in these C-R functions.
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Appendix F. Particulate Matter C-R Functions
Exhibit F-l. Concentration-Response (C-R) Functions for Particulate Matter and Long-Term Mortality
Endpoint Name
Pollutant
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
i Time
Beta
Std Error
Functional
Form
Notes
All Cause
pm2,
Krewski et
al.
2000
63 cities
30+
All
All
None
Annual
Avg
0.004626
0.001205
Log-linear
ACS reanalysis
All Cause
PM2,
Krewski et
al.
2000
50 cities
30+
All
All
None
Annual
Median
0.005348
0.001464
Log-linear
ACS reanalysis
All Cause
PM2,
Krewski et
al.
2000
nationwide
30+
All
All
None
Annual
Median
0.010394
0.002902
Log-linear
ACS reanalysis; RE
Ind Cities
All Cause
PM2,
Krewski et
al.
2000
nationwide
30+
All
All
None
Annual
Median
0.006058
0.003383
Log-linear
ACS reanalysis; RE
Reg Adj
All Cause
PM2,
Krewski et
al.
2000
6 cities
25+
All
All
None
Annual
Avg
0.013272
0.004070
Log-linear
Six Cities reanalysis
All Cause
PM2,
Pope et al.
1995
50 cities
30+
All
All
None
Annual
Median
0.006408
0.001509
Log-linear
All Cause
PM2,
Dockery et
al.
1993
6 cities
25+
All
All
None
Annual
Avg
0.012425
0.004228
Log-linear
All Cause
PM2,
Pope et al.
2002
61 cities
30+
All
All
None
Annual
Avg
0.004018
0.001642
Log-linear
'79-'83 air data
All Cause
PM2,
Pope et al.
2002
51 cities
30+
All
All
None
Annual
Avg
0.006015
0.002257
Log-linear
Average of '79-'83
and '99-'00 air data
All Cause
Sulfate
Pope et al.
2002
53 cities
30+
All
All
None
Annual
Avg
0.008964
0.001778
Log-linear
Cardiopulmonary
PM2,
Pope et al.
2002
61 cities
30+
All
All
None
Annual
Avg
0.005733
0.002167
Log-linear
'79-'83 air data
Cardiopulmonary
PM2,
Pope et al.
2002
51 cities
30+
All
All
None
Annual
Avg
0.008893
0.002914
Log-linear
Average of '79-'83
and '99-'00 air data
Cardiopulmonary
Sulfate
Pope et al.
2002
53 cities
30+
All
All
None
Annual
Avg
0.007506
0.002690
Log-linear
Lung Cancer
PM2,
Pope et al.
2002
61 cities
30+
All
All
None
Annual
Avg
0.007881
0.003463
Log-linear
'79-'83 air data
Lung Cancer
PM2,
Pope et al.
2002
51 cities
30+
All
All
None
Annual
Avg
0.012663
0.004265
Log-linear
Average of '79-'83
and '99-'00 air data
Lung Cancer
Sulfate
Pope et al.
2002
53 cities
30+
All
All
None
Annual
Avg
0.013962
0.004048
Log-linear
Infant
PM10
Woodruff et al.
1997
86 cities
<1
All
All
None
Annual
Avg
0.003922
0.001221
Logistic
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Appendix F. Particulate Matter C-R Functions
F .1 Long-term Mortality
There are two types of exposure to PM that may result in premature mortality. Short-term
exposure may result in excess mortality on the same day or within a few days of exposure. Long-term
exposure over, say, a year or more, may result in mortality in excess of what it would be if PM levels
were generally lower, although the excess mortality that occurs will not necessarily be associated with
any particular episode of elevated air pollution levels. In other words, long-term exposure may capture a
facet of the association between PM and mortality that is not captured by short-term exposure.
F .1.1 Mortality - Mean, All Cause (Krewski et al., 2000) - Reanalysis of Pope et al. (1995)
The Krewski et al. (2000) reanalysis of Pope et al. (1995) used a Cox proportional hazard model
to estimate the impact of long-term PM exposure. The original investigation followed 295,223
individuals15 ages 30 and over in 50 cities from September 1, 1982 to December 31, 1989, and related
their survival to median PM25 concentrations for 1979 to 1983. Krewski et al. (2000) independently
estimated city-specific annual mean values from EPA's Inhalable Particle Monitoring Network (IPMN)
for the same years (1979-1983). Krewski et al. (2000) followed Pope et al. (1995, Table 2) and reported
results for all-cause deaths, lung cancer (ICD-9 code: 162), cardiopulmonary deaths (ICD-9 codes: 401-
440 and 460-519), and "all other" deaths,16 and found that mean PM2 5 is significantly related to all-cause
and cardiopulmonary mortality. Krewski et al. included only PM, so it is unclear to what extent it may be
including the impacts of ozone or other gaseous pollutants.
Pope et al. (1995) is the better of the two published prospective cohort studies: it has a larger
population and includes more cities than the prospective cohort study by Dockery et al. (1993). Pope et
al.'s study has several further advantages. The population followed in this study was largely Caucasian
and middle class, decreasing the likelihood that interlocational differences in premature mortality were
due in part to differences in race, socioeconomic status, or related factors. In addition, the PM coefficient
in Pope et al. is likely to be biased downward, counteracting a possible upward bias associated with
historical air quality trends discussed earlier. One source of this downward bias is the generally healthier
and study population, in comparison to poorer minority populations. Krewski et al. (2000, Part II - Table
52) found that educational status was a strong effect modifier of the PM - mortality relationship in both
studies, with the strongest effect seen among the less educated. In fact, much of the differences in
magnitude of effect between the studies was made up when assessing risk across comparable levels of
educational attainment.
Another source of downward bias is that intercity movement of cohort members was not
considered in the original study and therefore could not be evaluated in the reanalysis. Migration across
study cities would result in exposures of cohort members being more similar than would be indicated by
assigning city-specific annual average pollution levels to each member of the cohort. The more intercity
migration there is, the more exposure will tend toward an intercity mean. If this is ignored, differences in
exposure levels, that are proxied by differences in city-specific annual average PM levels, will be
exaggerated, and will result in a downward bias of the PM coefficient (because a given difference in
mortality rates is being associated with a larger difference in PM levels than is actually the case).
15 The total study population was 552,138 in 151 cities, however, only 295,223 individuals resided in 50 cities with fine
particle data.
16 All-cause mortality includes accidents, suicides, homicides and legal interventions. The category "all other" deaths is
all-cause mortality less lung cancer and cardiopulmonary deaths.
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Appendix F. Particulate Matter C-R Functions
Single Pollutant Model
The coefficient and standard error are estimated from the relative risk (1.12) and 95% confidence
interval (1.06-1.19) associated with a change in annual mean PM25 exposure of 24.5 |ig/m3 (based on the
range from the original ACS study) (Krewski et al., 2000, Part II - Table 31).
Functional Form: Log-linear
Coefficient: 0.004626
Standard Error: 0.001205
Incidence Rate: county-specific annual all cause mortality rate per person ages 30 and older
Population: population of ages 30 and older
F .1.2 Mortality - Median, All Cause (Krewski et al., 2000) - Reanalysis of Pope et al.
(1995)
Krewski et al. (2000) performed an analysis of Pope et al. (2000) using independently estimated
city-specific annual median values as well. Fine particle estimates were obtained from EPA's Inhalable
Particle Monitoring Network (IPMN) for the years 1979-1983 for the same 50 cities. Overall, the
estimates showed good agreement with the median values used in the original investigation with one
exception. The median fine particle concentration for Denver dropped from 16.1 to 7.8 |ig/m3. resulting
in a larger range between the least and most polluted cities and a reduced relative risk. Since the original
estimate could not be audited, Denver is included in the subsequent C-R function as there is no reason to
believe that the monitoring data is invalid.
Single Pollutant Model
The coefficient and standard error are estimated from the relative risk (1.14) and 95% confidence
interval (1.06-1.22) associated with a change in annual median PM25 exposure of 24.5 |ig/nr' (based on
the range from the original ACS study) (Krewski et al., 2000, Part II - Table 31).
Functional Form: Log-linear
Coefficient: 0.005348
Standard Error: 0.001464
Incidence Rate: county-specific annual all cause mortality rate per person ages 30 and older
Population: population of ages 30 and older
F .1.3 Mortality - Median, Random Effects with Regional Adjustment (Krewski et al.,
2000) - Reanalysis of Pope et al. (1995)
Krewski et al. (2000) also performed an analysis of Pope et al. (2000) using
a random effects model to estimate a regionally-adjusted relative risk. The authors used an indicator
variable representing seven regions of the U.S. The regionally-adjusted estimate was comparable with the
results from the standard Cox Proportional Hazards Model, which assumes that all observations are
statistically independent.
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Appendix F. Particulate Matter C-R Functions
Single Pollutant Model
The coefficient and standard error are estimated from the relative risk (1.16) and 95% confidence
interval (0.99-1.37) associated with a change in annual median PM25 exposure of 24.5 |ig/m3 (based on
the range from the original ACS study) (Krewski et al., 2000, Part II - Table 46).
Functional Form: Log-linear
Coefficient: 0.006058
Standard Error: 0.003383
Incidence Rate: county-specific annual all cause mortality rate per person ages 30 and older
Population: population of ages 30 and older
F .1.4 Mortality - Median, Random Effects with Independent Cities (Krewski et al., 2000)
- Reanalysis of Pope et al. (1995)
Krewski et al. (2000) also performed an analysis of Pope et al. (2000) using a random effects
approach to estimate an independent cities model. This approach incorporates between-city variation into
second-stage modeling weights, thereby avoiding the assumption of independent observations. However,
potential regional patterns in mortality may be overlooked, because the approach assumes that city-
specific mortality rates are statistically independent. The independent cities estimate is considerably
larger than the standard Cox Proportional Hazards Model, which assumes that all observations are
statistically independent.
Single Pollutant Model
The coefficient and standard error are estimated from the relative risk (1.29) and 95% confidence
interval (1.12-1.48) associated with a change in annual median PM25 exposure of 24.5 |ig/m3 (based on
the range from the original ACS study) (Krewski et al., 2000, Part II - Table 46).
Functional Form: Log-linear
Coefficient: 0.010394
Standard Error: 0.002902
Incidence Rate: county-specific annual all cause mortality rate per person ages 30 and older
Population: population of ages 30 and older
F .1.5 Mortality (Krewski et al., 2000) - Reanalysis of Dockery et al. (1993)
Krewski et al. (2000) performed a validation and replication analysis of Dockery et al. (1993).
The originial investigators examined the relationship between PM exposure and mortality in a cohort of
8,111 individuals aged 25 and older, living in six U.S. cities. They surveyed these individuals in 1974-
1977 and followed their health status until 1991. While they used a smaller sample of individuals from
fewer cities than the study by Pope et al., they used improved exposure estimates, a slightly broader study
population (adults aged 25 and older; a higher proportion without a high school education), and a follow-
up period nearly twice as long as that of Pope et al. (1995). Krewski et al. (2000, Part II - Table 52)
found that educational status was a strong effect modifier of the PM - mortality relationship in both
studies, with the strongest effect seen among the less educated. Perhaps because of these differences,
Dockery et al. study found a larger effect of PM on premature mortality than that found by Pope et al.
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Appendix F. Particulate Matter C-R Functions
After an audit of the air pollution data, demographic variables, and cohort selection process,
Krewski et al. (2000) noted that a small portion of study participants were mistakenly censored early.
The following C-R function is based on the risk estimate from the audited data, with the inclusion of
those person-years mistakenly censored early.
Single Pollutant Model
The coefficient and standard error are estimated from the relative risk (1.28) and 95% confidence
interval (1.10-1.48) associated with a change in annual mean PM25 exposure of 18.6 |ig/m3 to 29.6 |ig/m3
(Krewski et al., 2000, Part I - Table 19c).
Functional Form: Log-linear
Coefficient: 0.013272
Standard Error: 0.004070
Incidence Rate: county-specific annual all cause mortality rate per person ages 25 and older
Population: population of ages 25 and older
F .1.6 Mortality, All Cause (Pope et al., 1995)
Pope et al. (1995) used a Cox proportional hazard model to estimate the impact of long-term PM
exposure. They followed 295,223 individuals17 ages 30 and over in 50 cities from September 1, 1982 to
December 31, 1989, and related their survival to median PM25 concentrations for 1979 to 1983. Pope et
al. (1995, Table 2) reported results for all-cause deaths, lung cancer (ICD-9 code: 162), cardiopulmonary
deaths (ICD-9 codes: 401-440 and 460-519), and "all other" deaths,18 and found that median PM25 is
significantly related to all-cause and cardiopulmonary mortality. Pope et al. included only PM, so it is
unclear to what extent it may be including the impacts of ozone or other gaseous pollutants.
Pope et al. (1995) is the better of the two published prospective cohort studies: it has a larger
population and includes more cities than the prospective cohort study by Dockery et al. (1993). Pope et
al.'s study has several further advantages. The population followed in this study was largely Caucasian
and middle class, decreasing the likelihood that interlocational differences in premature mortality were
due in part to differences in race, socioeconomic status, or related factors. In addition, the PM coefficient
in Pope et al. is likely to be biased downward, counteracting a possible upward bias associated with
historical air quality trends discussed earlier. One source of this downward bias is the generally healthier
study population, in comparison to poorer minority populations. Another source of downward bias is that
intercity movement of cohort members was not considered in this study. Migration across study cities
would result in exposures of cohort members being more similar than would be indicated by assigning
city-specific annual average pollution levels to each member of the cohort. The more intercity migration
there is, the more exposure will tend toward an intercity mean. If this is ignored, differences in exposure
levels, that are proxied by differences in city-specific annual average PM levels, will be exaggerated, and
will result in a downward bias of the PM coefficient (because a given difference in mortality rates is being
associated with a larger difference in PM levels than is actually the case).
17 The total study population was 552,138 in 151 cities, however, only 295,223 individuals resided in 50 cities with fine
particle data.
18 All-cause mortality includes accidents, suicides, homicides and legal interventions. The category "all other" deaths is
all-cause mortality less lung cancer and cardiopulmonary deaths.
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Appendix F. Particulate Matter C-R Functions
Single Pollutant Model
The coefficient and standard error are estimated from the relative risk (1.17) and 95% confidence
interval (1.09-1.26) associated with a change in annual median PM25 exposure of 24.5 |ig/m3 (Pope et al.,
1995, Table 2).
Functional Form: Log-linear
Coefficient: 0.006408
Standard Error: 0.001509
Incidence Rate: county-specific annual all cause mortality rate per person ages 30 and older
Population: population of ages 30 and older
F .1.7 Mortality, All Cause (Dockery et al., 1993)
Dockery et al. (1993) examined the relationship between PM exposure and mortality in a cohort
of 8,111 individuals aged 25 and older, living in six U.S. cities. They surveyed these individuals in 1974-
1977 and followed their health status until 1991. While they used a smaller sample of individuals from
fewer cities than the study by Pope et al., they used improved exposure estimates, a slightly broader study
population (adults aged 25 and older), and a follow-up period nearly twice as long as that of Pope et al.
(1995). Perhaps because of these differences, Dockery et al. study found a larger effect of PM on
premature mortality than that found by Pope et al.
Single Pollutant Model
The coefficient and standard error are estimated from the relative risk (1.26) and 95% confidence
interval associated (1.08-1.47) with a change in annual mean PM25 exposure of 18.6 |ig/m3 (Dockery et
al., 1993, Tables 1 and 5).
Functional Form: Log-linear
Coefficient: 0.012425
Standard Error: 0.004228
Incidence Rate: county-specific annual all cause mortality rate per person ages 25 and older
Population: population of ages 25 and older
F .1.8 Mortality, All Cause (Pope et al., 2002) - Based on ACS Cohort
The Pope et al. (2002) analysis is a longitudinal cohort tracking study that uses the same
American Cancer Society (ACS) cohort as the original Pope et al. (1995) study, and the Krewski et al.
(2000) reanalysis. Pope et al. (2002) analyzed survival data for the cohort from 1982 through 1998, 9
years longer than the original Pope study. Pope et al. (2002) also obtained PM2 5 data in 116 metropolitan
areas collected in 1999, and the first three quarters of 2000. This is more metropolitan areas with PM2 5
data than was available in the Krewski reanalysis (61 areas), or the original Pope study (50 areas),
providing a larger size cohort.
They used a Cox proportional hazard model to estimate the impact of long-term PM exposure
using three alternative measures of PM25 exposure; metropolitan area-wide annual mean PM levels from
the beginning of tracking period ('79-'83 PM data, conducted for 61 metropolitan areas with 359,000
individuals), annual mean PM from the end of the tracking period ('99-'00, for 116 areas with 500,000
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Appendix F. Particulate Matter C-R Functions
individuals), and the average annual mean PM levels of the two periods (for 51 metropolitan areas, with
319,000 individuals). PM levels were lower in '99-00 than in '79 - '83 in most cities, with the largest
improvements occurring in cities with the highest original levels.
Pope et al. (2002) followed Krewski et al. (2000) and Pope et al. (1995, Table 2) and reported
results for all-cause deaths, lung cancer (ICD-9 code: 162), cardiopulmonary deaths (ICD-9 codes: 401-
440 and 460-519), and "all other" deaths.19 Like the earlier studies, Pope et al. (2002) found that mean
PM2 5 is significantly related to all-cause and cardiopulmonary mortality. In addition, Pope et al. (2002)
found a significant relationship with lung cancer mortality, which was not found in the earlier studies.
None of the three studies found a significant relationship with "all other" deaths.
Pope et al. (2002) obtained ambient data on gaseous pollutants routinely monitored by EPA
during the 1982-1998 observation period, including S02, N02, CO, and ozone. They did not find
significant relationships between N02, CO, and ozone and premature mortality, but there were significant
relationships between S04 (as well as S02), and all-cause, cardiopulmonary, lung cancer and "all other"
mortality.
PM2 5 Function(s)
'79-'83 Exposure
The coefficient and standard error for PM25 using the '79-'83 PM data are estimated from the
relative risk (1.041) and 95% confidence interval (1.008-1.075) associated with a change in annual mean
exposure of 10.0 |ig/nr\ Pope et al. (2002, Table 2).20
Functional Form: Log-linear
Coefficient: 0.004018
Standard Error: 0.001642
Incidence Rate: county-specific annual all cause mortality rate per person ages 30 and older
Population: population of ages 30 and older
Average of'79-'83 and '99-'00 Exposure
The coefficient and standard error for PM25 using the average of '79-'83 and '99-'00 PM data are
estimated from the relative risk (1.062) and 95% confidence interval (1.016-1.110) associated with a
change in annual mean exposure of 10.0 |ig/nr\ Pope et al. (2002, Table 2).21
19 All-cause mortality includes accidents, suicides, homicides and legal interventions. The category "all other" deaths is
all-cause mortality less lung cancer and cardiopulmonary deaths.
20 Note that we used an unpublished, final version of the paper that presents the relative risks with one more significant
digit than that found in the published version. We chose to use this extra information to increase the precision of our estimates.
21 Note that we used an unpublished, final version of the paper that presents the relative risks with one more significant
digit than that found in the published version. We chose to use this extra information to increase the precision of our estimates.
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Appendix F. Particulate Matter C-R Functions
Functional Form: Log-linear
Coefficient: 0.006015
Standard Error: 0.002257
Incidence Rate: county-specific annual all cause mortality rate per person ages 30 and older
Population: population of ages 30 and older
S04 Function(s)
The coefficient and standard error for S04 using '80-'81 data are estimated from the relative risk
(1.060) and 95% confidence interval (1.036-1.084) associated with a change in annual mean exposure of
6.5 |ig/m3. The relative risk and confidence interval were provided by C.A. Pope III over the phone.
Functional Form: Log-linear
Coefficient: 0.008964
Standard Error: 0.001778
Incidence Rate: county-specific annual all cause mortality rate per person ages 30 and older
Population: population of ages 30 and older
F .1.9 Mortality, Cardiopulmonary (Pope et al., 2002) - Based on ACS Cohort
Pope et al. (2002) followed Krewski et al. (2000) and Pope et al. (1995, Table 2) and reported
results for all-cause deaths, lung cancer (ICD-9 code: 162), cardiopulmonary deaths (ICD-9 codes: 401-
440 and 460-519), and "all other" deaths.22 Like the earlier studies, Pope et al. (2002) found that mean
PM2 5 and S04 (as well as S02) is significantly related to all-cause and cardiopulmonary mortality. In
addition, Pope et al. (2002) found a significant relationship with lung cancer mortality, which was not
found in the earlier studies. None of the three studies found a significant relationship with "all other"
deaths.
PM2 5 Function(s)
'79-'83 Exposure
The coefficient and standard error for PM25 using the '79-'83 PM data are estimated from the
relative risk (1.059) and 95% confidence interval (1.015-1.105) associated with a change in annual mean
exposure of 10.0 |ig/nr\ Pope et al. (2002, Table 2).23
22 All-cause mortality includes accidents, suicides, homicides and legal interventions. The category "all other" deaths is
all-cause mortality less lung cancer and cardiopulmonary deaths.
23 Note that we used an unpublished, final version of the paper that presents the relative risks with one more significant
digit than that found in the published version. We chose to use this extra information to increase the precision of our estimates.
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Appendix F. Particulate Matter C-R Functions
Functional Form: Log-linear
Coefficient: 0.005733
Standard Error: 0.002167
Incidence Rate: county-specific annual cardiopulmonary mortality rate (ICD codes 401-440, 460-519)
per person ages 30 and older
Population: population of ages 30 and older
Average of'79-'83 and '99-'00 Exposure
The coefficient and standard error for PM25 using the average of '79-'83 and '99-'00 PM data are
estimated from the relative risk (1.093) and 95% confidence interval (1.033-1.158) associated with a
change in annual mean exposure of 10.0 |ig/nr\ Pope et al. (2002, Table 2).24
Functional Form: Log-linear
Coefficient: 0.008893
Standard Error: 0.002914
Incidence Rate: county-specific annual cardiopulmonary mortality rate (ICD codes 401-440, 460-519)
per person ages 30 and older
Population: population of ages 30 and older
S04 Function(s)
The coefficient and standard error for S04 using '80-'81 data are estimated from the relative risk
(1.050) and 95% confidence interval (1.015-1.087) associated with a change in annual mean exposure of
6.5 |ig/nr\ The relative risk and confidence interval were provided by C.A. Pope III over the phone.
Functional Form: Log-linear
Coefficient: 0.007506
Standard Error: 0.002690
Incidence Rate: county-specific annual cardiopulmonary mortality rate (ICD codes 401-440, 460-519)
per person ages 30 and older
Population: population of ages 30 and older
F .1.10 Mortality, Lung Cancer (Pope et al., 2002) - Based on ACS Cohort
Pope et al. (2002) followed Krewski et al. (2000) and Pope et al. (1995, Table 2) and reported
results for all-cause deaths, lung cancer (ICD-9 code: 162), cardiopulmonary deaths (ICD-9 codes: 401-
440 and 460-519), and "all other" deaths.25 Like the earlier studies, Pope et al. (2002) found that mean
PM2 5 S04 (as well as S02) is significantly related to all-cause and cardiopulmonary mortality. In
addition, Pope et al. (2002) found a significant relationship with lung cancer mortality, which was not
found in the earlier studies. None of the three studies found a significant relationship with "all other"
deaths.
24 Note that we used an unpublished, final version of the paper that presents the relative risks with one more significant
digit than that found in the published version. We chose to use this extra information to increase the precision of our estimates.
25 All-cause mortality includes accidents, suicides, homicides and legal interventions. The category "all other" deaths is
all-cause mortality less lung cancer and cardiopulmonary deaths.
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Appendix F. Particulate Matter C-R Functions
PM2 5 Function(s)
'79-'83 Exposure
The coefficient and standard error for PM25 using the '79-'83 PM data are estimated from the
relative risk (1.082) and 95% confidence interval (1.011-1.158) associated with a change in annual mean
exposure of 10.0 |ig/nr\ Pope et al. (2002, Table 2).26
Functional Form: Log-linear
Coefficient: 0.007881
Standard Error: 0.003463
Incidence Rate: county-specific annual lung cancer mortality rate (ICD code 162) per person ages 30 and
older
Population: population of ages 30 and older
Average of'79-'83 and '99-'00 Exposure
The coefficient and standard error for PM25 using the average of '79-'83 and '99-'00 PM data are
estimated from the relative risk (1.135) and 95% confidence interval (1.044-1.234) associated with a
change in annual mean exposure of 10.0 |ig/nr\ Pope et al. (2002, Table 2).27
Functional Form: Log-linear
Coefficient: 0.012663
Standard Error: 0.004265
Incidence Rate: county-specific annual lung cancer mortality rate (ICD code 162) per person ages 30 and
older
Population: population of ages 30 and older
S04 Function(s)
The coefficient and standard error for S04 using '80-'81 data are estimated from the relative risk
(1.095) and 95% confidence interval (1.040-1.153) associated with a change in annual mean exposure of
6.5 |ig/m3. The relative risk and confidence interval were provided by C.A. Pope III over the phone.
Functional Form: Log-linear
Coefficient: 0.013962
Standard Error: 0.004048
Incidence Rate: county-specific annual lung cancer mortality rate (ICD code 162) per person ages 30 and
older
Population: population of ages 30 and older
26 Note that we used an unpublished, final version of the paper that presents the relative risks with one more significant
digit than that found in the published version. We chose to use this extra information to increase the precision of our estimates.
27 Note that we used an unpublished, final version of the paper that presents the relative risks with one more significant
digit than that found in the published version. We chose to use this extra information to increase the precision of our estimates.
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F .1.11 Infant Mortality (Woodruff et al., 1997)
In a study of four million infants in 86 U.S. metropolitan areas conducted from 1989 to 1991,
Woodruff et al. (1997) found a significant link between PM10 exposure in the first two months of an
infant's life with the probability of dying between the ages of 28 days and 364 days. PM10 exposure was
significant for all-cause mortality. PM10 was also significant for respiratory mortality in average birth-
weight infants, but not low birth-weight infants.
In addition to the work by Woodruff et al., work in Mexico City (Loomis et al., 1999), the Czech
Republic (Bobak and Leon, 1992), Sao Paulo (Saldiva et al., 1994; Pereira et al., 1998), and Beijing
(Wang et al., 1997) provides additional evidence that particulate levels are significantly related to infant
or child mortality, low birth weight or intrauterine mortality.
Conceptually, neonatal or child mortality could be added to the premature mortality predicted by
Pope et al. (1995), because the Pope function covers only the population over 30 years old.28 However,
the EPA Science Advisory Board recently advised the Agency not to include post-neonatal mortality in
this analysis because the study is of a new endpoint and the results have not been replicated in other
studies (U.S. EPA, 1999a, p. 12). The estimated avoided incidences of neonatal mortality are estimated
and presented as a sensitivity analysis, and are not included in the primary analysis.
Single Pollutant Model
The coefficient and standard error are based on the odds ratio (1.04) and 95% confidence interval
(1.02-1.07) associated with a 10 /ig/m3 change in PM10 (Woodruff et al., 1997, Table 3).
Functional Form: Logistic
Coefficient: 0.003922
Standard Error: 0.001221
Incidence Rate: county-specific annual postneonatal29 infant deaths per infant under the age of one
Population: population of infants under one year old
28 Predicted neonatal mortality could not be added to the premature mortality predicted by the daily (short-term exposure)
mortality studies, however, because these studies cover all ages.
29 Post-neonatal refers to infants that are 28 days to 364 days old.
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Exhibit F-2. Concentration-Response (C-R) Functions for Particulate Matter and Short-Term Mortality
Endpoint Name
Pollutant
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time1
Beta
Std Error
Functional
Form
Notes
Non- Accidental
pm2,
Fairley
2003
Santa Clara
County
All
All
All
None
24-hr avg
0.003143
0.001283
Log-linear
Reanalysis of
Fairley, 1999
Non- Accidental
PM2,
Fairley
2003
Santa Clara
County
All
All
All
o3
24-hr avg
0.003404
0.001300
Log-linear
Reanalysis of
Fairley, 1999
Non-Accidental
PM2,
Ito
2003
Detroit, MI
All
All
All
None
24-hr avg
0.000740
0.000752
Log-linear
Reanalysis of
Lippmann et al.,
2000
Non-Accidental
PM2,
Klemm and
Mason
2003
6 Cities
All
All
All
None
24-hr avg
0.001193
0.000202
Log-linear
Reanalysis of
Klemm and Mason
et al., 2000
Non-Accidental
PM2,
Moolgavkar
2003
Los Angeles,
CA
All
All
All
None
24-hr avg
0.000588
0.000300
Log-linear
Reanalysis of
Moolgavkar,
2000a,b,c
Non-Accidental
PM2,
Schwartz et al.
1996
6 cities
All
All
All
None
24-hr avg
0.001433
0.000129
Log-linear
Standard and Lag
adjusted2
Non-Accidental
PM2,
Schwartz
2003
6 cities
All
All
All
None
24-hr avg
0.00137
0.00020
Log-linear
Standard and Lag
adjusted2
Chronic Lung
PM2,
Schwartz et al.
1996
6 cities
All
All
All
None
24-hr avg
0.003247
-
Log-linear
Lag adjusted2
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for more detail
on the specific averaging time used in the study.
2. Refer to the study summaries below for a discussion of the lag adjustment used for these functions.
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F .2 Short-term Mortality
Short-term mortality studies are those that typically link daily air pollution levels with daily
changes in mortality rates.
F .2.1 Short-Term Mortality, Non-Accidental (Fairley, 2003)
Using data from 1989-1996 in Santa Clara County, California, Fairley et al. (1999) examined the
relationship between daily non-accidental mortality and fluctuations in a variety of pollutants, including
PM2 5, coarse PM10 (i.e., PM2 5_10), nitrate (N03), S04, coefficient of haze (COH), ozone, CO, and N02.
They reported that PM25 and N03 were significant in single-pollutant models, as well as two-pollutant
models. PM25 was only insignificant when paired with PM10 and N03 and N03 was only insignificant
when paired with PM25. The other pollutants were insignificant when paired with either PM25 or N03.
The analysis by Fairly et al. (1999) relied on a generalized additive model based on the Splus
software. Because of potential bias from using Splus, Fairley (2003) conducted a reanalysis, and reported
that the conclusions of the original study were unchanged. Both PM2 5 and N03 appear significantly
related to non-accidental mortality.
Single Pollutant Model
The coefficient and standard error for PM2 5 are estimated from the relative risk (1.092) and 95%
confidence interval (1.018-1.172) for a 28 |ig/m3 increase in PM2 5 in the 0-day lag GAM stringent ('New
GAM') model (Fairley, 2003, Table la).
Functional Form: Log-linear
Coefficient: 0.003143
Standard Error: 0.001283
Incidence Rate: county-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
Multipollutant Model (PM2 5 and ozone)
In a model with 8-hour averaged ozone, the coefficient and standard error for PM2 5 are estimated
from the relative risk (1.100) and 95% confidence interval (1.024-1.181) for a 28 |ig/nr' increase in PM25
in the 0-day lag GAM stringent ('New GAM') model (Fairley, 2003, Table lb).
Functional Form: Log-linear
Coefficient: 0.003404
Standard Error: 0.001300
Incidence Rate: county-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
F .2.2 Short-Term Mortality, Non-Accidental (Ito, 2003)
Ito (2003) reanalyzed a study by Lippmann et al. (2000) who examined the associations between
PM components and daily mortality and elderly hospital admissions in Detroit, Michigan. The reanalysis
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by Ito reported that more generalized additive models with stringent convergence criteria and generalized
linear models resulted in smaller relative risk estimates.
Single Pollutant Model
The coefficient and standard error for PM2 5 are estimated from the relative risk (1.027) and 95%
confidence interval (0.974-1.083) for a 36 |ig/m3 increase in PM25 in the 3-day lag GAM stringent model
(Ito, 2003, Table 4).
Functional Form: Log-linear
Coefficient: 0.000740
Standard Error: 0.000752
Incidence Rate: region-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
F .2.3 Short-Term Mortality, Non-Accidental (Klemm and Mason, 2003)
Klemm and Mason (2003) reanalyzed a prior study by Klemm and Mason (2000), who conducted
a replication of work by Schwartz et al. (1996). In the updated work using more stringent convergence
criteria and generalized linear models, Klemm and Mason (2003) reported a generally smaller relationship
between daily PM25 levels and premature mortality.
Single Pollutant Model
The coefficient and standard error for PM2 5 are estimated from the relative risk (1.012) and 95%
confidence interval (0.008-1.016) for a 10 |ig/m3 increase in PM25 in the 0-day lag GAM stringent
('GAM 2002') model (Klemm and Mason, 2003, Table 1).
Functional Form: Log-linear
Coefficient: 0.001193
Standard Error: 0.000202
Incidence Rate: county-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
F .2.4 Short-Term Mortality, Non-Accidental (Moolgavkar, 2003)
Moolgavkar (2003) reanalyzed a study by Moolgavkar (2000b) who examined the relationships
between daily mortality and hospital admissions in Los Angeles and Cook Counties. The reanalysis by
Moolgavkar reported that more generalized additive models with stringent convergence criteria and
generalized linear models generally resulted in smaller relative risk estimates, and that gases such as CO
were often more closely associated with health endpoints than particulate matter.
Single Pollutant Model
The coefficient and standard error for PM2 5 are estimated from the relative risk (1.0059) and the
t-statistic (1.96) for a 10 |ig/m3 increase in PM25 in the 1-day lag GAM-30df stringent (10~8) model
(Moolgavkar, 2003, Table 1)
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Functional Form: Log-linear
Coefficient: 0.000588
Standard Error: 0.000300
Incidence Rate: county-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
F .2.5 Short-Term Mortality, Non-Accidental (Schwartz et al., 1996)
Schwartz et al. (1996) pooled the results from six cities in the U.S. and found a significant
relationship between daily PM25 concentration and non-accidental mortality.30 Abt Associates Inc.
(1996b, p. 52) used the six PM2 5 relative risks reported by Schwartz et al. in a three-step procedure to
estimate a pooled PM2 5 coefficient and its standard error. The first step estimates a random-effects
pooled estimate of P; the second step uses an "empirical Bayes" procedure to reestimate the p for each
study as a weighted average of the p reported for that location and the random effects pooled estimate; the
third step estimates the underlying distribution of p, and uses a Monte Carlo procedure to estimate the
standard error (Abt Associates Inc., 1996a, p. 65).
Single Pollutant Model
The C-R function to estimate the change in mortality associated with daily changes in PM25 is:
Functional Form: Log-linear
Coefficient: 0.001433 (Abt Associates Inc., 1996a, Exhibit 7.2)
Standard Error: 0.000129 (Abt Associates Inc., 1996a, Exhibit 7.2)
Incidence Rate: county-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
Single Pollutant Model, Lag Adjusted
Recent studies have found that an increase in PM levels on a given day can elevate mortality for
several days following the exposure (Samet et al., 2000; Schwartz, 2000b). These studies have reported
the results of distributed lag models for the relationship between PM10 and daily mortality. Schwartz
(2000b) examined the relationship between PM10 and daily mortality and reported results both for a single
day lag model and an unconstrained distributed lag model. The unconstrained distributed lag model
coefficient estimate is 0.0012818 and the single-lag model coefficient estimate is 0.0006479. A
distributed lag adjustment factor can be constructed as the ratio of the estimated coefficient from the
unconstrained distributed lag model to the estimated coefficient from the single-lag model reported in
Schwartz (2000). The ratio of these estimates is 1.9784. In order to estimate the full impact of daily PM
levels on daily mortality, we applied this ratio to the coefficient obtained from Schwartz et al. (1996) for
the association between PM25 and daily mortality.
In applying the ratio derived from a PM10 study to PM25, we assume that the same relationship
between the distributed lag and single day estimates would hold for PM2 5. Effect estimates for the PM10-
daily mortality relationship tend to be lower in magnitude than for PM2 5, because fine particles are
believed to be more closely associated with mortality than the coarse fraction of PM. If most of the
30 Schwartz et al. (1996, p. 929) defined non-accidental mortality as all-cause mortality less deaths due to accidents and
other external causes (ICD-9 codes: 800-999). Other external causes includes suicide, homicide, and legal intervention (National
Center for Health Statistics, 1994).
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Appendix F. Particulate Matter C-R Functions
increase in mortality is expected to be associated with the fine fraction of PM10, then it is reasonable to
assume that the same proportional increase in risk would be observed if a distributed lag model were
applied to the PM2 5 data.
The distributed lag model coefficient is estimated by multiplying the distributed lag adjustment
factor of 1.9784 with the pooled PM2 5 coefficient. Note that the distributed lag adjustment C-R function
is only run for the point estimate, as the standard error of this modified coefficient has not been estimated.
Functional Form: Log-linear
Coefficient: 0.001433
Lag Adjustment: 1.9784
Incidence Rate: county-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
F .2.6 Short-Term Mortality, Non-Accidental (Schwartz, 2003)
Schwartz et al. (1996) pooled the results from six cities in the U.S. and found a significant
relationship between daily PM25 concentration and non-accidental mortality.31 In a reanalysis of this
work, Schwartz (2003) reported that the coefficients are somewhat smaller and less stable, but that the
overall relationship between PM2 5 and mortality remained unchanged.
Single Pollutant Model
The coefficient and standard error are provided Schwartz (2003, Table 1) (see: combined
estimate, mean of lag 0 and 1, New Convergence - GAM stringent).
Functional Form: Log-linear
Coefficient: 0.00137
Standard Error: 0.0002
Incidence Rate: county-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
Single Pollutant Model, Lag Adjusted
As noted in the section on the Schwartz et al. (1996) C-R function, we have added a distributed
lag adjustment factor. The distributed lag model coefficient is estimated by multiplying the distributed
lag adjustment factor of 1.9784 with the PM25 coefficient. Note that the distributed lag adjustment C-R
function is only run for the point estimate, as the standard error of this modified coefficient has not been
estimated.
Functional Form: Log-linear
Coefficient: 0.00137 (Schwartz, 2003, Table 1)
Lag Adjustment: 1.9784
Incidence Rate: county-specific annual daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
31 Schwartz et al. (1996, p. 929) defined non-accidental mortality as all-cause mortality less deaths due to accidents and
other external causes (ICD-9 codes: 800-999). Other external causes includes suicide, homicide, and legal intervention (National
Center for Health Statistics, 1994).
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F .2.7 Short-Term Mortality, Chronic Lung Disease - Lag Adjusted (Schwartz et al., 1996)
Schwartz et al. (1996) evaluated the relationship between daily PM25 levels and short-term
mortality in six U.S. cities. Schwartz pooled results across the six cities and found statistically significant
associations between daily PM25 levels and non-accidental mortality (ICD codes <800), along with
mortality for ischemic heart disease (ICD codes 410-414), COPD (ICD codes 490-496), and pneumonia
(ICD codes 480-486). A smaller association was found for PM10 and no significant associations were
reported for PM10_2 5. The C-R function for chronic lung disease mortality is based on the results of a
single pollutant model using a two-day average of PM2 5 (Schwartz et al., 1996, Table 7). In order to
estimate the impact of daily PM2 5 levels on daily mortality if a distributed lag model had been fit, the
PM2 5 coefficient is adjusted as described below.
Single Pollutant Model
The PM25 coefficient is based on a reported 3.3% increase in COPD mortality associated with a
10 /ig/nr' change in two-day average PM25 levels (Schwartz et al., 1996, Table 7). This coefficient
(0.003247) is then multiplied by the distributed lag adjustment factor of 1.9784 to estimate a distributed
lag model coefficient.
Functional Form: Log-linear
Coefficient: 0.003247
Lag Adjustment: 1.9784
Incidence Rate: county-specific annual daily chronic lung disease mortality rate (ICD codes 490-496)
Population: population of all ages
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Exhibit F-3. Concentration-Response (C-R) Functions for Particulate Matter and Chronic Illness
Endpoint Name Pollutant Author Year Location
_ _ , Other . _ Functional
Age Race Gender _ „ , . Averaging Time Beta Std Error _
Pollutants Form
Chronic Bronchitis
Chronic Bronchitis,
Reversals
Chronic Bronchitis
PM2 5 Abbey etal. 1995
PM25 Abbey etal. 1995
SF, SD, South
Coast Air Basin
SF, SD, South
PM,r
Schwartz
Coast Air Basin
1993 53 cities
27+ All All None Annual Avg 0.0137 0.00680 Logistic
27+ All All None Annual Avg 0.0137 0.00680 Logistic
30+ All All None Annual Avg 0.0123 0.00434 Logistic
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F .3 Chronic Illness
Schwartz (1993) and Abbey et al. (1993; 1995c) provide evidence that PM exposure over a
number of years gives rise to the development of chronic bronchitis in the U.S., and a recent study by
McDonnell et al. (1999) provides evidence that ozone exposure is linked to the development of asthma in
adults. These results are consistent with research that has found chronic exposure to pollutants leads to
declining pulmonary functioning (Detels et al., 1991; Ackermann-Liebrich et al., 1997; Abbey et al.,
1998).32
F .3.1 Chronic Bronchitis (Abbey et al., 1995c, California)
Abbey et al. (1995c) examined the relationship between estimated PM25 (annual mean from 1966
to 1977), PM10 (annual mean from 1973 to 1977) and TSP (annual mean from 1973 to 1977) and the
same chronic respiratory symptoms in a sample population of 1,868 Californian Seventh Day Adventists.
The initial survey was conducted in 1977 and the final survey in 1987. To ensure a better estimate of
exposure, the study participants had to have been living in the same area for an extended period of time.
In single-pollutant models, there was a statistically significant PM2 5 relationship with development of
chronic bronchitis, but not for AOD or asthma; PM10 was significantly associated with chronic bronchitis
and AOD; and TSP was significantly associated with all cases of all three chronic symptoms. Other
pollutants were not examined. The C-R function is based on the results of the single pollutant model
presented in Table 2.
Single Pollutant Model (Chronic Bronchitis)
The estimated coefficient (0.0137) is presented for a one /ig/m3 change in PM2 5 (Abbey et al.,
1995c, Table 2). The standard error is calculated from the reported relative risk (1.81) and 95%
confidence interval (0.98-3.25) for a 45 /ig/m3 change in PM25 (Abbey et al., 1995c, Table 2).
Functional Form: Logistic
Coefficient: 0.0137
Standard Error: 0.00680
Incidence Rate: annual bronchitis incidence rate per person (Abbey et al., 1993, Table 3) = 0.00378
Population: population of ages 27 and older33 without chronic bronchitis = 95.57%34 of population 27+
Single Pollutant Model (Chronic Bronchitis, Reversals)
In developing the C-R function for chronic bronchitis, it is necessary to estimate its annual
incidence rate. The annual incidence rate is derived by taking the number of new cases (234), dividing by
the number of individuals in the sample (3,310), as reported by Abbey et al.(1993, Table 3), dividing by
32 There are a limited number of studies that have estimated the impact of air pollution on chronic bronchitis. An
important hindrance is the lack of health data and the associated air pollution levels over a number of years.
33 Using the same data set, Abbey et al. (1995a, p. 140) reported that the respondents in 1977 ranged in age from 27 to 95.
34 The American Lung Association (2002b, Table 4) reports a chronic bronchitis prevalence rate for ages 18 and over of
4.43% (American Lung Association, 2002b, Table 4).
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Appendix F. Particulate Matter C-R Functions
the ten years covered in the sample, and then multiplying by one minus the reversal rate.35 Reversals refer
to those cases of chronic bronchitis that were reported at the start of the Abbey et al. survey, but were
subsequently not reported at the end of the survey. Since we assume that chronic bronchitis is a
permanent condition, we subtract these reversals from the C-R function for chronic bronchitis.
Nevertheless, reversals may likely represent a real effect that should be included in an analysis.
The estimated coefficient (0.0137) is presented for a one /ig/m3 change in PM2 5 (Abbey et al.,
1995c, Table 2). The standard error is calculated from the reported relative risk (1.81) and 95%
confidence interval (0.98-3.25) for a 45 /ig/m3 change in PM25 (Abbey et al., 1995c, Table 2).
Functional Form: Logistic
Coefficient: 0.0137
Standard Error: 0.00680
Incidence Rate: annual bronchitis incidence rate per person for chronich bronchitis that eventually
resolves itself. Based on the percentage of reversals (46.6%) from Abbey et al. (1995a, Table 1) and
chronic bronchitis cases from (Abbey et al., 1993, Table 3) = 0.00325
Population: population of ages 27 and older36 without chronic bronchitis = 95.57%37 of population 27+
F .3.2 Chronic Bronchitis (Schwartz, 1993)
Schwartz (1993) examined survey data collected from 3,874 adults ranging in age from 30 to 74,
and living in 53 urban areas in the U.S. The survey was conducted between 1974 and 1975, as part of the
National Health and Nutrition Examination Survey, and is representative of the non-institutionalized U.S.
population. Schwartz (1993, Table 3) reported chronic bronchitis prevalence rates in the study population
by age, race, and gender. Non-white males under 52 years old had the lowest rate (1.7%) and white males
52 years and older had the highest rate (9.3%). The study examined the relationship between the
prevalence of reported chronic bronchitis, asthma, shortness of breath (dyspnea) and respiratory illness38,
and the annual levels of TSP, collected in the year prior to the survey (TSP was the only pollutant
examined in this study). TSP was significantly related to the prevalence of chronic bronchitis, and
marginally significant for respiratory illness. No effect was found for asthma or dyspnea. The C-R
function for PM10 is estimated from the results of the single pollutant model reported for TSP.
Single Pollutant Model
The estimated coefficient is based on the odds ratio ( 1.07) associated with 10 |ig/m3 change in
TSP (Schwartz, 1993, p. 9). Assuming that PM10 is 55 percent of TSP39 and that particulates greater than
ten micrometers are harmless, the coefficient is calculated by dividing the TSP coefficient by 0.55. The
35The percentage of reversals is estimated to be 46.6% based on Abbey et al. (1995a, Table 1).
36 Using the same data set, Abbey et al. (1995a, p. 140) reported that the respondents in 1977 ranged in age from 27 to
95.
37 The American Lung Association (2002b, Table 4) reports a chronic bronchitis prevalence rate for ages 18 and over of
4.43% (American Lung Association, 2002b, Table 4).
38 Respiratory illness defined as a significant condition, coded by an examining physician as ICD-8 code 460-519.
39 The conversion of TSP to PM10 is from ESEERCO (1994, p. V-5), who cited studies by EPA (1986) and the California
Air Resources Board (1982).
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Appendix F. Particulate Matter C-R Functions
standard error for the coefficient is calculated from the 95% confidence interval for the odds ratio (1.02 to
1.12) (Schwartz, 1993, p. 9).
Schwartz (1993) examined the prevalence of chronic bronchitis, not its incidence. To use
Schwartz's study and still estimate the change in incidence, there are at least two possible approaches.
The first is to simply assume that it is appropriate to use the baseline incidence of chronic bronchitis in a
C-R function with the estimated coefficient from Schwartz's study, to directly estimate the change in
incidence. The second is to estimate the percentage change in the prevalence rate for chronic bronchitis
using the estimated coefficient from Schwartz's study in a C-R function, and then to assume that this
percentage change applies to a baseline incidence rate obtained from another source. (That is, if the
prevalence declines by 25 percent with a drop in PM, then baseline incidence drops by 25 percent with
the same drop in PM.) This analysis is using the latter approach, and estimates a percentage change in
prevalence which is then applied to a baseline incidence rate. The scaling factor used in the C-R function
is the ratio of chronic bronchitis incidence rate (estimated from Abbey et al. (1993)) to chronic bronchitis
prevalence rate (estimated from American Lung Association (2002b, Table 4)).
Functional Form: Logistic
Coefficient: 0.0123
Standard Error: 0.00434
Prevalence Rate: annual chronic bronchitis prevalence rate per person (American Lung Association,
2002b, Table 4) = 0.0443
Population: population of ages 30 and older without chronic bronchitis = 95.57%40 of population 30+
Adjustment Factor: ratio of chronic bronchitis incidence to chronic bronchitis prevalence =
0.00378/0.0443 = 0.085 (Abbey et al., 1993, Table 3; American Lung Association, 2002b, Table 4)
40 The American Lung Association (2002b, Table 4) reports a chronic bronchitis prevalence rate for ages 18 and over of
4.43% (American Lung Association, 2002b, Table 4).
Abt Associates Inc. F-22 November 2003
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Appendix F. Particulate Matter C-R Functions
Exhibit F-4. Concentration-Response (C-R) Functions for Particulate Matter and Hospital Admissions
Endpoint Name Pollutant
Author
Year
Location
Age Race Gender
Other
Pollutants
Averaging
Time
Beta
Std
Error
Functional
Form
A1
Respiratory
pm2,
Burnett et al.
1997
A1
Respiratory
PM2,
Burnett et al.
1997
A1
Respiratory
PM2,
Burnett et al.
1997
A1
Respiratory
pm10-2,
Burnett et al.
1997
A1
Respiratory
PMlO-2.5
Burnett et al.
1997
A1
Respiratory
PMlO-2.5
Burnett et al.
1997
A1
Respiratory
PM10
Burnett et al.
1997
A1
Respiratory
PM10
Burnett et al.
1997
A1
Respiratory
PM10
Burnett et al.
1997
A1
Respiratory
pm2,
Burnett et al.
2001
A1
Respiratory
pm2,
Burnett et al.
2001
A1
Respiratory
PMlO-2.5
Burnett et al.
2001
A1
Respiratory
PMlO-2.5
Burnett et al.
2001
A1
Respiratory
PM10
Schwartz
1995
A1
Respiratory
PM10
Schwartz
1995
A1
Respiratory
PM10
Schwartz
1995
A1
Respiratory
PM10
Schwartz
1995
A1
Respiratory
pm2,
Thurston et al.
1994
A1
Respiratory
PM2,
Thurston et al.
1994
A1
Respiratory
PMlO-2.5
Thurston et al.
1994
A1
Respiratory
PM10
Thurston et al.
1994
A1
Respiratory
PM10
Thurston et al.
1994
Asthma
pm2,
Burnett et al.
1999
Asthma
PMio-2.5
Burnett et al.
1999
Notes
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
New Haven, CT
New Haven, CT
Tacoma, WA
Tacoma, WA
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
All
All
All
All
All
All
All
All
All All
All
All
All All
All
All
All
All
All
All
All
All
All
All
None
03
no2, o3,
so2
None
03
no2, o3;
so2
None
O,
24-hr avg
24-hr avg
0.003303
0.002422
0.001004
0.001039
Log-linear
Log-linear
24-hr avg -0.000091 0.000910 Log-linear
24-hr avg
24-hr avg
0.004787
0.004169
0.001404
0.001371
Log-linear
Log-linear
24-hr avg 0.001469 0.001791 Log-linear
24-hr avg
24-hr avg
0.002074
0.001870
0.000607
0.000592
Log-linear
Log-linear
All
All
All
^5 ^
Op
0
24-hr avg
0.000280
0.000778
Log-linear
<2
All
All
None
24-hr avg
0.008150
0.002477
Log-linear
<2
All
All
03
24-hr avg
0.000772
0.003218
Log-linear
<2
All
All
None
24-hr avg
0.010374
0.002752
Log-linear
<2
All
All
O3
24-hr avg
0.002717
0.003774
Log-linear
65+
All
All
None
24-hr avg
0.001165
0.000624
Log-linear
65+
All
All
O3
24-hr avg
0.001724
0.000930
Log-linear
65+
All
All
None
24-hr avg
0.001906
0.000650
Log-linear
65+
All
All
O3
24-hr avg
0.002267
0.001455
Log-linear
All
All
All
None
24-hr avg
0.0828
0.0367
Linear
All
All
All
O3
24-hr avg
0.0434
0.0429
Linear
All
All
All
None
24-hr avg
0.1228
0.0895
Linear
All
All
All
None
24-hr avg
0.0642
0.0290
Linear
All
All
All
O3
24-hr avg
0.0339
0.0344
Linear
All
All
All
None
24-hr avg
0.002499
0.000776
Log-linear
All
All
All
None
24-hr avg
0.004194
0.000999
Log-linear
Abt Associates Inc.
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November 2003
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Appendix F. Particulate Matter C-R Functions
Endpoint Name
Pollutant
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time
Beta
Std
Error
Functional
Form
Notes
Asthma
PM10-2,
Burnett et al.
1999
Toronto, CAN
All
All
All
co,o3
24-hr avg
0.003215
0.001058
Log-linear
Asthma
PM10
Burnett et al.
1999
Toronto, CAN
All
All
All
None
24-hr avg
0.001701
0.000502
Log-linear
Asthma
pm2,
Lin et al.
2002
Toronto, CAN
6-12
All
Male
None
24-hr avg
-0.004389
0.003130
Log-linear
Asthma
pm2,
Lin et al.
2002
Toronto, CAN
6-12
All
Male
CO, no2,
o3, so2
24-hr avg
-0.006653
0.003779
Log-linear
Asthma
pm2,
Lin et al.
2002
Toronto, CAN
6-12
All
Female
None
24-hr avg
0.006265
0.008377
Log-linear
Asthma
pm2,
Lin et al.
2002
Toronto, CAN
6-12
All
Female
CO, no2,
o3, so2
24-hr avg
-0.002172
0.005001
Log-linear
Asthma
PMio-2.5
Lin et al.
2002
Toronto, CAN
6-12
All
Male
None
24-hr avg
0.013492
0.004346
Log-linear
Asthma
PMio-2.5
Lin et al.
2002
Toronto, CAN
6-12
All
Male
CO, no2,
o3, so2
24-hr avg
0.016638
0.005007
Log-linear
Asthma
PMio-2.5
Lin et al.
2002
Toronto, CAN
6-12
All
Female
None
24-hr avg
0.021705
0.005583
Log-linear
Asthma
PMio-2.5
Lin et al.
2002
Toronto, CAN
6-12
All
Female
CO, no2,
o3, so2
24-hr avg
0.016638
0.006836
Log-linear
Asthma
PM10
Lin et al.
2002
Toronto, CAN
6-12
All
Male
None
24-hr avg
0.000672
0.002211
Log-linear
Asthma
PM10
Lin et al.
2002
Toronto, CAN
6-12
All
Male
CO, no2,
o3, so2
24-hr avg
0.001338
0.002865
Log-linear
Asthma
PM10
Lin et al.
2002
Toronto, CAN
6-12
All
Female
None
24-hr avg
0.004572
0.002906
Log-linear
Asthma
PM10
Lin et al.
2002
Toronto, CAN
6-12
All
Female
CO, no2,
o3, so2
24-hr avg
0.001997
0.003660
Log-linear
Asthma
pm2,
Sheppard et al.
2003
Seattle, WA
<65
All
All
None
24-hr avg
0.003324
0.001045
Log-linear
Reanalysis of
Sheppard et al.,
1999
Asthma
pm2,
Sheppard et al.
1999
Seattle, WA
<65
All
All
CO
24-hr avg
0.002505
0.001045
Log-linear
Asthma
PMlO-2.5
Sheppard et al.
1999
Seattle, WA
<65
All
All
None
24-hr avg
0.004217
0.001583
Log-linear
Asthma
PM10
Sheppard et al.
1999
Seattle, WA
<65
All
All
None
24-hr avg
0.002568
0.000767
Log-linear
Asthma
PM2,
Thurston et al.
1994
Toronto, CAN
All
All
All
None
24-hr avg
0.0334
0.0241
Linear
Asthma
PM2,
Thurston et al.
1994
Toronto, CAN
All
All
All
o3
24-hr avg
0.0132
0.0273
Linear
Asthma
PMlO-2.5
Thurston et al.
1994
Toronto, CAN
All
All
All
None
24-hr avg
0.0670
0.0571
Linear
Asthma
PM10
Thurston et al.
1994
Toronto, CAN
All
All
All
None
24-hr avg
0.0248
0.0180
Linear
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November 2003
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Appendix F. Particulate Matter C-R Functions
Endpoint Name Pollutant Author Year Location Age Race Gender
Other Averaging
Pollutants Time
Beta
Std Functional
Error Form
Notes
Asthma
Chronic Lung
Disease
Chronic Lung
Disease
Chronic Lung
Disease
Chronic Lung
Disease
Chronic Lung
Disease
Chronic Lung
Disease
Chronic Lung
Disease
Chronic Lung
Disease
Chronic Lung
Disease
Chronic Lung
Disease (less
Asthma)
Chronic Lung
Disease (less
Asthma)
Chronic Lung
Disease (less
Asthma)
Chronic Lung
Disease (less
Asthma)
PM,r
PM,
PM,
PM,
PM,
PM,
PM,
PM,
PM,r
PM,f
PM,
PM,
PM,r
PM,f
Thurston et al.
Ito
Lippmann et al.
Moolgavkar
1994 Toronto, CAN All All All O,
2003 Detroit, MI
2000 Detroit, MI
65+ All All None
65+ All All O,
Moolgavkar
Moolgavkar
Moolgavkar
Moolgavkar et
al.
Schwartz
Burnett et al.
Burnett et al.
2003 Los Angeles, CA 65+ All All None
Moolgavkar 2003 Los Angeles, CA 65+ All All N02
2000 Los Angeles, CA 65+ All All CO
2000 Los Angeles, CA 18-64 All All None
2000 Los Angeles, CA 18-64 All All CO
1997 Minneapolis, MN 65+ All All CO, 03
1994 Minneapolis, MN 65+ All All None
1999 Toronto, CAN All All All None
Moolgavkar 2000 Los Angeles, CA 18-64 All All CO
1999 Toronto, CAN All All All None
24-hr avg 0.0039 0.0208 Linear
Reanalysis of
24-hr avg 0.001169 0.002064 Log-linear Lippmann et al..
24-hr avg 0.001089 0.002420 Log-linear
2000
Reanalysis of
24-hr avg 0.001833 0.000519 Log-linear Moolgavkar,
2000b
Reanalysis of
24-hr avg 0.000419 0.000676 Log-linear Moolgavkar,
2000b
24-hr avg 0.0008 0.001000 Log-linear
24-hr avg 0.0022 0.000733 Log-linear
24-hr avg 0.0020 0.000909 Log-linear
24-hr avg 0.000877 0.000777 Log-linear
24-hr avg 0.003853 0.001461 Log-linear
24-hr avg 0.001868 0.000988 Log-linear
24-hr avg 0.0020 0.000909 Log-linear
24-hr avg 0.004830 0.001482 Log-linear
Burnett etal. 1999 Toronto, CAN All All All CO, 03 24-hr avg 0.003104 0.001634 Log-linear
Abt Associates Inc.
F-25
November 2003
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Appendix F. Particulate Matter C-R Functions
Endpoint Name
Pollutant
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time
Beta
Std
Error
Functional
Form
Notes
Chronic Lung
Disease (less
Asthma)
PM10
Burnett et al.
1999
Toronto, CAN
All
All
All
None
24-hr avg
0.001334
0.000547
Log-linear
Chronic Lung
Disease (less
Asthma)
PM10
Samet et al.
2000
14 cities
65+
All
All
None
24-hr avg
0.002839
0.001351
Log-linear
Chronic Lung
Disease (less
Asthma)
PM10
Schwartz
1994
Detroit, MI
65+
All
All
o3
24-hr avg
0.00202
0.00059
Log-linear
Pneumonia
pm2,
Burnett et al.
1999
Toronto, CAN
All
All
All
None
24-hr avg
0.004090
0.000672
Log-linear
Pneumonia
PM2,
Burnett et al.
1999
Toronto, CAN
All
All
All
no2, o3
24-hr avg
0.003279
0.000735
Log-linear
Pneumonia
PM10-2,
Burnett et al.
1999
Toronto, CAN
All
All
All
None
24-hr avg
0.003561
0.000890
Log-linear
Pneumonia
PM10
Burnett et al.
1999
Toronto, CAN
All
All
All
None
24-hr avg
0.002656
0.000446
Log-linear
Pneumonia
PM2,
Ito
2003
Detroit, MI
65+
All
All
None
24-hr avg
0.003979
0.001659
Log-linear
Reanalysis of
Lippmann et al.,
2000
Pneumonia
PM2,
Lippmann et al.
2000
Detroit, MI
65+
All
All
o3
24-hr avg
0.004480
0.001918
Log-linear
Pneumonia
PM10
Moolgavkar et
al.
1997
Minneapolis, MN
65+
All
All
no2, o3,
so2
24-hr avg
0.000498
0.000505
Log-linear
Pneumonia
PM10
Samet et al.
2000
14 cities
65+
All
All
None
24-hr avg
0.002049
0.000570
Log-linear
Pneumonia
PM10
Schwartz
1994
Minneapolis, MN
65+
All
All
None
24-hr avg
0.001570
0.000652
Log-linear
Pneumonia
PM10
Schwartz
1994
Minneapolis, MN
65+
All
All
o3
24-hr avg
0.001655
0.000709
Log-linear
Pneumonia
PM10
Schwartz
1994
Detroit, MI
65+
All
All
o3
24-hr avg
0.00115
0.00039
Log-linear
All
Cardiovascular
pm2,
Burnett et al.
1997
Toronto, CAN
All
All
All
None
24-hr avg
0.002775
0.001542
Log-linear
All
Cardiovascular
PM2,
Burnett et al.
1997
Toronto, CAN
All
All
All
o3
24-hr avg
0.001264
0.001620
Log-linear
All
Cardiovascular
PM2,
Burnett et al.
1997
Toronto, CAN
All
All
All
no2, o3,
so2
24-hr avg
-0.000639
0.001935
Log-linear
All
Cardiovascular
PMlO-2.5
Burnett et al.
1997
Toronto, CAN
All
All
All
None
24-hr avg
0.007446
0.002183
Log-linear
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November 2003
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Appendix F. Particulate Matter C-R Functions
Endpoint Name
Pollutant
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time
Beta
Std
Error
Functional
Form
Notes
All
Cardiovascular
PM10-2,
Burnett et al.
1997
Toronto, CAN
All
All
All
o3
24-hr avg
0.007039
0.002146
Log-linear
All
Cardiovascular
PMjo-2,
Burnett et al.
1997
Toronto, CAN
All
All
All
no2, o3,
so2
24-hr avg
0.004581
0.002727
Log-linear
All
Cardiovascular
PM10
Burnett et al.
1997
Toronto, CAN
All
All
All
None
24-hr avg
0.002278
0.001017
Log-linear
All
Cardiovascular
PM10
Burnett et al.
1997
Toronto, CAN
All
All
All
o3
24-hr avg
0.001733
0.001031
Log-linear
All
Cardiovascular
PM10
Burnett et al.
1997
Toronto, CAN
All
All
All
no2, o3,
so2
24-hr avg
-0.000281
0.001223
Log-linear
All
Cardiovascular
pm2,
Moolgavkar
2003
Los Angeles, CA
65+
All
All
None
24-hr avg
0.001568
0.000342
Log-linear
Reanalysis of
Moolgavkar,
2000a
All
Cardiovascular
pm2,
Moolgavkar
2003
Los Angeles, CA
65+
All
All
CO
24-hr avg
0.000389
0.000423
Log-linear
Reanalysis of
Moolgavkar,
2000a
All
Cardiovascular
pm2,
Moolgavkar
2000
Los Angeles, CA
18-64
All
All
None
24-hr avg
0.0014
0.000341
Log-linear
All
Cardiovascular
pm2,
Moolgavkar
2000
Los Angeles, CA
18-64
All
All
CO
24-hr avg
0.0009
0.000500
Log-linear
All
Cardiovascular
PM10
Samet et al.
2000
14 cities
65+
All
All
None
24-hr avg
0.001183
0.000111
Log-linear
Dysrhythmia
pm2,
Burnett et al.
1999
Toronto, CAN
All
All
All
None
24-hr avg
0.002355
0.000809
Log-linear
Dysrhythmia
pm2,
Burnett et al.
1999
Toronto, CAN
All
All
All
co,o3
24-hr avg
0.001356
0.000910
Log-linear
Dysrhythmia
PMio-2.5
Burnett et al.
1999
Toronto, CAN
All
All
All
None
24-hr avg
0.002000
0.001064
Log-linear
Dysrhythmia
PM10
Burnett et al.
1999
Toronto, CAN
All
All
All
None
24-hr avg
0.001616
0.000533
Log-linear
Dysrhythmia
PM2,
Ito
2003
Detroit, MI
65+
All
All
None
24-hr avg
0.001249
0.002033
Log-linear
Reanalysis of
Lippmann et al.,
2000
Dysrhythmia
PM2,
Lippmann et al.
2000
Detroit, MI
65+
All
All
o3
24-hr avg
0.002138
0.002525
Log-linear
Congestive
Heart Failure
PM2,
Ito
2003
Detroit, MI
65+
All
All
None
24-hr avg
0.003074
0.001292
Log-linear
Reanalysis of
Lippmann et al.,
2000
Abt Associates Inc.
F-27
November 2003
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Appendix F. Particulate Matter C-R Functions
^ ^ . . .. „ Other Averaging _ . Std Functional .. .
EndpointName Pollutant Author Year Location Age Race Gender _ Beta _ _ Notes
Pollutants Time Error Form
Heart^ailure ^^25 Lippmann et al. 2000 Detroit, MI 65+ All All 03 24-hr avg 0.004668 0.001650 Log-linear
, . Reanalysis of
ischemic Heart pM^ no 2QQ3 Detroitj m 65+ AU AU None 24-hr avg 0.001435 0.001156 Log-linear Lippmann et al.
Disease
Ischemic Heart
Disease
2000
Lippmann et al. 2000 Detroit, MI 65+ All All 03 24-hr avg 0.001116 0.001339 Log-linear
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for more
detail on the specific averaging time used in the study.
Abt Associates Inc.
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November 2003
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Appendix F. Particulate Matter C-R Functions
F .4 Hospitalizations
F .4.1 Hospital Admissions for All Respiratory (Burnett et al., 1997, Toronto)
Burnett et al. (1997) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada during the summers of 1992-1994. In a Poisson regression, all
respiratory admissions (ICD codes 464-466,480-486,490-494,496) were linked to coefficient of haze
(COH) and ozone; other PM measures were less strongly linked. In two pollutant models, they found that
CO, N02, and S02 were not significant, controlling for COH. They found that ozone was still significant,
controlling for COH. In multipollutant models with COH, 03, N02, and S02, both ozone and COH
remained signifcant. None of the other PM measures (PM10, PM10_2 5, PM2 5) were significant in four-
pollutant models. The PM C-R functions are based on results from single and multipollutant models.
PM2 5 Function(s)
Single Pollutant Model (PM2 5)
In a single pollutant model with adjustment for temperature and dew point, the PM2 5 coefficient
and standard error are based on a relative risk of 1.037 (t-statistic 3.29) for an 11 |ig/nr' increase in four-
day average PM25 (Burnett et al., 1997, Table 2, p. 617).
Functional Form: Log-linear
Coefficient: 0.003303
Standard Error: 0.001004
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (PM2 5 and ozone)
In a model with ozone, the PM25 coefficient and standard error are based on a relative risk of
1.027 (t-statistic 2.33) for an 11 |ig/m3 increase in four-day average PM25 (Burnett et al., 1997, Table 4, p.
618).
Functional Form: Log-linear
Coefficient: 0.002422
Standard Error: 0.001039
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (PM2 5, N02, ozone, and S02)
In a four-pollutant model with N02, 03, and S02, the PM2 5 coefficient and standard error are
based on a relative risk of 0.999 (t-statistic 0.10) for an 11 |ig/m3 increase in four-day average PM25
(Burnett et al., 1997, Table 6, p. 618).
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Appendix F. Particulate Matter C-R Functions
Functional Form: Log-linear
Coefficient: -0.000091
Standard Error: 0.000910
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
PM10 2 5 Function(s)
Single Pollutant Model
In a single pollutant model with adjustment for temperature and dew point, the PM10_2 5 coefficient
and standard error are based on a relative risk of 1.023 (t-statistic 3.41) for a 4.75 |ig/m3 increase in five-
day average PM10_25 (Burnett et al., 1997, Table 2, p. 617).
Functional Form: Log-linear
Coefficient: 0.004787
Standard Error: 0.001404
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (PM10_2 5 and ozone)
In a model with ozone, the PM10_2 5 coefficient and standard error are based on a relative risk of
1.020 (t-statistic 3.04) for a 4.75 |ig/nr' increase in five-day average PM10_25 (Burnett et al., 1997, Table 4,
p. 618).
Functional Form: Log-linear
Coefficient: 0.004169
Standard Error: 0.001371
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (PM10_2 5, N02, ozone, and S02)
In a four-pollutant model with N02, ozone, and S02, the PM10_2 5 coefficient and standard error are
based on a relative risk of 1.007 (t-statistic 0.82) for a 4.75 |ig/m3 increase in five-day average PM10_25
(Burnett et al., 1997, Table 6, p. 618).
Functional Form: Log-linear
Coefficient: 0.001469
Standard Error: 0.001791
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
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PM10 Function(s)
Single Pollutant Model
In a single pollutant model with adjustment for temperature and dew point, the PM10 coefficient
and standard error are based on a relative risk of 1.03 (t-statistic 3.42) for a 14.25 |ig/m3 increase in five-
day average PM10 (Burnett et al., 1997, Table 2, p. 617).
Functional Form: Log-linear
Coefficient: 0.002074
Standard Error: 0.000607
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (PM10 and ozone)
In a model with ozone, the PM10 coefficient and standard error are based on a relative risk of
1.027 (t-statistic 3.16) for a 14.25 |ig/m3 increase in five-day average PM10 (Burnett et al., 1997, Table 4,
p. 618).
Functional Form: Log-linear
Coefficient: 0.001870
Standard Error: 0.000592
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (PM10, N02, ozone, and S02)
In a four-pollutant model with N02, ozone, and S02, the PM10 coefficient and standard error are
based on a relative risk of 1.004 (t-statistic 0.36) for a 14.25 |ig/m3 increase in five-day average PM10
(Burnett et al., 1997, Table 6, p. 618).
Functional Form: Log-linear
Coefficient: 0.000280
Standard Error: 0.000778
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person (ICD
codes 464, 466, 480-487, 490-496)
Population: population of all ages
F .4.2 Hospital Admissions for All Respiratory (Burnett et al., 2001, Toronto)
Burnett et al. (2001) studied the association between air pollution and acute respiratory hospital
admissions (ICD codes 493, 466, 464.4, 480-486) in Toronto from 1980-1994, among children <2 years
of age. They collected hourly concentrations of the gaseous pollutants, CO, N02, S02, and ozone. Daily
measures of particulate matter were estimated for the May to August period of 1992-1994 using TSP,
sulfates, and coefficient of haze data. The authors report a positive association between ozone in the May
through August months and respiratory hospital admissions, for several single days after elevated ozone
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levels. The strongest association was found using a five-day moving average of ozone. No association
was found in the September through April months. In co-pollutant models with a particulate matter or
another gaseous pollutant, the ozone effect was only slightly diminished. The effects for PM and gaseous
pollutants were generally significant in single pollutant models but diminished in co-pollutant models
with ozone, with the exception of CO. The C-R functions for PM10_2 5 are based on a single pollutant and
co-pollutant model, using the four-day moving average of PM10_25. The C-R functions for PM2 5 are based
on a single pollutant and co-pollutant model, using the four-day moving average of PM2 5.
PM2 5 Function(s)
Single Pollutant Model
The single pollutant coefficient and standard error are based on a percent increase of 15.8 (t-stat
3.29) for an 18.0 |ig/m3 increase in four-day average PM25 (Burnett et al., 2001, Table 3).
Functional Form: Log-linear
Coefficient: 0.008150
Standard Error: 0.002477
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person <2
(ICD codes 464, 466, 480-487, 493)
Population: population of ages under 2
Multipollutant Model (PM2 5 and ozone)
In a model with ozone, the coefficient and standard error are based on a percent increase of 1.4 (t-
stat 0.24) for an 18.0 |ig/m3 increase in four-day average PM2 5 (Burnett et al., 2001, Table 3).
Functional Form: Log-linear
Coefficient: 0.000772
Standard Error: 0.003218
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person <2
(ICD codes 464, 466, 480-487, 493)
Population: population of ages under 2
PM10 2 5 Function(s)
Single Pollutant Model
The single pollutant coefficient and standard error are based on a percent increase of 18.3 (t-stat
3.77) for a 16.2 |ig/m3 increase in four-day average PM10_25 (Burnett et al., 2001, Table 3).
Functional Form: Log-linear
Coefficient: 0.010374
Standard Error: 0.002752
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person <2
(ICD codes 464, 466, 480-487, 493)
Population: population of ages under 2
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Multipollutant Model (PM10_2 5 and ozone)
In a model with ozone, the coefficient and standard error are based on a percent increase of 4.5 (t-
stat 0.72) for a 16.2 |ig/m3 increase in four-day average PM10_25 (Burnett et al., 2001, Table 3).
Functional Form: Log-linear
Coefficient: 0.002717
Standard Error: 0.003774
Incidence Rate: region-specific daily hospital admission rate for all respiratory disease per person <2
(ICD codes 464, 466, 480-487, 493)
Population: population of ages under 2
F .4.3 Hospital Admissions for All Respiratory (Schwartz, 1995, New Haven)
Schwartz (1995) examined the relationship between air pollution and respiratory hospital
admissions (ICD codes 460-519) for individuals 65 and older in New Haven, Connecticut, from January
1988 to December 1990. In single-pollutant models, PM10 and S02 were significant, while ozone was
marginally significant. In two-pollutant models, ozone was significant in a model with PM10 and not
significant in a model with S02, but had relatively stable coefficient estimates. PM10 was significant in
two-pollutant models with ozone and S02. S02 was significant only in the co-pollutant model with PM10.
The PM10 C-R functions are based on results from a single pollutant and two-pollutant model (PM10 and
ozone).
Single Pollutant Model
In a single-pollutant model, the coefficient and standard error are calculated from the relative risk
(1.06) and 95% confidence interval (1.00-1.13) for a 50 |ig/m3 increase in average daily PM10 levels
(Schwartz, 1995, Table 3, p. 534).
Functional Form: Log-linear
Coefficient: 0.001165
Standard Error: 0.000624
Incidence Rate: region-specific daily hospital admission rate for respiratory admissions per person 65+
(ICD codes 460-519)
Population: population of ages 65 and older
Multipollutant Model (PM10 and ozone)
In a model with ozone, the coefficient and standard error are estimated from the relative risk
(1.09) and 95% confidence interval (1.00-1.20) for a 50 |ig/m3 increase in average daily PM10 levels
(Schwartz, 1995, Table 3, p. 534).
Functional Form: Log-linear
Coefficient: 0.001724
Standard Error: 0.000930
Incidence Rate: region-specific daily hospital admission rate for respiratory admissions per person 65+
(ICD codes 460-519)
Population: population of ages 65 and older
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F .4.4 Hospital Admissions for All Respiratory (Schwartz, 1995, Tacoma)
Schwartz (1995) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Tacoma, Washington, from January 1988 to December 1990. In single-
pollutant models, PM10, ozone, and S02 were all significant. Ozone remained significant in two-pollutant
models with PM10 and S02, and had stable coefficient estimates. PM10 was significant in a two-pollutant
model with S02, but not in a model with ozone, although the central estimate remained stable. S02 was
not significant in two-pollutant models with ozone or PM10. The PM10 C-R functions are based on results
from a single pollutant and two-pollutant model (PM10 and ozone).
Single Pollutant Model
In a single-pollutant model, the coefficient and standard error are calculated from the relative risk
(1.10) and 95% confidence interval (1.03-1.17) for a 50 |ig/m3 increase in average daily PM10 levels
(Schwartz, 1995, Table 6, p. 535).
Functional Form: Log-linear
Coefficient: 0.001906
Standard Error: 0.000650
Incidence Rate: region-specific daily hospital admission rate for respiratory admissions per person 65+
(ICD codes 460-519)
Population: population of ages 65 and older
Multipollutant Model (PM10 and ozone)
In a model with PM10, the coefficient and standard error are estimated from the relative risk (1.12)
and 95% CI (0.97-1.29) for a 50 |ig/m3 increase in average daily PM10 levels (Schwartz, 1995, Table 6, p.
535).
Functional Form: Log-linear
Coefficient: 0.002267
Standard Error: 0.001455
Incidence Rate: region-specific daily hospital admission rate for respiratory admissions per person 65+
(ICD codes 460-519)
Population: population of ages 65 and older
F .4.5 Hospital Admissions for All Respiratory (Thurston et al., 1994, Toronto)
Thurston et al. (1994) examined the relationship between air pollution and hospital admissions
for individuals of all ages in Toronto, Canada, for six weeks in July and August 1986-1988. In single-
pollutant linear regression models, ozone and various measures of PM were linked to all respiratory
admissions (ICD codes 466, 480-482, 485, 490-493). In two-pollutant models, ozone was still
significant, but measures of PM were often not significant; only H+ was significant. The C-R functions
for PM2 5 and PM10 are based on results from the reported single pollutant models and co-pollutant models
with ozone. For PM10_2 5, results are reported only from a single pollutant model.
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PM2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the PM2 5 coefficient (0.0828) and standard error (0.0367) are
reported in Table 3 (Thurston et al., 1994, p. 281) for a unit |ig/m3 increase daily average PM25 levels.
Functional Form: Linear
Coefficient: 0.0828
Standard Error: 0.0367
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
Multipollutant Model (PM2 5 and ozone)
In a model with ozone, the PM25 coefficient (0.0434) and standard error (0.0429) are reported in
Table 3 (Thurston et al., 1994, p. 281) for a unit |ig/m3 increase daily average PM25 levels.
Functional Form: Linear
Coefficient: 0.0434
Standard Error: 0.0429
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
PM10 2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the PM10_25 coefficient (0.1228) and standard error (0.0895) are
reported in Table 3 (Thurston et al., 1994, p. 281) for a unit |ig/m3 increase daily average PM10_2 5 levels.
Functional Form: Linear
Coefficient: 0.1228
Standard Error: 0.0895
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
PM10 Function(s)
Single Pollutant Model
In a single pollutant model, the PM10 coefficient (0.0642) and standard error (0.0290) are reported
in Table 3 (Thurston et al., 1994, p. 281) for a unit |ig/m3 increase daily average PM10 levels.
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Functional Form: Linear
Coefficient: 0.0642
Standard Error: 0.0290
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
Multipollutant Model (PM10 and ozone)
In a model with ozone, the PM10 coefficient (0.0339) and standard error (0.0344) are reported in
Table 3 (Thurston et al., 1994, p. 281) for a unit |ig/nr' increase daily average PM10 levels.
Functional Form: Linear
Coefficient: 0.0339
Standard Error: 0.0344
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
F .4.6 Hospital Admissions for Asthma (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. The authors examined single pollutant log-
linear models for PM10, PM10_2 5, PM2 5, CO, N02, S02, and ozone and found all significantly associated
with asthma except S02. They estimated multiple pollutant models, where pollutants for best fitting
model were chosen using stepwise regression based on AIC criterion. Asthma admissions were linked to
ozone, CO, and PM10_2 5. The C-R functions for PM10_2 5 are based on the results of a single pollutant
model and three-pollutant model (03, CO, PM10_25). The C-R functions for PM25 and PM10are based on
the results of a single pollutant model.
PM2 5 Function(s)
Single Pollutant Model
The coefficient and standard error are based on the percent increase (4.60) and t-statistic (3.22)
reported in Table 3 (Burnett et al., 1999, p. 133) for an 18.0 |ig/m3 increase in three-day average PM25
levels.
Functional Form: Log-linear
Coefficient: 0.002499
Standard Error: 0.000776
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per person (ICD
code 493)
Population: population of all ages
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PM10 2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(5.25) and t-statistic (4.20) reported in Table 3 (Burnett et al., 1999, p. 133) for a 12.2 |ig/m3 increase in
three-day average PM10_25 levels.
Functional Form: Log-linear
Coefficient: 0.004194
Standard Error: 0.000999
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per person (ICD
code 493)
Population: population of all ages
Multipollutant Model (PM10_2 5, CO, and ozone)
In a model with ozone and CO, the PM10_2 5 coefficient and standard error are based on the percent
increase (4.00) reported in Table 5 (Burnett et al., 1999, p. 135) and the t-statistic obtained from the
authors (3.04)41 for a 12.2 |ig/m3 increase in three-day average PM10_25 levels.
Functional Form: Log-linear
Coefficient: 0.003215
Standard Error: 0.001058
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per person (ICD
code 493)
Population: population of all ages
PM10 Function(s)
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(5.27) and t-statistic (3.39) reported in Table 3 (Burnett et al., 1999, p. 133) for a 30.2 |ig/m3 increase in
three-day average PM10 levels.
Functional Form: Log-linear
Coefficient: 0.001701
Standard Error: 0.000502
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per person (ICD
code 493)
Population: population of all ages
41 Rick Burnett (co-author), personal communication.
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F .4.7 Hospital Admissions for Asthma (Lin et al., 2002, Toronto)
Lin et al. (2002) examined the association between ambient particulate matter in Toronto and
asthma hospitalizations in children (ages 6-12) between 1981 and 1993. The authors collected PM data
measured every six days for the period of 1984 to 1990.42 The authors analyzed the PM-asthma
hospitalization association using a case-crossover analysis (with unidirectional and bidirectional
controls)43 and a time series analysis with moving averages of PM ranging from 1 day to 7 days . They
estimated the effects on boys and girls separately and found an increasing association between PM10_2 5
and asthma hospitalizations as averaging time increased, with a leveling off around six or seven days.
This effect remained significant in a model with CO, N02, S02, and ozone. Results for gaseous pollutants
were not reported. They did not find a significant association for PM2 5 or PM10 in models other than the
unidirectional case-crossover analysis. The authors suggest that estimates from a unidirectional case-
crossover analysis may be significantly biased when time trends are present. The considerable difference
between the results from this model and the bidirectional and time series analyses suggest that this may be
the case.
The C-R functions for PM are based on the time series analysis rather than the bidirectional case-
crossover because the time series produces more stable estimates (i.e., the 95% confidence intervals are
always narrower than those from the case-crossover design) and this design is more commonly used in air
pollution epidemiology. The reported relative risks for PM10_2 5 increase as the number of days included
in the moving average increases - up through 7 days (the maximum number of days considered). This
suggests that the multi-day averages are capturing to some extent what is essentially a distributed lag
effect - that is, that PM10_25 even 7 days earlier has some impact on asthma hospitalization rates. We
therefore selected the model with the 7-day average for use in the single pollutant C-R functions. In
multipollutant models, only results using 5- and 6-day averages were reported, so the C-R functions are
based on 6-day averages.
PM2 5 Function(s) - Boys
Single Pollutant Model
The single pollutant coefficient and standard error for boys are based on the relative risk (0.96)
and 95% confidence interval (0.91-1.02) for a 9.3 |ig/m3 increase in 7-day average PM25 (Lin et al., 2002,
Table 3, p. 579)
Functional Form: Log-linear
Coefficient: -0.004389
Standard Error: 0.003130
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per male child ages
6-12 (ICD code 493)
Population: population of males, ages 6 through 12
42 For the remaining days, they estimated PM using TSP, sulfate, and coefficient of haze data.
43 In the case-crossover analysis, the same individual serves as a case and control. In the unidirectional model, the case
period is during the hospital visit and the control period is at some point well in advance of the case period. In the bidirectional
model, there are two control periods for each visit, one before the case period and one after the case period.
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Multipollutant Model (PM2 5, CO, N02, ozone, and S02)
In a model with CO, N02, ozone, and S02, the coefficient and standard error for boys are based
on the relative risk (0.94) and 95% confidence interval (0.88-1.01) for a 9.3 |ig/m3 increase in 6-day
average PM25 (Lin et al., 2002, Table 5, p. 580).
Functional Form: Log-linear
Coefficient: -0.006653
Standard Error: 0.003779
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per male child ages
6-12 (ICD code 493)
Population: population of males, ages 6 through 12
PM2 5 Function(s) - Girls
Single Pollutant Model
The single pollutant coefficient and standard error for girls are based on the relative risk (1.06)
and 95% confidence interval (0.98-1.13) for a 9.3 |ig/m3 increase in 7-day average PM25(Lin et al., 2002,
Table 4, p. 580)
Functional Form: Log-linear
Coefficient: 0.006265
Standard Error: 0.008377
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per female child
ages 6-12 (ICD code 493)
Population: population of females, ages 6 through 12
Multipollutant Model (PM2 5, CO, N02, ozone, and S02)
In a model with CO, N02, ozone, and S02, the coefficient and standard error for girls are based
on the relative risk (0.98) and 95% confidence interval (0.90-1.08) for a 9.3 |ig/m3 increase in 6-day
average PM25 (Lin et al., 2002, Table 5, p. 580).
Functional Form: Log-linear
Coefficient: -0.002172
Standard Error: 0.005001
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per female child
ages 6-12 (ICD code 493)
Population: population of females, ages 6 through 12
PM10 2 5 Function(s) - Boys
Single Pollutant Model
The single pollutant coefficient and standard error for boys are based on the relative risk (1.12)
and 95% confidence interval (1.04-1.20) for an 8.4 |ig/m3 increase in 7-day average PM10_25 (Lin et al.,
2002, Table 3, p. 579)
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Functional Form: Log-linear
Coefficient: 0.013492
Standard Error: 0.004346
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per male child ages
6-12 (ICD code 493)
Population: population of males, ages 6 through 12
Multipollutant Model (PM10_2 5, CO, N02, ozone, and S02)
In a model with CO, N02, ozone, and S02, the coefficient and standard error for boys are based
on the relative risk (1.15) and 95% confidence interval (1.06-1.25) for an 8.4 |ig/m3 increase in 6-day
average PM10_25 (Lin et al., 2002, Table 5, p. 580).
Functional Form: Log-linear
Coefficient: 0.016638
Standard Error: 0.005007
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per male child ages
6-12 (ICD code 493)
Population: population of males, ages 6 through 12
PM10 2 5 Function(s) - Girls
Single Pollutant Model
The single pollutant coefficient and standard error for girls are based on the relative risk (1.20)
and 95% confidence interval (1.09-1.31) for an 8.4 |ig/m3 increase in 7-day average PM10_25(Lin et al.,
2002, Table 4, p. 580)
Functional Form: Log-linear
Coefficient: 0.021705
Standard Error: 0.005583
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per female child
ages 6-12 (ICD code 493)
Population: population of females, ages 6 through 12
Multipollutant Model (PM10_2 5, CO, N02, ozone, and S02)
In a model with CO, N02, ozone, and S02, the coefficient and standard error for girls are based
on the relative risk (1.15) and 95% confidence interval (1.03-1.29) for an 8.4 |ig/m3 increase in 6-day
average PM10_25 (Lin et al., 2002, Table 5, p. 580).
Functional Form: Log-linear
Coefficient: 0.016638
Standard Error: 0.006836
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per female child
ages 6-12 (ICD code 493)
Population: population of females, ages 6 through 12
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PM10 Function(s) - Boys
Single Pollutant Model
The single pollutant coefficient and standard error for boys are based on the relative risk (1.01)
and 95% confidence interval (0.95-1.08) for a 14.8 |ig/m3 increase in 7-day average PM10(Lin et al.,
2002, Table 3, p. 579)
Functional Form: Log-linear
Coefficient: 0.000672
Standard Error: 0.002211
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per male child ages
6-12 (ICD code 493)
Population: population of males, ages 6 through 12
Multipollutant Model (PM10, CO, N02, ozone, and S02)
In a model with CO, N02, ozone, and S02, the coefficient and standard error for boys are based
on the relative risk (1.02) and 95% confidence interval (0.94-1.11) for a 14.8 |ig/m3 increase in 6-day
average PM10(Lin et al., 2002, Table 5, p. 580).
Functional Form: Log-linear
Coefficient: 0.001338
Standard Error: 0.002865
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per male child ages
6-12 (ICD code 493)
Population: population of males, ages 6 through 12
PM10 Function(s) - Girls
Single Pollutant Model
The single pollutant coefficient and standard error for girls are based on the relative risk (1.07)
and 95% confidence interval (0.98-1.16) for a 14.8 |ig/m3 increase in 7-day average PM10(Lin et al.,
2002, Table 4, p. 580)
Functional Form: Log-linear
Coefficient: 0.004572
Standard Error: 0.002906
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per female child
ages 6-12 (ICD code 493)
Population: population of females, ages 6 through 12
Multipollutant Model (PM10, CO, N02, ozone, and S02)
In a model with CO, N02, ozone, and S02, the coefficient and standard error for girls are based
on the relative risk (1.03) and 95% confidence interval (0.93-1.15) for a 14.8 |ig/m3 increase in 6-day
average PM10(Lin et al., 2002, Table 5, p. 580).
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Functional Form: Log-linear
Coefficient: 0.001997
Standard Error: 0.003660
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per female child
ages 6-12 (ICD code 493)
Population: population of females, ages 6 through 12
F .4.8 Hospital Admissions for Asthma (Sheppard et al., 1999; Sheppard, 2003)
Sheppard et al. (1999) studied the relation between air pollution in Seattle and nonelderly (<65)
hospital admissions for asthma from 1987 to 1994. They used air quality data for PM10, PM25, coarse
PM1010_2 5, S02, ozone, and CO in a Poisson regression model with control for time trends, seasonal
variations, and temperature-related weather effects.44 They found asthma hospital admissions associated
with PM10, PM25, PM10_2 5, CO, and ozone. They did not observe an association for S02. They found PM
and CO to be jointly associated with asthma admissions. The best fitting co-pollutant models were found
using ozone. However, ozone data was only available April through October, so they did not consider
ozone further. For the remaining pollutants, the best fitting models included PM25 and CO. Results for
other co-pollutant models were not reported.
In response to concerns that the work by Sheppard et al. (1999) may be biased because of the
Splus issue (discussed in Appendix D of this User Manual), Sheppard (2003) reanalyzed some of this
work, in particular Sheppard reanalyzed the original study's PM25 single pollutant model.
PM2 5 Function(s)
Single Pollutant Model (Sheppard, 2003)
The coefficient and standard error are based on the relative risk (1.04) and 95% confidence
interval (1.01-1.06) for a 11.8 |ig/m3 increase in PM25 in the 1-day lag GAM stringent model (Sheppard,
2003, pp. 228-229).
Functional Form: Log-linear
Coefficient: 0.003324
Standard Error: 0.001045
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per person <65 (ICD
code 493)
Population: population of ages 65 and under
Multipollutant Model (PM2 5 and CO) (Sheppard et al., 1999)
The coefficient and standard error for the co-pollutant model with CO are calculated from a
relative risk of 1.03 (95% CI 1.01-1.06) for an 11.8 i-ig/m3 increase45 in PM25 (Sheppard et al., 1999, p.
28).
44 PM2 5 levels were estimated from light scattering data.
45 The reported IQR change in the abstract and text is smaller than reported in Table 3. We assume the change reported in
the abstract and text to be correct because greater number of significant figures are reported.
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Functional Form: Log-linear
Coefficient: 0.002505
Standard Error: 0.001045
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per person <65 (ICD
code 493)
Population: population of ages 65 and under
PM10 2 5 Function(s)
Single Pollutant Model (Sheppard et al., 1999)
The single pollutant coefficient and standard error are calculated from a relative risk of 1.04 (95%
CI 1.01-1.07) for a 9.3 i-ig/m3 increase46 in PM10_25 (Sheppard et al., 1999, p. 27).
Functional Form: Log-linear
Coefficient: 0.004217
Standard Error: 0.001583
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per person <65 (ICD
code 493)
Population: population of ages 65 and under
PM10 Function(s)
Single Pollutant Model (Sheppard et al., 1999)
The single pollutant coefficient and standard error are calculated from a relative risk of 1.05 (95%
CI 1.02-1.08) for a 19 i-ig/m3 increase47 in PM10 (Sheppard et al., 1999, p. 27).
Functional Form: Log-linear
Coefficient: 0.002568
Standard Error: 0.000767
Incidence Rate: region-specific daily hospital admission rate for asthma admissions per person <65 (ICD
code 493)
Population: population of ages 65 and under
F .4.9 Hospital Admissions for Asthma (Thurston et al., 1994, Toronto)
Thurston et al. (1994) examined the relationship between air pollution and hospital admissions
for individuals of all ages in Toronto, Canada, for six weeks in July and August 1986-1988. In single-
pollutant linear regression models, ozone was strongly associated with asthma admissions (ICD code 493)
and various measures of PM were marginally significant. In two-pollutant models, ozone remained
46 The reported IQR change in the abstract and text is smaller than reported in Table 3. We assume the change reported in
the abstract and text to be correct because greater number of significant figures are reported.
47 The reported IQR change in the abstract and text is smaller than reported in Table 3. We assume the change reported in
the abstract and text to be correct because greater number of significant figures are reported.
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significant, but measures of PM were often not significant. The C-R functions for PM2 5 and PM10 are
based on results from the reported single pollutant models and co-pollutant models with ozone. For PM10.
25, results are reported only from a single pollutant model.
PM2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the PM2 5 coefficient (0.0334) and standard error (0.0241) are
reported in Table 4 (Thurston et al., 1994, p. 282) for a unit |ig/m3 increase daily average PM25 levels.
Functional Form: Linear
Coefficient: 0.0334
Standard Error: 0.0241
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
Multipollutant Model (PM2 5 and ozone)
In a model with ozone, the PM25 coefficient (0.0132) and standard error (0.0273) are reported in
Table 4 (Thurston et al., 1994, p. 282) for a unit |ig/m3 increase daily average PM25 levels.
Functional Form: Linear
Coefficient: 0.0132
Standard Error: 0.0273
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
PM10 2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the PM10_25 coefficient (0.0670) and standard error (0.0571) are
reported in Table 4 (Thurston et al., 1994, p. 282) for a unit |ig/m3 increase daily average PM10_2 5 levels.
Functional Form: Linear
Coefficient: 0.0670
Standard Error: 0.0571
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
PM10 Function(s)
Single Pollutant Model
In a single pollutant model, the PM10 coefficient (0.0248) and standard error (0.0180) are reported
in Table 4 (Thurston et al., 1994, p. 282) for a unit |ig/m3 increase daily average PM10 levels.
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Functional Form: Linear
Coefficient: 0.0248
Standard Error: 0.0180
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
Multipollutant Model (PM10 and ozone)
In a model with ozone, the PM10 coefficient (0.0039) and standard error (0.0208) are reported in
Table 4 (Thurston et al., 1994, p. 282) for a unit |ig/nr' increase daily average PM10 levels.
Functional Form: Linear
Coefficient: 0.0039
Standard Error: 0.0208
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
F .4.10 Hospital Admissions for Chronic Lung Disease (Lippmann et al., 2000; Ito, 2003)
Lippmann et al. (2000) studied the association between particulate matter and daily mortality and
hospitalizations among the elderly in Detroit, MI. Data were analyzed for two separate study periods,
1985-1990 and 1992-1994. The 1992-1994 study period had a greater variety of data on PM size and was
the main focus of the report. The authors collected hospitalization data for a variety of cardiovascular and
respiratory endpoints. They used daily air quality data for PM10, PM25, and PM10_25 in a Poisson
regression model with generalized additive models (GAM) to adjust for nonlinear relationships and
temporal trends. In single pollutant models, all PM metrics were statistically significant for pneumonia
(ICD codes 480-486), PM10_2 5 and PM10 were significant for ischemic heart disease (ICD code 410-414),
and PM25 and PM10 were significant for heart failure (ICD code 428). There were positive, but not
statistically significant associations, between the PM metrics and COPD (ICD codes 490-496) and
dysrhythmia (ICD code 427). In separate co-pollutant models with PM and either ozone, S02, N02, or
CO, the results were generally comparable. The PM2 5 C-R functions are based on results of the single
pollutant model and co-pollutant model with ozone.
In response to concerns with the Splus issue, Ito (2003) reanalyzed the study by Lippmann et al.
(2000). The reanalysis by Ito reported that more generalized additive models with stringent convergence
criteria and generalized linear models resulted in smaller relative risk estimates. Not all of the original
results were replicated, so we present here a mix of C-R functions from the reanalysis and from the
original study (when the reanalyzed results were not available).
Single Pollutant Model (Ito, 2003)
The coefficient and standard error are based on the relative risk (1.043) and 95% confidence
interval (0.902-1.207) for a 36 |ig/nr' increase in PM25 in the 3-day lag GAM stringent model (Ito, 2003,
Table 8).
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Functional Form: Log-linear
Coefficient: 0.001169
Standard Error: 0.002064
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 65+ (ICD codes 490-496)
Population: population of ages 65 and older
Multipollutant Model (PM2 5 and ozone) (Lippmann et al., 2000)
The co-pollutant coefficient and standard error are calculated from a relative risk of 1.040 (95%
CI 0.877-1.234) for a 36 |ig/m3 increase in PM25 (Lippmann et al., 2000, Table 14, p. 26).
Functional Form: Log-linear
Coefficient: 0.001089
Standard Error: 0.002420
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 65+ (ICD codes 490-496)
Population: population of ages 65 and older
F .4.11 Hospital Admissions for Chronic Lung Disease (Moolgavkar, 2000c; Moolgavkar,
2003)
Moolgavkar (2000c) examined the association between air pollution and COPD hospital
admissions (ICD 490-496) in the Chicago, Los Angeles, and Phoenix metropolitan areas. He collected
daily air pollution data for ozone, S02, N02, CO, and PM10 in all three areas. PM2 5 data was available
only in Los Angeles. The data were analyzed using a Poisson regression model with generalized
additive models to adjust for temporal trends. Separate models were run for 0 to 5 day lags in each
location. Among the 65+ age group in Chicago and Phoenix, weak associations were observed between
the gaseous pollutants and admissions. No consistent associations were observed for PM10. In Los
Angeles, marginally significant associations were observed for PM2 5, which were generally lower than
for the gases. In co-pollutant models with CO, the PM2 5 effect was reduced. Similar results were
observed in the 0-19 and 20-64 year old age groups.
In response to concerns with the Splus issue, Moolgavkar (2003) reanalyzed his earlier study. In
the reanalysis, he reported that more generalized additive models with stringent convergence criteria and
generalized linear models resulted in smaller relative risk estimates. Not all of the original results were
replicated, so we present here a mix of C-R functions from the reanalysis and from the original study
(when the reanalyzed results were not available).
The PM2 5 C-R functions for the 65+ age group are based on the reanalysis in Moolgavkar
(Moolgavkar, 2003) of the single and co-pollutant models (PM2 5 and CO). The PM25 C-R functions for
the 20-64 age group are based on the original study's single and co-pollutant models (PM25 and CO).
Since the true PM effect is most likely best represented by a distributed lag model, then any single lag
model should underestimate the total PM effect. As a result, we selected the lag models with the greatest
effect estimates for use in the C-R functions.
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Appendix F. Particulate Matter C-R Functions
Ages 65 and older
Single Pollutant Model (Moolgavkar, 2003)
The coefficient and standard error are calculated from an estimated percentage change of 1.8548
and t-statistic of 3.53 for a 10 |ig/m3 increase in PM25 in the 2-day lag GAM-30df stringent (10~8) model
(Moolgavkar, 2003, Table 17).
Functional Form: Log-linear
Coefficient: 0.001833
Standard Error: 0.000519
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 65+ (ICD codes 490-496)
Population: population of ages 65 and older
Multipollutant Model (PM2 5 and N02) (Moolgavkar, 2003)
In a model with PM2 5 and N02, the coefficient and standard error are calculated from the
estimated percentage change of 0.4240 and t-statistic of 0.62 for a 10 |ig/m3 increase in PM2 5 in the 0-day
lag GAM-lOOdf stringent (10~8) model (Moolgavkar, 2003, Table 19).
Functional Form: Log-linear
Coefficient: 0.000419
Standard Error: 0.000676
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 65+ (ICD codes 490-496)
Population: population of ages 65 and older
Multipollutant Model (PM2 5 and CO) (Moolgavkar, 2000c)
In a model with CO, the coefficient and standard error are calculated from an estimated percent
change of 0.849 and t-statistic of 0.8 for a 10 |ig/m3 increase in PM25 in the two-day lag model
(Moolgavkar, 2000c, Table 3, p. 80).
Functional Form: Log-linear
Coefficient: 0.0008
Standard Error: 0.001000
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 65+ (ICD codes 490-496)
Population: population of ages 65 and older
48 In a log-linear model, the percent change is equal to (RR - 1) * 100. In this study, Moolgavkar defines and reports the
"estimated" percent change as (log RR * 100). Because the relative risk is close to 1, RR-1 and log RR are essentially the same.
For example, a true percent change of 2.0 would result in a relative risk of 1.020 and coefficient of 0.001980. The "estimated"
percent change, as reported by Moolgavkar, of 2.0 results in a relative risk of 1.020201 and coefficient of 0.002.
49 In a log-linear model, the percent change is equal to (RR - 1) * 100. In this study, Moolgavkar defines and reports the
"estimated" percent change as (log RR * 100). Because the relative risk is close to 1, RR-1 and log RR are essentially the same.
For example, a true percent change of 0.8 would result in a relative risk of 1.008 and coefficient of 0.000797. The "estimated"
percent change, as reported by Moolgavkar, of 0.8 results in a relative risk of 1.008032 and coefficient of 0.0008.
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Appendix F. Particulate Matter C-R Functions
Ages 18 to 6450
Single Pollutant Model (Moolgavkar, 2000c)
The single pollutant coefficient and standard error are calculated from an estimated percent
change of 2,251 and t-statistic of 3.0 for a 10 |ig/m3 increase in PM2 5 in the two-day lag model
(Moolgavkar, 2000c, Table 4, p. 81).
Functional Form: Log-linear
Coefficient: 0.0022
Standard Error: 0.000733
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 18-64 (ICD codes 490-492, 494-496)52
Population: population of ages 18 to 64
Multipollutant Model (PM2 5 and CO) (Moolgavkar, 2000c)
In a model with CO, the coefficient and standard error are calculated from an estimated percent
change of 2.053 and t-statistic of 2.2 for a 10 |ig/m3 increase in PM25 in the two-day lag model
(Moolgavkar, 2000c, Table 4, p. 81).
Functional Form: Log-linear
Coefficient: 0.0020
Standard Error: 0.000909
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 18-64 (ICD codes 490-492, 494-496)54
Population: population of ages 18 to 64
50 Although Moolgavkar (2000c) reports results for the 20-64 year old age range, for comparability to other studies, we
apply the results to the population of ages 18 to 64.
51 In a log-linear model, the percent change is equal to (RR - 1) * 100. In this study, Moolgavkar defines and reports the
"estimated" percent change as (log RR * 100). Because the relative risk is close to 1, RR-1 and log RR are essentially the same.
For example, a true percent change of 2.2 would result in a relative risk of 1.022 and coefficient of 0.002176. The "estimated"
percent change, as reported by Moolgavkar, of 2.2 results in a relative risk of 1.022244 and coefficient of 0.0022.
52 Moolgavkar (2000c) reports results for ICD codes 490-496. In order to avoid double counting non-elderly asthma
hospitalizations (ICD code 493) with Sheppard et al. (1999) in a total benefits estimation, we have excluded ICD code 493 from the
baseline incidence rate used in this function.
53 In a log-linear model, the percent change is equal to (RR - 1) * 100. In this study, Moolgavkar defines and reports the
"estimated" percent change as (log RR * 100). Because the relative risk is close to 1, RR-1 and log RR are essentially the same.
For example, a true percent change of 2.0 would result in a relative risk of 1.020 and coefficient of 0.001980. The "estimated"
percent change, as reported by Moolgavkar, of 2.0 results in a relative risk of 1.020201 and coefficient of 0.002.
54 Moolgavkar (2000c) reports results for ICD codes 490-496. In order to avoid double counting non-elderly asthma
hospitalizations (ICD code 493) with Sheppard et al. (1999) in a total benefits estimation, we have excluded ICD code 493 from the
baseline incidence rate used in this function.
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F .4.12 Hospital Admissions for Chronic Lung Disease (Moolgavkar et al., 1997,
Minneapolis)
Moolgavkar et al. (1997) examined the relationship between air pollution and chronic lung
disease hospital admissions (ICD codes 490-496) for individuals 65 and older in Minneapolis-St. Paul,
Minnesota, from January 1986 to December 1991. In a Poisson regression, they found no significant
effect for any of the pollutants (PM10, ozone, or CO). The effect for ozone was marginally significant.
The PM10 C-R function is based on the results from a three-pollutant model (ozone, CO, PM10) to
estimate chronic lung disease incidence. The model with a 100 df smoother was reported to be optimal
(p. 368).
Multipollutant Model (PM10, CO, and ozone)
In a model with ozone and CO, the estimated PM10 coefficient and standard error are based on a
1.77 percent increase in admissions (95% CI -1.3, 4.9) due to a PM10 change of 20 |ig/m3 (Moolgavkar
et al., 1997, Table 4 and p. 366).
Functional Form: Log-linear
Coefficient: 0.000877
Standard Error: 0.000777
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 65+ (ICD codes 490-496)
Population: population of ages 65 and older
F .4.13 Hospital Admissions for Chronic Lung Disease (Schwartz, 1994a, Minneapolis)
Schwartz (1994c) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Minneapolis, MN, from January 1986 to December 1989. In single-
pollutants models, PM10 was significantly related to chronic lung disease. Ozone was not significantly
linked to chronic lung disease and the results were not reported. The PM10 C-R function is based on the
results of the single-pollutant model with "spline" smoothing.
Single Pollutant Model
In a model with spline functions to adjust for time and weather, the coefficient and standard
error are based on the relative risk (1.47) and 95% confidence interval (1.10-1.95) associated with a 100
|ig/nr' increase in two-day average PM10 levels (Schwartz, 1994c, Table 4, p. 369) .
Functional Form: Log-linear
Coefficient: 0.003853
Standard Error: 0.001461
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 65+ (ICD codes 490-496)
Population: population of ages 65 and older
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F .4.14 Hospital Admissions for Chronic Lung Disease (less Asthma) (Burnett et al., 1999,
Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. The authors examined single pollutant
log-linear models for PM10, PM10_25, PM25, CO, N02, S02, and ozone and found PM10_2 5, PM10, and
ozone significantly associated with chronic lung disease (ICD codes 490-492, 496). They estimated
multiple pollutant models, where pollutants for the best fitting model were chosen using stepwise
regression based on AIC criterion. In a three pollutant model, admissions for chronic obstructive
pulmonary disease (COPD) were linked to ozone and PM10_2 5. A non-significant association was found
with CO. The C-R functions for PM2 5 and PM10 are based on the results of a single pollutant model.
The C-R functions for PM10_2 5 are based on the results of a single pollutant model and three-pollutant
model (03, CO, PM10_2 5).
PM2 5 Function(s)
Single Pollutant Model
The coefficient and standard error are based on the percent increase (3.42) and t-statistic (1.89)
reported in Table 3 (Burnett et al., 1999, p. 133) for an 18.0 |ig/m ' increase in two-day average PM2 5
levels.
Functional Form: Log-linear
Coefficient: 0.001868
Standard Error: 0.000988
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person (ICD codes 490-492, 494-496)
Population: population of all ages
PM10 2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(6.07) and t-statistic (3.26) reported in Table 3 (Burnett et al., 1999, p. 133) for a 12.2 |ig/m3 increase in
three-day average PM10_2 5 levels.
Functional Form: Log-linear
Coefficient: 0.004830
Standard Error: 0.001482
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person (ICD codes 490-492, 494-496)
Population: population of all ages
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Multipollutant Model (PM10_2 5, CO, and ozone)
In a model with ozone and CO, the PM10_2 5 coefficient and standard error are based on the
percent increase (3.86) reported in Table 5 (Burnett et al., 1999, p. 135) and the t-statistic obtained from
the authors (1.90)55 for a 12.2 |ig/nr' increase in three-day average PM10_2 5 levels.
Functional Form: Log-linear
Coefficient: 0.003104
Standard Error: 0.001634
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person (ICD codes 490-492, 494-496)
Population: population of all ages
PM10 Function(s)
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(4.11) and t-statistic (2.44) reported in Table 3 (Burnett et al., 1999, p. 133) for a 30.2 |ig/m3 increase in
three-day average PM10 levels.
Functional Form: Log-linear
Coefficient: 0.001334
Standard Error: 0.000547
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person (ICD codes 490-492, 494-496)
Population: population of all ages
F .4.15 Hospital Admissions for Chronic Lung Disease (less Asthma) (Moolgavkar, 2000c)
Moolgavkar (2000c) examined the association between air pollution and COPD hospital
admissions (ICD 490-496) in the Chicago, Los Angeles, and Phoenix metropolitan areas. He collected
daily air pollution data for ozone, S02, N02, CO, and PM10 in all three areas. PM2 5 data was available
only in Los Angeles. The data were analyzed using a Poisson regression model with generalized
additive models to adjust for temporal trends. Separate models were run for 0 to 5 day lags in each
location. Among the 65+ age group in Chicago and Phoenix, weak associations were observed between
the gaseous pollutants and admissions. No consistent associations were observed for PM10. In Los
Angeles, marginally significant associations were observed for PM2 5, which were generally lower than
for the gases. In co-pollutant models with CO, the PM2 5 effect was reduced. Similar results were
observed in the 0-19 and 20-64 year old age groups.
The PM2 5 C-R functions are based on the single and co-pollutant models (PM2 5 and CO)
reported for the 20-64 and 65+ age groups. Since the true PM effect is most likely best represented by a
distributed lag model, then any single lag model should underestimate the total PM effect. As a result,
we selected the lag models with the greatest effect estimates for use in the C-R functions.
55 Rick Burnett (co-author), personal communication.
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Ages 18 to 6456
Multipollutant Model (PM2 5 and CO)
In a model with CO, the coefficient and standard error are calculated from an estimated percent
change of 2.057 and t-statistic of 2.2 for a 10 |ig/m3 increase in PM25 in the two-day lag model
(Moolgavkar, 2000c, Table 4, p. 81).
Functional Form: Log-linear
Coefficient: 0.0020
Standard Error: 0.000909
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease admissions per
person 18-64 (ICD codes 490-492, 494-496)58
Population: population of ages 18 to 64
F .4.16 Hospital Admissions for Chronic Lung Disease (less Asthma) (Samet et al., 2000,14
Cities)
Samet et al. (2000) examined the relationship between air pollution and hospital admissions for
individuals of ages 65 and over in 14 cities across the country.59 Cities were selected on the basis of
available air pollution data for at least four years between 1985 and 1994 during which at least 50% of
days had observations between the city-specific start and end of measurements. Hospital admissions
were obtained from the Health Care Financing Administration (HCFA) for the years 1992 and 1993.
Poisson regression was used in the analysis with unconstrained distributed lag models to examine the
possibility that air pollution affects hospital admissions on not only the same day but on later days as
well. The use of unconstrained distributed lags has the advantages of (1) not inappropriately biasing
down risk estimates due to tight constraints (e.g. one day lag) and (2) not leaving the often arbitrary
choice of lag period to the investigator's discretion. The C-R functions are based on the pooled estimate
across all 14 cities, using the unconstrained distributed lag model and fixed or random effects estimates,
depending on the results of a test for heterogeneity.
For this analysis, the unadjusted, base models for the effect of PM10 on hospital admissions were
used. The authors performed a second-stage regression to estimate the impact of S02 and 03 on the
PM10 - hospitalization effect. For ozone, the PM10 effect in each city was regressed on the correlation
between ozone and particulate matter (the slope of a PM10 vs. 03 regression) in that city. The fitted line
for this regression will have a slope of zero if there is no relationship, meaning that the effect of PM10 is
56 Although Moolgavkar (2000c) reports results for the 20-64 year old age range, for comparability to other studies, we
apply the results to the population of ages 18 to 64.
57 In a log-linear model, the percent change is equal to (RR - 1) * 100. In this study, Moolgavkar defines and reports the
"estimated" percent change as (log RR * 100). Because the relative risk is close to 1, RR-1 and log RR are essentially the same.
For example, a true percent change of 2.0 would result in a relative risk of 1.020 and coefficient of 0.001980. The "estimated"
percent change, as reported by Moolgavkar, of 2.0 results in a relative risk of 1.020201 and coefficient of 0.002.
58 Moolgavkar (2000c) reports results for ICD codes 490-496. In order to avoid double counting non-elderly asthma
hospitalizations (ICD code 493) with Sheppard et al. (1999) in a total benefits estimation, we have excluded ICD code 493 from the
baseline incidence rate used in this function.
59 The cities under investigation include: Birmingham, Boulder, Canton, Chicago, Colorado Springs, Detroit,
Minneapolis/St. Paul, Nashville, New Haven, Pittsburgh, Provo/Orem, Seattle, Spokane, Youngstown.
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not dependent on the correlation between PM10 and 03. The adjusted point estimate was obtained by
determining the PM10 effect when the correlation between the pollutants is zero (i.e. the y-intercept of
the fitted line). The effect of 03 adjustment on the PM10 - hospitalization relationship appeared to be
minimal except for the case of COPD. In this case, adjustment increased the point estimate of the
independent particulate matter effect. The variance of this estimate, however, was quite large and the
confidence intervals of the adjusted and unadjusted estimates overlapped substantially. For these
reasons, there appeared to be little impact of 03 adjustment.60 Furthermore, the statistical power and
robustness of this second-stage approach to co-pollutant adjustment are in question because of the small
number of observations used in the regression (14 cities) and the potential for one or two observations to
dramatically impact the results.61 Finally, for the case of COPD, adjustment led to an increased PM10
independent effect, meaning that if the adjustment is valid, the impact on hospital admissions will be
underestimated rather than overestimated.
Single Pollutant Model
The estimated PM10 coefficient is based on a 2.88 percent increase (RR =
due to a PM10 change of 10.0 ng/m3 (Samet et al., 2000, Part II - Table 14)62. The
estimated from the reported lower (0.19 percent) and upper bounds (5.64 percent)
(Samet et al., 2000, Part II - Table 14).
Functional Form: Log-linear
Coefficient: 0.002839
Standard Error: 0.001351
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease per person 65+
(ICD codes 490-492, 494-496)
Population: population of ages 65 and older
1.0288) in admissions
standard error is
of the percent increase
F .4.17 Hospital Admissions for Chronic Lung Disease (less Asthma) (Schwartz, 1994b,
Detroit)
Schwartz (1994b) examined the relationship between air pollution and hospital admissions (ICD
codes 491-492, 494-496) for individuals 65 and older in Detroit, Michigan, from January 1986 to
December 1989. In a two-pollutant Poisson regression model, Schwartz found both PM10 and ozone
significantly linked to pneumonia and COPD. The authors state that effect estimates were relatively
unchanged compared to the unreported single pollutant models. No significant associations were found
between either pollutant and asthma admissions. The C-R function for chronic lung disease incidence is
based on the results of the "basic" co-pollutant model (PM10 and ozone) presented in Table 4 (p. 651).
Multipollutant Model (PM10 and ozone)
60 Joel Schwartz (co-author), personal communication.
61 Commentary from the Health Review Committee (Samet et al., 2000, p.77) states that "[w]hile the approach used in the
morbidity analysis is novel...the question arises as to the adequacy of statistical power for performing these analyses."
62 The random effects estimate of the unconstrained distributed lag model was chosen for COPD admissions since the chi-
square test of heterogeneity was significant (see Samet et al., 2000, Part II - Table 15).
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The PM10 coefficient and standard error are reported in Table 4 (Schwartz, 1994b, p. 651) for a
one |ig/m3 increase in daily average PM10 levels.
Functional Form: Log-linear
Coefficient: 0.00202
Standard Error: 0.00059
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease per person 65+
(ICD codes 490-492, 494-496)
Population: population of ages 65 and older
F .4.18 Hospital Admissions for Pneumonia (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada from 1980 to 1994. The authors examined single pollutant
log-linear models for PM10, PM10_2 5, PM2 5, CO, N02, S02, and ozone and found all significantly
associated with pneumonia and other respiratory infections (ICD codes 464,466,480-487,494). They
estimated multi-pollutant models, where pollutants for the best fitting model were chosen using stepwise
regression based on AIC criterion. Respiratory infection admissions were linked to ozone, N02, and
PM2 5. The C-R functions for PM10_2 5 and PM10 are based on the results of a single pollutant model. The
C-R functions for PM2 5 are based on the results of a single pollutant model and three-pollutant model
(ozone, N02, PM25).
PM2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(7.64) and t-statistic (6.09) reported in Table 3 (Burnett et al., 1999, p. 133) for an 18.0 |ig/m3 increase in
three-day average PM25 levels.
Functional Form: Log-linear
Coefficient: 0.004090
Standard Error: 0.000672
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person (ICD codes 464,
466, 480-487)
Population: population of all ages
Multipollutant Model (PM2 5, N02, and ozone)
In a model with ozone and N02, the PM2 5 coefficient and standard error are based on the percent
increase (6.08) reported in Table 5 (Burnett et al., 1999, p. 135) and the t-statistic obtained from the
authors (4.46)63 for an 18.0 |ig/m3 increase in three-day average PM25 levels.
63 Rick Burnett (co-author), personal communication.
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Functional Form: Log-linear
Coefficient: 0.003279
Standard Error: 0.000735
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person (ICD codes 464,
466, 480-487)
Population: population of all ages
PM10 2 5 Function(s)
Single Pollutant Model
The coefficient and standard error are based on the percent increase (4.44) and t-statistic (4.00)
reported in Table 3 (Burnett et al., 1999, p. 133) for a 12.2 |ig/m3 increase in three-day average PM10_2 5
levels.
Functional Form: Log-linear
Coefficient: 0.003561
Standard Error: 0.000890
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person (ICD codes 464,
466, 480-487)
Population: population of all ages
PM10 Function(s)
Single Pollutant Model
The coefficient and standard error are based on the percent increase (8.35) and t-statistic (5.96)
reported in Table 3 (Burnett et al., 1999, p. 133) for a 30.2 |ig/m3 increase in three-day average PM10
levels.
Functional Form: Log-linear
Coefficient: 0.002656
Standard Error: 0.000446
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person (ICD codes 464,
466, 480-487)
Population: population of all ages
F .4.19 Hospital Admissions for Pneumonia (Lippmann et al., 2000; Ito, 2003)
Lippmann et al. (2000) studied the association between particulate matter and daily mortality
and hospitalizations among the elderly in Detroit, MI. Data were analyzed for two separate study
periods, 1985-1990 and 1992-1994. The 1992-1994 study period had a greater variety of data on PM
size and was the main focus of the report. The authors collected hospitalization data for a variety of
cardiovascular and respiratory endpoints. They used daily air quality data for PM10, PM25, and PM10_25
in a Poisson regression model with generalized additive models (GAM) to adjust for nonlinear
relationships and temporal trends. In single pollutant models, all PM metrics were statistically
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significant for pneumonia (ICD codes 480-486), PM10_2 5 and PM10 were significant for ischemic heart
disease (ICD code 410-414), and PM25 and PM10 were significant for heart failure (ICD code 428).
There were positive, but not statistically significant associations, between the PM metrics and COPD
(ICD codes 490-496) and dysrhythmia (ICD code 427). In separate co-pollutant models with PM and
either ozone, S02, N02, or CO, the results were generally comparable.
In response to concerns with the Splus issue, Ito (2003) reanalyzed the study by Lippmann et al.
(2000). The reanalysis by Ito reported that more generalized additive models with stringent convergence
criteria and generalized linear models resulted in smaller relative risk estimates. Not all of the original
results were replicated, so we present here a mix of C-R functions from the reanalysis and from the
original study (when the reanalyzed results were not available). The PM25 C-R functions are based on
results of the single pollutant model and co-pollutant model with ozone.
Single Pollutant Model (Ito, 2003)
The estimated PM2 5 coefficient and standard error are based on a relative risk of 1.154 (95% CI
-1.027, 1.298) due to a PM25 change of 36 |ig/nr' in the 1-day lag GAM stringent model (Ito, 2003,
Table 7).
Functional Form: Log-linear
Coefficient: 0.003979
Standard Error: 0.001659
Incidence Rate: region-specific daily hospital admission rate for pneumonia admissions per person 65+
(ICD codes 480-487)
Population: population of ages 65 and older
Multipollutant Model (PM2 5 and ozone) (Lippmann et al., 2000)
The co-pollutant coefficient and standard error are calculated from a relative risk of 1.175 (95%
CI 1.026-1.345) for a 36 |ig/m3 increase in PM25 (Lippmann et al., 2000, Table 14, p. 26).
Functional Form: Log-linear
Coefficient: 0.004480
Standard Error: 0.001918
Incidence Rate: region-specific daily hospital admission rate for pneumonia admissions per person 65+
(ICD codes 480-487)
Population: population of ages 65 and older
F .4.20 Hospital Admissions for Pneumonia (Moolgavkar et al., 1997, Minneapolis)
Moolgavkar et al. (1997) examined the relationship between air pollution and hospital
admissions for individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to
December 1991. In a four pollutant Poisson model examining pneumonia admissions (ICD codes 480-
487) in Minneapolis, ozone was significant, while N02, S02, and PM10 were not significant. The PM10
C-R function is based on the results from the four-pollutant model to estimate pneumonia incidence.
The model with a 130 df smoother was reported to be optimal (p. 368).
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Multipollutant (PM10, N02, ozone, and S02)
In a model with N02 and ozone, the estimated PM10 coefficient and standard error are based on a
1.00 percent increase in admissions (95% CI -1.0, 3.0) due to a PM10 change of 20 |ig/m3 (Moolgavkar et
al., 1997, Table 4, p. 366)
Functional Form: Log-linear
Coefficient: 0.000498
Standard Error: 0.000505
Incidence Rate: region-specific daily hospital admission rate for pneumonia admissions per person 65+
(ICD codes 480-487)
Population: population of ages 65 and older
F .4.21 Hospital Admissions for Pneumonia (Samet et al., 2000,14 Cities)
Samet et al. (2000) examined the relationship between air pollution and hospital admissions for
individuals of ages 65 and over in 14 cities across the country.64 Cities were selected on the basis of
available air pollution data for at least four years between 1985 and 1994 during which at least 50% of
days had observations between the city-specific start and end of measurements. Hospital admissions
were obtained from the Health Care Financing Administration (HCFA) for the years 1992 and 1993.
Poisson regression was used in the analysis with unconstrained distributed lag models to examine the
possibility that air pollution affects hospital admissions on not only the same day but on later days as
well. The use of unconstrained distributed lags has the advantages of (1) not inappropriately biasing
down risk estimates due to tight constraints (e.g. one day lag) and (2) not leaving the often arbitrary
choice of lag period to the investigator's discretion. The C-R functions are based on the pooled estimate
across all 14 cities, using the unconstrained distributed lag model and fixed or random effects estimates,
depending on the results of a test for heterogeneity.
For this analysis, the unadjusted, base models for the effect of PM10 on hospital admissions were
used. The authors performed a second-stage regression to estimate the impact of S02 and 03 on the
PM10 - hospitalization effect. For ozone, the PM10 effect in each city was regressed on the correlation
between ozone and particulate matter (the slope of a PM10 vs. 03 regression) in that city. The fitted line
for this regression will have a slope of zero if there is no relationship, meaning that the effect of PM10 is
not dependent on the correlation between PM10 and 03. The adjusted point estimate was obtained by
determining the PM10 effect when the correlation between the pollutants is zero (i.e. the y-intercept of
the fitted line). The effect of 03 adjustment on the PM10 - hospitalization relationship appeared to be
minimal except for the case of COPD. In this case, adjustment increased the point estimate of the
independent particulate matter effect. The variance of this estimate, however, was quite large and the
confidence intervals of the adjusted and unadjusted estimates overlapped substantially. For these
reasons, there appeared to be little impact of 03 adjustment.65 Furthermore, the statistical power and
robustness of this second-stage approach to co-pollutant adjustment are in question because of the small
number of observations used in the regression (14 cities) and the potential for one or two observations to
64The cities under investigation include: Birmingham, Boulder, Canton, Chicago, Colorado Springs, Detroit,
Minneapolis/St. Paul, Nashville, New Haven, Pittsburgh, Provo/Orem, Seattle, Spokane, Youngstown.
65 Joel Schwartz (co-author), personal communication.
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dramatically impact the results.66 Finally, for the case of COPD, adjustment led to an increased PM10
independent effect, meaning that if the adjustment is valid, the impact on hospital admissions will be
underestimated rather than overestimated.
Single Pollutant Model
The estimated PM10 coefficient is based on a 2.07 percent increase (RR =
due to a PM10 change of 10.0 ng/m3 (Samet et al., 2000, Part II - Table 14)67. The
estimated from the reported lower (0.94 percent) and upper bounds (3.22 percent)
(Samet et al., 2000, Part II - Table 14).
Functional Form: Log-linear
Coefficient: 0.002049
Standard Error: 0.000570
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person 65+ (ICD codes
480-487)
Population: population of ages 65 and older
1.0207) in admissions
standard error is
of the percent increase
F .4.22 Hospital Admissions for Pneumonia (Schwartz, 1994a, Minneapolis)
Schwartz (1994a) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to December 1989. In
single-pollutant Poission regression models, both ozone and PM10 were significantly associated with
pneumonia admissions. In a two-pollutant model, Schwartz found PM10 significantly related to
pneumonia; ozone was weakly linked to pneumonia. The results were not sensitive to the methods used
to control for seasonal patterns and weather. The PM10 C-R functions are based on the results of the
single pollutant model and the two-pollutant model (PM10 and ozone) with "spline" smoothing.
Single Pollutant Model
The single pollutant coefficient and standard error are based on the relative risk (1.17) and 95%
confidence interval (1.03-1.33) for a 100 |ig/m3 increase in daily average PM10 levels (Schwartz, 1994a,
p. 369).
Functional Form: Log-linear
Coefficient: 0.001570
Standard Error: 0.000652
Incidence Rate: region-specific daily hospital admission rate for pneumonia admissions per person 65+
(ICD codes 480-487)
Population: population of ages 65 and older.
66 Commentary from the Health Review Committee (Samet et al., 2000, p.77) states that "[w]hile the approach used in the
morbidity analysis is novel...the question arises as to the adequacy of statistical power for performing these analyses."
67 The random effects estimate of the unconstrained distributed lag model was chosen for pneumonia admissions since the
chi-square test of heterogeneity was significant (see Samet et al., 2000, Part II - Table 15).
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Multipollutant Model (PM10 and ozone)
In a model with ozone and spline functions to adjust for time and weather, the coefficient and
standard error are based on the relative risk (1.18) and 95% confidence interval (1.03, 1.36) for a 100
|ig/nr' increase in daily average PM10 levels (Schwartz, 1994a, Table 4).
Functional Form: Log-linear
Coefficient: 0.001655
Standard Error: 0.000709
Incidence Rate: region-specific daily hospital admission rate for pneumonia admissions per person 65+
(ICD codes 480-487)
Population: population of ages 65 and older
F .4.23 Hospital Admissions for Pneumonia (Schwartz, 1994b, Detroit)
Schwartz (1994b) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Detroit, Michigan, from January 1986 to December 1989. In a two-pollutant
Poisson regression model, Schwartz found both PM10 and ozone significantly linked to pneumonia and
COPD. The authors state that effect estimates were relatively unchanged compared to the unreported
single pollutant models. No significant associations were found between either pollutant and asthma
admissions. The PM10 C-R function for pneumonia incidence is based on results of the co-pollutant
model (PM10 and ozone).
Multipollutant Model (PM10 and ozone)
The PM10 coefficient and standard error are reported in Table 4 (Schwartz, 1994b, p. 651) for a
one |ig/m3 increase in daily average PM10 levels.
Functional Form: Log-linear
Coefficient: 0.00115
Standard Error: 0.00039
Incidence Rate: region-specific daily hospital admission rate for pneumonia admissions per person 65+
(ICD codes 480-487)
Population: population of ages 65 and older
F .4.24 Hospital Admissions for All Cardiovascular (Burnett et al., 1997, Toronto)
Burnett et al. (1997) examined the relationship between air pollution and cardiac hospital
admissions (ICD codes 410-414,427,428) for individuals of all ages in Toronto, Canada during the
summers of 1992-1994. In a Poisson regression, cardiac admissions were linked to coefficient of haze
(COH) and ozone; other PM measures were less strongly linked. In two pollutant models, they found
that CO, N02, and S02 were not significant, controlling for COH. They found that ozone was still
significant, controlling for COH. In multi-pollutant models with COH, ozone, N02, and S02, both ozone
and COH remained significant. None of the other PM measures (PM10, PM10_2 5, PM2 5) were significant
in four-pollutant models. PM C-R functions are based on the results of single and multipollutant models.
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PM2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the PM2 5 coefficient and standard error are based on a relative risk
ofl.031 (t-statistic 1.8) for an 11 |_ig/m3 increase in four-day average PM25 (Burnett et al., 1997, Table 2,
p. 617).
Functional Form: Log-linear
Coefficient: 0.002775
Standard Error: 0.001542
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
Multipollutant Model (PM2 5 and ozone)
In a model with ozone, the PM2 5 coefficient and standard error are based on a relative risk of
1.014 (t-statistic 0.78) for an 11 |ig/m3 increase in four-day average PM25 (Burnett et al., 1997, Table 5,
p. 618).
Functional Form: Log-linear
Coefficient: 0.001264
Standard Error: 0.001620
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
Multipollutant Model (PM2 5, N02, ozone, and S02)
In a four-pollutant model with N02, ozone, and S02, the PM2 5 coefficient and standard error are
based on a relative risk of 0.993 (t-statistic 0.33) for an 11 |ig/m3 increase in four-day average PM2 5
(Burnett et al., 1997, Table 6, p. 618).
Functional Form: Log-linear
Coefficient: -0.000639
Standard Error: 0.001935
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
PM10 2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the PM10_2 5 coefficient and standard error are based on a relative
risk of 1.036 (t-statistic 3.41) for a 4.75 |ig/m3 increase in four-day average PM10_25 (Burnett et al., 1997,
Table 2, p. 617).
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Functional Form: Log-linear
Coefficient: 0.007446
Standard Error: 0.002183
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
Multipollutant Model (PM10_2 5 and ozone)
In a model with ozone, the PM10_2 5 coefficient and standard error are based on a relative risk of
1.034 (t-statistic 3.28) for a 4.75 |ig/m3 increase in four-day average PM10_25 (Burnett et al., 1997, Table
5, p. 618).
Functional Form: Log-linear
Coefficient: 0.007039
Standard Error: 0.002146
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
Multipollutant Model (PM10_2 5, N02, ozone, and S02)
In a four-pollutant model with N02, ozone, and S02, the PM10_2 5 coefficient and standard error
are based on a relative risk of 1.022 (t-statistic 1.68) for a 4.75 |ig/m3 increase in four-day average PM10.
25 (Burnett et al., 1997, Table 6, p. 618).
Functional Form: Log-linear
Coefficient: 0.004581
Standard Error: 0.002727
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
PM10 Function(s)
Single Pollutant Model
In a single pollutant model, the PM10 coefficient and standard error are based on a relative risk
of 1.033 (t-statistic 2.24) for a 14.25 |ig/m3 increase in four-day average PM10 (Burnett et al., 1997,
Table 2, p. 617).
Functional Form: Log-linear
Coefficient: 0.002278
Standard Error: 0.001017
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
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Multipollutant Model (PM10 and ozone)
In a model with ozone, the PM10 coefficient and standard error are based on a relative risk of
1.025 (t-statistic 1.68) for a 14.25 |ig/m3 increase in four-day average PM10 (Burnett et al., 1997, Table 5,
p. 618).
Functional Form: Log-linear
Coefficient: 0.001733
Standard Error: 0.001031
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
Multipollutant Model (PM10, N02, ozone, and S02)
In a four-pollutant model with N02, ozone, and S02, the PM10 coefficient and standard error are
based on a relative risk of 0.996 (t-statistic 0.23) for a 14.25 |ig/m3 increase in four-day average PM10
(Burnett et al., 1997, Table 6, p. 618).
Functional Form: Log-linear
Coefficient: -0.000281
Standard Error: 0.001223
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
F .4.25 Hospital Admissions for All Cardiovascular (Moolgavkar, 2000b; Moolgavkar,
2003)
Moolgavkar (2000a) examined the association between air pollution and cardiovascular hospital
admissions (ICD 390-448) in the Chicago, Los Angeles, and Phoenix metropolitan areas. He collected
daily air pollution data for ozone, S02, N02, CO, and PM10 in all three areas. PM2 5 data was available
only in Los Angeles. The data were analyzed using a Poisson regression model with generalized
additive models to adjust for temporal trends. Separate models were run for 0 to 5 day lags in each
location. Among the 65+ age group, the gaseous pollutants generally exhibited stronger effects than
PM10 or PM25. The strongest overall effects were observed for S02 and CO. In a single pollutant model,
PM2 5 was statistically significant for lag 0 and lag 1. In co-pollutant models with CO, the PM2 5 effect
dropped out and CO remained significant. For ages 20-64, S02 and CO exhibited the strongest effect
and any PM25 effect dropped out in co-pollutant models with CO.
In response to concerns with the Splus issue, Moolgavkar (2003) reanalyzed his earlier study. In
the reanalysis, he reported that more generalized additive models with stringent convergence criteria and
generalized linear models resulted in smaller relative risk estimates. Not all of the original results were
replicated, so we present here a mix of C-R functions from the reanalysis and from the original study
(when the reanalyzed results were not available). The PM25 C-R functions are based on single pollutant
and co-pollutant (PM2 5 and CO) models.
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Ages 65 and older
Single Pollutant Model (Moolgavkar, 2003)
The single pollutant coefficient and standard error are calculated from an estimated percent
change of 1.5868 and t-statistic of 4.59 for a 10 |ig/m3 increase in PM25 in the 0-day lag GAM-30df
stringent (10~8) model (Moolgavkar, 2003, Table 12).
Functional Form: Log-linear
Coefficient: 0.001568
Standard Error: 0.000342
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular admissions per
person 65+ (ICD codes 390-429)
Population: population of ages 65 and older.
Multipollutant Model (PM2 5 and CO) (Moolgavkar, 2003)
In a model with PM2 5 and CO, the single pollutant coefficient and standard error are calculated
from an estimated percent change of 0.3959 and t-statistic of 0.92 for a 10 |ig/m3 increase in PM25 in the
0-day lag GAM-lOOdf stringent (10~8) model (Moolgavkar, 2003, Table 14).
Functional Form: Log-linear
Coefficient: 0.000389
Standard Error: 0.000423
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular admissions per
person 65+ (ICD codes 390-429)
Population: population of ages 65 and older
Ages 18 to 6469
Single Pollutant Model (Moolgavkar, 2000b)
The single pollutant coefficient and standard error are calculated from an estimated percent
change of 1 A10 and t-statistic of 4.1 for a 10 |ig/m3 increase in PM2 5 in the zero lag model (Moolgavkar,
2000a, Table 4, p. 1203).
68 In a log-linear model, the percent change is equal to (RR - 1) * 100. In this study, Moolgavkar defines and reports the
"estimated" percent change as (log RR * 100). Because the relative risk is close to 1, RR-1 and log RR are essentially the same.
For example, a true percent change of 2.2 would result in a relative risk of 1.022 and coefficient of 0.002176. The "estimated"
percent change, as reported by Moolgavkar, of 2.2 results in a relative risk of 1.022244 and coefficient of 0.0022.
69 Although Moolgavkar (2000a) reports results for the 20-64 year old age range, for comparability to other studies, we
apply the results to the population of ages 18 to 64.
70 In a log-linear model, the percent change is equal to (RR - 1) * 100. In a similar hospitalization study by Moolgavkar
(2000c), he defines and reports the "estimated" percent change as (log RR * 100). Because the relative risk is close to 1, RR-1 and
log RR are essentially the same. For example, a true percent change of 1.4 would result in a relative risk of 1.014 and coefficient of
0.00139. Assuming that the 1.4 is the "estimated" percent change described previously would result in a relative risk of 1.014098
and coefficient of 0.0014. We assume that the "estimated" percent changes reported in this study reflect the definition from
(Moolgavkar, 2000c).
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Functional Form: Log-linear
Coefficient: 0.0014
Standard Error: 0.000341
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular admissions per
person ages 18 to 64 (ICD codes 390-409, 411-45 9)71
Population: population of ages 18 to 64
Multipollutant Model (PM2 5 and CO) (Moolgavkar, 2000b)
In a model with CO, the coefficient and standard error are calculated from an estimated percent
change of 0.972 and t-statistic of 1.8 for a 10 |ig/m3 increase in PM25 in the zero lag model (Moolgavkar,
2000a, Table 4, p. 1203).
Functional Form: Log-linear
Coefficient: 0.0009
Standard Error: 0.000500
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular admissions per
person ages 18 to 64 (ICD codes 390-409, 411-45 9)73
Population: population of ages 18 to 64
F .4.26 Hospital Admissions for All Cardiovascular (Samet et al., 2000,14 Cities)
Samet et al. (2000) examined the relationship between air pollution and hospital admissions for
individuals of ages 65 and over in 14 cities across the country.74 Cities were selected on the basis of
available air pollution data for at least four years between 1985 and 1994 during which at least 50% of
days had observations between the city-specific start and end of measurements. Hospital admissions
were obtained from the Health Care Financing Administration (HCFA) for the years 1992 and 1993.
Poisson regression was used in the analysis with unconstrained distributed lag models to examine the
possibility that air pollution affects hospital admissions on not only the same day but on later days as
well. The use of unconstrained distributed lags has the advantages of (1) not inappropriately biasing
71 Moolgavkar (2000a) reports results that include ICD code 410 (heart attack). In the benefits analysis, avoided nonfatal
heart attacks are estimated using the results reported by Peters et al. (2001). The baseline rate in the Peters et al. function is a
modified heart attack hospitalization rate (ICD code 410), since most, if not all, nonfatal heart attacks will require hospitalization.
In order to avoid double counting heart attack hospitalizations, we have excluded ICD code 410 from the baseline incidence rate
used in this function.
72 In a log-linear model, the percent change is equal to (RR - 1) * 100. In a similar hospitalization study by Moolgavkar
(2000c), he defines and reports the "estimated" percent change as (log RR * 100). Because the relative risk is close to 1, RR-1 and
log RR are essentially the same. For example, a true percent change of 0.9 would result in a relative risk of 1.009 and coefficient of
0.000896. Assuming that the 0.9 is the "estimated" percent change described previously would result in a relative risk of 1.009041
and coefficient of 0.0009. We assume that the "estimated" percent changes reported in this study reflect the definition from
(Moolgavkar, 2000c).
73 Moolgavkar (2000a) reports results that include ICD code 410 (heart attack). In the benefits analysis, avoided nonfatal
heart attacks are estimated using the results reported by Peters et al. (2001). The baseline rate in the Peters et al. function is a
modified heart attack hospitalization rate (ICD code 410), since most, if not all, nonfatal heart attacks will require hospitalization.
In order to avoid double counting heart attack hospitalizations, we have excluded ICD code 410 from the baseline incidence rate
used in this function.
74 The cities under investigation include: Birmingham, Boulder, Canton, Chicago, Colorado Springs, Detroit,
Minneapolis/St. Paul, Nashville, New Haven, Pittsburgh, Provo/Orem, Seattle, Spokane, Youngstown.
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Appendix F. Particulate Matter C-R Functions
down risk estimates due to tight constraints (e.g. one day lag) and (2) not leaving the often arbitrary
choice of lag period to the investigator's discretion. The C-R functions are based on the pooled estimate
across all 14 cities, using the unconstrained distributed lag model and fixed or random effects estimates,
depending on the results of a test for heterogeneity.
For this analysis, the unadjusted, base models for the effect of PM10 on hospital admissions were
used. The authors performed a second-stage regression to estimate the impact of S02 and 03 on the
PM10 - hospitalization effect. For ozone, the PM10 effect in each city was regressed on the correlation
between ozone and particulate matter (the slope of a PM10 vs. 03 regression) in that city. The fitted line
for this regression will have a slope of zero if there is no relationship, meaning that the effect of PM10 is
not dependent on the correlation between PM10 and 03. The adjusted point estimate was obtained by
determining the PM10 effect when the correlation between the pollutants is zero (i.e. the y-intercept of
the fitted line). The effect of 03 adjustment on the PM10 - hospitalization relationship appeared to be
minimal except for the case of COPD. In this case, adjustment increased the point estimate of the
independent particulate matter effect. The variance of this estimate, however, was quite large and the
confidence intervals of the adjusted and unadjusted estimates overlapped substantially. For these
reasons, there appeared to be little impact of 03 adjustment.75 Furthermore, the statistical power and
robustness of this second-stage approach to co-pollutant adjustment are in question because of the small
number of observations used in the regression (14 cities) and the potential for one or two observations to
dramatically impact the results.76 Finally, for the case of COPD, adjustment led to an increased PM10
independent effect, meaning that if the adjustment is valid, the impact on hospital admissions will be
underestimated rather than overestimated.
Single Pollutant Model
The estimated PM10 coefficient is based on a 1.19 percent increase (RR =
due to a PM10 change of 10.0 ng/m3 (Samet et al., 2000, Part II - Table 14)77. The
estimated from the reported lower (0.97 percent) and upper bounds (1.41 percent)
(Samet et al., 2000, Part II - Table 14).
Functional Form: Log-linear
Coefficient: 0.001183
Standard Error: 0.000111
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
65+ (ICD codes 390-459)
Population: population of ages 65 and older
F .4.27 Hospital Admissions for Dysrhythmias (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada froml980 to 1994. The authors examined single pollutant
log-linear models for PM10, PM10_2 5, PM2 5, CO, N02, S02, and 03 and found PM2 5, PM10, and CO
75 Joel Schwartz (co-author), personal communication.
76 Commentary from the Health Review Committee (Samet et al., 2000, p.77) states that "[w]hile the approach used in the
morbidity analysis is novel...the question arises as to the adequacy of statistical power for performing these analyses."
1.0119) in admissions
standard error is
of the percent increase
77 The fixed effects estimate of the unconstrained distributed lag model was chosen for CVD admissions since the chi-
square test of heterogeneity was non-significant (see Samet et al., 2000, Part II - Table 15).
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Appendix F. Particulate Matter C-R Functions
significantly associated with admissions. They estimated multiple pollutant models, where pollutants for
best fitting model were chosen using stepwise regression based on AIC criterion. The final model for
dysrhythmias admissions included 03, CO, and PM25. CO was significantly associated with admissions,
while 03 and PM2 5 were marginally significant. The C-R functions are based on the reported single
pollutant and multipollutant models for PM2 5 and single pollutant models for other PM measures.
PM2 5 Function(s)
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(4.33) and t-statistic (2.91) reported in Table 3 (Burnett et al., 1999, p. 133) for an 18.0 |ig/m3 increase in
daily average PM2 5 concentration.
Functional Form: Log-linear
Coefficient: 0.002355
Standard Error: 0.000809
Incidence Rate: region-specific daily hospital admission rate for dysrhythmia disease per person (ICD
code 427)
Population: population of all ages
Multipollutant Model (PM2 5, CO, and ozone)
In a model with ozone and CO, the PM2 5 coefficient and standard error are based on the percent
increase (2.47) reported in Table 5 (Burnett et al., 1999, p. 135) and the t-statistic obtained from the
authors (1.49)78 for an 18.0 |ig/m3 increase in daily average PM25 concentration.
Functional Form: Log-linear
Coefficient: 0.001356
Standard Error: 0.000910
Incidence Rate: region-specific daily hospital admission rate for dysrhythmia disease per person (ICD
code 427)
Population: population of all ages
PM10 2 5 Function(s)
Single Pollutant Model
The coefficient and standard error are based on the percent increase (2.47) and t-statistic (1.88)
reported in Table 3 (Burnett et al., 1999, p. 133) for a 12.2 |ig/m3 increase in daily average PM10_25
concentration.
78 Rick Burnett (co-author), personal communication.
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Functional Form: Log-linear
Coefficient: 0.002000
Standard Error: 0.001064
Incidence Rate: region-specific daily hospital admission rate for dysrhythmia disease per person (ICD
code 427)
Population: population of all ages
PM10 Function(s)
Single Pollutant Model
The coefficient and standard error are based on the percent increase (5.00) and t-statistic (4.25)
reported in Table 3 (Burnett et al., 1999, p. 133) for a 30.2 |ig/m3 increase in daily average PM10
concentration.
Functional Form: Log-linear
Coefficient: 0.001616
Standard Error: 0.000533
Incidence Rate: region-specific daily hospital admission rate for dysrhythmia disease per person (ICD
code 427)
Population: population of all ages
F .4.28 Hospital Admissions for Dysrhythmia (Lippmann et al., 2000; Ito, 2003)
Lippmann et al. (2000) studied the association between particulate matter and daily mortality
and hospitalizations among the elderly in Detroit, MI. Data were analyzed for two separate study
periods, 1985-1990 and 1992-1994. The 1992-1994 study period had a greater variety of data on PM
size and was the main focus of the report. The authors collected hospitalization data for a variety of
cardiovascular and respiratory endpoints. They used daily air quality data for PM10, PM25, and PM10_25
in a Poisson regression model with generalized additive models (GAM) to adjust for nonlinear
relationships and temporal trends. In single pollutant models, all PM metrics were statistically
significant for pneumonia (ICD codes 480-486), PM10_2 5 and PM10 were significant for ischemic heart
disease (ICD code 410-414), and PM2 5 and PM10 were significant for heart failure (ICD code 428).
There were positive, but not statistically significant associations, between the PM metrics and COPD
(ICD codes 490-496) and dysrhythmia (ICD code 427). In separate co-pollutant models with PM and
either ozone, S02, N02, or CO, the results were generally comparable.
In response to concerns with the Splus issue, Ito (2003) reanalyzed the study by Lippmann et al.
(2000). The reanalysis by Ito reported that more generalized additive models with stringent convergence
criteria and generalized linear models resulted in smaller relative risk estimates. Not all of the original
results were replicated, so we present here a mix of C-R functions from the reanalysis and from the
original study (when the reanalyzed results were not available).
Single Pollutant Model (Ito, 2003)
The co-pollutant coefficient and standard error are calculated from a relative risk of 1.046 (95%
CI 0.906-1.207) for a 36 |ig/m3 increase in PM25 in the 1-day lag GAM stringent model (Ito, 2003, Table
10).
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Functional Form: Log-linear
Coefficient: 0.001249
Standard Error: 0.002033
Incidence Rate: region-specific daily hospital admission rate for dysrhythmia admissions per person
65+ (ICD code 427)
Population: population of ages 65 and older
Multipollutant Model (PM2 5 and ozone) (Lippmann et al., 2000)
The co-pollutant coefficient and standard error are calculated from a relative risk of 1.080 (95%
CI 0.904-1.291) for a 36 |ig/nr' increase in PM25 (Lippmann et al., 2000, Table 14, p. 27).
Functional Form: Log-linear
Coefficient: 0.002138
Standard Error: 0.002525
Incidence Rate: region-specific daily hospital admission rate for dysrhythmia admissions per person
65+ (ICD code 427)
Population: population of ages 65 and older
F .4.29 Hospital Admissions for Congestive Heart Failure (Lippmann et al., 2000; Ito,
2003)
Lippmann et al. (2000) studied the association between particulate matter and daily mortality
and hospitalizations among the elderly in Detroit, MI. Data were analyzed for two separate study
periods, 1985-1990 and 1992-1994. The 1992-1994 study period had a greater variety of data on PM
size and was the main focus of the report. The authors collected hospitalization data for a variety of
cardiovascular and respiratory endpoints. They used daily air quality data for PM10, PM25, and PM10_25
in a Poisson regression model with generalized additive models (GAM) to adjust for nonlinear
relationships and temporal trends. In single pollutant models, all PM metrics were statistically
significant for pneumonia (ICD codes 480-486), PM10_2 5 and PM10 were significant for ischemic heart
disease (ICD code 410-414), and PM2 5 and PM10 were significant for congestive heart failure (ICD code
428). There were positive, but not statistically significant associations, between the PM metrics and
COPD (ICD codes 490-496) and dysrhythmia (ICD code 427). In separate co-pollutant models with PM
and either ozone, S02, N02, or CO, the results were generally comparable.
In response to concerns with the Splus issue, Ito (2003) reanalyzed the study by Lippmann et al.
(2000). The reanalysis by Ito reported that more generalized additive models with stringent convergence
criteria and generalized linear models resulted in smaller relative risk estimates. Not all of the original
results were replicated, so we present here a mix of C-R functions from the reanalysis and from the
original study (when the reanalyzed results were not available).
Single Pollutant Model (Ito, 2003)
The co-pollutant coefficient and standard error are calculated from a relative risk of 1.117 (95%
CI 1.020-1.224) for a 36 |ig/m3 increase in PM25 in the 1-day lag GAM stringent model (Ito, 2003, Table
11).
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Functional Form: Log-linear
Coefficient: 0.003469
Standard Error: 0.001293
Incidence Rate: region-specific daily hospital admission rate for congestive heart failure admissions per
person 65+ (ICD code 428)
Population: population of ages 65 and older
Multipollutant Model (PM2 5 and ozone) (Lippmann et al., 2000)
The co-pollutant coefficient and standard error are calculated from a relative risk of 1.183 (95%
CI 1.053-1.329) for a 36 |ig/nr' increase in PM25 (Lippmann et al., 2000, Table 14, p. 27).
Functional Form: Log-linear
Coefficient: 0.004668
Standard Error: 0.001650
Incidence Rate: region-specific daily hospital admission rate for congestive heart failure admissions per
person 65+ (ICD code 428)
Population: population of ages 65 and older
F .4.30 Hospital Admissions for Ischemic Heart Disease (Lippmann et al., 2000; Ito, 2003)
Lippmann et al. (2000) studied the association between particulate matter and daily mortality
and hospitalizations among the elderly in Detroit, MI. Data were analyzed for two separate study
periods, 1985-1990 and 1992-1994. The 1992-1994 study period had a greater variety of data on PM
size and was the main focus of the report. The authors collected hospitalization data for a variety of
cardiovascular and respiratory endpoints. They used daily air quality data for PM10, PM25, and PM10_25
in a Poisson regression model with generalized additive models (GAM) to adjust for nonlinear
relationships and temporal trends. In single pollutant models, all PM metrics were statistically
significant for pneumonia (ICD codes 480-486), PM10_2 5 and PM10 were significant for ischemic heart
disease (ICD code 410-414), and PM2 5 and PM10 were significant for heart failure (ICD code 428).
There were positive, but not statistically significant associations, between the PM metrics and COPD
(ICD codes 490-496) and dysrhythmia (ICD code 427). In separate co-pollutant models with PM and
either ozone, S02, N02, or CO, the results were generally comparable.
In response to concerns with the Splus issue, Ito (2003) reanalyzed the study by Lippmann et al.
(2000). The reanalysis by Ito reported that more generalized additive models with stringent convergence
criteria and generalized linear models resulted in smaller relative risk estimates. Not all of the original
results were replicated, so we present here a mix of C-R functions from the reanalysis and from the
original study (when the reanalyzed results were not available).
Single Pollutant Model (Ito, 2003)
The co-pollutant coefficient and standard error are calculated from a relative risk of 1.053 (95%
CI 0.971-1.143) for a 36 |ig/m3 increase in PM25 in the 1-day lag GAM stringent model (Ito, 2003, Table
9)
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Functional Form: Log-linear
Coefficient: 0.001435
Standard Error: 0.001156
Incidence Rate: region-specific daily hospital admission rate for ischemic heart disease admissions per
person 65+ (ICD codes 411-414)79
Population: population of ages 65 and older
Multipollutant Model (PM2 5 and ozone) (Lippmann et al., 2000)
The co-pollutant coefficient and standard error are calculated from a relative risk of 1.041 (95%
CI 0.947-1.144) for a 36 |ig/nr' increase in PM25 (Lippmann et al., 2000, Table 14, p. 27).
Functional Form: Log-linear
Coefficient: 0.001116
Standard Error: 0.001339
Incidence Rate: region-specific daily hospital admission rate for ischemic heart disease admissions per
person 65+ (ICD codes 411-414)80
Population: population of ages 65 and older
79 Lippmann et al. (2000) reports results for ICD codes 410-414. In the benefits analysis, avoided nonfatal heart attacks
are estimated using the results reported by Peters et al. (2001). The baseline rate in the Peters et al. function is a modified heart
attack hospitalization rate (ICD code 410), since most, if not all, nonfatal heart attacks will require hospitalization. In order to avoid
double counting heart attack hospitalizations, we have excluded ICD code 410 from the baseline incidence rate used in this function.
80 Lippmann et al. (2000) reports results for ICD codes 410-414. In the benefits analysis, avoided nonfatal heart attacks
are estimated using the results reported by Peters et al. (2001). The baseline rate in the Peters et al. function is a modified heart
attack hospitalization rate (ICD code 410), since most, if not all, nonfatal heart attacks will require hospitalization. In order to avoid
double counting heart attack hospitalizations, we have excluded ICD code 410 from the baseline incidence rate used in this function.
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Exhibit F-5. Concentration-Response (C-R) Functions for Particulate Matter and Emergency Room Visits
Endpoint Name
Pollutant
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time1
Beta
Std Error
Functional
Form
Asthma
pm2,
Norris et al.
1999
Seattle, WA
<18
All
All
None
24-hr avg
0.014712
0.003492
Log-linear
Asthma
PM2,
Norris et al.
1999
Seattle, WA
<18
All
All
no2, so2
24-hr avg
0.016527
0.004139
Log-linear
Asthma
PM10
Norris et al.
1999
Seattle, WA
<18
All
All
None
24-hr avg
0.011296
0.003480
Log-linear
Asthma
PM10
Norris et al.
1999
Seattle, WA
<18
All
All
no2, so2
24-hr avg
0.011296
0.004220
Log-linear
Asthma
PM10
Schwartz et al.
1993
Seattle, WA
<65
All
All
None
24-hr avg
0.00367
0.00126
Log-linear
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for
more detail on the specific averaging time used in the study.
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F .5 Emergency Room Visits
F .5.1 Emergency Room Visits for Asthma (Norris et al., 1999)
Norris et al. (1999) examined the relation between air pollution in Seattle and childhood (<18)
hospital admissions for asthma from 1995 to 1996. The authors used air quality data for PM10, light
scattering (used to estimate fine PM), CO, S02, N02, and 03 in a Poisson regression model with
adjustments for day of the week, time trends, temperature, and dew point. They found significant
associations between asthma ER visits and light scattering (converted to PM25), PM10, and CO. No
association was found between 03, N02, or S02 and asthma ER visits, although 03 had a significant
amount of missing data. In multipollutant models with either PM metric (light scattering or PM10) and
N02 and S02, the PM coefficients remained significant while the gaseous pollutants were not associated
with increased asthma ER visits. The PM C-R functions are based on results of the single and
multipollutant models reported.
PM2 5 Function(s)
Single Pollutant Model
The single pollutant coefficient and standard error are calculated from a relative risk of 1.15
(95% CI 1.08-1.23) for a 9.5 i-ig/m3 increase in PM25 (Norris et al., 1999, Table 4, p. 492).
Functional Form: Log-linear
Coefficient: 0.014712
Standard Error: 0.003492
Incidence Rate: region-specific daily emergency room rate for asthma admissions per person <18 (ICD
code 493)
Population: population of ages under 18
Multipollutant Model (PM2 5, N02 and S02)
In a model with N02 and S02, the PM2 5 coefficient and standard error are calculated from a
relative risk of 1.17 (95% CI 1.08-1.26) for a 9.5 i-ig/m3 increase in PM25 (Norris et al., 1999, p. 491).
Functional Form: Log-linear
Coefficient: 0.016527
Standard Error: 0.004139
Incidence Rate: region-specific daily emergency room rate for asthma admissions per person <18 (ICD
code 493)
Population: population of ages under 18
PM10 Function(s)
Single Pollutant Model
The single pollutant coefficient and standard error are calculated from a relative risk of 1.14
(95% CI 1.05-1.23) for an 11.6 |_ig/m3 increase in PM10 (Norris etal., 1999, Table 4, p. 492).
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Functional Form: Log-linear
Coefficient: 0.011296
Standard Error: 0.003480
Incidence Rate: region-specific daily emergency room rate for asthma admissions per person <18 (ICD
code 493)
Population: population of ages under 18
Multipollutant Model (PM10, N02; and S02)
In a model with N02 and S02, the PM10 coefficient and standard error are calculated from a
relative risk of 1.14 (95% CI 1.04-1.26) for an 11.6 i-ig/m3 increase in PM10 (Norris et al., 1999, p. 491).
Functional Form: Log-linear
Coefficient: 0.011296
Standard Error: 0.004220
Incidence Rate: region-specific daily emergency room rate for asthma admissions per person <18 (ICD
code 493)
Population: population of ages under 18
F .5.2 Emergency Room Visits for Asthma (Schwartz et al., 1993, Seattle)
Schwartz et al. (1993) examined the relationship between air quality and emergency room visits
for asthma (ICD codes 493,493.01,493.10,493.90,493.91) in persons under 65 and 65 and over, living in
Seattle from September 1989 to September 1990. Using single-pollutant models they found daily levels
of PM10 linked to ER visits in individuals ages under 65, and they found no effect in individuals ages 65
and over. They did not find a significant effect for S02 and ozone in either age group. The results of the
single pollutant model for PM10 are used in this analysis.
Single Pollutant Model
The PM10 coefficient and standard error are reported by Schwartz et al. (1993, p. 829) for a unit
|ig/m3 increase in four-day average PM10 levels.
Functional Form: Log-linear
Coefficient: 0.00367
Standard Error: 0.00126
Incidence Rate: region-specific daily emergency room rate for asthma admissions per person <65 (ICD
code 493)
Population: population of ages under 65
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Exhibit F-6. Concentration-Response (C-R) Functions for Particulate Matter and Acute Effects
Endpoint Name Pollutant
Author
Year
Location
. _ ,, Other Averaging
Age Race Gender _ „ , . ,
& Pollutants Time1
Beta Std Error
Functional
Form
Acute Bronchitis
Acute Myocardial
Infarction, Nonfatal
Acute Myocardial
Infarction, Nonfatal
Acute Myocardial
Infarction, Nonfatal
Any of 19 Respiratory
Symptoms
Lower Respiratory
Symptoms
Lower Respiratory
Symptoms
Lower Respiratory
Symptoms
Minor Restricted Activity
Days
School Loss Days, All
Cause
School Loss Days, All
Cause
School Loss Days, All
Cause
School Loss Days, All
Cause
School Loss Days,
Illness-Related
School Loss Days,
Respiratory-Related
^¥orkLoss^Da^s^^_^^_
PM2
pm2
PM1(
PM1(
PM1(
PM2
pm2
pm2
pm2
PM1(
PM1(
PM1(
PM1(
PM1(
PM1(
PM,
Dockery et al.
Peters et al.
Peters et al.
Peters et al.
Krupnick
1996 24 communities 8-12 All
2001 Boston, MA
2001 Boston, MA
2001 Boston, MA
18+ All
18+ All
18+ All
1990 Los Angeles, CA 18-64 All
Schwartz and Neas 2000 6 cities
Schwartz and Neas 2000 6 cities
Schwartz et al.
Ostro and
Rothschild
Chen et al.
Gilliland et al.
Ransom and Pope
Ransom and Pope
Gilliland et al.
Gilliland et al.
Ostro
1994 6 cities
1989 nationwide
7-14 All
7-14 All
7-14 All
18-64 All
2000 Washoe Co, NV 6-11 All
Southern „ . ..
2001 ^ ... . 9-10 All
California
1992 Provo, UT 6-11 All
1992 Orem, UT
Southern
2001
2001
California
Southern
California
1987 nationwide
6-11 All
9-10 All
9-10 All
18-64 All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
None
None
None
None
o3
None
pm10.2,
None
o3
co,o3
None
None
None
None
None
None
Annual Avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
0.027212
0.024121
0.021954
0.016894
0.000461
0.019012
0.016976
0.01823
0.00741
-0.015400
0.020539
0.021921
0.02115
0.005543
-0.004395
0.0046
0.017096
0.009285
0.015000
0.006870
0.000239
0.006005
0.006680
0.00586
0.00070
0.004400
0.004894
0.00461
0.00460
0.009387
0.017569
0.00036
Logistic
Logistic
Logistic
Logistic
Linear
Logistic
Logistic
Logistic
Log-linear
Linear
Log-linear
Linear
Linear
Log-linear
Log-linear
Log-linear
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for
more detail on the specific averaging time used in the study.
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F .6 Acute Effects
F .6.1 Acute Bronchitis (Dockery et al., 1996)
Dockery et al. (1996) examined the relationship between PM and other pollutants on the
reported rates of asthma, persistent wheeze, chronic cough, and bronchitis, in a study of 13,369 children
ages 8-12 living in 24 communities in U.S. and Canada. Health data were collected in 1988-1991, and
single-pollutant models were used in the analysis to test a number of measures of particulate air
pollution. Dockery et al. found that annual level of sulfates and particle acidity were significantly
related to bronchitis, and PM21 and PM10 were marginally significantly related to bronchitis.81 They
also found nitrates were linked to asthma, and sulfates linked to chronic phlegm. It is important to note
that thestudy examined annual pollution exposures, and the authors did not rule out that acute (daily)
exposures could be related to asthma attacks and other acute episodes. Earlier work, by Dockery et al.
(1989), based on six U.S. cities, found acute bronchitis and chronic cough significantly related to PM15.
Because it is based on a larger sample, the Dockery et al. (1996) study is the better study to develop a C-
R function linking PM2 5 with bronchitis.
Bronchitis was counted in the study only if there were "reports of symptoms in the past 12
months" (Dockery et al., 1996, p. 501). It is unclear, however, if the cases of bronchitis are acute and
temporary, or if the bronchitis is a chronic condition. Dockery et al. found no relationship between PM
and chronic cough and chronic phlegm, which are important indicators of chronic bronchitis. For this
analysis, we assumed that the C-R function based on Dockery et al. is measuring acute bronchitis. The
C-R function is based on results of the single pollutant model reported in Table 1.
Single Pollutant Model
The estimated logistic coefficient and standard error are based on the odds ratio (1.50) and 95%
confidence interval (0.91-2.47) associated with being in the most polluted city (PM21 =20.7 |ig/m3)
versus the least polluted city (PM21 =5.8 |ig/m3) (Dockery et al., 1996, Tables 1 and 4). The original
study used PM21, however, we use the PM21 coefficient and apply it to PM2 5 data.
Functional Form: Logistic
Coefficient: 0.027212
Standard Error: 0.017096
Incidence Rate: annual bronchitis incidence rate per person = 0.043 (American Lung Association,
2002a, Table 11)
Population: population of ages 8-12
F .6.2 Acute Myocardial Infarction (Heart Attacks), Nonfatal (Peters et al., 2001)
Peters et al. (2001) studied the relationship between increased particulate air pollution and onset
of heart attacks in the Boston area from 1995 to 1996. The authors used air quality data for PM10, PM10_
25, PM2 5,"black carbon", 03, CO, N02, and S02 in a case-crossover analysis. For each subject, the case
period was matched to three control periods, each 24 hours apart. In univariate analyses, the authors
observed a positive association between heart attack occurrence and PM2 5 levels hours before and days
before onset. The authors estimated multivariate conditional logistic models including two-hour and
81 The original study measured PM21, however when using the study's results we use PM25.
difference, assuming that the adverse effects ofPM21 and PM25 are comparable.
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Appendix F. Particulate Matter C-R Functions
twenty-four hour pollutant concentrations for each pollutant. They found significant and independent
associations between heart attack occurrence and both two-hour and twenty-four hour PM2 5
concentrations before onset. Significant associations were observed for PM10 as well. None of the other
particle measures or gaseous pollutants were significantly associated with acute myocardial infarction for
the two hour or twenty-four hour period before onset.
The patient population for this study was selected from health centers across the United States.
The mean age of participants was 62 years old, with 21% of the study population under the age of 50. In
order to capture the full magnitude of heart attack occurrence potentially associated with air pollution
and because age was not listed as an inclusion criteria for sample selection, we apply an age range of 18
and over in the C-R function. According to the National Hospital Discharge Survey, there were no
hospitalizations for heart attacks among children <15 years of age in 1999 and only 5.5% of all
hospitalizations occurred in 15-44 year olds (Popovic, 2001, Table 10).
PM2 5 Function(s)
Single Pollutant Model
The coefficient and standard error are calculated from an odds ratio of 1.62 (95% CI 1.13-2.34)
for a 20 |ig/m3 increase in twenty-four hour average PM25 (Peters et al., 2001, Table 4, p. 2813).
Functional Form: Logistic
Coefficient: 0.024121
Standard Error: 0.009285
Incidence Rate: region-specific daily nonfatal heart attack rate per person 18+ = 93% of region-specific
daily heart attack hospitalization rate (ICD code 410)82
Population: population of ages 18 and older
PM10 2 5 Function(s)
Single Pollutant Model
The coefficient and standard error are calculated from an odds ratio of 1.39 (95% CI 0.89-2.15)
for a 15 |ig/m3 increase in twenty-four hour average PM10_2 5 (Peters et al., 2001, Table 4, p. 2813).
Functional Form: Logistic
Coefficient: 0.021954
Standard Error: 0.015000
Incidence Rate: region-specific daily nonfatal heart attack rate = 93% of region-specific daily heart
attack hospitalization rate (ICD code 410)83
Population: population of all ages
82 This estimate assumes that all heart attacks that are not instantly fatal will result in a hospitalization. In addition,
Rosamond et al. (1999) report that approximately six percent of male and eight percent of female hospitalized heart attack patients
die within 28 days (either in or outside of the hospital). We applied a factor of 0.93 to the number of hospitalizations to estimate the
number of nonfatal heart attacks per year.
83 This estimate assumes that all heart attacks that are not instantly fatal will result in a hospitalization. In addition,
Rosamond et al. (1999) report that approximately six percent of male and eight percent of female hospitalized heart attack patients
die within 28 days (either in or outside of the hospital). We applied a factor of 0.93 to the number of hospitalizations to estimate the
number of nonfatal heart attacks per year.
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PM10Function(s)
Single Pollutant Model
The coefficient and standard error are calculated from an odds ratio of 1.66 (95% CI 1.11-2.49)
for a 30 |ig/m3 increase in twenty-four hour average PM10 (Peters et al., 2001, Table 4, p. 2813).
Functional Form: Logistic
Coefficient: 0.016894
Standard Error: 0.006870
Incidence Rate: region-specific daily nonfatal heart attack rate = 93% of region-specific daily heart
attack hospitalization rate (ICD code 410)84
Population: population of all ages
F .6.3 Any of 19 Respiratory Symptoms (Krupnick et al., 1990)
Krupnick et al. (1990) estimated the impact of air pollution on the incidence of any of 19
respiratory symptoms or conditions in 570 adults and 756 children living in three communities in Los
Angeles, California from September 1978 to March 1979. Krupnick et al. (1990) listed 13 specific
"symptoms or conditions": head cold, chest cold, sinus trouble, croup, cough with phlegm, sore throat,
asthma, hay fever, doctor-diagnosed ear infection, flu, pneumonia, bronchitis, and bronchiolitis. The
other six symptoms or conditions are not specified.
In their analysis, they included COH, ozone, N02, and S02, and they used a logistic regression
model that takes into account whether a respondent was well or not the previous day. A key difference
between this and the usual logistic model, is that the model they used includes a lagged value of the
dependent variable. In single-pollutant models, daily 03, COH, and S02 were significantly related to
respiratory symptoms in adults. Controlling for other pollutants, they found that ozone was still
significant. The results were more variable for COH and S02, perhaps due to collinearity. N02 had no
significant effect. No effect was seen in children for any pollutant. The results from the two-pollutant
model with COH and ozone are used to develop a C-R function.
Multipollutant Model (PM10 and ozone)
The C-R function used to estimate the change in ARD2 associated with a change in daily
average PM10 concentration is based on Krupnick et al. (1990, p. 12):85
AARD2= j3*PMm - A PMw ¦pop,
Functional Form: Linear
84 This estimate assumes that all heart attacks that are not instantly fatal will result in a hospitalization. In addition,
Rosamond et al. (1999) report that approximately six percent of male and eight percent of female hospitalized heart attack patients
die within 28 days (either in or outside of the hospital). We applied a factor of 0.93 to the number of hospitalizations to estimate the
number of nonfatal heart attacks per year.
85 Krupnick and Kopp (1988, p. 2-24) and ESEERCO (1994, p. V-32) used the same C-R functional form as that used
here.
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Coefficient: first derivative of the stationary probability = 0.000461
Standard Error: 0.000239
Population: population of ages 18-64 years86
The logistic regression model used by Krupnick et al. (1990) takes into account whether a
respondent was well or not the previous day. Following Krupnick et al. (p. 12), the probability that one
is sick is on a given day is:
prob ability (ARD2)= -—
1
probability(yARD2 \ sickness or not t , )= pi = ~—p^+^.ardi, t+x-p > f°r /= •
where:
X = the matrix of explanatory variables
p0 = the probability of sickness on day t, given wellness on day t-1, and
Pi = the probability of sickness on day t, given sickness on day t-1.
In other words, the transition probabilities are estimated using a logistic function; the key
difference between this and the usual logistic model, is that the model includes a lagged value of the
dependent variable.
To calculate the impact of COH (or other pollutants) on the probability of ARD2, it is possible,
in principle, to estimate ARD2 before the change in COH and after the change:
hARD2= ARD2after - ARD2before .
However the full suite of coefficient estimates are not available.87 Rather than use the full suite
of coefficient values, the impact of COH on the probability of probability of ARD2 may be
approximated by the derivative of ARD2 with respect to COH:
dprobability(ARD2) /v('~ A)'/^//{a +0~ Ai)]
86 Krupnick et al. (1990, Table 1) reported the age distribution in their complete data, but they did not report the ages of
individuals that were considered "adult." This analysis assumes that individuals 18 and older were considered adult. Only a small
percentage (0.6%) of the study population is above the age of 60, so the C-R function was limited to the adult population, up
through the age of 65.
87 The model without N02 (Krupnick et al., 1990, Table V equation 3) was used in this analysis, but the full suite of
coefficient estimates for this model were not reported. Krupnick et al. (1990, Table IV) reported all of the estimated coefficients for
a model of children and for a model of adults when four pollutants were included (ozone, COH, S02, and N02). However, because
of high collinearity between N02 and COH, N02 was dropped from some of the reported analyses (Krupnick et al., p. 10), and the
resulting coefficient estimates changed substantially (see Krupnick et al., 1990, Table IV). Both the ozone and COH coefficients
dropped by about a factor of two or more.
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where PC0H is the reported logistic regression coefficient for COH. Since COH data are not available for
the benefits analysis, an estimated PM10 logistic regression coefficient is used based on the following
assumed relationship between PM10, COH, and TSP:
COH=0.\ \ 6 TSP
PMW = 0.5 5TSP
=> COH = 0.2109- PMW
=> J3PMio = 0.2109-J3coh = 0.2109 0.0088= 0.001856.
This analysis uses PC0H = 0.0088 (Krupnick et al., 1990, Table V equation 3). The conversion
from COH to TSP is based on study-specific information provided to ESEERCO (1994, p. V-32). The
conversion of TSP to PM10 is from also from ESEERCO (1994, p. V-5), which cited studies by EPA
(1986) and the California Air Resources Board (1982).
The change in the incidence of ARD2 associated with a given change in COH is then estimated
by:
(9ARD2 AARD2
dPMl0 ~ APMW
AARD2 .
=> = /?
A PMW ^ PM10
=* AARD2=j3*PMio-APM10 .
This analysis uses transition probabilities obtained from Krupnick et al. as reported by
ESEERCO (1994, p. V-32), for the adult population: p: = 0.7775 and p0 = 0.0468. This implies:
0.0468(1-0.7775)0.001856f0.7775,+(1-0.0468)1
J3PM = j1 l- —= 0.000461.
10 (1-0.7775+0.0468)
The standard error for the coefficient is derived using the reported standard error of the logistic
regression coefficient in Krupnick et al. (1990, Table V):
^ PPMlM = 0.2109.0COH, hlgh = 0.2109(0.0088+ (1.960.0046))= 0.003757
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0.0468(1- 0.7775)0.003757[0.7775+ (l-0.0468)]
(l- 0.7775+ 0.0468):
• P'pm wh = ~ ^' 1——7—1 : —= 0.000934
' PMl0, high n nnnc- n ri/l/ScA2
ftPM1(j, high PpM10 (0.000934-0.000461)
=a000236
A, - 0 2 100-/? ... - 0 2 I <)<> (0.00X8-1I 0 0046I)- - 4. I0
0.0468(1-0.7775)(-4.55510"5 >[0.7775+(1-0.0468)]
(l- 0.7775+ 0.0468):
———=—113210
(0.000461+1.13210 ')
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Appendix F. Particulate Matter C-R Functions
Multipollutant Model (PM2 5 and PM10_2 5)
In a model with PM10_25, the PM25 coefficient and standard error are calculated from the reported
odds ratio (1.29) and 95% confidence interval (1.06-1.57) associated with a 15 ng/m3 change in PM25
(Schwartz and Neas, 2000, Table 2).
Functional Form: Logistic
Coefficient: 0.016976
Standard Error: 0.006680
Incidence Rate: daily lower respiratory symptom incidence rate per person = 0.0012 (Schwartz et al.,
1994, Table 2)
Population: population of ages 7 to 14
F .6.5 Lower Respiratory Symptoms (Schwartz et al., 1994)
Schwartz et al. (1994) used logistic regression to link lower respiratory symptoms in children
with S02, N02, ozone, PM10, PM2 5, sulfate and H+ (hydrogen ion). Children were selected for the study
if they were exposed to indoor sources of air pollution: gas stoves and parental smoking. The study
enrolled 1,844 children into a year-long study that was conducted in different years (1984 to 1988) in six
cities. The students were in grades two through five at the time of enrollment in 1984. By the
completion of the final study, the cohort would then be in the eighth grade (ages 13-14); this suggests an
age range of 7 to 14.
In single pollutant models S02, N02, PM2 5, and PM10 were significantly linked to cough. In
two-pollutant models, PM10 had the most consistent relationship with cough; ozone was marginally
significant, controlling for PM10. In models for upper respiratory symptoms, they reported a marginally
significant association for PM10. In models for lower respiratory symptoms, they reported significant
single-pollutant models, using S02, 03, PM2 5, PM10, S04, and H+. The PM2 5 C-R function is based on
the single pollutant model reported in Table 5.
Single Pollutant Model
The coefficient and standard error are calculated from the reported odds ratio (1.44) and 95%
confidence interval (1.15-1.82) associated with a 20 //g/m3 change in PM25 (Schwartz et al., 1994, Table
5).
Functional Form: Logistic
Coefficient: 0.018232
Standard Error: 0.005856
Incidence Rate: daily lower respiratory symptom incidence rate per person = 0.0012 (Schwartz et al.,
1994, Table 2)
Population: population of ages 7 to 14
F .6.6 Minor Restricted Activity Days: Ostro and Rothschild (1989)
Ostro and Rothschild (1989) estimated the impact of PM2 5 and ozone on the incidence of minor
restricted activity days (MRADs) and respiratory-related restricted activity days (RRADs) in a national
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sample of the adult working population, ages 18 to 65, living in metropolitan areas.88 The annual
national survey results used in this analysis were conducted in 1976-1981. Controlling for PM2 5, two-
week average ozone has highly variable association with RRADs and MRADs. Controlling for ozone,
two-week average PM25 was significantly linked to both health endpoints in most years. The C-R
function for PM is based on this co-pollutant model.
The study is based on a "convenience" sample of non-elderly individuals. Applying the C-R
function to this age group is likely a slight underestimate, as it seems likely that elderly are at least as
susceptible to PM as individuals under 65. The elderly appear more likely to die due to PM exposure
than other age groups (e.g., Schwartz, 1994d, p. 30) and a number of studies have found that hospital
admissions for the elderly are related to PM exposures (e.g., Schwartz, 1994b; Schwartz, 1994c).
Multipollutant Model (PM2 5 and ozone)
Using the results of the two-pollutant model, we developed separate coefficients for each year in
the analysis, which were then combined for use in this analysis. The coefficient is a weighted average of
the coefficients in Ostro and Rothschild (1989, Table 4) using the inverse of the variance as the weight:
( 1981
P=
Pi
= 1916°'/3t
1981
V i=\9H6a'pi J
= 0.00741.
The standard error of the coefficient is calculated as follows, assuming that the estimated year-
specific coefficients are independent:
( 1981
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Appendix F. Particulate Matter C-R Functions
Functional Form: Log-linear
Coefficient: 0.00741
Standard Error: 0.00070
Incidence Rate: daily incidence rate for minor restricted activity days (MRAD) = 0.02137 (Ostro and
Rothschild, 1989, p. 243)
Population: adult population ages 18 to 64
F .6.7 School Loss Days, All Cause (Chen et al., 2000)
Chen et al. (2000) studied the association between air pollution and elementary school
absenteeism (grades 1-6)89 in Washoe County, Nevada. Daily absence data were available for all
elementary schools in the Washoe Country School District. The authors regressed daily total absence
rate on the three air pollutants, meteorological variables, and indicators for day of the week, month, and
holidays. They reported statistically significant associations between both ozone and CO and daily total
absence rate for grades one through six. PM10 was negatively associated with absence rate, after
adjustment for ozone, CO, and meteorological and temporal variables. The C-R function for PM is
based on the results from a multiple linear regression model with CO, ozone, and PM10.
Multipollutant Model (PM10, CO, and ozone)
The coefficient and standard error are presented in Table 3 (Chen et al., 2000, p. 1008) for a unit
|ig/m3 increase in daily PM10 concentration.
The reported coefficient represents an absolute increase in absenteeism rate for a unit increase in
PM10. If we apply this study to other locations, we assume that the same absolute increase will occur for
a unit increase in PM10, regardless of the baseline rate. If the study location has a particularly high
baseline rate, we may be overestimating decreases in absenteeism nationally, and vice-versa. As an
example, consider if the baseline absenteeism rate were 10% in the study and 5% nationally. An
absolute increase in absence rate of 2% associated with a given increase in PM10 reflects a relative
increase in absence rate of 20% for the study population. However, in the national estimate, we would
assume the same absolute increase of 2%, but this would reflect a relative increase in the absenteeism
rate of 40%.
An alternative approach is to estimate apply the relative increase in absenteeism rate in the C-R
function by adjusting the results by the ratio of the national absenteeism rate to the study-specific rate.
As a result, the percent increase in absenteeism rate associated with an increase in PM10 is extrapolated
nationally rather than the absolute increase in absenteeism rate. The incidence derivation section above
describes the data used to estimate national and study-specific absence rates.
In addition to this scaling factor, there are two other scaling factors which are applied to the
function. A scaling factor of 0.01 is used to convert the beta from a percentage (x 100) per unit increase
of PM10 to a proportion per unit increase of PM10. As a result it can be applied directly to the national
population of school children ages 6 through 11 to estimate the number of absences avoided.
The final scaling factor is used to adjust for the proportion of school days in the full year. In the
modeling program, the function is applied to every day in the year, however, in reality, school absences
89 Assuming that most children start kindergarten at age 5, the corresponding ages for grades 1 through 6 would be 6
through 11.
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will be avoided only on school days. Using an estimate of 180 school days per year, we estimate that
49.3% of the days in a given year are school days (180/365). The C-R function parameters are shown
below.
Functional Form: Linear
Coefficient: -0.015400
Standard Error: 0.004400
Population: population of children ages 6-11
Scaling Factor 1: Ratio of national school absence rate to study-specific school absence rate90 = 1.081
Scaling Factor 2: Convert beta in percentage terms to a proportion = 0.01
Scaling Factor 3: Proportion of days in the year that are school days91 = 0.493
F .6.8 School Loss Days, All Cause (Gilliland et al., 2001)
Gilliland et al. (2001) examined the association between air pollution and school absenteeism
among 4th grade school children (ages 9-10) in 12 southern Californian communities. The study was
conducted from January through June 1996. The authors used school records to collect daily absence
data and parental telephone interviews to identify causes. They defined illness-related absences as
respiratory or non-respiratory. A respiratory illness was defined as an illness that included at least one of
the following: runny nose/sneezing, sore throat, cough, earache, wheezing, or asthma attack. The
authors used 15 and 30 day distributed lag models to quantify the association between ozone, PM10, and
N02 and incident school absences. Ozone levels were positively associated with all school absence
measures and significantly associated with all illness-related school absences (non-respiratory illness,
respiratory illness, URI and LRI). Neither PM10 nor N02 was significantly associated with illness-
related school absences, but PM10 was associated with non-illness related absences. The C-R function
for PM10 is based on the results of the single pollutant model.
Gilliland et al. (2001) defines an incident absence as an absence that followed attendance on the
previous day and the incidence rate as the number of incident absences on a given day over the
population at risk for an absence on a given day (i.e. those children who were not absent on the previous
day). Since school absences due to air pollution may last longer than one day, an estimate of the average
duration of school absences could be used to calculated the total avoided school loss days from an
estimate of avoided new absences. A simple ratio of the total absence rate divided by the new absence
rate would provide an estimate of the average duration of school absences, which could be applied to the
estimate of avoided new absences as follows:
totalAbsences
Duration=
new Absences
A Tola/Absences = -[incidence ¦ (e /?APMltl - !)]• duration- pop
90 National school absence rate of 5.50% obtained from the U.S. Department of Education (1996, Table 42-1). Study-
specific school absence rate of 5.09% obtained from Chen et al. (2000, Table 1).
91 Using an estimate of 180 school days per year, we estimate that 49.3% of the days in a given year are school days
(180/365).
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Since the function is log-linear, the baseline incidence rate (in this case, the rate of new
absences) is multiplied by duration, which reduces to the total school absence rate. Therefore, the same
result would be obtained by using a single estimate of the total school absence rate in the C-R function.
Using this approach, we assume that the same relationship observed between pollutant and new school
absences in the study would be observed for total absences on a given day. As a result, the total school
absence rate is used in the function below. The derivation of this rate is described in the section on
baseline incidence rate estimation.
Single Pollutant Model
For all absences, the coefficient and standard error are based on a percent increase of 22.8
percent (95% CI 11.6 percent, 35.2 percent) associated with a 10 ng/m3 increase in daily average PM10
concentration (2001, Table 6, p. 52).
A scaling factor is used to adjust for the number of school days in the ozone season. In the
modeling program, the function is applied to every day in the year, however, in reality, school absences
will be avoided only on school days. Using an estimate of 180 school days per year, we estimate that
49.3% of the days in a given year are school days (180/365).
In addition, not all children are at-risk for a new school absence, as defined by the study. On
average, 5.5% of school children are absent from school on a given day (U.S. Department of Education,
1996, Table 42-1). Only those who are in school on the previous day are at risk for a new absence (1-
0.055 = 94.5%). As a result, a factor of 94.5% is used in the function to estimate the population of
school children at-risk for a new absence.
Functional Form: Log-linear
Coefficient: 0.020539
Standard Error: 0.004894
Incidence Rate: daily school absence rate = 0.055 (U.S. Department of Education, 1996, Table 42-1)
Population: population of children ages 9-10 not absent from school on a given day92 = 94.5% of
children ages 9-10
Scaling Factor: Proportion of school days in a year93 = 0.493
F .6.9 School Loss Days, All Cause (Ransom and Pope, 1992, Provo)
Ransom and Pope (1992) studied the relationship between particulate air pollution and
elementary school absenteeism (grades 1-6)94 in Utah Valley from 1985 to 1990. The authors identified
school absences using weekly attendance data from the Provo School District and daily attendance data
from an elementary school in Orem, Utah. The authors regressed school absence rates on PM10,weather
variables, day of the week, month of the year, and indicators for holidays or extended weekends. The
authors report that a four week moving average of PM10 provided the best model fit. They found a
92 The proportion of children not absent from school on a given day (5.5%) is based on 1996 data from the U.S.
Department of Education (1996, Table 42-1).
93 Using an estimate of 180 school days per year, we estimate that 49.3% of the days in a given year are school days
(180/365).
94 Assuming that most children start kindergarten at age 5, the corresponding ages for grades 1 through 6 would be 6
through 11.
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statistically significant association between increases in PM10 and absence rates in Provo and Orem, after
adjustment for weather variables and temporal trends. The C-R function for PM10 is based on results of
the linear regression model in the Provo School District for grades 1-6 (Ransom and Pope, 1992, Table
3, p. 211).
Single Pollutant Model
For Provo, the coefficient and standard error for a 100 |ig/m3 increase in four-week average
PM10 concentration are reported as 2.1921 and 0.4610, respectively (Ransom and Pope, 1992, Table 3, p.
211).
The reported coefficient represents an absolute increase in absenteeism rate for a unit increase in
PM10. If we apply this study to other locations, we assume that the same absolute increase will occur for
a unit increase in PM10, regardless of the baseline rate. If the study location has a particularly high
baseline rate, we may be overestimating decreases in absenteeism nationally, and vice-versa. As an
example, consider if the baseline absenteeism rate were 10% in the study and 5% nationally. An
absolute increase in absence rate of 2% associated with a given increase in PM10 reflects a relative
increase in absence rate of 20% for the study population. However, in the national estimate, we would
assume the same absolute increase of 2%, but this would reflect a relative increase in the absenteeism
rate of 40%.
An alternative approach is to estimate apply the relative increase in absenteeism rate in the C-R
function by adjusting the results by the ratio of the national absenteeism rate to the study-specific rate.
As a result, the percent increase in absenteeism rate associated with an increase in PM10 is extrapolated
nationally rather than the absolute increase in absenteeism rate. The incidence derivation section above
describes the data used to estimate national and study-specific absence rates.
An additional scaling factor is used to adjust for the proportion of school days in the full year.
In the modeling program, the function is applied to every day in the year, however, in reality, school
absences will be avoided only on school days. Using an estimate of 180 school days per year, we
estimate that 49.3% of the days in a given year are school days (180/365). The C-R function parameters
are shown below.
Functional Form: Linear
Coefficient: 0.021921
Standard Error: 0.00461
Population: population of children ages 6-11
Scaling Factor 1: Ratio of national school absence rate to study-specific school absence rate95 = 1.211
Scaling Factor 2: Proportion of school days in a year96 = 0.493
95 National school absence rate of 5.5% obtained from the U.S. Department of Education (1996, Table 42-1). Study-
specific school absence rate of 4.54% obtained from Ransom and Pope (1992, Table 2).
96 Using an estimate of 180 school days per year, we estimate that 49.3% of the days in a given year are school days
(180/365).
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F .6.10 School Loss Days, All Cause (Ransom and Pope, 1992, Orem)
Ransom and Pope (1992) studied the relationship between particulate air pollution and
elementary school absenteeism (grades 1-6)97 in Utah Valley from 1985 to 1990. The authors identified
school absences using weekly attendance data from the Provo School District and daily attendance data
from an elementary school in Orem, Utah. The authors regressed school absence rates on PM10,weather
variables, day of the week, month of the year, and indicators for holidays or extended weekends. The
authors report that a four week moving average of PM10 provided the best model fit. They found a
statistically significant association between increases in PM10 and absence rates in Provo and Orem, after
adjustment for weather variables and temporal trends. The C-R function for PM10 is based on results of
the linear regression model for grades 1-6 in Orem, Utah (Ransom and Pope, 1992, Table 4, p. 212).
Single Pollutant Model
For Orem, the coefficient and standard error for a 100 |ig/m3 increase in four-week average PM10
concentration are reported as 2.115 and 0.4600, respectively (Ransom and Pope, 1992, Table 4, p. 212).
The reported coefficient represents an absolute increase in absenteeism rate for a unit increase in
PM10. If we apply this study to other locations, we assume that the same absolute increase will occur for
a unit increase in PM10, regardless of the baseline rate. If the study location has a particularly high
baseline rate, we may be overestimating decreases in absenteeism nationally, and vice-versa. As an
example, consider if the baseline absenteeism rate were 10% in the study and 5% nationally. An
absolute increase in absence rate of 2% associated with a given increase in PM10 reflects a relative
increase in absence rate of 20% for the study population. However, in the national estimate, we would
assume the same absolute increase of 2%, but this would reflect a relative increase in the absenteeism
rate of 40%.
An alternative approach is to estimate apply the relative increase in absenteeism rate in the C-R
function by adjusting the results by the ratio of the national absenteeism rate to the study-specific rate.
As a result, the percent increase in absenteeism rate associated with an increase in PM10 is extrapolated
nationally rather than the absolute increase in absenteeism rate. The incidence derivation section above
describes the data used to estimate national and study-specific absence rates.
An additional scaling factor is used to adjust for the proportion of school days in the full year.
In the modeling program, the function is applied to every day in the year, however, in reality, school
absences will be avoided only on school days. Using an estimate of 180 school days per year, we
estimate that 49.3% of the days in a given year are school days (180/365). The C-R function parameters
are shown below.
97 Assuming that most children start kindergarten at age 5, the corresponding ages for grades 1 through 6 would be 6
through 11.
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Functional Form: Linear
Coefficient: 0.02115
Standard Error: 0.00460
Population: population of children ages 6-11
Scaling Factor 1: Ratio of national school absence rate to study-specific school absence rate98 = 1.076
Scaling Factor 2: Proportion of school days in a year" = 0.493
F .6.11 School Loss Days, Illness-Related (Gilliland et al., 2001)
Gilliland et al. (2001) examined the association between air pollution and school absenteeism
among 4th grade school children (ages 9-10) in 12 southern Californian communities. The study was
conducted from January through June 1996. The authors used school records to collect daily absence
data and parental telephone interviews to identify causes. They defined illness-related absences as
respiratory or non-respiratory. A respiratory illness was defined as an illness that included at least one of
the following: runny nose/sneezing, sore throat, cough, earache, wheezing, or asthma attack. The
authors used 15 and 30 day distributed lag models to quantify the association between ozone, PM10, and
N02 and incident school absences. Ozone levels were positively associated with all school absence
measures and significantly associated with all illness-related school absences (non-respiratory illness,
respiratory illness, URI and LRI). Neither PM10 nor N02 was significantly associated with illness-
related school absences, but PM10 was associated with non-illness related absences. The C-R function
for PM10 is based on the results of the single pollutant model.
Gilliland et al. (2001) defines an incident absence as an absence that followed attendance on the
previous day and the incidence rate as the number of incident absences on a given day over the
population at risk for an absence on a given day (i.e. those children who were not absent on the previous
day). Since school absences due to air pollution may last longer than one day, an estimate of the average
duration of school absences could be used to calculated the total avoided school loss days from an
estimate of avoided new absences. A simple ratio of the total absence rate divided by the new absence
rate would provide an estimate of the average duration of school absences, which could be applied to the
estimate of avoided new absences as follows:
totalAbsences
Duration = —
new Absences
A TotalAbsences = -[incidence ¦ (e-P-APMl° _ ] . duration ¦ pop
Since the function is log-linear, the baseline incidence rate (in this case, the rate of new
absences) is multiplied by duration, which reduces to the total school absence rate. Therefore, the same
result would be obtained by using a single estimate of the total school absence rate in the C-R function.
Using this approach, we assume that the same relationship observed between pollutant and new school
absences in the study would be observed for total absences on a given day. As a result, the total school
98 National school absence rate of 5.50% obtained from the U.S. Department of Education (1996, Table 42-1). Study-
specific school absence rate of 5.11% obtained from Ransom and Pope (1992, Table 1).
99 Using an estimate of 180 school days per year, we estimate that 49.3% of the days in a given year are school days
(180/365).
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absence rate is used in the function below. The derivation of this rate is described in the section on
baseline incidence rate estimation.
Single Pollutant Model
For total illness-related absences, the coefficient and standard error are based on a percent
increase of 5.7 percent (95% CI -12.1 percent, 27.0 percent) associated with a 10 ng/m3 increase in daily
average PM10 concentration (2001, Table 6, p. 52).
A scaling factor is used to adjust for the number of school days in the ozone season. In the
modeling program, the function is applied to every day in the year, however, in reality, school absences
will be avoided only on school days. Using an estimate of 180 school days per year, we estimate that
49.3% of the days in a given year are school days (180/365).
In addition, not all children are at-risk for a new school absence, as defined by the study. On
average, 5.5% of school children are absent from school on a given day (U.S. Department of Education,
1996, Table 42-1). Only those who are in school on the previous day are at risk for a new absence (1-
0.055 = 94.5%). As a result, a factor of 94.5% is used in the function to estimate the population of
school children at-risk for a new absence.
Functional Form: Log-linear
Coefficient: 0.005543
Standard Error: 0.009387
Incidence Rate: region-specific daily illness-related school absence rate (Adams et al., 1999, Table 47),
assuming 180 school days per year.
Population: population of children ages 9-10 not absent from school on a given day100 = 94.5% of
children ages 9-10
Scaling Factor: Proportion of school days in a year101 = 0.493
F .6.12 School Loss Days, Respiratory Illness-Related (Gilliland et al., 2001)
Gilliland et al. (2001) examined the association between air pollution and school absenteeism
among 4th grade school children (ages 9-10) in 12 southern Californian communities. The study was
conducted from January through June 1996. The authors used school records to collect daily absence
data and parental telephone interviews to identify causes. They defined illness-related absences as
respiratory or non-respiratory. A respiratory illness was defined as an illness that included at least one of
the following: runny nose/sneezing, sore throat, cough, earache, wheezing, or asthma attack. The
authors used 15 and 30 day distributed lag models to quantify the association between ozone, PM10, and
N02 and incident school absences. Ozone levels were positively associated with all school absence
measures and significantly associated with all illness-related school absences (non-respiratory illness,
respiratory illness, URI and LRI). Neither PM10 nor N02 was significantly associated with illness-
related school absences, but PM10 was associated with non-illness related absences.
100 The proportion of children not absent from school on a given day (5.5%) is based on 1996 data from the U.S.
Department of Education (1996, Table 42-1).
101 Using an estimate of 180 school days per year, we estimate that 49.3% of the days in a given year are school days
(180/365).
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Gilliland et al. (2001) defines an incident absence as an absence that followed attendance on the
previous day and the incidence rate as the number of incident absences on a given day over the
population at risk for an absence on a given day (i.e. those children who were not absent on the previous
day). Since school absences due to air pollution may last longer than one day, an estimate of the average
duration of school absences could be used to calculated the total avoided school loss days from an
estimate of avoided new absences. A simple ratio of the total absence rate divided by the "incident" rate
would provide an estimate of the average duration of school absences, which could be applied to the
estimate of avoided new absences as follows:
Duration =
totalAbsences
newAbsences
kTotalAbsences = - incidence ¦(e~li'APMl'> - 1 )\-duration- pop
Since the function is log-linear, the baseline incidence rate (in this case, the rate of new
absences) is multiplied by duration, which reduces to the total school absence rate. Therefore, the same
result would be obtained by using a single estimate of the total school absence rate in the C-R function.
Using this approach, we assume that the same relationship observed between pollutant and new school
absences in the study would be observed for total absences on a given day. As a result, the total school
absence rate is used in the function below. The derivation of this rate is described in the section on
baseline incidence rate estimation.
Single Pollutant Model
For respiratory illness-related absences, the coefficient and standard error are based on a percent
increase of -4.3 percent (95% CI -32.2 percent, 35.0 percent) associated with a 10 /ig/m3 increase in
daily average PM10 concentration (2001, Table 6, p. 52).
A scaling factor is used to adjust for the number of school days in the ozone season. In the
modeling program, the function is applied to every day in the year, however, in reality, school absences
will be avoided only on school days. Using an estimate of 180 school days per year, we estimate that
49.3% of the days in a given year are school days (180/365).
In addition, not all children are at-risk for a new school absence, as defined by the study. On
average, 5.5% of school children are absent from school on a given day (U.S. Department of Education,
1996, Table 42-1). Only those who are in school on the previous day are at risk for a new absence (1-
0.055 = 94.5%). As a result, a factor of 94.5% is used in the function to estimate the population of
school children at-risk for a new absence.
Functional Form: Log-linear
Coefficient: -0.004395
Standard Error: 0.017569
Incidence Rate: region-specific daily respiratory illness-related school absence rate (Adams et al., 1999,
Table 47), assuming 180 school days per year.
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Population: population of children ages 9-10 not absent from school on a given day102 = 94.5% of
children ages 9-10
Scaling Factor: Proportion of school days in a year103 = 0.493
F .6.13 Work Loss Days (Ostro, 1987)
Ostro (1987) estimated the impact of PM2 5 on the incidence of work-loss days (WLDs),
restricted activity days (RADs), and respiratory-related RADs (RRADs) in a national sample of the adult
working population, ages 18 to 65, living in metropolitan areas.104 The annual national survey results
used in this analysis were conducted in 1976-1981. Ostro reported that two-week average PM2 5 levels105
were significantly linked to work-loss days, RADs, and RRADs, however there was some year-to-year
variability in the results. Separate coefficients were developed for each year in the analysis (1976-1981);
these coefficients were pooled. The coefficient used in the concentration-response function presented
here is a weighted average of the coefficients in Ostro (1987, Table III) using the inverse of the variance
as the weight.
The study is based on a "convenience" sample of non-elderly individuals. Applying the C-R
function to this age group is likely a slight underestimate, as it seems likely that elderly are at least as
susceptible to PM as individuals under 65. The elderly appear more likely to die due to PM exposure
than other age groups (e.g., Schwartz, 1994d, p. 30) and a number of studies have found that hospital
admissions for the elderly are related to PM exposures (e.g., Schwartz, 1994b; Schwartz, 1994c). On the
other hand, the number of workers over the age of 65 is relatively small; it was approximately 3% of the
total workforce in 2001(U.S. Bureau of the Census, 2002, Table 561).
Single Pollutant Model
The coefficient used in the C-R function is a weighted average of the coefficients in Ostro (1987,
Table III) using the inverse of the variance as the weight:
P
( 1981 R \
1 jr
2 = 1976 <->
1981
V z = 1976 (7pi )
0.0046.
102 The proportion of children not absent from school on a given day (5.5%) is based on 1996 data from the U.S.
Department of Education (1996, Table 42-1).
103 Using an estimate of 180 school days per year, we estimate that 49.3% of the days in a given year are school days
(180/365).
104 The study population is based on the Health Interview Survey (HIS), conducted by the National Center for Health
Statistics. In publications from this ongoing survey, non-elderly adult populations are generally reported as ages 18-64. From the
study, it is not clear if the age range stops at 65 or includes 65 year olds. We apply the C-R function to individuals ages 18-64 for
consistency with other studies estimating impacts to non-elderly adult populations.
105 The study used a two-week average pollution concentration; the C-R function uses a daily average, which is assumed
to be a reasonable approximation.
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The standard error of the coefficient is calculated as follows, assuming that the estimated year-
specific coefficients are independent:
Functional Form: Log-linear
Coefficient: 0.0046
Standard Error: 0.00036
Incidence Rate: daily work-loss-day incidence rate per person ages 18 to 64 = 0.00595 (U.S. Bureau of
the Census, 1997, No. 22; Adams et al., 1999, Table 41)
Population: adult population ages 18 to 64
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i = 1976LJ pi
i= 1976 V pi
!=1976
= pl J \
This eventually reduces down to:
0.00036
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Appendix F. Particulate Matter C-R Functions
Exhibit F-7. Concentration-Response (C-R) Functions for Particulate Matter and Asthma-Related Effects
Endpoint Name Pollutant Author Year Location
_ _ , Other Averaging _ _ Functional
Age Race Gender _ „ , . , Beta Std Error „
Pollutants Time1 Form
Notes
Acute Bronchitis
Acute Bronchitis
Asthma Exacerbation,
Asthma Attacks
Asthma Exacerbation,
Cough
Asthma Exacerbation,
Cough
Asthma Exacerbation,
Cough
Asthma Exacerbation,
Cough
Asthma Exacerbation,
Cough
Asthma Exacerbation,
Moderate or Worse
Asthma Exacerbation,
One or More Symptoms
Asthma Exacerbation,
One or More Symptoms
Asthma Exacerbation,
Shortness of Breath
Asthma Exacerbation,
Shortness of Breath
Asthma Exacerbation,
Shortness of Breath
Asthma Exacerbation,
Shortness of Breath
PM,
PM„
PM„
PM,
PM,
PM„
PM„
PM,
PM,
PM„
McConnell et
al.
McConnell et
al.
Whittemore
and Korn
1999
1999
1980
Ostro et al. 2001
Ostro et al. 2001
2001
2001
PM,„ Vedaletal. 1998
Southern
California
Southern
California
Los Angeles,
CA
Los Angeles,
CA
Los Angeles,
CA
Los Angeles,
CA
Los Angeles,
CA
Vancouver,
CAN
9-15 All All None
9-15 All All None
All All All O,
8-13 Black All None
8-13 Black All None
8-13 Black All None
8-13 Black All None
6-13 All All None
PM„ Ostro etal. 1991 Denver, CO All All All None
2000 Seattle, WA 5-13 All All None
Yu et al.
Ostro et al.
Ostro et al.
Ostro et al.
Ostro et al.
2000 Seattle, WA 5-13 All All CO, SO,
1995
2001
2001
2001
Los Angeles,
CA
Los Angeles,
CA
Los Angeles,
CA
Los Angeles,
CA
7-12 Black All None
8-13 Black All None
8-13 Black All None
8-13 Black All None
Annual Avg 0.022431 0.015957 Logistic
Annual Avg 0.017709 0.006612 Logistic
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
24-hr avg
0.001436 0.000558 Logistic
0.000985 0.000747 Logistic
0.003177 0.001156 Logistic
0.005606 0.001639 Logistic
0.013126 0.003241 Logistic
0.007696 0.003786 Logistic
0.0006 0.0003
0.009531 0.003032 Logistic
Day with
symptoms
New onset of
symptoms
Day with
symptoms
New onset of
symptoms
Linear (log
of pollutant)
0.004879 0.005095 Logistic
0.008412 0.003631 Logistic
0.002565 0.001335 Logistic
0.003177 0.001550 Logistic
0.007708 0.002639 Logistic
Day with
symptoms
New onset of
symptoms
Day with
symptoms
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Endpoint Name
Pollutant
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time1
Beta
Std Error
Functional
Form
Notes
Asthma Exacerbation,
Shortness of Breath
PM10
Ostro et al.
2001
Los Angeles,
CA
8-13
Black
All
None
24-hr avg
0.010725
0.003850
Logistic
New onset of
symptoms
Asthma Exacerbation,
Wheeze
pm2,
Ostro et al.
2001
Los Angeles,
CA
8-13
Black
All
None
24-hr avg
0.001942
0.000803
Logistic
Day with
symptoms
Asthma Exacerbation,
Wheeze
pm2,
Ostro et al.
2001
Los Angeles,
CA
8-13
Black
All
None
24-hr avg
0.002565
0.001030
Logistic
New onset of
symptoms
Asthma Exacerbation,
Wheeze
PM10
Ostro et al.
2001
Los Angeles,
CA
8-13
Black
All
None
24-hr avg
0.002307
0.001733
Logistic
Day with
symptoms
Asthma Exacerbation,
Wheeze
PM10
Ostro et al.
2001
Los Angeles,
CA
8-13
Black
All
None
24-hr avg
0.006666
0.002957
Logistic
New onset of
symptoms
Chronic Phlegm
pm2,
McConnell et
al.
1999
Southern
California
9-15
All
All
None
Annual Avg
0.063701
0.025580
Logistic
Chronic Phlegm
PM10
McConnell et
al.
1999
Southern
California
9-15
All
All
None
Annual Avg
0.039049
0.011512
Logistic
Upper Respiratory
Symptoms
PM10
Pope et al.
1991
Utah Valley
9-11
All
All
None
24-hr avg
0.0036
0.0015
Logistic
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for more detail
on the specific averaging time used in the study.
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F .7 Asthma-Related Effects
F .7.1 Acute Bronchitis (McConnell et al., 1999)
McConnell et al. (1999) examined the relationship between air pollution and bronchitic
symptoms among asthmatic 4th, 7th, and 10th grade children in southern California.106 The authors
collected information on the prevalence of bronchitis, chronic cough, and chronic phlegm among
children with and without a history of asthma and/or wheeze. They used annual measurements of ozone,
PM10, PM25, N02, and acids in a logistic regression model with adjustments for personal covariates.
Neither bronchitis, cough, or phlegm were associated with any of the pollutants among children with no
history of wheeze or asthma or a history of wheeze without diagnosed asthma. Among asthmatics, PM10
was significantly associated with bronchitis and phlegm; PM2 5 was significantly associated with phlegm
and marginally associated with bronchitis; N02 and acids were both significantly associated with
phlegm; and ozone was not significantly associated with any of the endpoints.
Bronchitis was defined in the study by the question: "How many times in the past 12 months did
your child have bronchitis?" (McConnell et al., 1999, p. 757). It is unclear, however, if the cases of
bronchitis are acute and temporary, or if the bronchitis is a chronic condition. McConnell et al. found a
relationship between PM and chronic phlegm but none with chronic cough, each of which may be
indicators of chronic bronchitis. For this analysis, we assumed that the C-R function based on
McConnell et al. is measuring acute bronchitis. The PM C-R functions for bronchitis among asthmatics
are based on the results of the single pollutant model reported in Table 3.
pm25
Single Pollutant Model
The estimated logistic coefficient and standard error are based on the odds ratio (1.4) and 95%
confidence interval (0.9-2.3) associated with an increase in yearly mean 2-week average PM25 of 15
|ig/m3. (McConnell et al., 1999, Table 3)
Functional Form: Logistic
Coefficient: 0.022431
Standard Error: 0.015957
Incidence Rate: annual incidence rate of one or more episodes of bronchitis per asthmatic = 0.326
(McConnell et al., 1999, Table 2)
Population: population of asthmatics ages 9 to 15 = 5.67%107 of population ages 9 to 15
106 Assuming that a child enters kindergarten at age 5, 4th grade corresponds to age 9 and 10th grade corresponds to age 15.
We therefore applied the results of this study to children ages 9 to 15.
107 The American Lung Association (2002c, Table 7) estimates asthma prevalence for children ages 5 to 17 at 5.67%
(based on data from the 1999 National Health Interview Survey).
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PM10
Single Pollutant Model
The estimated logistic coefficient and standard error are based on the odds ratio (1.4) and 95%
confidence interval (1.1-1.8) associated with an increase in annual average PM10 of 19 |ig/nr\
(McConnell et al., 1999, Table 3)
Functional Form: Logistic
Coefficient: 0.017709
Standard Error: 0.006612
Incidence Rate: annual incidence rate of one or more episodes of bronchitis per asthmatic = 0.326
(McConnell et al., 1999, Table 2)
Population: population of asthmatics ages 9 to 15 = 5.67%108 of population ages 9 to 15
F .7.2 Asthma Attacks (Whittemore and Korn, 1980)
Whittemore and Korn (1980) examined the relationship between air pollution and asthma attacks
in a survey of 443 children and adults, living in six communities in southern California during three 34-
week periods in 1972-1975. The analysis focused on TSP and oxidants (Ox). Respirable PM, N02, S02
were highly correlated with TSP and excluded from the analysis. In a two pollutant model, daily levels
of both TSP and oxidants were significantly related to reported asthma attacks. The results from this
model were used, and the oxidant result was adjusted so it may be used with ozone data.
Multipollutant Model (PM10 and ozone)
The PM10 C-R function is based on the results of a co-pollutant model of TSP and ozone
(Whittemore and Korn, 1980, Table 5). Assuming that PM10 is 55 percent of TSP109 and that particulates
greater than ten micrometers are harmless, the coefficient is calculated by dividing the TSP coefficient
(0.00079) by 0.55. The standard error is calculated from the two-tailed p-value (<0.01) reported by
Whittemore and Korn (1980, Table 5), which implies a t-value of at least 2.576 (assuming a large
number of degrees of freedom).
Functional Form: Logistic
Coefficient: 0.001436
Standard Error: 0.000558
Incidence Rate: daily incidence of asthma attacks = 0.0550110
Population: population of asthmatics of all ages = 3.86% of the population of all ages (American Lung
Association, 2002c, Table 7)
108 The American Lung Association (2002c, Table 7) estimates asthma prevalence for children ages 5 to 17 at 5.67%
(based on data from the 1999 National Health Interview Survey).
109 The conversion of TSP to PM10 is from ESEERCO (1994, p. V-5), who cited studies by EPA (1986) and the California
Air Resources Board (1982).
110 Based on an analysis of the 1999 National Health Interview Survey, the daily incidence of wheezing attacks for adult
asthmatics is estimated to be 0.0550. In the same survey, wheezing attacks for children were examined, however, the number of
wheezing attacks per year were censored at 12 (compared to censoring at 95 for adults). Due to the potential for underestimation of
the number of children's wheezing attacks, we used the adult rate for all individuals.
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F .7.3 Asthma Exacerbation, Cough (Ostro et al., 2001)
Ostro et al. (2001) studied the relation between air pollution in Los Angeles and asthma
exacerbation in African-American children (8 to 13 years old) from August to November 1993. They
used air quality data for PM10, PM25, N02, and 03 in a logistic regression model with control for age,
income, time trends, and temperature-related weather effects.111 Asthma symptom endpoints were
defined in two ways: "probability of a day with symptoms" and "onset of symptom episodes". New
onset of a symptom episode was defined as a day with symptoms followed by a symptom-free day. The
authors found cough prevalence associated with PM10 and PM25 and cough incidence associated with
PM25 PM10, and N02. Ozone was not significantly associated with cough among asthmatics. The PM
C-R functions are based on the results of single pollutant models looking at both the probability of
symptoms and the onset of new symptoms.
PM2 5 Function(s)
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on an odds ratio of 1.03 (95% CI 0.98-1.07) for a 30
|ig/m3 increase in 12-hour average PM25 concentration (Ostro et al., 2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: 0.000985
Standard Error: 0.000747
Incidence Rate: daily cough rate per person (Ostro et al., 2001, p.202) = 0.145
Population: asthmatic African-American population ages 8 to 13 = 7.26%112 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on an odds ratio of 1.10 (95% CI 1.03-1.18) for a 30
|ig/m ' increase in 12-hour average PM2 5 concentration.
The C-R function based on this model will estimate the number of new onset episodes of cough
avoided. In order to convert this estimate to the total number of episodes avoided, the results are
adjusted by an estimate of the duration of symptom episodes. The average duration can be estimated
from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the probability of a
new onset episode. For cough, this ratio is 2.2 (14.5% divided by 6.7%) (Ostro et al., 2001, p.202).
In addition, not all children are at-risk for a new onset of cough, as defined by the study. On
average, 14.5% of African-American asthmatics have cough on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day are at-risk for a new onset episode (1-0.145 =
111 The authors note that there were 26 days in which PM2 5 concentrations were reported higher than PM10 concentrations.
The majority of results the authors reported were based on the full dataset. These results were used for the basis for the C-R
functions.
112 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5
to 17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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85.5%). As a result, a factor of 85.5% is used in the function to estimate the population of African-
American 8 to 13 year old children at-risk for a new cough episode.
Functional Form: Logistic
Coefficient: 0.003177
Standard Error: 0.001156
Incidence Rate: daily new onset cough (incidence) rate per person (Ostro et al., 2001, p.202) = 0.067
Population: asthmatic African-American population ages 8 to 13 at-risk for a new episode of cough =
6.21% of African-American population ages 8 to 13 multiplied (85. 5% at-risk113 times 7.26%
asthmatic114)
Adjustment Factor: average number of consecutive days with a cough episode (days) = 2.2
PM10 Function(s)
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on an odds ratio of 1.10 (95% CI 1.04-1.16) for a 17
|ig/m ' increase in daily average PM10 concentration (Ostro et al., 2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: 0.005606
Standard Error: 0.001639
Incidence Rate: daily cough rate per person (Ostro et al., 2001, p.202) = 0.145
Population: asthmatic African-American population ages 8 to 13 = 7.26%115 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on an odds ratio of 1.25 (95% CI 1.12-1.39) for a 17
l-ig/m3 increase in daily average PM10 concentration (Ostro et al., 2001, Table 5, p.204).
The C-R function based on this model will estimate the number of new onset episodes of cough
avoided. In order to convert this estimate to the total number of episodes avoided, the results are
adjusted by an estimate of the duration of symptom episodes. The average duration can be estimated
from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the probability of a
new onset episode. For cough, this ratio is 2.2 (14.5% divided by 6.7%) (Ostro et al., 2001, p.202).
In addition, not all children are at-risk for a new onset of cough, as defined by the study. On
average, 14.5% of African-American asthmatics have cough on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day are at-risk for a new onset episode (1-0.145 =
113 On average, 17.3% of African-American asthmatics have cough episodes on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day (1-0.145 = 85.5%) are at-risk for a new onset episode.
114 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5
to 17 at 7.26% (based on data from the 1999 National Health Interview Survey).
115 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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Appendix F. Particulate Matter C-R Functions
85.5%). As a result, a factor of 85.5% is used in the function to estimate the population of African-
American 8 to 13 year old children at-risk for a new cough episode.
Functional Form: Logistic
Coefficient: 0.013126
Standard Error: 0.003241
Incidence Rate: daily new onset cough (incidence) rate per person (Ostro et al., 2001, p.202) = 0.067
Population: asthmatic African-American population ages 8 to 13 at-risk for a new episode of cough =
6.21% of African-American population ages 8 to 13 multiplied (85. 5% at-risk116 times 7.26%
asthmatic117)
Adjustment Factor: average number of consecutive days with a cough episode (days) = 2.2
F .7.4 Asthma Exacerbation, Cough (Vedal et al., 1998)
Vedal et al. (1998) studied the relationship between air pollution and respiratory symptoms
among asthmatics and non-asthmatic children (ages 6 to 13) in Port Alberni, British Columbia, Canada.
Four groups of elementary school children were sampled from a prior cross-sectional study: (1) all
children with current asthma, (2) children without doctor diagnosed asthma who experienced a drop in
FEV after exercise, (3) children not in groups 1 or 2 who had evidence of airway obstruction, and (4) a
control group of children with matched by classroom. The authors used logistic regression and
generalized estimating equations to examine the association between daily PM10 levels and daily
increases in various respiratory symptoms among these groups. In the entire sample of children, PM10
was significantly associated with cough, phlegm, nose symptoms, and throat soreness. Among children
with diagnosed asthma, the authors report a significant association between PM10 and cough symptoms,
while no consistent effects were observed in the other groups. Since the study population has an over-
representation of asthmatics, due to the sampling strategy, the results from the full sample of children are
not generalizeable to the entire population. The C-R function presented below is based on results among
asthmatics only.
Single Pollutant Model
The PM10coefficient and standard error are based on an increase in odds of 8% (95% CI 0-16%)
reported in the abstract for a 10 |ig/m3 increase in daily average PM10.
Functional Form: Logistic
Coefficient: 0.007696
Standard Error: 0.003786
Incidence Rate: daily cough rate per person (Vedal et al., 1998, Table 1, p. 1038) = 0.086
Population: asthmatic population ages 6 to 13 = 5.67%118 of population ages 6 to 13
116 On average, 17.3% of African-American asthmatics have cough episodes on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day (1-0.145 = 85.5%) are at-risk for a new onset episode.
117 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5
to 17 at 7.26% (based on data from the 1999 National Health Interview Survey).
118 The American Lung Association (2002c, Table 7) estimates asthma prevalence for children 5-17 at 5.67% (based on
data from the 1999 National Health Interview Survey).
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F .7.5 Asthma Exacerbation, Moderate or Worse (Ostro et al., 1991)
Ostro et al. (1991) examined the effect of air pollution on asthmatics, ages 18 to 70, living in
Denver, Colorado from December 1987 to February 1988. The respondents in this study were asked to
record daily a subjective rating of their overall asthma status each day (0=none, l=mild, 2=moderate,
3=severe, 4=incapacitating). Ostro et al. then examined the relationship between moderate (or worse)
asthma and H+, sulfate, S02, PM25, estimated PM25, PM10, nitrate, and nitric acid. Daily levels of H+
were linked to cough, asthma, and shortness of breath. PM2 5 was linked to asthma. Sulfate was linked
to shortness of breath. No effects seen for other pollutants. The C-R function is based on a single-
pollutant linear regression model where the log of the pollutant is used.
Single Pollutant Model
Two PM2 5 coefficients are presented, both equal 0.0006, however only one is significant. The
coefficient based on data that does not include estimates of missing PM2 5 values is not significant (std
error = 0.0053); the coefficient that includes estimates of missing PM2 5 values (estimated using a
function of sulfate and nitrate) is significant at p < 0.5 (std error = 0.0003). The latter coefficient is used
here. The C-R function to estimate the change in the number of days with moderate (or worse) asthma is
as follows:
A Days Moderate/Worse Asthma-- /?ln
^ PM ^
1 1V1 2.5, after
pm2
.5, before J
¦pop,
Functional Form: Linear (using log of the pollutant)
Coefficient: 0.0006
Standard Error: 0.0003
Population: population of asthmatics of all ages119 = 3.86% of the population of all ages (American
Lung Association, 2002c, Table 7)
F .7.6 Asthma Exacerbation, One or More Symptoms (Yu et al., 2000)
Yu et al. (2000) examined the association between air pollution and asthmatic symptoms among
mild to moderate asthmatic children ages 5-13 in Seattle. They collected air quality data for CO, S02,
PM10, and PMj 0and asked study subjects to record symptoms daily. They used logistic regression
models with generalized estimating equations in two different approaches. A "marginal approach" was
used to estimate the impact of air pollution on asthma symptoms and a "transition approach" was used to
estimate the association conditioned on the previous day's outcome. The primary endpoint, odds of at
least one asthma symptom, was significantly associated with CO, PM10, and PMj 0 in single pollutant
models. In multipollutant models, CO remained significant while PM effects declined slightly. The
magnitude of the effects were similar between the "marginal" and "transition" approaches. The C-R
function is based on the results of the "transition approach," where the previous day's symptoms is an
explanatory variable.
119 The C-R function is applied to asthmatics of all ages, although the study population consists of asthmatics between the
ages of 18 and 70. It seems reasonable to assume that individuals over the age of 70 are at least as susceptible as individuals in the
study population. It also seems reasonable to assume that individuals under the age of 18 are also susceptible. For example,
controlling for oxidant levels, Whittemore and Korn (1980) found TSP significantly related to asthma attacks in a study population
comprised primarily (59 percent) of individuals less than 16 years of age.
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Single Pollutant Model
The single pollutant PM10 coefficient and standard error are based on the odds ratio (1.10) and
95% confidence interval (1.03-1.16) for a 10 |ig/m3 increase in one-day lagged daily average PM10 (Yu
etal., 2000, Table 4, p. 1212).
Functional Form: Logistic
Coefficient: 0.009531
Standard Error: 0.003032
Incidence Rate: daily rate of at least one asthma episode per person (Yu et al.,
0.60
Population: asthmatic population ages 5 to 13 = 5.67%120 of population ages 5
Multipollutant Model (PM10, CO, S02)
The C-R function is based on the results of the "transition approach," where the previous day's
symptoms is an explanatory variable. The multipollutant PM10 coefficient and standard error are based
on the odds ratio (1.05) and 95% confidence interval (0.95-1.16) for a 10 |ig/m3 increase in one-day
lagged daily average PM10 (Yu et al., 2000, Table 4, p. 1212).
Functional Form: Logistic
Coefficient: 0.004879
Standard Error: 0.005095
Incidence Rate: daily rate of at least one asthma episode per person (Yu et al., 2000, Table 2, p. 1212) =
0.60
Population: asthmatic population ages 5 to 13 = 5.67%121 of population ages 5 to 13
2000, Table 2, p. 1212) =
to 13
F .7.7 Asthma Exacerbation, Shortness of Breath (Ostro et al., 1995)
Using a logistic regression estimation, Ostro et al. (1995) estimated the impact of PM10, ozone,
N02, and S02 on the incidence of coughing, shortness of breath, and wheezing in 83 African-American
asthmatic children ages 7-12 living in Los Angeles from August through September 1992. Regression
results show both PM10 and ozone significantly linked to shortness of breath; the beginning of an asthma
episode was also significantly linked to ozone. No effect was seen for N02 and S02. Results for single-
pollutant models only were presented in the published paper. The C-R function is based on the model
with adjustment for respiratory infection, temperature, and outdoor mold levels.
Single Pollutant Model
The PM10 coefficient and standard error are based on the odds ratio (1.60) and 95% confidence
interval (1.07-2.37) (Ostro et al., 1995, Table 3) associated with a change in daily mean PM10 of 55.87
/ig/m3 (Ostro et al., 1995, Table 2).
120 The American Lung Association (2002c, Table 7) estimates asthma prevalence for children 5 to 17 at 5.67% (based on
data from the 1999 National Health Interview Survey).
121 The American Lung Association (2002c, Table 7) estimates asthma prevalence for children 5 to 17 at 5.67% (based on
data from the 1999 National Health Interview Survey).
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Functional Form: Logistic
Coefficient: 0.008412
Standard Error: 0.003631
Incidence Rate: daily shortness of breath incidence rate per person (Ostro et al., 1995, p. 715) = 0.056
Population: asthmatic African-American population ages 7 to 12 = 7.26%122 of African-American
population ages 7 to 12
F .7.8 Asthma Exacerbation, Shortness of Breath (Ostro et al., 2001)
Ostro et al. (2001) studied the relationship between air pollution in Los Angeles and asthma
exacerbation in African-American children (8 to 13 years old) from August to November 1993. They
used air quality data for PM10, PM25, N02, and ozone in a logistic regression model with control for age,
income, time trends, and temperature-related weather effects. Asthma symptom endpoints were defined
in two ways: "probability of a day with symptoms" and "new onset of a symptom episode". New onset
of a symptom episode was defined as a day with symptoms followed by a symptom-free day. The
authors found that both the prevalent and incident episodes of shortness of breath were associated with
PM2 5 and PM10. Neither ozone nor N02 were significantly associated with shortness of breath among
asthmatics. The PM C-R functions are based on the results of single pollutant models looking at both
the probability of symptoms and the onset of new symptoms.
PM2 5 Function(s)
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on an odds ratio of 1.08 (95% CI 1.00-1.17) for a 30
l-ig/m3 increase in 12-hour average PM25 concentration (Ostro et al., 2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: 0.002565
Standard Error: 0.001335
Incidence Rate: daily shortness of breath rate per person (Ostro et al., 2001, p.202) = 0.074
Population: asthmatic African-American population ages 8 to 13 = 7.26%123 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on an odds ratio of 1.10 (95% CI 1.00-1.20) for a 30
|ig/m ' increase in 12-hour average PM25 concentration (Ostro et al., 2001, Table 5, p.204).
The C-R function based on this model will estimate the number of new onset episodes of
shortness of breath avoided. In order to convert this estimate to the total number of episodes avoided,
the results are adjusted by an estimate of the duration of symptom episodes. The average duration can be
estimated from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the
probability of a new onset episode. For shortness of breath, this ratio is 2.0 (7.4% divided by 3.7%)
(Ostro et al., 2001, p.202).
122 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
123 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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In addition, not all children are at-risk for a new onset of shortness of breath, as defined by the
study. On average, 7.4% of African-American asthmatics have shortness of breath episodes on a given
day (Ostro et al., 2001, p.202). Only those who are symptom-free on the previous day are at-risk for a
new onset episode (1-0.074 = 92.6%). As a result, a factor of 92.6% is used in the function to estimate
the population of African-American 8 to 13 year old children at-risk for a new shortness of breath
episode.
Functional Form: Logistic
Coefficient: 0.003177
Standard Error: 0.001550
Incidence Rate: daily new onset shortness of breath (incidence) rate per person (Ostro et al., 2001,
p.202) = 0.037
Population: asthmatic African-American population ages 8 to 13 at-risk for anew episode of shortness
of breath = 6.72% of African-American population ages 8 to 13 multiplied (92. 6% at-risk124 times 7.26%
asthmatic125)
Adjustment Factor: average number of consecutive days with a shortness of breath episode (days) =
2.0
PM10 Function(s)
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on an odds ratio of 1.14 (95% CI 1.04-1.24) for a 17
|ig/m3 increase in daily average PM10 concentration (Ostro et al., 2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: 0.007708
Standard Error: 0.002639
Incidence Rate: daily shortness of breath rate per person (Ostro et al., 2001, p.202) = 0.074
Population: asthmatic African-American population ages 8 to 13 = 7.26%126 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on an odds ratio of 1.20 (95% CI 1.06-1.37) for a 17
|ig/m3 increase in daily average PM10 concentration (Ostro et al., 2001, Table 5, p.204).
The C-R function based on this model will estimate the number of new onset episodes of
shortness of breath avoided. In order to convert this estimate to the total number of episodes avoided,
the results are adjusted by an estimate of the duration of symptom episodes. The average duration can be
estimated from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the
124 On average, 7.4% of African-American asthmatics have shortness of breath episodes on a given day (Ostro et al., 2001,
p.202). Only those who are symptom-free on the previous day (1-0.074 = 92.6%) are at-risk for a new onset episode.
125 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
126 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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probability of a new onset episode. For shortness of breath, this ratio is 2.0 (7.4% divided by 3.7%)
(Ostro et al., 2001, p.202).
In addition, not all children are at-risk for a new onset of shortness of breath, as defined by the
study. On average, 7.4% of African-American asthmatics have shortness of breath episodes on a given
day (Ostro et al., 2001, p.202). Only those who are symptom-free on the previous day are at-risk for a
new onset episode (1-0.074 = 92.6%). As a result, a factor of 92.6% is used in the function to estimate
the population of African-American 8 to 13 year old children at-risk for a new shortness of breath
episode.
Functional Form: Logistic
Coefficient: 0.010725
Standard Error: 0.003850
Incidence Rate: daily new onset shortness of breath (incidence) rate per person (Ostro et al., 2001,
p.202) = 0.037
Population: asthmatic African-American population ages 8 to 13 at-risk for anew episode of shortness
of breath = 6.72% of African-American population ages 8 to 13 multiplied (92. 6% at-risk127 times 7.26%
asthmatic128)
Adjustment Factor: average number of consecutive days with a shortness of breath episode (days) =
2.0
F .7.9 Asthma Exacerbation, Wheeze (Ostro et al., 2001)
Ostro et al. (2001) studied the relation between air pollution in Los Angeles and asthma
exacerbation in African-American children (8 to 13 years old) from August to November 1993. They
used air quality data for PM10, PM2 5, N02, and 03 in a logistic regression model with control for age,
income, time trends, and temperature-related weather effects. Asthma symptom endpoints were defined
in two ways: "probability of a day with symptoms" and "onset of symptom episodes". New onset of a
symptom episode was defined as a day with symptoms followed by a symptom-free day. The authors
found both the prevalence and incidence of wheeze associated with PM2 5 PM10, and N02. Ozone was
not significantly associated with wheeze among asthmatics. The PM C-R functions are based on the
results of single pollutant models looking at both the probability of symptoms and the onset of new
symptoms.
PM2 5 Function(s)
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on an odds ratio of 1.06 (95% CI 1.01-1.11) for a 30
l-ig/m3 increase in 12-hour average PM25 concentration (Ostro et al., 2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: 0.001942
Standard Error: 0.000803
127 On average, 7.4% of African-American asthmatics have shortness of breath episodes on a given day (Ostro et al., 2001,
p.202). Only those who are symptom-free on the previous day (1-0.074 = 92.6%) are at-risk for a new onset episode.
128 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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Incidence Rate: daily wheeze rate per person (Ostro et al., 2001, p.202) = 0.173
Population: asthmatic African-American population ages 8 to 13 = 7.26%129 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on an odds ratio of 1.08 (95% CI 1.01-1.14) for a 30
|ig/m3 increase in 12-hour average PM25 concentration (Ostro et al., 2001, Table 5, p.204).
The C-R function based on this model will estimate the number of new onset episodes of wheeze
avoided. In order to convert this estimate to the total number of episodes avoided, the results are
adjusted by an estimate of the duration of symptom episodes. The average duration can be estimated
from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the probability of a
new onset episode. For wheeze, this ratio is 2.3 (17.3% divided by 7.6%) (Ostro et al., 2001, p.202).
In addition, not all children are at-risk for a new onset of wheeze, as defined by the study. On
average, 17.3% of African-American asthmatics have wheeze on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day are at-risk for a new onset episode (1-0.173 =
82.7%). As a result, a factor of 82.7% is used in the function to estimate the population of African-
American 8 to 13 year old children at-risk for a new wheeze episode.
Functional Form: Logistic
Coefficient: 0.002565
Standard Error: 0.001030
Incidence Rate: daily new onset wheeze (incidence) rate per person (Ostro et al., 2001, p.202) = 0.076
Population: asthmatic African-American population ages 8 to 13 at-risk for a new episode of wheeze =
6.00% of African-American population ages 8 to 13 multiplied (82. 7% at-risk130 times 7.26%
asthmatic131)
Adjustment Factor: average number of consecutive days with a wheeze episode (days) = 2.3
PM10 Function(s)
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on an odds ratio of 1.04 (95% CI 0.98-1.10) for a 17
|ig/m3 increase in daily average PM10 concentration (Ostro et al., 2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: 0.002307
Standard Error: 0.001733
Incidence Rate: daily wheeze rate per person (Ostro et al., 2001, p.202) = 0.173
129 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5
to 17 at 7.26% (based on data from the 1999 National Health Interview Survey).
130 On average, 17.3% of African-American asthmatics have wheeze episodes on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day (1-0.173 = 82.7%) are at-risk for a new onset episode.
131 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5
to 17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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Population: asthmatic African-American population ages 8 to 13 = 7.26%132 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on an odds ratio of 1.12 (95% CI 1.01-1.23) for a 17
|ig/m3 increase in daily average PM10 concentration (Ostro et al., 2001, Table 5, p.204).
The C-R function based on this model will estimate the number of new onset episodes of wheeze
avoided. In order to convert this estimate to the total number of episodes avoided, the results are
adjusted by an estimate of the duration of symptom episodes. The average duration can be estimated
from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the probability of a
new onset episode. For wheeze, this ratio is 2.3 (17.3% divided by 7.6%) (Ostro et al., 2001, p.202).
In addition, not all children are at-risk for a new onset of wheeze, as defined by the study. On
average, 17.3% of African-American asthmatics have wheeze on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day are at-risk for a new onset episode (1-0.173 =
82.7%). As a result, a factor of 82.7% is used in the function to estimate the population of African-
American 8 to 13 year old children at-risk for a new wheeze episode.
Functional Form: Logistic
Coefficient: 0.006666
Standard Error: 0.002957
Incidence Rate: daily new onset wheeze (incidence) rate per person (Ostro et al., 2001, p.202) = 0.076
Population: asthmatic African-American population ages 8 to 13 at-risk for a new episode of wheeze =
6.00% of African-American population ages 8 to 13 multiplied (82. 7% at-risk133 times 7.26%
asthmatic134)
Adjustment Factor: average number of consecutive days with a wheeze episode (days) = 2.3
F .7.10 Chronic Phlegm (McConnell et al., 1999)
McConnell et al. (1999) examined the relationship between air pollution and bronchitic
symptoms among asthmatic 4th, 7th, and 10th grade children in southern California.135 The authors
collected information on the prevalence of bronchitis, chronic cough, and chronic phlegm among
children with and without a history of asthma and/or wheeze. They used annual measurements of ozone,
PM10, PM25, N02, and acids in a logistic regression model with adjustments for personal covariates.
Neither bronchitis, cough, or phlegm were associated with any of the pollutants among children with no
history of wheeze or asthma or a history of wheeze without diagnosed asthma. Among asthmatics, PM10
was significantly associated with bronchitis and phlegm; PM2 5 was significantly associated with phlegm
132 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5
to 17 at 7.26% (based on data from the 1999 National Health Interview Survey).
133 On average, 17.3% of African-American asthmatics have wheeze episodes on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day (1-0.173 = 82.7%) are at-risk for a new onset episode.
134 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
135 Assuming that a child enters kindergarten at age 5,4th grade corresponds to age 9 and 10th grade corresponds to age 15.
We therefore applied the results of this study to children ages 9 to 15.
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and marginally associated with bronchitis; N02 and acids were both significantly associated with
phlegm; and ozone was not significantly associated with any of the endpoints.
Phlegm was defined in the study by the question: "Other than with colds, does this child usually
seem congested in the chest or bring up phlegm?" (McConnell et al., 1999, p. 757). The authors refer to
this definition as "chronic phlegm" and we also assume that the term "usually" refers to chronic, rather
than acute, phlegm. The PM C-R functions for chronic phlegm among asthmatics are based on the
results of the single pollutant model reported in Table 3.
pm25
Single Pollutant Model
The estimated logistic coefficient and standard error are based on the odds ratio (2.6) and 95%
confidence interval (1.2-5.4) associated with an increase in yearly mean 2-week average PM2 5 of 15
|ig/m\ (McConnell et al., 1999, Table 3)
Functional Form: Logistic
Coefficient: 0.063701
Standard Error: 0.025580
Incidence Rate: annual incidence rate of phlegm per asthmatic = 0.257 (McConnell et al., 1999, Table
2)
Population: population of asthmatics ages 9 to 15 = 5.67%136 of population ages 9 to 15
PM10
Single Pollutant Model
The estimated logistic coefficient and standard error are based on the odds ratio (2.1) and 95%
confidence interval (1.4-3.3) associated with an increase in annual average PM10 of 19 |ig/m\
(McConnell et al., 1999, Table 3)
Functional Form: Logistic
Coefficient: 0.039049
Standard Error: 0.011512
Incidence Rate: annual incidence rate of phlegm per asthmatic = 0.257 (McConnell et al., 1999, Table
2)
Population: population of asthmatics ages 9 to 15 = 5.67%137 of population ages 9 to 15
F .7.11 Upper Respiratory Symptoms (Pope et al., 1991)
Using logistic regression, Pope et al. (1991) estimated the impact of PM10 on the incidence of a
variety of minor symptoms in 55 subjects (34 "school-based" and 21 "patient-based") living in the Utah
136 The American Lung Association (2002c, Table 7) estimates asthma prevalence for children ages 5 to 17 at 5.67%
(based on data from the 1999 National Health Interview Survey).
137 The American Lung Association (2002c, Table 7) estimates asthma prevalence for children ages 5 to 17 at 5.67%
(based on data from the 1999 National Health Interview Survey).
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Valley from December 1989 through March 1990. The children in the Pope et al. study were asked to
record respiratory symptoms in a daily diary. With this information, the daily occurrences of upper
respiratory symptoms (URS) and lower respiratory symptoms (LRS) were related to daily PM10
concentrations. Pope et al. describe URS as consisting of one or more of the following symptoms:
runny or stuffy nose; wet cough; and burning, aching, or red eyes. Levels of ozone, N02, and S02 were
reported low during this period, and were not included in the analysis. The sample in this study is
relatively small and is most representative of the asthmatic population, rather than the general
population. The school-based subjects (ranging in age from 9 to 11) were chosen based on "a positive
response to one or more of three questions: ever wheezed without a cold, wheezed for 3 days or more out
of the week for a month or longer, and/or had a doctor say the 'child has asthma' (Pope et al., 1991, p.
669)." The patient-based subjects (ranging in age from 8 to 72) were receiving treatment for asthma and
were referred by local physicians. Regression results for the school-based sample (Pope et al., 1991,
Table 5) show PM10 significantly associated with both upper and lower respiratory symptoms. The
patient-based sample did not find a significant PM10 effect. The results from the school-based sample
are used here.
Single Pollutant Model
The coefficient and standard error for a one ng/m3 change in PM10 is reported in Table 5.
Functional Form: Logistic
Coefficient: 0.0036
Standard Error: 0.0015
Incidence Rate: daily upper respiratory symptom incidence rate per person = 0.3419 (Pope et al., 1991,
Table 2)
Population: asthmatic population ages 9 to 11 = 5.67%138 of population ages 9 to 11
138 The American Lung Association (2002c, Table 7) estimates asthma prevalence for children ages 5 to 17 at 5.67%
(based on data from the 1999 National Health Interview Survey).
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Exhibit F-8. Concentration-Response (C-R) Functions for Particulate Matter and Welfare Effects
Endpoint Name
Pollutant
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time
Beta
Std Error
Functional
Form
Household
Soiling Damage
PM10
ESEERCO
1994
nationwide
All
All
All
None
Annual avg -
-
--
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F-109
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Appendix F. Particulate Matter C-R Functions
F .8 Welfare Effects
F .8.1 Household Soiling Damage (ESEERCO, 1994)
Particulate matter air pollution has been shown to result in dirtier clothes, which in turn results
in higher annual cleaning costs for consumers. One benefit of reduced particulate matter, then, is the
consequent reduction in cleaning costs for consumers. Several studies have provided estimates of the
cost to households of PM soiling. The study that is cited by ESEERCO (1994) as one of the most
sophisticated and is relied upon by EPA in its 1988 Regulatory Impact Analysis for S02 is Manuel et al.
(1982). Using a household production function approach and household expenditure data from the
1972-73 Bureau of Labor Statistics Consumer Expenditure Survey for over twenty cities in the United
States, Manuel et al. estimated the annual cost of cleaning per |ig/m3 PM per household as $ 1.55 ($0.59
per person times 2.63 persons per household). This estimate is low compared with others (e.g., estimates
provided by Cummings et al. (1985) and Watson and Jaksch (1982) are about eight times and five times
greater, respectively). The ESEERCO report notes, however, that the Manuel estimate is probably
downward biased because it does not include the time cost of do-it-yourselfers. Estimating that these
costs may comprise at least half the cost of PM-related cleaning costs, they double the Manuel estimate
to obtain a point estimate of $3.10 (reported by ESEERCO in 1992 dollars as $2.70).
The Manuel et al. (1982) study measured particulate matter as TSP rather than PM10 or PM2 5. If
a one |ig/m3 increase in TSP causes $1.55 worth of cleaning expenses per household, the same unit
dollar value can be used for PM10 (or PM2 5) only if particle size doesn't matter ~ i.e., only if particles of
all sizes are equally soiling. Suppose, for example, that PM10 is 75% of TSP and that all particles are
equally soiling. Then 75% of the damage caused by a one |ig/m3 increase in TSP is due to PM10. This is
(0.75)($1.55) = $1.16. However, this corresponds to a 0.75 |ig/m3 increase in PM10. A one |ig/m3
increase in PM10 would therefore yield a dollar soiling damage of $1.16/0.75 = $1.55.
Suppose, however, that only PM10 matters. Then the $1.55 underestimates the impact of a one
|ig/m3 increase in PM10, because it corresponds to a less than one |ig/m3 increase in PM10 (e.g., a 0.75
|ig/m3 increase in PM10). In this case, the correct unit value per unit of PM10 would be ($1.55)/0.75 =
$2.07. If only PM10 matters, then either (1) the dollar value can be adjusted by dividing it by the
percentage of TSP that is PM10 and PM10 can be used in the soiling damage function, or (2) the dollar
value can be left unadjusted and TSP, rather than PM10, can be used in the soiling damage function.
Finally, it is possible that, while both PM10 and PM25 are components of TSP that cause
consumer cleaning costs, the remaining portion of TSP has a greater soiling capability than either the
PM10 or PM2 5 component. In this case, using either PM10 or PM2 5 air quality data with a household
soiling function based on TSP would yield overestimates of the PM10- or PM2 5-related consumer
cleaning costs avoided by reductions in concentration of these pollutants.
There is, however, insufficient information on the relative soiling capabilities of the different
components of TSP. We have assumed that all components of TSP have an equivalent soiling capacity.
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Appendix G: Ozone Concentration-Response Functions
In this Appendix, we present the concentration-response (C-R) functions used to estimate ozone-
related adverse health effects. Each sub-section has an Exhibit with a brief description of the C-R
function and the underlying parameters. Following each Exhibit, we present a brief summary of each of
the studies and any items that are unique to the study.
Note that the main text describes the methods that we used to choose these C-R functions from
the wide range available in the literature. In addition, Appendix D mathematically derives the standard
types of C-R functions that we encountered in the epidemiological literature, such as, log-linear, logistic
and linear, so we simply note here the type of functional form. Finally, Appendix E presents a detailed
description of the sources for the incidence and prevalence data used in these C-R functions.
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Appendix G. Ozone C-R Functions
Exhibit G-l. Concentration-Response (C-R) Functions for Ozone and Short-Term Mortality
Endpoint Name
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time1
Functional
Form
Beta
Std Error
Notes
Non-Accidental
Fairley
2003
Santa Clara County
All
All
All
None
8-hr max
Log-linear
0.001558
0.000871
Reanalysis of
Fairley, 1999
Non-Accidental
Fairley
2003
Santa Clara County
All
All
All
pm2,
8-hr max
Log-linear
0.002828
0.002668
Reanalysis of
Fairley, 1999
Non-Accidental
Ito and Thurston
1996
Chicago, IL
All
All
All
None
1-hr max
Log-linear
0.000953
0.000208
Non-Accidental
Ito and Thurston
1996
Chicago, IL
All
All
All
PM10
1-hr max
Log-linear
0.000634
0.000251
Non-Accidental
Kinney et al.
1995
Los Angeles, CA
All
All
All
None
1-hr max
Log-linear
0.000138
0.000087
Non-Accidental
Kinney et al.
1995
Los Angeles, CA
All
All
All
PM10
1-hr max
Log-linear
0
0.000214
Non-Accidental
Moolgavkar et al.
1995
Philadelphia, PA
All
All
All
S02, TSP
24-hr avg
Log-linear
0.000611
0.000216
Non-Accidental
Samet et al.
1997
Philadelphia, PA
All
All
All
None
24-hr avg
Log-linear
0.001115
0.000372
Non-Accidental
Samet et al.
1997
Philadelphia, PA
All
All
All
CO, no2,
S02, TSP
24-hr avg
Log-linear
0.000936
0.000312
Non-Accidental
WHO Working
Group
2003
Europe
All
All
All
2
1-hr max
Log-linear
0.000784
0.000250
Non-Accidental
WHO Working
Group
2003
Europe
All
All
All
2
8-hr avg
Log-linear
0.001174
0.000299
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for more
detail on the specific averaging time used in the study.
2. The WHO Working Group meta-study is unclear as to whether some of the studies used in the meta-study included other pollutants in their ozone models.
Abt Associates Inc.
G-2
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Appendix G. Ozone C-R Functions
G .1 Short-term Mortality
Exhibit G-1 summarizes the C-R functions used to estimate the relationship between ozone and
short-term mortality. Detailed summaries of each of the studies used to generate the functions are
described below, along with the parameters used in each of the functions.
G .1.1 Short-Term Mortality, Non-Accidental (Fairley, 2003)
Using data from 1989-1996 in Santa Clara County, California, Fairley et al. (1999) examined the
relationship between daily non-accidental mortality and fluctuations in a variety of pollutants, including
PM25, coarse PM10 (i.e., PM25_10), nitrate (N03), S04, coefficient of haze (COH), ozone, CO, andN02.
They reported that PM25 and N03 were significant in single-pollutant models, as well as two-pollutant
models. PM25 was only insignificant when paired with PM10 and N03 and N03 was only insignificant
when paired with PM25. The other pollutants were insignificant when paired with either PM2 5 or N03.
The analysis by Fairly et al. (1999) relied on a generalized additive model based on the Splus
software. Because of potential bias from using Splus, Fairley (2003) conducted a reanalysis, and
reported that the conclusions of the original study were unchanged. Both PM2 5 and N03 appear
significantly related to non-accidental mortality.
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the relative risk
(1.031) and 95% confidence interval (0.997-1.066) reported for a 19.6 ppb increase in daily 8-hour
maximum ozone concentration in the 0-day lag GAM stringent ('New GAM') model (Fairley, 2003,
Table la).
Functional Form: Log-linear
Coefficient: 0.001558
Standard Error: 0.000871
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
Multipollutant Model (ozone and PM2 5)
In a co-pollutant model with PM2 5, the coefficient and standard error are based on the relative
risk (1.057) and 95% confidence interval (0.954-1.171) reported for a 19.6 ppb increase in daily 8-hour
maximum ozone concentration in the 0-day lag GAM stringent ('New GAM') model (Fairley, 2003,
Table lb).
Functional Form: Log-linear
Coefficient: 0.002828
Standard Error: 0.002668
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
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G-3
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Appendix G. Ozone C-R Functions
G .1.2 Short-Term Mortality, Non-Accidental (Ito and Thurston, 1996, Chicago)
Ito and Thurston (1996) examined the relationship between daily non-accidental mortality and
air pollution levels in Cook County, Illinois from 1985 to 1990. They examined daily levels of ozone,
PM10, S02, and CO, and found a significant relationship for ozone and PM10 with both pollutants in the
model; no significant effects were found for S02 and CO. In single pollutant models the effects were
slightly larger. The C-R functions for ozone are based on results from both the single and co-pollutant
models.
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the relative risk
(1.10) and 95% confidence interval (1.06-1.15) reported for a 100 ppb increase in daily one-hour
maximum ozone concentration (Ito and Thurston, 1996, p. 87).
Functional Form: Log-linear
Coefficient: 0.000953
Standard Error: 0.000208
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
Multipollutant Model (ozone and PM10)
In a co-pollutant model with PM10, the coefficient (0.000634) and standard error (0.000251)
were obtained directly from the author because the published paper reported incorrect information.
Functional Form: Log-linear
Coefficient: 0.000634
Standard Error: 0.000251
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
G .1.3 Short-Term Mortality, Non-Accidental (Kinney et al., 1995, Los Angeles)
Kinney et al. (1995) examined the relationship between daily non-accidental mortality and air
pollution levels in Los Angeles, California from 1985 to 1990. They examined ozone, PM10, and CO,
and found a significant relationship for each pollutant in single pollutant models. The effect for ozone
dropped to zero with the inclusion of PM10 in the model, while the effect for CO and PM10 appeared co-
pollutant ozone models.
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the relative risk
(1.02) and 95% confidence interval (1.00-1.05) reported for a 143 ppb increase in daily one-hour
maximum ozone levels (Kinney et al., 1995, Table 2, p. 64).
Functional Form: Log-linear
Coefficient: 0.000138
Standard Error: 0.000087
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
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Appendix G. Ozone C-R Functions
Population: population of all ages
Multipollutant Model (ozone and PM10)
In a model with PM10, the coefficient and standard error are based on the relative risk (1.00) and
95% confidence interval (0.94-1.06) reported for a 143 ppb increase in daily one-hour maximum ozone
concentration (Kinney et al., 1995, Table 2, p. 64).
Functional Form: Log-linear
Coefficient: 0
Standard Error: 0.000214
Incidence: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
G .1.4 Short-Term Mortality, Non-Accidental (Moolgavkar et al., 1995, Philadelphia)
Moolgavkar et al. (1995) examined the relationship between daily non-accidental mortality and
air pollution levels in Philadelphia, Pennsylvania from 1973 to 1988. They examined ozone, TSP, and
S02 in a three-pollutant model, and found a significant relationship for ozone and S02; TSP was not
significant. In season-specific models, ozone was significantly associated with mortality only in the
summer months. The C-R function for ozone is based on the full-year three-pollutant model reported in
Table 5 (Moolgavkar et al., 1995, p. 482).
Multipollutant Model (ozone, S02, TSP)
The coefficient and standard error are based on the relative risk (1.063) and 95% confidence
interval (1.018-1.108) associated with a 100 ppb increase in daily average ozone (Moolgavkar et al.,
1995, p. 482, Table 5).
Functional Form: Log-linear
Coefficient: 0.000611
Standard Error: 0.000216
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
G .1.5 Short-Term Mortality, Non-Accidental (Samet et al., 1997, Philadelphia)
Samet et al. (1997) examined the relationship between daily non-accidental mortality and air
pollution levels in Philadelphia, Pennsylvania from 1974 to 1988. They examined ozone, TSP, S02,
N02, and CO in a Poisson regression model. In single pollutant models, ozone, S02, TSP, and CO were
significantly associated with mortality. In a five-pollutant model, they found a positive statistically
significant relationship for each pollutant except N02. The C-R functions for ozone are based on the
single pollutant and five-pollutant model (ozone, CO, N02, S02, and TSP) reported in Table 9 (Samet et
al., 1997, p. 20).
Abt Associates Inc.
G-5
November 2003
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Appendix G. Ozone C-R Functions
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(2.28) and t-statistic (3) associated with a 20.219 ppb increase in two-day average ozone (Samet et al.,
1997, p. 20, Table 9).
Functional Form: Log-linear
Coefficient: 0.001115
Standard Error: 0.000372
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
Multipollutant Model (ozone, CO, N02, S02, and TSP)
In a model with CO, N02, S02, and TSP, the ozone coefficient and standard error are based on
the percent increase (1.91) and t-statistic (3) associated with a 20.219 ppb increase in two-day average
ozone (Samet et al., 1997, p. 20, Table 9).
Functional Form: Log-linear
Coefficient: 0.000936
Standard Error: 0.000312
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages
G .1.6 Short-Term Mortality, Non-Accidental (World Health Organization (WHO)
Working Group, 2003, Europe)
The World Health Organization (WHO 2003, p. 44) conducted a meta-analysis of time-series
studies conducted between 1996 and 2001. The results of the analysis are preliminary, so we have
presented it as an alternative estimate of the relationship between ozone and premature mortality. We
consider two sets of results: one based on the 1-hour maximum and the other based on the 8-hour
average.
1-Hour Maximum Model
In a model with the daily 1-hour maximum the relative risk is 1.004 associated with a 10 ug/m3
change in ozone, with a 5th and 95th estimate of 1.001 and 1.006 (WHO 2003, p. 44). In calculating the
coefficient and standard error for the C-R function, we assume a conversion of 1.963 ug/m3 per ppb.
This is the standard conversion at 25° C and one atmosphere. We have used this function with a
population of all ages, as well as just the population ages 65 and up.
Functional Form: Log-linear
Coefficient: 0.000784
Standard Error: 0.000250
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages & ages 65+
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G-6
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Appendix G. Ozone C-R Functions
8-Hour Average Model
In a model with the daily 8-hour average the relative risk is 1.006 associated with a 10 ug/m3
change in ozone, with a 5th and 95th estimate of 1.003 and 1.009 (WHO 2003, p. 44). The paper is not
completely clear on how the 8-hour average should be calculated, so we have assumed the average
between the hours of 9:00 am and 4:59 pm. In calculating the coefficient and standard error for the C-R
function, we assume a conversion of 1.963 ug/m3 per ppb. This is the standard conversion at 25° C and
one atmosphere. We have used this function with a population of all ages, as well as just the population
ages 65 and up.
Functional Form: Log-linear
Coefficient: 0.001174
Standard Error: 0.000299
Incidence Rate: county-level daily non-accidental mortality rate (ICD codes <800) per person
Population: population of all ages & ages 65+
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Appendix G. Ozone C-R Functions
Exhibit G-2. Concentration-Response (C-R) Functions for Ozone and Chronic Illness
Endpoint Name
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time1
Functional
Form
Beta
Std Error
Chronic Asthma
McDonnell et al.
1999
SF, SD, South
Coast Air Basin
27+
All
Male
None
annual avg 8-
hr avg
Logistic
0.0277
0.0135
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for
more detail on the specific averaging time used in the study.
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G-8
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Appendix G. Ozone C-R Functions
G .2 Chronic Illness
Exhibit G-2 summarizes the C-R function ((McDonnell et al., 1999)) used to estimate the
relationship between ozone and chronic asthma. A more detailed summary of McDonnell et al. (1999),
and the parameters used in the function, is described below.
G .2.1 Chronic Asthma (McDonnell et al., 1999)
McDonnell et al. (1999) used the same cohort of Seventh-Day Adventists as Abbey et al.
(1995b), and examined the association between air pollution and the onset of asthma in adults between
1977 and 1992. Males who did not report doctor-diagnosed asthma in 1977, but reported it in 1987 or
1992, had significantly higher ozone exposures, controlling for other covariates; no significant effect
was found between ozone exposure and asthma in females. No significant effect was reported for
females or males due to exposure to PM, N02, S02, or S04. The C-R function for ozone is based on the
single pollutant model for males reported in Table 5 (McDonnell et al., 1999, 1999, p. 117).
Single Pollutant Model
The coefficient and standard error for males is reported in Table 5 for a unit increase in annual
average eight-hour ozone concentrations.139
Functional Form: Logistic
Coefficient: 0.0277
Standard Error: 0.0135
Incidence Rate: annual asthma incidence rate per person = 0.00219 (McDonnell et al., 1999, 1999,
Table 4)
Population: non-asthmatic males age 27 and over = 97.9%140 of males 27+
139 The eight-hour ozone concentration is defined as 9:00 A.M. to 4:59 P.M. The study used the 1973-1992 mean 8-hour
average ambient ozone concentration (McDonnell et al., 1999, p. 113).
140 The prevalence of asthma among males 27 and older (2.10 percent) was estimated from the 2000 National Health
Interview Survey (NHIS) public use data, available at ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Datasets/NHIS/2000.
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Appendix G. Ozone C-R Functions
Exhibit G-3. Concentration-Response (C-R) Functions for Ozone and Hospital Admissions
Endpoint Name
Author
Year
Location
Age Race Gender
Other
Pollutants
Averaging
Time1
Functional
Form
Beta
Std Error
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
All Respiratory
Asthma
Asthma
Asthma
Asthma
Asthma
Asthma
Chronic Lung Disease
Chronic Lung Disease
(less Asthma)
Chronic Lung Disease
(less Asthma)
Burnett et al.
Burnett et al.
Burnett et al.
Burnett et al.
Burnett et al.
Burnett et al.
Burnett et al.
Schwartz
Schwartz
Schwartz
Schwartz
Thurston et al.
Thurston et al.
Thurston et al.
Burnett et al.
Burnett et al.
Sheppard et al.
Thurston et al.
Thurston et al.
Thurston et al.
Moolgavkar et al.
Burnett et al.
Burnett et al.
1997
1997
1997
Toronto, CAN
Toronto, CAN
Toronto, CAN
1997 Toronto, CAN
2001
2001
2001
1995
1995
1995
1995
1994
1994
1994
1999
1999
1999
1994
1994
1994
1997
All
All
All
Toronto, CAN
Toronto, CAN
Toronto, CAN
New Haven, CT
New Haven, CT
Tacoma, WA
Tacoma, WA
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Toronto, CAN
Seattle, WA
Toronto, CAN
Toronto, CAN
Toronto, CAN
Minneapolis, MN
All
All
All
All All
<2
<2
<2
65+
65+
65+
65+
All
All
All
All
All
<65
All
All
All
65+
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
1999 Toronto, CAN
1999 Toronto, CAN
All All
All All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
None
pm2,
PMin.,
no2
so2
None
PM2,
PMio-2.5
None
PM10
None
PM10
None
pm2,
PM10
None
CO, PM1(
None
None
pm2,
PM10
CO, PM,r
None
CO, PM,r
8-hr avg
8-hr avg
8-hr avg
1-hr max
1-hr max
1-hr max
24-hr avg
24-hr avg
24-hr avg
24-hr avg
1-hr max
1-hr max
1-hr max
24-hr avg
24-hr avg
8-hr avg
1-hr max
1-hr max
1-hr max
24-hr avg
Log-linear
Log-linear
Log-linear
8-hr avg Log-linear
Log-linear
Log-linear
Log-linear
Log-linear
Log-linear
Log-linear
Log-linear
Linear
Linear
Linear
Log-linear
Log-linear
Log-linear
Linear
Linear
Linear
Log-linear
24-hr avg Log-linear
24-hr avg Log-linear
0.005394
0.004985
0.005231
0.004985
0.006607
0.006309
0.005702
0.002284
0.002652
0.007472
0.007147
0.0528
0.0404
0.0388
0.003143
0.002497
0.002913
0.0346
0.0265
0.029
0.002743
0.003608
0.003027
0.001052
0.001093
0.001070
0.001070
0.001378
0.001834
0.001901
0.001323
0.001398
0.002638
0.002565
0.0197
0.0233
0.0241
0.000679
0.000718
0.001079
0.0124
0.0142
0.0146
0.001699
0.000853
0.001105
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November 2003
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Appendix G. Ozone C-R Functions
Endpoint Name
Author
Year
Location
Age Race Gender
Other
Pollutants
Averaging Functional
Time1 Form
Beta
Std Error
Chronic Lung Disease
(less Asthma)
Schwartz
1994
Detroit, MI
65+
All
All
PM10
Pneumonia
Burnett et al.
1999
Toronto, CAN
All
All
All
None
Pneumonia
Burnett et al.
1999
Toronto, CAN
All
All
All
no2, pm2 5
Pneumonia
Moolgavkar et al.
1997
Minneapolis, MN
65+
All
All
no2, pm10,
so2
Pneumonia
Schwartz
1994
Detroit, MI
65+
All
All
PM10
Pneumonia
Schwartz
1994
Minneapolis, MN
65+
All
All
None
Pneumonia
Schwartz
1994
Minneapolis, MN
65+
All
All
PM10
All Cardiovascular
Burnett et al.
1997
Toronto, CAN
All
All
All
None
All Cardiovascular
Burnett et al.
1997
Toronto, CAN
All
All
All
pm2,
All Cardiovascular
Burnett et al.
1997
Toronto, CAN
All
All
All
pm10-2,
All Cardiovascular
Burnett et al.
1997
Toronto, CAN
All
All
All
no2, pm25.
so2
Dysrhythmia
Burnett et al.
1999
Toronto, CAN
All
All
All
None
Dysrhythmia
Burnett et al.
1999
Toronto, CAN
All
All
All
CO, PM2 5
24-hr avg
Log-linear
0.00549
0.00205
24-hr avg
Log-linear
0.002218
0.000517
24-hr avg
Log-linear
0.001977
0.000520
24-hr avg
Log-linear
0.003696
0.001030
24-hr avg
Log-linear
0.00521
0.0013
24-hr avg
Log-linear
0.003479
0.001616
24-hr avg
Log-linear
0.003977
0.001865
8-hr avg
Log-linear
0.006208
0.001612
8-hr avg
Log-linear
0.005231
0.001503
8-hr avg
Log-linear
0.005313
0.001420
8-hr avg
Log-linear
0.005639
0.001512
24-hr avg
Log-linear
0.001769
0.001035
24-hr avg
Log-linear
0.001685
0.001034
1. The averaging time refers to the metric used in the
more detail on the specific averaging time used in the
benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for
study.
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Appendix G. Ozone C-R Functions
G .3 Hospital Admissions
Exhibit G-3 summarizes the C-R functions used to estimate the relationship between ozone and
hospital admissions. Detailed summaries of each of the studies used to generate the functions are
described below, along with the parameters used in each of the functions.
G .3.1 Hospital Admissions for All Respiratory (Burnett et al., 1997, Toronto)
Burnett et al. (1997) examined the relationship between air pollution and hospital admissions
(ICD codes 464-466, 480-486, 490-494, 496) for individuals of all ages in Toronto, Canada during the
summers of 1992-1994. In a Poisson regression model, all respiratory admissions were linked to
coefficient of haze (COH) and ozone; other PM measures were less strongly linked. In two pollutant
models with COH, they found that CO, N02, and S02 were not significant, while ozone remained
significant. In multipollutant models with COH, ozone, N02, and S02, both ozone and COH remained
significant. None of the other PM measures (PM10, PM10_2 5, PM2 5) were significant in four-pollutant
models. The ozone C-R functions are based on the results from the single pollutant model and
multipollutant models with PM co-pollutants.
Single Pollutant Model
In a single pollutant model with adjustment for temperature and dew point, the coefficient and
standard error are based on the relative risk (1.064) and t-statistic (5.13) reported for an 11.5 ppb
increase in 12-hour average ozone (1997, Table 2, p. 617).
Functional Form: Log-linear
Coefficient: 0.005394
Standard Error: 0.001052
Incidence Rate: region-specific daily hospital admission rate for all respiratory admissions per person
(ICD 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (ozone and PM2 5)
In a model with PM2 5, the coefficient and standard error are based on the relative risk (1.059)
and t-statistic (4.56) reported for an 11.5 ppb increase in 12-hour average ozone (1997, Table 4, p. 618).
Functional Form: Log-linear
Coefficient: 0.004985
Standard Error: 0.001093
Incidence Rate: region-specific daily hospital admission rate for all respiratory admissions per person
(ICD 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (ozone and PM10_2 5)
In a model with PM10_2 5, the coefficient and standard error are based on the relative risk (1.062)
and t-statistic (4.89) reported for an 11.5 ppb increase in 12-hour average ozone (1997, Table 4, p. 618).
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Functional Form: Log-linear
Coefficient: 0.005231
Standard Error: 0.001070
Incidence Rate: region-specific daily hospital admission rate for all respiratory admissions per person
(ICD 464, 466, 480-487, 490-496)
Population: population of all ages
Multipollutant Model (ozone, N02, PM25, and S02)
In a four-pollutant model with N02, PM25, and S02, the coefficient and standard error are based
on the relative risk (1.059) and t-statistic (4.66) reported for an 11.5 ppb increase in 12-hour average
ozone (1997, Table 6, p. 618).
Functional Form: Log-linear
Coefficient: 0.004985
Standard Error: 0.001070
Incidence Rate: region-specific daily hospital admission rate for all respiratory admissions per person
(ICD 464, 466, 480-487, 490-496)
Population: population of all ages
G .3.2 Hospital Admissions for All Respiratory (Burnett et al., 2001, Toronto)
Burnett et al. (2001) studied the association between air pollution and acute respiratory hospital
admissions (ICD codes 493, 466, 464.4, 480-486) in Toronto from 1980-1994, among children less than
2 years of age. They collected hourly concentrations of the gaseous pollutants, CO, N02, S02, and
ozone. Daily measures of particulate matter were estimated for the May to August period of 1992-1994
using TSP, sulfates, and coefficient of haze data. The authors report a positive association between
ozone in the May through August months and respiratory hospital admissions, for several single days
after elevated ozone levels.
The strongest association was found using a five-day moving average of ozone. No association
was found in the September through April months. In co-pollutant models with a particulate matter or
another gaseous pollutant, the ozone effect was only slightly diminished. The effects for PM and
gaseous pollutants were generally significant in single pollutant models but diminished in co-pollutant
models with ozone, with the exception of CO. The C-R functions for ozone are based on a single
pollutant and two co-pollutant models, using the five-day moving average of one-hour max ozone.
Single Pollutant Model141
The single pollutant coefficient and standard error are based on a percent increase (34.8) and
95% confidence interval of the percent increase (19.3 percent, 52.3 percent) for a 45.2 ppb change in the
five-day moving average of one-hour max ozone (Burnett et al., 2001, Table 2 and p. 448).
141 The authors present seven single-pollutant models: the first six of these use single lags of 0 days, 1 day, up to 5
days. The seventh model uses a 5-day moving average of 0-day, 1-day, 2-day, 3-day and 4-day lagged 1-hour maximum ozone
concentrations. The authors describe the 5-day moving average model as an attempt to "more fully characterize this pattern of
temporally distributed effects" (p. 448). It shows a percentage increase of 34.8%, substantially larger than the percentage increase
from any of the single lag models. This suggests that the 5-day moving average is indeed capturing some of the effect of each of the
days that were shown to have an effect, individually, in the single lag models.
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Functional Form: Log-linear
Coefficient: 0.006607
Standard Error: 0.0001378
Incidence Rate: region-specific daily hospital admission rate for all respiratory admissions per person
less than 2 years of age (ICD codes 464, 466, 480-487, 493)
Population: population less than 2 years of age
Multipollutant Model (ozone and PM2 5)
In a model with PM2 5, the coefficient and standard error are based on the percent increase (33.0)
and t-statistic (3.44) associated with a 45.2 ppb increase in the five-day moving average of one-hour max
ozone (Burnett et al., 2001, Table 3).
Functional Form: Log-linear
Coefficient: 0.006309
Standard Error: 0.001834
Incidence Rate: region-specific daily hospital admission rate for all respiratory admissions per person
less than 2 years of age (ICD codes 464, 466, 480-487, 493)
Population: population less than 2 years of age
Multipollutant Model (ozone and PM10_2 5)
In a model with PM10_2 5, the coefficient and standard error are based on the percent increase
(29.4) and t-statistic (3.00) associated with a 45.2 ppb increase in the five-day moving average of one-
hour max ozone (Burnett et al., 2001, Table 3).
Functional Form: Log-linear
Coefficient: 0.005702
Standard Error: 0.001901
Incidence Rate: region-specific daily hospital admission rate for all respiratory admissions per person
less than 2 years of age (ICD codes 464, 466, 480-487, 493)
Population: population less than 2 years of age
G .3.3 Hospital Admissions for All Respiratory (Schwartz, 1995, New Haven)
Schwartz (1995) examined the relationship between air pollution and respiratory hospital
admissions (ICD codes 460-519) for individuals 65 and older in New Haven, Connecticut, from January
1988 to December 1990. In single-pollutant models, PM10 and S02 were significant, while ozone was
marginally significant. In a co-pollutant model with ozone and PM10, both pollutants were significant.
PM10 remained significant in a model with S02, while ozone was marginally significant when adjusted
for S02. S02 was significant in a co-pollutant model with PM10 but not with ozone. The ozone C-R
functions are based on results from the single pollutant model and co-pollutant model with PM10.
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Appendix G. Ozone C-R Functions
Single Pollutant Model
In a single-pollutant model, the coefficient and standard error are calculated from the relative
risk (1.03) and 95% confidence interval (1.02-1.05) for a 50 |ig/m ' increase in average daily ozone levels
(Schwartz, 1995, Table 3, p. 534).142
Functional Form: Log-linear
Coefficient: 0.002284
Standard Error: 0.001323
Incidence Rate: region-specific daily hospital admission rate for respiratory admissions per person 65+
(ICD codes 460-519)
Population: population of ages 65 and older
Multipollutant Model (ozone and PM10)
In a model with PM10, the coefficient and standard error are estimated from the relative risk
(1.07) and 95% confidence interval (1.00-1.15) for a 50 |ig/m3 increase in average daily ozone levels
(Schwartz, 1995, Table 3, p. 534).143
Functional Form: Log-linear
Coefficient: 0.002652
Standard Error: 0.001398
Incidence Rate: region-specific daily hospital admission rate for respiratory admissions per person 65+
(ICD codes 460-519)
Population: population of ages 65 and older
G .3.4 Hospital Admissions for All Respiratory (Schwartz, 1995, Tacoma)
Schwartz (1995) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Tacoma, Washington, from January 1988 to December 1990. In single-
pollutant models, PM10, ozone, and S02 were all significant. Ozone remained significant in separate co-
pollutant models with PM10 and S02. PM10 remained significant in a co-pollutant model with S02, but
not in a co-pollutant model with ozone. S02 was not significant in either of the co-pollutant models.
The ozone C-R functions are based on results from the single pollutant model and co-pollutant model
with PM10.
142 To calculate the coefficient, a conversion of 1.96 |_ig/m3 per ppb is used, based on a density of ozone of 1.96 grams per
liter (at 25 degrees Celsius). Since there are 1000 liters in a cubic meter and a million |_ig in a gram, this density means that there are
1.96 billion |_ig of ozone in a cubic meter of ozone. If a cubic meter has just one ppb of ozone, then this means that this particular
cubic meter has 1.96 |_ig of ozone (i.e., one ppb = 1.96 |_ig/m3).
143 To calculate the coefficient, a conversion of 1.96 |_ig/m3 per ppb is used, based on a density of ozone of 1.96 grams per
liter (at 25 degrees Celsius). Since there are 1000 liters in a cubic meter and a million |_ig in a gram, this density means that there are
1.96 billion |_ig of ozone in a cubic meter of ozone. If a cubic meter has just one ppb of ozone, then this means that this particular
cubic meter has 1.96 |_ig of ozone (i.e., one ppb = 1.96 |_ig/m3).
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Single Pollutant Model
In a single-pollutant model, the coefficient and standard error are calculated from the relative
risk (1.21) and 95% confidence interval (1.06-1.38) for a 50 |ig/m' increase in average daily ozone levels
(Schwartz, 1995, Table 6, p. 535)144
Functional Form: Log-linear
Coefficient: 0.007472
Standard Error: 0.002638
Incidence Rate: region-specific daily hospital admission rate for respiratory admissions per person 65+
(ICD codes 460-519)
Population: population of ages 65 and older
Multipollutant Model (ozone and PM10)
In a model with PM10, the coefficient and standard error are estimated from the relative risk
(1.20) and 95% confidence interval (1.06-1.37) for a 50 |ig/m3 increase in average daily ozone levels
(Schwartz, 1995, Table 6, p. 535).145
Functional Form: Log-linear
Coefficient: 0.007147
Standard Error: 0.002565
Incidence Rate: region-specific daily hospital admission rate for respiratory admissions per person 65+
(ICD codes 460-519)
Population: population of ages 65 and older
G .3.5 Hospital Admissions for All Respiratory (Thurston et al., 1994, Toronto)
Thurston et al. (1994) examined the relationship between air pollution and hospital admissions
for individuals of all ages in Toronto, Canada, for six weeks in July and August 1986-1988. In single-
pollutant linear regression models, ozone and various measures of PM were linked to all respiratory
admissions (ICD codes 466, 480-482, 485, 490-493). In two-pollutant models, ozone was still
significant, but measures of PM were often not significant; only H+ was significant. The C-R functions
for ozone are based on results from single and multipollutant models.
Single Pollutant Model
In a single pollutant model, the ozone coefficient (0.0528) and standard error (0.0197) are
reported in Table 3 (Thurston et al., 1994, p. 281) for a unit ppb increase in one-hour maximum ozone
levels.
144 To calculate the coefficient, a conversion of 1.96 |_ig/m3 per ppb is used, based on a density of ozone of 1.96 grams per
liter (at 25 degrees Celsius). Since there are 1000 liters in a cubic meter and a million |_ig in a gram, this density means that there are
1.96 billion |_ig of ozone in a cubic meter of ozone. If a cubic meter has just one ppb of ozone, then this means that this particular
cubic meter has 1.96 |_ig of ozone (i.e., one ppb = 1.96 |_ig/m3).
145To calculate the coefficient, a conversion of 1.96 |_ig/m3 per ppb is used, based on a density of ozone of 1.96 grams per
liter (at 25 degrees Celsius). Since there are 1000 liters in a cubic meter and a million |_ig in a gram, this density means that there are
1.96 billion |_ig of ozone in a cubic meter of ozone. If a cubic meter has just one ppb of ozone, then this means that this particular
cubic meter has 1.96 |_ig of ozone (i.e., one ppb = 1.96 |_ig/m3).
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Functional Form: Linear
Coefficient: 0.0528
Standard Error: 0.0197
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
Multipollutant Model (ozone and PM2 5)
In a model with PM2 5, the ozone coefficient (0.0404) and standard error (0.0233) are reported in
Table 3 (Thurston et al., 1994, p. 281) for a unit ppb increase in one-hour maximum ozone levels.
Functional Form: Linear
Coefficient: 0.0404
Standard Error: 0.0233
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
Multipollutant Model (ozone and PM10)
In a model with PM10, the ozone coefficient (0.0388) and standard error (0.0241) are reported in
Table 3 (Thurston et al., 1994, p. 281) for a unit ppb increase in one-hour maximum ozone levels.
Functional Form: Linear
Coefficient: 0.0388
Standard Error: 0.0241
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
G .3.6 Hospital Admissions for Asthma (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada from 1980 to 1994. The authors examined single pollutant
log-linear models for PM10, PM10_2 5, PM2 5, CO, N02, S02, and ozone and found all significantly
associated with asthma except S02. They estimated multi-pollutant models, where pollutants for best
fitting model were chosen using stepwise regression based on AIC criterion. Asthma admissions were
linked to ozone, CO, and PM10_2 5. The C-R functions for ozone are based on the results of a single
pollutant model and three pollutant model (ozone, CO, PM10_25).146
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(6.32) and t-statistic (4.63) reported in Table 3 (Burnett et al., 1999, p. 133) for a 19.5 ppb increase in
three-day average ozone concentration.
146 Burnett et al. (1999) reports results for co-pollutant models with ozone and various PM metrics as well, however,
standard errors were not provided so these estimates were not used to derive C-R functions.
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Functional Form: Log-linear
Coefficient: 0.003143
Standard Error: 0.000679
Incidence Rate: region-specific daily hospital admission rate for asthma per person (ICD code 493)
Population: population of all ages
Multipollutant Model (ozone, CO, and PM10_2 5)
In a model with PM10_2 5 and CO, the ozone coefficient and standard error are based on the
percent increase (4.99) reported in Table 5 (Burnett et al., 1999, p. 135) and the t-statistic obtained from
the authors (3.48)147 for a 19.5 ppb increase in three-day average ozone concentration.
Functional Form: Log-linear
Coefficient: 0.002497
Standard Error: 0.000718
Incidence Rate: region-specific daily hospital admission rate for asthma per person
(ICD code 493)
Population: population of all ages
G .3.7 Hospital Admissions for Asthma (Sheppard et al., 1999, Seattle)
Sheppard et al. (1999) studied the relationship between air pollution in Seattle and nonelderly
(<65) hospital admissions for asthma from 1987 to 1994. They used air quality data for PM10, PM25,
PM10_2 5, S02, ozone, and CO in a Poisson regression model with control for time trends, seasonal
variations, and temperature-related weather effects.148 They found asthma hospital admissions associated
with PM10, PM25, PM10_25, CO, and ozone. They did not observe an association for S02. They found PM
and CO to be jointly associated with asthma admissions. The best fitting co-pollutant models were
found using ozone. However, ozone data was only available April through October, so they did not
consider ozone further. For the remaining pollutants, the best fitting models included PM2 5 and CO.
Results for other co-pollutant models were not reported. The ozone C-R function is based on the results
of a single pollutant model.
Single Pollutant Model
The single pollutant coefficient and standard error are calculated from the relative risk (1.06) and
95% confidence interval (1.02-1.11) associated witha20 ppb increase in eight-hour average ozone
(Sheppard et al., 1999, p. 27).
Functional Form: Log-linear
Coefficient: 0.002913
Standard Error: 0.001079
Incidence Rate: region-specific daily hospital admission rate for asthma per person <65 (ICD code 493)
Population: population of ages 65 and under
147 Rick Burnett (co-author), personal communication.
148 PM2 5 levels were estimated from light scattering data.
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G .3.8 Hospital Admissions for Asthma (Thurston et al., 1994, Toronto)
Thurston et al. (1994) examined the relationship between air pollution and hospital admissions
for individuals of all ages in Toronto, Canada, for six weeks in July and August 1986-1988. In single-
pollutant linear regression models, ozone was strongly associated with asthma admissions (ICD code
493) and various measures of PM were marginally significant. In two-pollutant models, ozone remained
significant, but measures of PM were often not significant. The C-R functions for ozone are based on
results from single and multipollutant models.
Single Pollutant Model
In a single pollutant model, the ozone coefficient (0.0346) and standard error (0.0124) are
reported in Table 4 (Thurston et al., 1994, p. 282) for a unit ppb increase in one-hour maximum ozone
levels.
Functional Form: Linear
Coefficient: 0.0346
Standard Error: 0.0124
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
Multipollutant Model (ozone and PM2 5)
In a model with PM2 5, the ozone coefficient (0.0265) and standard error (0.0142) are reported in
Table 4 (Thurston et al., 1994, p. 282) for a unit ppb increase in one-hour maximum ozone levels.
Functional Form: Linear
Coefficient: 0.0265
Standard Error: 0.0142
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
Multipollutant Model (ozone and PM10)
In a model with PM10, the ozone coefficient (0.0290) and standard error (0.0146) are reported in
Table 4 (Thurston et al., 1994, p. 282) for a unit ppb increase in one-hour maximum ozone levels.
Functional Form: Linear
Coefficient: 0.0290
Standard Error: 0.0146
Baseline Pop: baseline population in Toronto = 2,400,000 (U.S. EPA, 1997, Table D-7)
Population: population of all ages
G .3.9 Hospital Admissions for Chronic Lung Disease (Moolgavkar et al., 1997,
Minneapolis)
Moolgavkar et al. (1997) examined the relationship between air pollution and hospital
admissions (ICD codes 490-496) for individuals 65 and older in Minneapolis-St. Paul, Minnesota, from
January 1986 to December 1991. In a Poisson regression, they found no significant effect for any of the
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pollutants (PM10, ozone, or CO). The effect for ozone was marginally significant. The model with a 100
df smoother was reported to be optimal (p. 368). The C-R function is based on the results from a three-
pollutant model (ozone, CO, PM10) using the 100 df smoother.
Multipollutant Model (ozone, CO, PM10)
In a model with CO and PM10, the estimated coefficient and standard error are based on the
percent increase (4.2) and 95% confidence interval of the percent increase (-1.0-9.4) associated with a
change in daily average ozone levels of 15 ppb (Moolgavkar et al., 1997, Table 4 and p. 366).
Functional Form: Log-linear
Coefficient: 0.002743
Standard Error: 0.001699
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease per person 65+
(ICD codes 490-496)
Population: population of ages 65 and older
G .3.10 Hospital Admissions for Chronic Lung Disease (less Asthma) (Burnett et al.,
1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada from 1980 to 1994. The authors examined single pollutant
log-linear models for PM10, PM10_2 5, PM2 5, CO, N02, S02, and ozone and found PM10_2 5, PM10, and
ozone significantly associated with chronic lung disease (ICD codes 490-492, 496). They estimated
multi-pollutant models, where pollutants for the best fitting model were chosen using stepwise
regression based on AIC criterion. In a three pollutant model, admissions for chronic obstructive
pulmonary disease (COPD) were linked to ozone and PM10_2 5. A non-significant association was found
with CO. The C-R functions for ozone are based on the results of a single pollutant model and three-
pollutant model (ozone, CO, PM10_25).149
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(7.29) and t-statistic (4.23) reported in Table 3 (Burnett et al., 1999, p. 133) for a 19.5 ppb increase in
three-day average ozone concentration.
Functional Form: Log-linear
Coefficient: 0.003608
Standard Error: 0.000853
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease per person (ICD
codes 490-492, 494-496)
Population: population of all ages
149 Burnett et al. (1999) reports results for co-pollutant models with ozone and various PM metrics as well, however,
standard errors were not provided so these estimates were not used to derive C-R functions.
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Multipollutant Model (ozone, CO, and PM10_2 5)
In a model with PM10_2 5 and CO, the ozone coefficient and standard error are based on the
percent increase (6.08) reported in Table 5 (Burnett et al., 1999, p. 135) and the t-statistic obtained from
the authors (2.74)150 for a 19.5 ppb increase in three-day average ozone concentration.
Functional Form: Log-linear
Coefficient: 0.003027
Standard Error: 0.001105
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease per person (ICD
codes 490-492, 494-496)
Population: population of all ages
G .3.11 Hospital Admissions for Chronic Lung Disease (less Asthma) (Schwartz,
1994b, Detroit)
Schwartz (1994b) examined the relationship between air pollution and hospital admissions (ICD
codes 491-492, 494-496) for individuals 65 and older in Detroit, Michigan, from January 1986 to
December 1989. In a two-pollutant Poisson regression model, Schwartz found both PM10 and ozone
significantly linked to pneumonia and COPD. The authors state that effect estimates were relatively
unchanged compared to the unreported single pollutant models. No significant associations were found
between either pollutant and asthma admissions. The C-R function for chronic lung disease incidence is
based on the results of the "basic" co-pollutant model (ozone and PM10) presented in Table 4 (p. 651).151
Multipollutant Model (ozone and PM10)
The coefficient and standard error for the "basic" model are reported in Table 4 (Schwartz,
1994b, p.651) for a one ppb change in daily average ozone.
Functional Form: Log-linear
Coefficient: 0.00549
Standard Error: 0.00205
Incidence Rate: region-specific daily hospital admission rate for chronic lung disease per person 65+
(ICD codes 490-492, 494-496)
Population: population of ages 65 and older
G .3.12 Hospital Admissions for Pneumonia (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions for
individuals of all ages in Toronto, Canada from 1980 to 1994. The authors examined single pollutant
log-linear models for PM10, PM10_2 5, PM2 5, CO, N02, S02, and ozone and found all significantly
associated with pneumonia and other respiratory infections (ICD codes 464, 466, 480-487, 494). They
estimated multipollutant models, where pollutants for the best fitting model were chosen using stepwise
150 Rick Burnett (co-author), personal communication.
151 Schwartz (1994b) also reports results using generalized additive models to fit time and temperature variables, however
no standard error or confidence intervals were reported.
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regression based on AIC criterion. Pneumonia and respiratory infection admissions were linked to
ozone, N02, and PM25. The C-R functions for ozone are based on the results of a single pollutant model
and three-pollutant model (ozone, N02, PM25).152
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(4.42) and t-statistic (4.29) reported in Table 3 (Burnett et al., 1999, p. 133) for a 19.5 ppb increase in
two-day average ozone concentration.
Functional Form: Log-linear
Coefficient: 0.002218
Standard Error: 0.000517
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person (ICD codes 464,
466, 480-487)
Population: population of all ages
Multipollutant Model (ozone, N02, PM2 5)
In a model with PM2 5 and N02, the ozone coefficient and standard error are based on the percent
increase (3.93) reported in Table 5 (Burnett et al., 1999, p. 135) and the t-statistic obtained from the
authors (3.80)153 for a 19.5 ppb increase in two-day average ozone concentration.
Functional Form: Log-linear
Coefficient: 0.001977
Standard Error: 0.000520
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person (ICD codes 464,
466, 480-487)
Population: population of all ages
G .3.13 Hospital Admissions for Pneumonia (Moolgavkar et al., 1997, Minneapolis)
Moolgavkar et al. (1997) examined the relationship between air pollution and pneumonia
hospital admissions (ICD 480-487) for individuals 65 and older in Minneapolis-St. Paul, Minnesota,
from January 1986 to December 1991. In a four pollutant Poisson model examining pneumonia
admissions in Minneapolis, ozone was significant, while N02, S02, and PM10 were not significant. The
model with a 130 df smoother was reported to be optimal (p. 368). The ozone C-R function is based on
the results from the four-pollutant model with a 130 df smoother.
Multipollutant Model (ozone, N02, PM10,and S02)
In a model with N02, PM10,and S02, the estimated coefficient and standard error are based on
the percent increase (5.7) and 95% confidence interval of the percent increase (2.5-8.9) associated with
an increase in daily average ozone levels of 15 ppb (Moolgavkar et al., 1997, Table 4 and p. 366).
152 Burnett et al. (1999) reports results for co-pollutant models with ozone and various PM metrics as well, however,
standard errors were not provided so these estimates were not used to derive C-R functions.
153 Rick Burnett (co-author), personal communication.
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Functional Form: Log-linear
Coefficient: 0.003696
Standard Error: 0.00103
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person 65+ (ICD codes
480-487)
Population: population of ages 65 and older
G .3.14 Hospital Admissions for Pneumonia (Schwartz, 1994b, Detroit)
Schwartz (1994b) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Detroit, Michigan, from January 1986 to December 1989. In a two-pollutant
Poisson regression model, Schwartz found both PM10 and ozone significantly linked to pneumonia and
COPD. The authors state that effect estimates were relatively unchanged compared to the unreported
single pollutant models. No significant associations were found between either pollutant and asthma
admissions. The PM10 C-R function for pneumonia incidence is based on results of the "basic" co-
pollutant model (ozone and PM10).154
Multipollutant Model (ozone and PM10)
The ozone C-R function for pneumonia incidence is based on the coefficient and standard error
for the "basic" co-pollutant model presented in Table 4 (Schwartz, 1994b, p. 651).
Functional Form: Log-linear
Coefficient: 0.00521
Standard Error: 0.0013
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person 65+ (ICD codes
480-487)
Population: population of ages 65 and older
G .3.15 Hospital Admissions for Pneumonia (Schwartz, 1994a, Minneapolis)
Schwartz (1994a) examined the relationship between air pollution and hospital admissions for
individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to December 1989. In
single-pollutant Poisson regression models, both ozone and PM10 were significantly associated with
pneumonia admissions. In a two-pollutant model, Schwartz found PM10 significantly related to
pneumonia; ozone was weakly linked to pneumonia. The results were not sensitive to the methods used
to control for seasonal patterns and weather. The ozone C-R functions are based on the results of the
single pollutant model and the two-pollutant model (PM10 and ozone) with spline smoothing for
temporal patterns and weather.
Single Pollutant Model
The single pollutant coefficient and standard error are based on the relative risk (1.19) and 95%
confidence interval (1.02-1.40) for a 50 ppb increase in daily average ozone levels (Schwartz, 1994a, p.
369).
154 Schwartz (1994b) also reports results using generalized additive models to fit time and temperature variables, however
no standard error or confidence intervals were reported.
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Functional Form: Log-linear
Coefficient: 0.003479
Standard Error: 0.001616
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person 65+ (ICD codes
480-487)
Population: population of ages 65 and older
Multipollutant Model (ozone and PM10)
In a model with PM10 and spline functions to adjust for time and weather, the coefficient and
standard error are based on the relative risk (1.22) and 95% confidence interval (1.02, 1.47) for a 50 ppb
increase in daily average ozone levels (Schwartz, 1994a, Table 4).
Functional Form: Log-linear
Coefficient: 0.003977
Standard Error: 0.001865
Incidence Rate: region-specific daily hospital admission rate for pneumonia per person 65+ (ICD codes
480-487)
Population: population of ages 65 and older
G .3.16 Hospital Admissions for All Cardiovascular (Burnett et al., 1997, Toronto)
Burnett et al. (1997) examined the relationship between air pollution and cardiac hospital
admissions (ICD codes 410-414, 427, 428) for individuals of all ages in Toronto, Canada during the
summers of 1992-1994. In a Poisson regression model, cardiac admissions were linked to coefficient of
haze (COH) and ozone; other PM measures were less strongly linked. In two pollutant models, they
found that CO, N02, and S02 were not significant, controlling for COH. They found that ozone was still
significant, controlling for COH. In multi-pollutant models with COH, ozone, N02, and S02, both ozone
and COH remained significant. None of the other PM measures (PM10, PM10_2 5, PM2 5) were significant
in four-pollutant models. The ozone C-R functions are based on the results from the single pollutant
model and multipollutant models with PM co-pollutants.
Single Pollutant Model
In a single pollutant model with adjustment for temperature and dew point, the ozone coefficient
and standard error are based on the relative risk (1.074) and t-statistic (3.85) reported for an 11.5 ppb
increase in the three-day average of 12-hour average ozone (Burnett et al., 1997, Table 2, p. 617).
Functional Form: Log-linear
Coefficient: 0.006208
Standard Error: 0.001612
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
Multipollutant Model (ozone and PM2 5)
In a model with PM2 5, the ozone coefficient and standard error are based on the relative risk
(1.062) and t-statistic (3.48) reported for an 11.5 ppb increase in the three-day average of 12-hour
average ozone (Burnett et al., 1997, Table 5, p. 618).
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Appendix G. Ozone C-R Functions
Functional Form: Log-linear
Coefficient: 0.005231
Standard Error: 0.001503
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
Multipollutant Model (ozone and PM10_2 5)
In a model with PM10_2 5, the ozone coefficient and standard error are based on the relative risk
(1.063) and t-statistic (3.74) reported for an 11.5 ppb increase in the three-day average of 12-hour
average ozone (Burnett et al., 1997, Table 5, p. 618).
Functional Form: Log-linear
Coefficient: 0.005313
Standard Error: 0.001421
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
Multipollutant Model (ozone, N02, PM2 5, S02)
In a four-pollutant model with PM2 5, N02, and S02, the ozone coefficient and standard error are
based on the relative risk (1.067) and t-statistic (3.73) reported for an 11.5 ppb increase in the three-day
average of 12-hour average ozone (Burnett et al., 1997, Table 6, p. 618).
Functional Form: Log-linear
Coefficient: 0.005639
Standard Error: 0.001512
Incidence Rate: region-specific daily hospital admission rate for all cardiovascular disease per person
(ICD codes 410-414, 427, 428)
Population: population of all ages
G .3.17 Hospital Admissions for Dysrhythmia (Burnett et al., 1999, Toronto)
Burnett et al. (1999) examined the relationship between air pollution and hospital admissions
(ICD 427) for individuals of all ages in Toronto, Canada from 1980 to 1994. The authors examined
single pollutant log-linear models for PM10, PM10_2 5, PM2 5, CO, N02, S02, and ozone and found PM2 5,
PM10, and CO significantly associated with admissions. They estimated multiple pollutant models,
where pollutants for best fitting model were chosen using stepwise regression based on AIC criterion.
The final model for dysrhythmia admissions included ozone, CO, and PM25. CO was significantly
associated with admissions, while ozone and PM2 5 were marginally significant. The C-R functions for
ozone are based on the results of a single pollutant model and three-pollutant model (ozone, CO, and
pm25).155
155 Burnett et al. (1999) reports results for co-pollutant models with ozone and various PM metrics as well, however,
standard errors were not provided so these estimates were not used to derive C-R functions.
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Appendix G. Ozone C-R Functions
Single Pollutant Model
In a single pollutant model, the coefficient and standard error are based on the percent increase
(3.51) and t-statistic (1.71) reported in Table 3 (Burnett et al., 1999, p. 133) for a 19.5 ppb increase in
three-day average ozone concentration.
Functional Form: Log-linear
Coefficient: 0.001769
Standard Error: 0.001035
Incidence Rate: region-specific daily hospital admission rate for dysrhythmia per person (ICD code
427)
Population: population of all ages
Multipollutant Model (ozone, CO, PM2 5)
In a model with PM2 5 and CO, the ozone coefficient and standard error are based on the percent
increase (3.34) reported in Table 5 (Burnett et al., 1999, p. 135) and the t-statistic obtained from the
authors (1.63)156 for a 19.5 ppb increase in three-day average ozone concentration.
Functional Form: Log-linear
Coefficient: 0.001685
Standard Error: 0.001034
Incidence Rate: region-specific daily hospital admission rate for dysrhythmia per person (ICD code
427)
Population: population of all ages
156 Rick Burnett (co-author), personal communication.
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Appendix G. Ozone C-R Functions
Exhibit G-4. Concentration-Response (C-R) Functions for Ozone and Emergency Room Visits
Endpoint Name
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time1
Functional
Form
Beta
Std Error
Asthma
Cody et al.
1992
New Jersey (Northern)
All
All
All
so2
5-hr avg
Linear
0.0203
0.00717
Asthma
Jaffe et al.
2003
Ohio cities
5-34
All
All
None
8-hr max
Log-linear
0.002956
0.001486
Asthma
Norris et al.
1999
Seattle, WA
<18
All
All
None
8-hr avg
Log-linear
0.004305
0.003826
Asthma
Schwartz et al.
1993
Seattle, WA
<65
All
All
None
24-hr avg
Log-linear
-0.002031
0.002812
Asthma
Stieb et al.
1996
New Brunswick, CAN
All
All
All
None
1-hr max
Quadratic
0.00004
0.00002
Asthma
Stieb et al.
1996
New Brunswick, CAN
All
All
All
None
24-hr avg
Quadratic
0.0001
0.00004
Asthma
Weisel et al.
1995
New Jersey (Northern and
Central)
All
All
All
None
5-hr avg
Linear
0.0443
0.00723
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for
more detail on the specific averaging time used in the study.
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Appendix G. Ozone C-R Functions
G .4 Emergency Room Visits
Exhibit G-4 summarizes the C-R functions used to estimate the relationship between ozone and
emergency room visits. Detailed summaries of each of the studies used to generate the functions are
described below, along with the parameters used in each of the functions.
G .4.1 Emergency Room Visits for Asthma (Cody et al., 1992, Northern NJ)
Cody et al. (1992) examined the relationship between ER visits and air pollution for persons of
all ages in central and northern New Jersey, from May to August in 1988-1989. In a two pollutant
multiple linear regression model, ozone was linked to asthma visits, and no effect was seen for S02.
They modeled PM10 in separate analysis because of limited (every sixth day) sampling. No significant
effect was seen for PM10. The C-R function for ozone is based on results of a co-pollutant model with
S02 (Cody et al., 1992, Table 6, p. 191).
Multipollutant Model (ozone and S02)
The ozone coefficient and standard error are reported per 1 ppm increment of five-hour ozone
levels, which are converted to a 1 ppb increment by dividing by 1,000 (Cody et al., 1992, Table 6, p.
191).
Functional Form: Linear
Coefficient: 0.0203
Standard Error: 0.00717
Baseline Population: baseline population of Northern New Jersey157 = 4,436,976
Population: population of all ages
G .4.2 Emergency Room Visits for Asthma (Jaffe et al., 2003)
Jaffe et al. (2003) examined the relationship between ER visits and air pollution for persons ages
5-34 in Cleveland, Columbus, and Cincinnati, Ohio, from 1991 through 1996. In single-pollutant
Poisson regression models, ozone and S02 were linked to asthma visits, and no significant effect was
seen forN02 and PM10.
Single Pollutant Model
The ozone coefficient and standard error are reported per 10 ppb increment of the maximum
daily 8-hour average ozone level (Jaffe et al., 2003, Table 3). We used the results from the three cities
combined. The relative risk is 1.03, with a 95 percent confidence interval of 1.00 to 1.06.
Functional Form: Log-linear
Coefficient: 0.002956
Standard Error: 0.001486
Incidence: asthma ER rate for ages 0-17, 18-24, and 25-34
Population: population of ages from 5 to 34
157 The population estimate is based on the 1990 population for the eight counties containing hospitals or in the central
core of the study. Cody et al. (1992, Figure 1) presented a map of the study area; the counties are: Bergen, Essex, Hudson,
Middlesex, Morris, Passaic, Somerset, and Union.
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Appendix G. Ozone C-R Functions
G .4.3 Emergency Room Visits for Asthma (Norris et al., 1999)
Norris et al. (1999) examined the relation between air pollution in Seattle and childhood (<18)
hospital admissions for asthma from 1995 to 1996. The authors used air quality data for PM10, light
scattering (used to estimate fine PM), CO, S02, N02, and ozone in a Poisson regression model with
adjustments for day of the week, time trends, temperature, and dew point. They found significant
associations between asthma ER visits and light scattering (converted to PM25), PM10, and CO. No
association was found between ozone, N02, or S02 and asthma ER visits, although ozone had a
significant amount of missing data. In multi-pollutant models with either PM metric (light scattering or
PM10) and N02 and S02, the PM coefficients remained significant while the gaseous pollutants were not
associated with increased asthma ER visits. The C-R function for ozone is based on the result of a single
pollutant model.
Single Pollutant Model
The coefficient and standard error are calculated from a relative risk of 1.02 (95% CI 0.98-1.05)
for a 4.6 ppb increase in maximum eight-hour ozone levels (Norris et al., 1999, p. 491).
Functional Form: Log-linear
Coefficient: 0.004305
Standard Error: 0.003826
Incidence Rate: region-specific daily emergency room rate for asthma per person <18 (ICD code 493)
Population: population of ages under 18
G .4.4 Emergency Room Visits for Asthma (Schwartz et al., 1993, Seattle)
Schwartz et al. (1993) examined the relationship between air quality and emergency room visits
for asthma (ICD codes 493, 493.01, 493.10, 493.90, 493.91) in persons under 65 and 65 and over, living
in Seattle from September 1989 to September 1990. Using single-pollutant models they found daily
levels of PM10 linked to ER visits in individuals ages under 65, and they found no effect in individuals
ages 65 and over. They did not find a significant effect for S02 and ozone in either age group. The C-R
function is based on the results of the single pollutant model for ozone.
Single Pollutant Model
The ozone coefficient and standard error are based on the relative risk (0.97) and 95%
confidence interval (0.89-1.05) for a 15 ppb increase in daily ozone levels (Schwartz et al., 1993, p.
829).
Functional Form: Log-linear
Coefficient: -0.002031
Standard Error: 0.002812
Incidence Rate: region-specific daily emergency room rate for asthma per person <65 (ICD code 493)
Population: population of ages under 65
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Appendix G. Ozone C-R Functions
G .4.5 Emergency Room Visits for Asthma (Stieb et al., 1996, New Brunswick)
Stieb et al. (1996) examined the relationship between ER visits and air pollution for persons of
all ages in St. John, New Brunswick, Canada, from May through September in 1984-1992. Ozone was
significantly linked to ER visits, especially when ozone levels exceeded 75 ppb. The authors reported
results from a linear model, quadratic model, and linear-quadratic model using daily average and 1-hour
maximum ozone. In the linear model, ozone was borderline significant. In the quadratic and linear-
quadratic models, ozone was highly significant. This is consistent with the author's conclusion that
"only ozone appeared to have a nonlinear relationship with visit rates" (p. 1356) and that "quadratic,
linear-quadratic, and indicator models consistently fit the data better than the linear model..." (p. 1358).
The linear term in the linear-quadratic model is negative, implying that at low ozone levels, increases in
ozone are associated with decreases in risk. Since this does not seem biologically plausible, the ozone
C-R functions described here are based on the results of the quadratic regression models presented in
Table 2 (Stieb et al., 1996, p. 1356).
Single Pollutant Model (one-hour max ozone)
The coefficient and standard error of the quadratic model are reported in Table 2 (Stieb et al.,
1996, p. 1356) for a 1 ppb increase in 1-hour daily maximum ozone levels. The C-R function to estimate
avoided emergency visits derived from a quadratic regression model is shown below:
A Asthma ER Visits= Ba^ePop^°xbaSeUne)2" (C>Xcontrol)2 ]pop,
Functional Form: Quadratic
Coefficient: 0.00004
Standard Error: 0.00002
Baseline Population: baseline population of St. John, New Brunswick (Stieb et al., 1996, p. 1354) =
125,000
Population: population of all ages
Single Pollutant Model (daily average ozone)
The coefficient and standard error of the quadratic model are reported in Table 2 (p. 1356) for
a 1 ppb increase in daily average ozone levels. The C-R function to estimate avoided emergency visits
derived from a quadratic regression model is shown below:
A Asthma ER Visits= ) 2 " (P Control ) ' } P°P ,
Functional Form: Quadratic
Coefficient: 0.0001
Standard Error: 0.00004
Baseline Population: baseline population of St. John, New Brunswick (Stieb et al., 1996, p. 1354) =
125,000
Population: population of all ages
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Appendix G. Ozone C-R Functions
G .4.6 Emergency Room Visits for Asthma (Weisel et al., 1995, Northern NJ)
Weisel et al. (1995) examined the relationship between ER visits and air pollution for persons of
all ages in central and northern New Jersey, from May to August in 1986-1990. A significant
relationship was reported for ozone. The C-R function is based on the results of the single pollutant
models reported by Weisel et al. (1995, Table 2).
Single Pollutant Model
The coefficient (P) used in the C-R function is a weighted average of the coefficients in Weisel
et al. (1995, Table 2) using the inverse of the variance as the weight:
The standard error of the coefficient (ap) is calculated as follows, assuming that the estimated
year-specific coefficients are independent:
Functional Form: Linear
Coefficient: 0.0443
Standard Error: 0.00723
Baseline Population: baseline population of Northern New Jersey158 = 4,436,976
Population: population of all ages
158 The population estimate is based on the 1990 population for the eight counties containing hospitals or in the central
core of the study. Cody et al. (1992, Figure 1) presented a map of the study area; the counties are: Bergen, Essex, Hudson,
Middlesex, Morris, Passaic, Somerset, and Union.
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0.0443
( 1990 f> \
Z-Sr]
i= 1986 v
f 1990
\ ( 1990
1990
z = 1986
z = 1986^ p.
1990
z=1986
V z = 1986 ^ f3i J \
This eventually reduces down to:
0.00723
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Appendix G. Ozone C-R Functions
Exhibit G-5. Concentration-Response (C-R) Functions for Ozone and Acute Effects
Endpoint Name
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time1
Functional
Form
Beta
Std Error
Any of 19 Respiratory
Symptoms
Minor Restricted Activity
Days
School Loss Days, All Cause
School Loss Days, All Cause
School Loss Days, Illness-
Related
Krupnick
Ostro and Rothschild
Chen et al.
Gilliland et al.
Gilliland et al.
1990
1989
2000
2001
2001
Los Angeles, CA
nationwide
Washoe Co, NV
Southern California
Southern California
18-64
18-64
6-11
9-10
9-10
All
All
All
All
All
All
All
All
All
All
COH
PM2,
CO, PM10
None
None
1-hr max
24-hr avg
1-hr max
8-hr avg
8-hr avg
Linear
Log-linear
Linear
Log-linear
Log-linear
0.000137
0.0022
0.013247
0.00755
0.024398
0.000070
0.000658
0.004985
0.004527
0.008138
School Loss Days,
Respiratory-Related
Worker Productivity
Gilliland et al.
Crocker and Horst
2001
1981
Southern California
nationwide
9-10
18-64
All
All
All
All
None
None
8-hr avg
24-hr avg
Log-linear
Linear
0.030188
0.14
0.014436
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for
more detail on the specific averaging time used in the study.
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Appendix G. Ozone C-R Functions
G .5 Acute Morbidity
Exhibit G-5 summarizes the C-R functions used to estimate the relationship between ozone and
acute morbidity. Detailed summaries of each of the studies used to generate the functions are described
below, along with the parameters used in each of the functions.
G .5.1 Any of 19 Respiratory Symptoms: Krupnick (1990)
Krupnick et al. (1990) estimated the impact of air pollution on the incidence of any of 19
respiratory symptoms or conditions in 570 adults and 756 children living in three communities in Los
Angeles, California from September 1978 to March 1979. Krupnick et al. (1990) listed 13 specific
"symptoms or conditions": head cold, chest cold, sinus trouble, croup, cough with phlegm, sore throat,
asthma, hay fever, doctor-diagnosed ear infection, flu, pneumonia, bronchitis, and bronchiolitis. The
other six symptoms or conditions are not specified.
In their analysis, they included coefficient of haze (COH, a measure of particulate matter
concentrations), ozone, N02, and S02, and they used a logistic regression model that takes into account
whether a respondent was well or not the previous day. A key difference between this and the usual
logistic model, is that the model they used includes a lagged value of the dependent variable. In single-
pollutant models, daily ozone, COH, and S02 were significantly related to respiratory symptoms in
adults. Controlling for other pollutants, they found that ozone was still significant. The results were
more variable for COH and S02, perhaps due to collinearity. N02 had no significant effect. No effect
was seen in children for any pollutant. The results from the two-pollutant model with COH and ozone
are used to develop a C-R function.
Multipollutant Model (ozone and coefficient of haze)
The C-R function used to estimate the change in ARD2 associated with a change in daily one-
hour maximum ozone159 is based on Krupnick et al. (1990, p. 12):160
l\ARD2= 0*-A03-pop ,
Functional Form: Linear
Coefficient: first derivative of the stationary probability = 0.000137
Standard Error: 0.0000697
Population: population of ages 18-64 years161
The logistic regression model used by Krupnick et al. (1990) takes into account whether a
respondent was well or not the previous day. Following Krupnick et al. (p. 12), the probability that one
is sick is on a given day is:
159Krupnick et al. (1990) used parts per hundred million (pphm) to measure ozone; the coefficient used here is based on
ppb.
160Krupnick and Kopp (1988, p. 2-24) and ESEERCO (1994, p. V-32) used the same C-R functional form as that used
here.
161The coefficient estimates are based on the sample of "adults," and assumes that individuals 18 and older were
considered adult. According to Krupnick et al. (1990, Table 1), about 0.6 percent of the study sample was over the age of 60. This
is a relatively small fraction, so it is further assumed that the results do not apply to individuals 65 years of age and older.
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probability (ARD2)=- ^0
1-Pi + Po
1
pt = probability(ARD2\sicknessornott_l )=-—p0+pvARD2t t+x-p >f°r '=0,1.
where:
X = the matrix of explanatory variables
p0 = the probability of sickness on day t, given wellness on day t-1, and
Pi = the probability of sickness on day t, given sickness on day t-1.
In other words, the transition probabilities are estimated using a logistic function; the key
difference between this and the usual logistic model, is that the model includes a lagged value of the
dependent variable.
To calculate the impact of ozone (or other pollutants) on the probability of ARD2, it is possible,
in principle, to estimate ARD2 before the change in ozone and after the change:
lS.ARD2= ARD2 after - ARD2 before .
However the full suite of coefficient estimates are not available.162 Rather than use the full suite
of coefficient values, the impact of ozone on the probability of ARD2 may be approximated by the
derivative of ARD2 with respect to ozone:163
cprobability(ARD2) Poi}~ + Po)\
^ = (i-p1+p0y '
where P is the reported logistic regression coefficient for ozone. The change in the incidence of ARD2
associated with a given change in ozone is then estimated by:
3mD2 AARD2
c03 = A 03
AARD2^^
A 03
162The model without N02 (Krupnick et al., 1990, Table V equation 3) was used in this analysis, but the full suite of
coefficient estimates for this model were not reported. Krupnick et al. (Table IV) reported all of the estimated coefficients for a
model of children and for a model of adults when four pollutants were included (ozone, COH, S02, and N02). However, because of
high collinearity between N02 and COH, N02 was dropped from some of the reported analyses (Krupnick et al., p. 10), and the
resulting coefficient estimates changed substantially (see Krupnick et al., Table V). Both the ozone and COH coefficients dropped
by about a factor of two or more.
163The derivative result is reported by Krupnick et al. (1990, p. 12).
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=> ^ARD2=0*-^O3 .
This analysis uses transition probabilities obtained from Krupnick et al. as reported by
ESEERCO (1994, p. V-32) for the adult population: p: = 0.7775 and p0 = 0.0468. This implies:
. 0.0468(1- 0.7775>0.00055[0.7775+ (1-0.0468)1
B = - -3—^ —=0.000137 .
(1-0.7775+0.0468)
The standard error for the coefficient is derived using the reported standard error of the logistic
regression coefficient in Krupnick et al. (1990, Table V):
phigh = 0.00055+ (1.96-0.00027)= 0.00108
0.0468(1- 0.7775)0.00108f0.7775+(l-0.0468)l
' Ate* = ' 7—' -= 0.000268
s (1-0.7775+0.0468)
PhiSh-P (0.000268-0.000137)
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Appendix G. Ozone C-R Functions
national survey results used in this analysis were conducted in 1976-1981. Controlling for PM25, two-
week average ozone had a highly variable association with RRADs and MRADs. Controlling for ozone,
two-week average PM25 was significantly linked to both health endpoints in most years. The C-R
function for ozone is based on the co-pollutant model with PM2 5.
The study is based on a "convenience" sample of non-elderly individuals. Applying the C-R
function to this age group is likely a slight underestimate, as it seems likely that elderly are at least as
susceptible to ozone as individuals under 65. A number of studies have found that hospital admissions
for the elderly are related to ozone exposures (e.g., Schwartz, 1994b; Schwartz, 1995).
Multipollutant Model (ozone and PM2 5)
The coefficient and standard error used in the C-R function are based on a weighted average of
the coefficients in Ostro and Rothschild (1989, Table 4). The derivation of these estimates is described
below.
Functional Form: Log-linear
Coefficient: 0.00220
Standard Error: 0.000658
Incidence Rate: daily incidence rate for minor restricted activity days (MRAD) = 0.02137 (Ostro and
Rothschild, 1989, p. 243)
Population: adult population ages 18 to 64
The coefficient used in the C-R function is a weighted average of the coefficients in Ostro and
Rothschild (1989, Table 4) using the inverse of the variance as the weight:165
f 1981
P
^ J"
= 1976
1981
V z = 1976 <->
0.00220.
The standard error of the coefficient is calculated as follows, assuming that the estimated year-
specific coefficients are independent:
f 1981
n
\
( i98i n
Pi
£ #
1981
= X var
7=1976
/
/=1976
P
z= 1976 &
P
1981
I
V ;=1976
1
)
Y
V
)
_2
V °p
•YJ
This reduces down to:
consistency with other studies estimating impacts to non-elderly adult populations.
165 The calculation of the MRAD coefficient and its standard error is exactly analogous to the calculation done for the
work-loss days coefficient based on Ostro (1987).
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Appendix G. Ozone C-R Functions
CTp - ^=>
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Appendix G. Ozone C-R Functions
in school during weekdays for all of May, two weeks in June, one week in August, and all of September.
This corresponds to approximately 2.75 months out of the 5 month season, resulting in an estimate of
39.3% of days (2.75/5*5/7). The C-R function parameters are shown below.
Functional Form: Linear
Coefficient: 0.013247
Standard Error: 0.004985
Population: population of children ages 6-11
Scaling Factor 1: Ratio of national school absence rate to study-specific school absence rate167 = 1.081
Scaling Factor 2: Convert beta in percentage terms to a proportion = 0.01
Scaling Factor 3: Proportion of days that are school days in the ozone season168 = 0.393
G .5.4 School Loss Days, All Cause (Gilliland et al., 2001)
Gilliland et al. (2001) examined the association between air pollution and school absenteeism
among 4th grade school children (ages 9-10) in 12 southern Californian communities. The study was
conducted from January through June 1996. The authors used school records to collect daily absence
data and parental telephone interviews to identify causes. They defined illness-related absences as
respiratory or non-respiratory. A respiratory illness was defined as an illness that included at least one of
the following: runny nose/sneezing, sore throat, cough, earache, wheezing, or asthma attack. The
authors used 15 and 30 day distributed lag models to quantify the association between ozone, PM10, and
N02 and incident school absences. Ozone levels were positively associated with all school absence
measures and significantly associated with all illness-related school absences (non-respiratory illness,
respiratory illness, URI and LRI). Neither PM10 nor N02 was significantly associated with illness-
related school absences, but PM10 was associated with non-illness related absences. The C-R function
for ozone is based on the results of the single pollutant model.
Gilliland et al. (2001) defines an incident absence as an absence that followed attendance on the
previous day and the incidence rate as the number of incident absences on a given day over the
population at risk for an absence on a given day (i.e. those children who were not absent on the previous
day). Since school absences due to air pollution may last longer than one day, an estimate of the average
duration of school absences could be used to calculated the total avoided school loss days from an
estimate of avoided new absences. A simple ratio of the total absence rate divided by the new absence
rate would provide an estimate of the average duration of school absences, which could be applied to the
estimate of avoided new absences as follows:
totalAbsences
Duration= -
newAbsences
A TotalAbsences= - ^incidence-(e~/3 A°3 -1) -duration-pop
167 National school absence rate of 5.5% obtained from the U.S. Department of Education (1996, Table 42-1). Study-
specific school absence rate of 5.09% obtained from Chen et al. (2000, Table 1).
168 Ozone is modeled for the 5 months from May 1 through September 30. We assume that children are in school during
weekdays for all of May, 2 weeks in June, 1 week in August, and all of September. This corresponds to approximately 2.75 months
out of the 5 month season, resulting in an estimate of 39.3% of days (2.75/5*5/7).
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Appendix G. Ozone C-R Functions
Since the function is log-linear, the baseline incidence rate (in this case, the rate of new
absences) is multiplied by duration, which reduces to the total school absence rate. Therefore, the same
result would be obtained by using a single estimate of the total school absence rate in the C-R function.
Using this approach, we assume that the same relationship observed between pollutant and new school
absences in the study would be observed for total absences on a given day. As a result, the total school
absence rate is used in the function below. The derivation of this rate is described in the section on
baseline incidence rate estimation.
Single Pollutant Model
For all absences, the coefficient and standard error are based on a percent increase of 16.3
percent (95% CI -2.6 percent, 38.9 percent) associated with a 20 ppb increase in 8-hour average ozone
concentration (2001, Table 6, p. 52).
A scaling factor is used to adjust for the number of school days in the ozone season. In the
modeling program, the function is applied to every day in the ozone season (May 1 - September 30),
however, in reality, school absences will be avoided only on school days. We assume that children are
in school during weekdays for all of May, two weeks in June, one week in August, and all of September.
This corresponds to approximately 2.75 months out of the 5 month season, resulting in an estimate of
39.3% of days (2.75/5*5/7).
In addition, not all children are at-risk for a new school absence, as defined by the study. On
average, 5.5% of school children are absent from school on a given day (U.S. Department of Education,
1996, Table 42-1). Only those who are in school on the previous day are at risk for a new absence (1-
0.055 = 94.5%). As a result, a factor of 94.5% is used in the function to estimate the population of
school children at-risk for a new absence.
Functional Form: Log-linear
Coefficient: 0.007550
Standard Error: 0.004527
Incidence Rate: daily school absence rate = 0.055 (U.S. Department of Education, 1996, Table 42-1)
Population: population of children ages 9-10 not absent from school on a given day169 = 94.5% of
children ages 9-10
Scaling Factor: Proportion of days that are school days in the ozone season170 = 0.3 93
G .5.5 School Loss Days, Illness-Related (Gilliland et al., 2001)
Gilliland et al. (2001) examined the association between air pollution and school absenteeism
among 4th grade school children (ages 9-10) in 12 southern Californian communities. The study was
conducted from January through June 1996. The authors used school records to collect daily absence
data and parental telephone interviews to identify causes. They defined illness-related absences as
respiratory or non-respiratory. A respiratory illness was defined as an illness that included at least one of
the following: runny nose/sneezing, sore throat, cough, earache, wheezing, or asthma attack. The
169 The proportion of children not absent from school on a given day (5.5%) is based on 1996 data from the U.S.
Department of Education (1996, Table 42-1).
170 Ozone is modeled for the 5 months from May 1 through September 30. We assume that children are in school during
weekdays for all of May, 2 weeks in June, 1 week in August, and all of September. This corresponds to approximately 2.75 months
out of the 5 month season, resulting in an estimate of 39.3% of days (2.75/5*5/7).
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Appendix G. Ozone C-R Functions
authors used 15 and 30 day distributed lag models to quantify the association between ozone, PM10, and
N02 and incident school absences. Ozone levels were positively associated with all school absence
measures and significantly associated with all illness-related school absences (non-respiratory illness,
respiratory illness, URI and LRI). Neither PM10 nor N02 was significantly associated with illness-
related school absences, but PM10 was associated with non-illness related absences. The C-R function
for ozone is based on the results of the single pollutant model.
Gilliland et al. (2001) defines an incident absence as an absence that followed attendance on the
previous day and the incidence rate as the number of incident absences on a given day over the
population at risk for an absence on a given day (i.e. those children who were not absent on the previous
day). Since school absences due to air pollution may last longer than one day, an estimate of the average
duration of school absences could be used to calculated the total avoided school loss days from an
estimate of avoided new absences. A simple ratio of the total absence rate divided by the new absence
rate would provide an estimate of the average duration of school absences, which could be applied to the
estimate of avoided new absences as follows:
totalAbsences
Duration- —
newAbsences
A I ola!A bsences- - [ incidence{ e ~ ^ -1) -duration-pop
Since the function is log-linear, the baseline incidence rate (in this case, the rate of new
absences) is multiplied by duration, which reduces to the total school absence rate. Therefore, the same
result would be obtained by using a single estimate of the total school absence rate in the C-R function.
Using this approach, we assume that the same relationship observed between pollutant and new school
absences in the study would be observed for total absences on a given day. As a result, the total school
absence rate is used in the function below. The derivation of this rate is described in the section on
baseline incidence rate estimation.
Single Pollutant Model
For total illness-related absences, the coefficient and standard error are based on a percent
increase of 62.9 percent (95% CI 18.4 percent, 124.1 percent) associated with a 20 ppb increase in 8-
hour average ozone concentration (2001, Table 6, p. 52).
A scaling factor is used to adjust for the number of school days in the ozone season. In the
modeling program, the function is applied to every day in the ozone season (May 1 - September 30),
however, in reality, school absences will be avoided only on school days. We assume that children are
in school during weekdays for all of May, two weeks in June, one week in August, and all of September.
This corresponds to approximately 2.75 months out of the 5 month season, resulting in an estimate of
39.3% of days (2.75/5*5/7).
In addition, not all children are at-risk for a new school absence, as defined by the study. On
average, 5.5% of school children are absent from school on a given day (U.S. Department of Education,
1996, Table 42-1). Only those who are in school on the previous day are at risk for a new absence (1-
0.055 = 94.5%). As a result, a factor of 94.5% is used in the function to estimate the population of
school children at-risk for a new absence.
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Appendix G. Ozone C-R Functions
Functional Form: Log-linear
Coefficient: 0.024398
Standard Error: 0.008138
Incidence Rate: region-specific daily illness-related school absence rate (Adams et al., 1999, Table 47),
assuming 180 school days per year.
Population: population of children ages 9-10 not absent from school on a given day171 = 94.5% of
children ages 9-10
Scaling Factor: Proportion of days that are school days in the ozone season172 = 0.3 93
G .5.6 School Loss Days, Respiratory Illness-Related (Gilliland et al., 2001)
Gilliland et al. (2001) examined the association between air pollution and school absenteeism
among 4th grade school children (ages 9-10) in 12 southern Californian communities. The study was
conducted from January through June 1996. The authors used school records to collect daily absence
data and parental telephone interviews to identify causes. They defined illness-related absences as
respiratory or non-respiratory. A respiratory illness was defined as an illness that included at least one of
the following: runny nose/sneezing, sore throat, cough, earache, wheezing, or asthma attack. The
authors used 15 and 30 day distributed lag models to quantify the association between ozone, PM10, and
N02 and incident school absences. Ozone levels were positively associated with all school absence
measures and significantly associated with all illness-related school absences (non-respiratory illness,
respiratory illness, URI and LRI). Neither PM10 nor N02 was significantly associated with illness-
related school absences, but PM10 was associated with non-illness related absences. The C-R function
for ozone is based on the results of the single pollutant model.
Gilliland et al. (2001) defines an incident absence as an absence that followed attendance on the previous
day and the incidence rate as the number of incident absences on a given day over the population at risk
for an absence on a given day (i.e. those children who were not absent on the previous day). Since
school absences due to air pollution may last longer than one day, an estimate of the average duration of
school absences could be used to calculated the total avoided school loss days from an estimate of
avoided new absences. A simple ratio of the total absence rate divided by the new absence rate would
provide an estimate of the average duration of school absences, which could be applied to the estimate of
avoided new absences as follows:
totalAbsences
Duration= -
newAbsences
A 7 otalA bsences- - [ incidence-( e ~°5 -1) -duration-pop
Since the function is log-linear, the baseline incidence rate (in this case, the rate of new
absences) is multiplied by duration, which reduces to the total school absence rate. Therefore, the same
result would be obtained by using a single estimate of the total school absence rate in the C-R function.
171 The proportion of children not absent from school on a given day (5.5%) is based on 1996 data from the U.S.
Department of Education (1996, Table 42-1).
172 Ozone is modeled for the 5 months from May 1 through September 30. We assume that children are in school during
weekdays for all of May, 2 weeks in June, 1 week in August, and all of September. This corresponds to approximately 2.75 months
out of the 5 month season, resulting in an estimate of 39.3% of days (2.75/5*5/7).
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Appendix G. Ozone C-R Functions
Using this approach, we assume that the same relationship observed between pollutant and new school
absences in the study would be observed for total absences on a given day. As a result, the total school
absence rate is used in the function below. The derivation of this rate is described in the section on
baseline incidence rate estimation.
Single Pollutant Model
For respiratory illness-related absences, the coefficient and standard error are based on a percent
increase of 82.9 percent (95% CI 3.9 percent, 222.0 percent) associated with a 20 ppb increase in 8-hour
average ozone concentration (2001, Table 6, p. 52).
A scaling factor is used to adjust for the number of school days in the ozone season. In the
modeling program, the function is applied to every day in the ozone season (May 1 - September 30),
however, in reality, school absences will be avoided only on school days. We assume that children are
in school during weekdays for all of May, two weeks in June, one week in August, and all of September.
This corresponds to approximately 2.75 months out of the 5 month season, resulting in an estimate of
39.3% of days (2.75/5*5/7).
In addition, not all children are at-risk for a new school absence, as defined by the study. On
average, 5.5% of school children are absent from school on a given day (U.S. Department of Education,
1996, Table 42-1). Only those who are in school on the previous day are at risk for a new absence (1-
0.055 = 94.5%). As a result, a factor of 94.5% is used in the function to estimate the population of
school children at-risk for a new absence.
Functional Form: Log-linear
Coefficient: 0.030188
Standard Error: 0.014436
Incidence Rate: region-specific daily respiratory illness-related school absence rate (Adams et al., 1999,
Table 47), assuming 180 school days per year.
Population: population of children ages 9-10 not absent from school on a given day173 = 94.5% of
children ages 9-10
Scaling Factor: Proportion of days that are school days in the ozone season174 = 0.3 93
G .5.7 Worker Productivity: Crocker and Horst (1981)
To monetize benefits associated with increased worker productivity resulting from improved
ozone air quality, we used information reported in Crocker and Horst (1981) and summarized in EPA
(1994). Crocker and Horst examined the impacts of ozone exposure on the productivity of outdoor
citrus workers. The study measured productivity impacts as the change in income associated with a
change in ozone exposure, given as the elasticity of income with respect to ozone concentration (-
173 The proportion of children not absent from school on a given day (5.5%) is based on 1996 data from the U.S.
Department of Education (1996, Table 42-1).
174 Ozone is modeled for the 5 months from May 1 through September 30. We assume that children are in school during
weekdays for all of May, 2 weeks in June, 1 week in August, and all of September. This corresponds to approximately 2.75 months
out of the 5 month season, resulting in an estimate of 39.3% of days (2.75/5*5/7).
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Appendix G. Ozone C-R Functions
0.1427).175 The reported elasticity translates a ten percent reduction in ozone to a 1.4 percent increase in
income. Given the national median daily income for outdoor workers engaged in strenuous activity
reported by the U.S. Census Bureau (2002), $68 per day (2000$),176 a ten percent reduction in ozone
yields about $0.97 in increased daily wages. We adjust the national median daily income estimate to
reflect regional variations in income using a factor based on the ratio of county median household
income to national median household income. No information was available for quantifying the
uncertainty associated with the central valuation estimate. Therefore, no uncertainty analysis was
conducted for this endpoint.
Single Pollutant Model
The C-R function for estimating changes in worker productivity is shown below:
Qi— Qo
Aproductivity= /?———•dailyincome¦ pop-,
Qi
Functional Form: Linear
Coefficient: 0.1427
Daily Income: median daily income for outdoor workers177
Population: population of adults 18 to 64 employed as farm workers.
175 The relationship estimated by Crocker and Horst between wages and ozone is a log-log relationship. Therefore the
elasticity of wages with respect to ozone is a constant, equal to the coefficient of the log of ozone in the model.
176 The national median daily income for workers engaged in "farming, forestry, and fishing" from the U.S. Census
Bureau (2002, Table 621, p. 403) is used as a surrogate for outdoor workers engaged in strenuous activity.
177 The national median daily income for workers engaged in "farming, forestry, and fishing" was obtained from the U.S.
Census Bureau (2002, Table 621, p. 403) and is used as a surrogate for outdoor workers engaged in strenuous activity. This national
median daily income ($68) is then scaled by the ratio of national median income to county median income to estimate county
median daily income for outdoor workers.
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Appendix G. Ozone C-R Functions
Exhibit G-6. Concentration-Response (C-R) Functions for Ozone and Asthma-Related Effects
Endpoint Name
Author
Year
Location
Age
Race
Gender
Other
Pollutants
Averaging
Time1
Functional
Form
Beta
Std Error
Notes
Asthma Exacerbation,
Asthma Attacks
Whittemore
and Korn
1980
Los Angeles, CA
All
All
All
TSP
1-hr max
Logistic
0.001843
0.000715
Asthma Exacerbation,
Cough
Ostro et al.
2001
Los Angeles, CA
8-13
Black
All
None
1-hr max
Logistic
-0.001814
0.000824
Probability of
symptoms
Asthma Exacerbation,
Cough
Ostro et al.
2001
Los Angeles, CA
8-13
Black
All
None
1-hr max
Logistic
-0.003196
0.001456
Probability of a new
onset of symptoms
Asthma Exacerbation,
Shortness of Breath
Ostro et al.
1995
Los Angeles, CA
7-12
Black
All
None
1-hr max
Logistic
0.003834
0.001859
Asthma Exacerbation,
Shortness of Breath
Ostro et al.
2001
Los Angeles, CA
8-13
Black
All
None
1-hr max
Logistic
0.000249
0.001140
Probability of
symptoms
Asthma Exacerbation,
Shortness of Breath
Ostro et al.
2001
Los Angeles, CA
8-13
Black
All
None
1-hr max
Logistic
0
0.001835
Probability of a new
onset of symptoms
Asthma Exacerbation,
Wheeze
Ostro et al.
2001
Los Angeles, CA
8-13
Black
All
None
1-hr max
Logistic
-0.001547
0.000815
Probability of
symptoms
Asthma Exacerbation,
Wheeze
Ostro et al.
2001
Los Angeles, CA
8-13
Black
All
None
1-hr max
Logistic
-0.001282
0.001212
Probability of a new
onset of symptoms
1. The averaging time refers to the metric used in the benefits model. This may differ slightly from the averaging time used in the study. Refer to the study summaries below for
more detail on the specific averaging time used in the study.
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Appendix G. Ozone C-R Functions
G .6 Asthma-Related Effects
Exhibit G-6 summarizes the C-R functions used to estimate the relationship between ozone and
asthma-related effects. Detailed summaries of each of the studies used to generate the functions are
described below, along with the parameters used in each of the functions.
G .6.1 Asthma Attacks (Whittemore and Korn, 1980)
Whittemore and Korn (1980) examined the relationship between air pollution and asthma attacks
in a survey of 443 children and adults, living in six communities in southern California during three 34-
week periods in 1972-1975. The analysis focused on TSP and oxidants (Ox). Respirable PM, N02, S02
were highly correlated with TSP and excluded from the analysis. In a two pollutant model, daily levels
of both TSP and oxidants were significantly related to reported asthma attacks. The results from this
model were used, and the oxidant result was adjusted so it may be used with ozone data.
Multipollutant Model (ozone and PM10)
The daily one-hour ozone coefficient is based on an oxidant coefficient (1.66) estimated from
data expressed in ppm. The coefficient is converted to ppb by dividing by 1,000 and to ozone by
multiplying by 1.11,178 The standard error is calculated from the two-tailed p-value (<0.01) reported by
Whittemore and Korn (1980, Table 5), which implies a t-value of at least 2.576 (assuming a large
number of degrees of freedom).
Functional Form: Logistic
Coefficient: 0.001843
Standard Error: 0.000715
Incidence Rate: daily incidence of asthma attacks = 0.0550179
Population: population of asthmatics of all ages = 3.86% of the population of all ages (American Lung
Association, 2002c, Table 7)
G .6.2 Asthma Exacerbation, Cough (Ostro et al., 2001)
Ostro et al. (2001) studied the relation between air pollution in Los Angeles and asthma
exacerbation in African-American children (8 to 13 years old) from August to November 1993. They
used air quality data for PM10, PM2 5, N02, and 03 in a logistic regression model with control for age,
178 The study used oxidant measurements in ppm (Whittemore and Korn, 1980, p. 688); these have been converted to
ozone measurements in ppb, assuming ozone comprises 90% of oxidants (i.e., 1.11 *ozone=oxidant). It is assumed that the harm of
oxidants is caused by ozone. The view expressed in the Ozone Staff Paper (U.S. EPA, 1996, p.164) is consistent with assuming that
ozone is the oxidant of concern at normal ambient concentrations: "Further, among the photochemical oxidants, the acute-exposure
chamber, field, and epidemiological human health data base raises concern only for ozone at levels of photochemical oxidants
commonly reported in ambient air. Thus, the staff recommends that ozone remain as the pollutant indicator for protection of public
health from exposure to all photochemical oxidants found in the ambient air."
179 Based on an analysis of the 1999 National Health Interview Survey, the daily incidence of wheezing attacks for adult
asthmatics is estimated to be 0.0550. In the same survey, wheezing attacks for children were examined, however, the number of
wheezing attacks per year were censored at 12 (compared to censoring at 95 for adults). Due to the potential for underestimation of
the number of children's wheezing attacks, we used the adult rate for all individuals.
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Appendix G. Ozone C-R Functions
income, time trends, and temperature-related weather effects.180 Asthma symptom endpoints were
defined in two ways: "probability of a day with symptoms" and "onset of symptom episodes". New
onset of a symptom episode was defined as a day with symptoms followed by a symptom-free day. The
authors found cough prevalence associated with PM10 and PM25 and cough incidence associated with
PM25 PM10, and N02. Ozone was not significantly associated with cough among asthmatics. The ozone
C-R functions are based on the results of single pollutant models looking at both the probability of
symptoms and the onset of new symptoms.
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on the odds ratio (0.93) and 95% confidence
interval (0.87-0.99) reported for a 40 ppb increase in one-hour maximum ozone levels (Ostro et al.,
2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: -0.001814
Standard Error: 0.000824
Incidence Rate: daily cough rate per person (Ostro et al., 2001, p.202) = 0.145
Population: asthmatic African-American population ages 8 to 13 = 7.26%181 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on the odds ratio (0.88) and 95% confidence
interval (0.78-0.98) reported for a 40 ppb increase in one-hour maximum ozone levels (Ostro et al.,
2001, Table 5, p.204).
The C-R function based on this model will estimate the number of new onset episodes of cough
avoided. In order to convert this estimate to the total number of episodes avoided, the results are
adjusted by an estimate of the duration of symptom episodes. The average duration can be estimated
from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the probability of a
new onset episode. For cough, this ratio is 2.2 (14.5% divided by 6.7%) (Ostro et al., 2001, p.202).
In addition, not all children are at-risk for a new onset of cough, as defined by the study. On
average, 14.5% of African-American asthmatics have cough on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day are at-risk for a new onset episode (1-0.145 =
85.5%). As a result, a factor of 85.5% is used in the function to estimate the population of African-
American 8 to 13 year old children at-risk for a new cough episode.
180 The authors note that there were 26 days in which PM2 5 concentrations were reported higher than PM10 concentrations.
The majority of results the authors reported were based on the full dataset. These results were used for the basis for the C-R
functions.
181 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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Appendix G. Ozone C-R Functions
Functional Form: Logistic
Coefficient: -0.003196
Standard Error: 0.001456
Incidence Rate: daily new onset cough rate per person (Ostro et al., 2001, p.202) = 0.067
Population: asthmatic African-American population ages 8 to 13 at-risk for a new episode of cough =
6.21% of African-American population ages 8 to 13 (85.5% at-risk182 times 7.26% asthmatic183)
Scaling Factor: average number of consecutive days with a cough episode (days) = 2.2
G .6.3 Asthma Exacerbation, Shortness of Breath (Ostro et al., 1995)
Using a logistic regression estimation, Ostro et al. (1995) estimated the impact of PM10, ozone,
N02, and S02 on the incidence of coughing, shortness of breath, and wheezing in 83 African-American
asthmatic children ages 7-12 living in Los Angeles from August through September 1992. Regression
results show both PM10 and ozone significantly linked to shortness of breath; the beginning of an asthma
episode was also significantly linked to ozone. No effect was seen for N02 and S02. Results for single-
pollutant models only were presented in the published paper. The C-R function is based on the model
with adjustment for respiratory infection, temperature, and outdoor mold levels (Ostro et al., 1995,
Table 3).
Single Pollutant Model
The ozone coefficient and standard error are based on the odds ratio (1.36) and 95% confidence
interval (1.02-1.83) (Ostro et al., 1995, Table 3) associated with a change in one-hour daily maximum
ozone of 8.02 pphm (80.2 ppb) (Ostro et al., 1995, Table 2).
Functional Form: Logistic
Coefficient: 0.003834
Standard Error: 0.001859
Incidence Rate: daily shortness of breath incidence rate per person (Ostro et al., 1995, p. 715) = 0.056
Population: asthmatic African-American population ages 7 to 12 = 7.26%184 of African-American
population ages 7 to 12
G .6.4 Asthma Exacerbation, Shortness of Breath (Ostro et al., 2001)
Ostro et al. (2001) studied the relationship between air pollution in Los Angeles and asthma
exacerbation in African-American children (8 to 13 years old) from August to November 1993. They
used air quality data for PM10, PM2 5, N02, and ozone in a logistic regression model with control for age,
income, time trends, and temperature-related weather effects. Asthma symptom endpoints were defined
in two ways: "probability of a day with symptoms" and "new onset of a symptom episode". New onset
182 On average, 14.5% of African-American asthmatics have cough episodes on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day (1-0.145 = 85.5%) are at-risk for a new onset episode.
183 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
184 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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Appendix G. Ozone C-R Functions
of a symptom episode was defined as a day with symptoms followed by a symptom-free day. The
authors found that both the prevalent and incident episodes of shortness of breath were associated with
PM2 5 and PM10. Neither ozone nor N02 were significantly associated with shortness of breath among
asthmatics. The ozone C-R functions are based on the results of single pollutant models looking at both
the probability of symptoms and the onset of new symptoms.
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on the odds ratio (1.01) and 95% confidence
interval (0.92-1.10) reported for a 40 ppb increase in one-hour maximum ozone levels (Ostro et al.,
2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: 0.000249
Standard Error: 0.001140
Incidence Rate: daily shortness of breath rate per person (Ostro et al., 2001, p.202) = 0.074
Population: asthmatic African-American population ages 8 to 13 = 7.26%185 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on the odds ratio (1.00) and 95% confidence
interval (0.87-1.16) reported for a 40 ppb increase in one-hour maximum ozone levels (Ostro et al.,
2001, Table 5, p.204).
The C-R function based on this model will estimate the number of new onset episodes of
shortness of breath avoided. In order to convert this estimate to the total number of episodes avoided,
the results are adjusted by an estimate of the duration of symptom episodes. The average duration can be
estimated from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the
probability of a new onset episode. For shortness of breath, this ratio is 2.0 (7.4% divided by 3.7%)
(Ostro et al., 2001, p.202).
In addition, not all children are at-risk for a new onset of shortness of breath, as defined by the
study. On average, 7.4% of African-American asthmatics have shortness of breath episodes on a given
day (Ostro et al., 2001, p.202). Only those who are symptom-free on the previous day are at-risk for a
new onset episode (1-0.074 = 92.6%). As a result, a factor of 92.6% is used in the function to estimate
the population of African-American 8 to 13 year old children at-risk for a new shortness of breath
episode.
Functional Form: Logistic
Coefficient: 0
Standard Error: 0.001835
Incidence Rate: daily new onset shortness of breath rate per person (Ostro et al., 2001, p.202) = 0.037
185 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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Appendix G. Ozone C-R Functions
Population: asthmatic African-American population ages 8 to 13 at-risk for anew episode of shortness
of breath = 6.72% of African-American population ages 8 to 13 (92.6% at-risk186 times 7.26%
asthmatic187)
Scaling Factor: average number of consecutive days with a shortness of breath episode (days) = 2.0
G .6.5 Asthma Exacerbation, Wheeze (Ostro et al., 2001)
Ostro et al. (2001) studied the relation between air pollution in Los Angeles and asthma
exacerbation in African-American children (8 to 13 years old) from August to November 1993. They
used air quality data for PM10, PM25, N02, and 03 in a logistic regression model with control for age,
income, time trends, and temperature-related weather effects. Asthma symptom endpoints were defined
in two ways: "probability of a day with symptoms" and "onset of symptom episodes". New onset of a
symptom episode was defined as a day with symptoms followed by a symptom-free day. The authors
found both the prevalence and incidence of wheeze associated with PM2 5 PM10, and N02. Ozone was
not significantly associated with wheeze among asthmatics. The ozone C-R functions are based on the
results of single pollutant models looking at both the probability of symptoms and the onset of new
symptoms.
Single Pollutant Model (probability of symptoms)
The coefficient and standard error are based on the odds ratio (0.94) and 95% confidence
interval (0.88-1.00) reported for a 40 ppb increase in one-hour maximum ozone levels (Ostro et al.,
2001, Table 4, p.204).
Functional Form: Logistic
Coefficient: -0.001547
Standard Error: 0.000815
Incidence Rate: daily wheeze rate per person (Ostro et al., 2001, p.202) = 0.173
Population: asthmatic African-American population ages 8 to 13 = 7.26%188 of African-American
population ages 8 to 13
Single Pollutant Model (probability of a new onset of symptoms)
The coefficient and standard error are based on the odds ratio (0.95) and 95% confidence
interval (0.86-1.04) reported for a 40 ppb increase in one-hour maximum ozone levels (Ostro et al.,
2001, Table 5, p.204).
The C-R function based on this model will estimate the number of new onset episodes of wheeze
avoided. In order to convert this estimate to the total number of episodes avoided, the results are
adjusted by an estimate of the duration of symptom episodes. The average duration can be estimated
186 On average, 7.4% of African-American asthmatics have shortness of breath episodes on a given day (Ostro et al., 2001,
p.202). Only those who are symptom-free on the previous day (1-0.074 = 92.6%) are at-risk for a new onset episode.
187 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
188 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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Appendix G. Ozone C-R Functions
from Ostro et al. (2001) using the ratio of the probability of a symptom episode to the probability of a
new onset episode. For wheeze, this ratio is 2.3 (17.3% divided by 7.6%) (Ostro et al., 2001, p.202).
In addition, not all children are at-risk for a new onset of wheeze, as defined by the study. On
average, 17.3% of African-American asthmatics have wheeze on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day are at-risk for a new onset episode (1-0.173 =
82.7%). As a result, a factor of 82.7% is used in the function to estimate the population of African-
American 8 to 13 year old children at-risk for a new wheeze episode.
Functional Form: Logistic
Coefficient: -0.001282
Standard Error: 0.001212
Incidence Rate: daily new onset wheeze rate per person (Ostro et al., 2001, p.202) = 0.076
Population: asthmatic African-American population ages 8 to 13 at-risk for a new episode of wheeze =
6.00% of African-American population ages 8 to 13 (82.7% at-risk189 times 7.26% asthmatic190)
Scaling Factor: average number of consecutive days with a wheeze episode (days) = 2.3
189 On average, 17.3% of African-American asthmatics have wheeze episodes on a given day (Ostro et al., 2001, p.202).
Only those who are symptom-free on the previous day (1-0.173 = 82.7%) are at-risk for a new onset episode.
190 The American Lung Association (2002c, Table 9) estimates asthma prevalence for African-American children ages 5 to
17 at 7.26% (based on data from the 1999 National Health Interview Survey).
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Appendix H. Economic Valuation of Health Effects
Appendix H: Economic Value of Health Effects
This appendix first presents an overview of valuation, and then presents the unit values that are
available in BenMAP for each of the health endpoints included in the current suite of C-R functions.
Wherever possible, we present a distribution of the unit value, characterizing the uncertainty surrounding
any point estimate. The mean of the distribution is taken as the point estimate of the unit value, and the
distribution itself is used to characterize the uncertainty surrounding the unit value, which feeds into the
uncertainty surrounding the monetary benefits associated with reducing the incidence of the health
endpoint. Below we give detailed descriptions of the derivations of unit values and their distributions, as
well as tables listing the unit values and their distributions, available for each health endpoint. The
definitions of the distributions and their parameters is given in Exhibit H-l 1, at the end of this Appendix.
H.l Overview of Valuation
Reductions in ambient concentrations of air pollution generally lower the risk of future adverse
health affects by a fairly small amount for a large population. A lower risk for everyone means that
fewer cases of the adverse health effect are expected, although we don't know ex ante which cases will
be avoided. For example, the analysis may predict 100 hospital admissions for respiratory illnesses
avoided, but the analysis does not estimate which individuals will be spared those cases of respiratory
illness that would have required hospitalization. The health benefits conferred on individuals by a
reduction in pollution concentrations are, then, actually reductions in the risk of having to endure certain
health problems. These benefits (reductions in risk) may not be the same for all individuals (and could
be zero for some individuals). Likewise, the WTP for a given benefit is likely to vary from one
individual to another. In theory, the total social value associated with the decrease in risk of a given
health problem resulting from a given reduction in pollution concentrations is generally taken to be the
sum of everyone's WTP for the benefits they receive:
where B is the benefit (i.e., the reduction in risk of having to endure the health problem conferred on the
ilh individual by the reduction in pollution concentrations, WTP^B,) is the ilh individual's WTP for that
benefit, and N is the number of people exposed to the pollution.191 If a reduction in pollution
concentrations affects the risks of several health endpoints, the total health-related social value of the
reduction in pollution concentrations is:
where BtJ is the benefit related to the jlh health endpoint (i.e., the reduction in risk of having to endure the
jlh health problem) conferred on the ilh individual by the reduction in pollution concentrations, and
WTP^B,,) is the ilh individual's WTP for that benefit.
The reduction in risk of each health problem for each individual is not known, however (nor is
each individual's WTP for each possible risk reduction he or she might receive). Instead,
epidemiological studies allow us to estimate the number of cases of an adverse health effect that would
i= 1
/=1 j=l
191 WTP may also include altruism
would be enjoyed by others.
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Appendix H. Economic Valuation of Health Effects
be avoided by a given reduction in pollutant concentrations. Therefore, in practice, benefit analyses take
an ex post approach and estimate the value of a statistical health problem avoided. If we have an
estimate of the average individual's WTP for the risk reduction conferred upon him, we can derive from
that an estimate of the value of a statistical case avoided. Suppose, for example, that a given reduction in
pollutant concentrations results in a decrease in mortality risk of 1/10,000. Then for every 10,000
individuals, one individual would be expected to die in the absence of the reduction in pollutant
concentrations (who would not be expected to die in the presence of the reduction in pollutant
concentrations). If the average individual's WTP for this 1/10,000 decrease in mortality risk is $100,
then the value of a statistical life is 10,000 x $100, or $1 million. In general, the ex ante WTP for a risk
reduction of x can be converted into an ex post value of a statistical case avoided by dividing the average
individual's WTP for the risk reduction of x by x (e.g. $100/0.0001 = $1,000,000). The same type of
calculation can produce values for statistical incidences of other health endpoints.
The value of a statistical case avoided is referred to here as a "unit value." The total dollar
value for a specific health effect is the number of statistical cases of the health effect avoided times the
unit value for that health effect. Whereas ideally the unit value would reflect the underlying WTP for the
ex ante risk reduction (as in the above example), in practice we usually have estimates of the value of the
ex post statistical case avoided. Sometimes those values come from contingent valuation studies, in
which study participants are queried about their WTP to avoid a specific adverse health effect.
Sometimes, when WTP estimates are not available, WTP is approximated by other measures, most
notably cost of illness measures.
An individual's WTP to avoid an adverse health effect will include, at a minimum, the amount
of money he would have to pay for medical expenses associated with the illness. Because medical
expenditures are to a significant extent shared by society, via medical insurance, Medicare, etc.,
however, the medical expenditures actually incurred by the individual are likely to be less than the total
medical cost to society. The total value to society of an individual's avoidance of an adverse health
effect, then, might be thought of as having two components: (1) the cost of the illness (COI) to society,
including the total value of the medical resources used (some portion of which will be paid by the
individual), plus the value of the lost productivity, as well as (2) the WTP of the individual, as well as
that of others, to avoid the pain and suffering resulting from the illness.
These two components might be rephrased as (1) the market component and (2) the non-market
component. When an individual becomes ill, there is some amount of resources (medical goods and
services) that are used to address the illness. The value of those resources, whoever pays the bill, is the
market component of the value of avoiding the illness - i.e., the value of the resources that would not
have to be used up if the individual had not incurred the illness. This may be a small value - e.g., the
cost of aspirin used for a headache, or a very large value - e.g., the value of medical goods and services
used to treat someone who goes to the hospital with a life-threatening illness. The COI approach
attempts to estimate the total value of the medical resources used up as well as the value of the
individual's time lost as a result of the illness. Because this method does not include the value of
avoiding the pain and suffering resulting from the illness (a potentially large component), it is generally
believed to underestimate the total value of avoiding the illness, perhaps substantially.
The contingent valuation method attempts to elicit from people what they would be willing to
pay to avoid the illness. Because of the distortion in the market for medical goods and services, whereby
individuals generally do not pay the full value of the medical resources used to address their illnesses,
however, this method too is likely to understate the total value of avoiding the illness.
Although the COI and contingent valuation approaches to valuing health effects avoided are the
two most common methods, other methods have been used in certain circumstances. The method the
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Appendix H. Economic Valuation of Health Effects
benefit analyst chooses to value a particular health endpoint will depend in part on what is available.
Benefit analysts typically do not do primary research to generate data for valuation to be used in a
benefit analysis - it is too expensive and time consuming. Instead, the benefit analyst uses data or
estimates that have been collected or generated by researchers and can be readily obtained in publicly
available databases or in the open literature. The unit values currently available for use in BenMap are
all of this type.
Sometimes more than one estimate of a unit value for a health effect is available. For chronic
bronchitis, for example, we have both a WTP estimate and COI estimates. In that case, you may select
one or pool two or more estimates. As research continues and new unit values become available, the
database of unit values available for use in BenMAP will be updated. The discussion below refers to the
set of unit values that are currently available for use in BenMAP. Unless otherwise stated, all unit values
are in 2000$.
H.2 Mortality
The economics literature concerning the appropriate method for valuing reductions in premature
mortality risk is still developing. The adoption of a value for the projected reduction in the risk of
premature mortality is the subject of continuing discussion within the economics and public policy
analysis communities. Issues such as the appropriate discount rate and whether there are factors, such as
age or the quality of life, that should be taken into consideration when estimating the value of avoided
premature mortality are still under discussion. BenMAP currently offers a variety of options reflecting
the uncertainty surrounding the unit value for premature mortality.
H.2.1 Value of a Statistical Life Based on 26 Studies
One unit value available in BenMAP is $6.3 million. This estimate is the mean of a distribution
fitted to 26 "value of statistical life" (VSL) estimates that appear in the economics literature and that
have been identified in the Section 812 Reports to Congress as "applicable to policy analysis." This
represents an intermediate value from a variety of estimates, and it is a value EPA has frequently used in
Regulatory Impact Analyses (RIAs) as well as in the Section 812 Retrospective and Prospective
Analyses of the Clean Air Act.
The VSL approach and the set of selected studies mirrors that of Viscusi (1992) (with the
addition of two studies), and uses the same criteria as Viscusi in his review of value-of-life studies. The
$6.3 million estimate is consistent with Viscusi's conclusion (updated to 2000$) that "most of the
reasonable estimates of the value of life are clustered in the $3.8 to $8.9 million range." Five of the 26
studies are contingent valuation (CV) studies, which directly solicit WTP information from subjects; the
rest are wage-risk studies, which base WTP estimates on estimates of the additional compensation
demanded in the labor market for riskier jobs. Because this VSL-based unit value does not distinguish
among people based on the age at their death or the quality of their lives, it can be applied to all
premature deaths.
H.2.2 Value of a Statistical Life Based on Selected Studies
In addition to the value of a statistical based on the results of 26 studies, we have included four
alternatives based loosely on the results of recent work by Mrozek and Taylor (2002) and Viscusi and
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Appendix H. Economic Valuation of Health Effects
Aldy (2003). Each of the four alternatives has a mean value of $5.5 million (2000$), but with a different
distributions: normal, uniform, triangular, and beta. Exhibit H-l presents the distribution parameters for
the suite of mortality valuations currently available in BenMAP.
Exhibit H-l. Unit Values Available for Mortality
Basis for Estimate" Age Range at Unit Value Distribution of Parameters of
Death
min. max.
(VSL)
(2000$)
Unit Value**
Distribution
PI P2
VSL, based on 26 value-of-life studies.
0
99
$6,324,101
Weibull
5.32E-6
1.509588
VSL based on range from $1 million to $10 million -
95% CI of assumed normal distribution.
0
99
$5,500,000
Normal
2,295,960.54
--
VSL based on range from $1 million to $10 million -
assumed uniform distribution.
0
99
$5,500,000
Uniform
1,000,000
10,000,000
VSL based on range from $1 million to $10 million -
assumed triangular distribution.
0
99
$5,500,000
Triangular
1,000,000
10,000,000
VSL based on range from $1 million to $10 million -
0
99
$5,500,000
Beta
1.95
1.95
95% CI of assumed beta distribution. B
1 The original value of a statistical life was calculated in 1990 $. We have used a factor of 1.3175, based on the All-Items CPI-U.
b The Beta distribution in this instance also has a scale parameter equal to 10993993.6.
H.3 Chronic Illness
This sub-section presents the unit values developed for chronic bronchitis, chronic asthma, and
non-fatal myocardial infarctions.
H.3.1 Chronic Bronchitis
PM-related chronic bronchitis is expected to last from the initial onset of the illness throughout
the rest of the individual's life. WTP to avoid chronic bronchitis would therefore be expected to
incorporate the present discounted value of a potentially long stream of costs (e.g., medical expenditures
and lost earnings) as well as WTP to avoid the pain and suffering associated with the illness. Both WTP
and COI estimates are currently available in BenMAP.
Unit Value Based on Two Studies of WTP
Two contingent valuation studies, Viscusi et al. (1991) and Krupnick and Cropper (1992),
provide estimates of WTP to avoid a case of chronic bronchitis. Viscusi et al. (1991) and Krupnick and
Cropper (1992) were experimental studies intended to examine new methodologies for eliciting values
for morbidity endpoints. Although these studies were not specifically designed for policy analysis, they
can be used to provide reasonable estimates of WTP to avoid a case of chronic bronchitis. As with other
contingent valuation studies, the reliability of the WTP estimates depends on the methods used to obtain
the WTP values. The Viscusi et al. and the Krupnick and Cropper studies are broadly consistent with
current contingent valuation practices, although specific attributes of the studies may not be.
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The study by Viscusi et al. (1991) uses a sample that is larger and more representative of the
general population than the study by Krupnick and Cropper (1992), which selects people who have a
relative with the disease. However, the chronic bronchitis described to study subjects in the Viscusi
study is severe, whereas a pollution-related case may be less severe.
The relationship between the severity of a case of chronic bronchitis and WTP to avoid it was
estimated by Krupnick and Cropper (1992). We used that estimated relationship to derive a relationship
between WTP to avoid a severe case of chronic bronchitis, as described in the Viscusis study, and WTP
to avoid a less severe case. The estimated relationship (see Table 4 in Krupnick and Cropper) can be
written as:
In (WTP)= cc+ /J^sev
where a denotes all the other variables in the regression model and their coefficients, p is the coefficient
of sev, estimated to be 0.18, and sev denotes the severity level (a number from 1 to 13). Let x (< 13)
denote the severity level of a pollution-related case of chronic bronchitis, and 13 denote the highest
severity level (as described in Viscusi et al., 1991). Then
In (WTP13)= ex+/3* 13
and
In(WTPx )= cr+ j8*x.
Subtracting one equation from the other,
In (WTP13 )- In (WTPX )= fi*( 13- x)
or
f wtp13)
ln,lF# =^(13-*>
Exponentiating and rearranging terms,
WTPX = WTP13 *e-p*(13-x).
There is uncertainty surrounding the exact values of WTP13; x, and P, and this uncertainty can be
incorporated in the equation, if you request that the analysis be carried out in "uncertainty mode." The
distribution of WTP to avoid a severe case of chronic bronchitis, WTPI3 ,is based on the distribution of
WTP responses in the Viscusi et al. (1991) study. The distribution of x, the severity level of an average
case of pollution-related chronic bronchitis, is modeled as a triangular distribution centered at 6.5, with
endpoints at 1.0 and 12.0. And the distribution of P is normal with mean = 0.18 and std. dev.= 0.0669
(the estimate of b and standard error reported in Krupnick and Cropper, 1992).
In uncertainty mode, BenMAP uses a Monte Carlo approach. On each Monte Carlo iteration,
random draws for these three variables are made, and the resulting WTPX is calculated from the equation
above. Because this function is non-linear, the expected value of WTP for a pollution-related case of CB
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Appendix H. Economic Valuation of Health Effects
cannot be obtained by using the expected values of the three uncertain inputs in the function (doing that
will substantially understate mean WTP). A Monte Carlo analysis suggests, however, that the mean
WTP to avoid a case of pollution-related chronic bronchitis is about $340,000. Therefore, if you request
that the analysis be carried out in "point estimate" mode, that is the unit value that is used.
Alternative Cost of Illness Estimates
Cost of illness estimates for chronic bronchitis were derived from estimates of annual medical
costs and annual lost earnings by Cropper and Krupnick (1990). This study estimated annual lost
earnings resulting from chronic bronchitis as a function of age at onset of the illness, for the following
age categories: 25-43, 35-44, 45-54, and 55-65 (see Cropper and Krupnick, Table 8). Annual medical
expenses were estimated for 10-years age groups (0-9, 10-19, 20-29, ..., 80-89). We derived estimates of
the present discounted value of the stream of medical and opportunity costs for people whose age of
onset is 30, 40, 50, 60, 70, and 80. Medical costs (which are in 1977$ in the Cropper and Krupnick
study) were inflated to 2000$ using the CPI-U for medical care; lost earnings (opportunity costs) were
inflated to 2000$ using the Employment Cost Index for Wages and Salaries. Life expectancies were
assumed to be unaffected by the illness.192 For example, an individual at age 70 has a life expectancy of
14.3 more years, and we assumed that someone whose age of onset of chronic bronchitis is 70 will also
live for 14.3 more years. We also assumed that opportunity costs at ages 66 and over were zero. Present
discounted values were calculated using three and seven percent discount rates.
For each of the two discount rates, there are three cost of illness unit values for chronic
bronchitis available in BenMAP, for the following age categories: 27-44, 45-64, and 65+. These are the
age categories that were used in the epidemiological study that estimated a concentration-response
function for chronic bronchitis (Abbey et al., 1995b). The estimate for the 27-44 age group is an
average of the present discounted values calculated for ages 30 and 40; the estimate for the 45-64 age
category is an average of the present discounted values calculated for ages 50 and 60; and the estimate
for the 65+ age category is an average of the present discounted values calculated for ages 70 and 80.
The suite of unit values available for use in BenMAP are shown in Exhibit H-2 below.
Exhibit H-2. Unit Values Available for Chronic Bronchitis
Basis for Estimate
Age of
Onset
min
max.
Present
Discounted
Value of
Medical
Costs
Present
Discounted
Value of
Opportunity
Costs
Unit
Value
Distribution
WTP: average severity
30 99
N/A
N/A
$340,482
custom
COI: med costs + wage loss, 3% DR
27 44
$18,960
$135,463
$154,422
none
45 64
$23,759
$76,029
$99,788
none
65 99
$11,088
$0
$11,088
none
COI: med costs + wage loss, 7% DR
27 44
$7,886
$80,444
$88,331
none
45 64
$14,390
$59,577
$73,967
none
65 99
$9,030
$0
$9,030
none
192 Source of life expectancies: National Vital Statistics Reports, Volume 47, No. 19, June 30, 1999.
expectancy at selected ages by race and sex: United States, 1997.
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H.3.2 Chronic Bronchitis Reversals
The unit value for chronic bronchitis reversals assumes that this is chronic bronchitis with a
severity level of 1. The method for generating a distribution of unit values in BenMAP is therefore the
same as the WTP-based unit value method for chronic bronchitis (see above), with x=l. The mean of
this distribution is $150,221.
H.3.3 Chronic Asthma
Two studies have estimated WTP to avoid chronic asthma in adults. Blumenschein and
Johannesson (1998) used two different contingent valuation (CV) methods, the dichotomous choice
method and a bidding game, to estimate mean willingness to pay for a cure for asthma. The mean WTP
elicited from the bidding game was $189 per month, or $2,268 per year (in 1996$). The mean WTP
elicited from the dichotomous choice approach was $343 per month, or $4,116 per year (in 1996$).
Using $2,268 per year, a three percent discount rate, and 1997 life expectancies for males in the United
States (National Center for Health Statistics, 1999, Table 5), the present discounted value of the stream
of annual WTPs is $47,637 (in 2000$).
O'Conor and Blomquist (1997) estimated WTP to avoid chronic asthma from estimates of risk-
risk tradeoffs. Combining the risk-risk tradeoffs with a statistical value of life, the annual value of
avoiding asthma can be derived. Assuming a value of a statistical life of $6 million, they derived an
annual WTP to avoid asthma of $1500 (O'Connor and Blomquist, 1997, p. 677). For a value of a
statistical life of $5,894,400 (in 1997 $), the corresponding implied annual value of avoiding chronic
asthma, based on O'Conor and Blomquist would be $1,474. Assuming a three percent discount rate and
1997 life expectancies for males in the United States, the present discounted value of the stream of
annual WTPs would be $30,257 (in 2000$). A unit value, based on a three percent discount rate, is the
average of the two estimates, or $38,947. Following the method used for the §812 Prospective analysis,
the uncertainty surrounding the WTP to avoid a case of chronic asthma among adult males was
characterized by a triangular distribution on the range determined by the two study-specific WTP
estimates.
A second unit value, using a seven percent discount rate, is also available for use in BenMAP.
The method used to derive this unit value is the same as that described above for the three percent
discount rate unit value. The unit values available for use in BenMAP are summarized in Exhibit H-3
below.
Exhibit H-3. Unit Values Available for Chronic Asthma
Basis for Estimate
Age Range
Unit Value
Distribution of
Unit Value
Parameters of
Distribution
min.
max.
PI
P2
WTP: 3% DR (Discount Rate)
27
99
$38,947
triangular
$30,257
$47,637
WTP: 7% DR
27
99
$25,357
triangular
$19,699
$31,015
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H.3.4 Non-Fatal Myocardial Infarctions (Heart Attacks)
In the absence of a suitable WTP value for reductions in the risk of non-fatal heart attacks, there
are a variety of cost-of-illness unit values available for use in BenMAP. These cost-of-illness unit values
incorporate two components: the direct medical costs and the opportunity cost (lost earnings) associated
with the illness event. Because the costs associated with a heart attack extend beyond the initial event
itself, the unit values include costs incurred over five years. Using age-specific annual lost earnings
estimated by Cropper and Krupnick (1990), and a three percent discount rate, we estimated the following
present discounted values in lost earnings over 5 years due to a heart attack: $8,774 for someone
between the ages of 25 and 44, $12,932 for someone between the ages of 45 and 54, and $74,746 for
someone between the ages of 55 and 65. The corresponding age-specific estimates of lost earnings using
a seven percent discount rate are $7,855, $11,578, and $66,920, respectively. Cropper and Krupnick do
not provide lost earnings estimates for populations under 25 or over 65. As such we do not include lost
earnings in the cost estimates for these age groups.
We have found three possible sources of estimates of the direct medical costs of a myocardial
infarction (MI) in the literature:
Wittels et al. (1990) estimated expected total medical costs of MI over 5 years to be $51,211 (in
1986$) for people who were admitted to the hospital and survived hospitalization. (There does
not appear to be any discounting used.) Wittels et al. was used to value coronary heart disease in
the 812 Retrospective Analysis of the Clean Air Act. Using the CPI-U for medical care, the
Wittels estimate is $109,474 in year 2000$. This estimated cost is based on a medical cost
model, which incorporated therapeutic options, projected outcomes and prices (using
"knowledgeable cardiologists" as consultants). The model used medical data and medical
decision algorithms to estimate the probabilities of certain events and/or medical procedures
being used. The authors note that the average length of hospitalization for acute MI has
decreased over time (from an average of 12.9 days in 1980 to an average of 11 days in 1983).
Wittels et al. used 10 days as the average in their study. It is unclear how much further the
length of stay (LOS) for MI may have decreased from 1983 to the present. The average LOS for
ICD code 410 (MI) in the year-2000 AHQR HCUP database is 5.5 days. However, this may
include patients who died in the hospital (not included among our non-fatal MI cases), whose
LOS was therefore substantially shorter than it would be if they hadn't died.
Eisenstein et al. (2001) estimated 10-year costs of $44,663, in 1997$ (using a three percent
discount rate), or $49,651 in 2000$ for MI patients, using statistical prediction (regression)
models to estimate inpatient costs. Only inpatient costs (physician fees and hospital costs) were
included.
Russell et al. (1998) estimated first-year direct medical costs of treating nonfatal MI of $15,540
(in 1995$), and $1,051 annually thereafter. Converting to year 2000$, that would be $18,880 for
a 5-year period, using a three percent discount rate, or $17,850, using a seven percent discount
rate.
The age group-specific estimates of opportunity cost over a five-year period are combined with
the medical cost estimates from each of the three studies listed above. Because opportunity costs are
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derived for each of five age groups, there are 3 x 5 = 15 unit values for each of 2 discount rates, or 30
unit values available for use in BenMAP.193 These are given in Exhibit H-4 below.
193 We were unable to achieve complete consistency, unfortunately, because of limitations in the input studies. For
example, although we calculated opportunity costs over a five-year period using a 3 percent and a 7 percent discount rate, we were
not able to do the same for medical costs, except for the medical costs estimated by Russell et al. (in which they estimate an annual
cost). Wittels et al. appear to have used no discounting in their estimate; Eisenstein et al. used a 3 percent discount rate. Similarly,
although almost all cost estimates (opportunity costs and medical costs) are for a 5-year period, the medical cost estimate reported
by Eisenstein et al. is for a 10-year period. There was no reasonable method for inferring from that study what costs over a 5-year
period would be.
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Exhibit H-4 Unit Values Available for Myocardial Infarction
Basis of Estimate
Age Range
Min Max
Medical Cost11
Opportunity
Cost"
Total Cost
COI: 5 yrs med, 5 yrs wages, 3% DR,
0
24
$109,474
$0
$109,474
Wittels (1990)
25
44
$109,474
$9,033
$118,507
45
54
$109,474
$13,313
$122,787
55
65
$109,474
$76,951
$186,425
66
99
$109,474
$0
$109,474
COI: 10 yrs med, 5 yrs wages, 3% DR,
0
24
$49,651
$0
$49,651
Eisenstein (2001)
25
44
$49,651
$9,033
$58,683
45
54
$49,651
$13,313
$62,964
55
65
$49,651
$76,951
$126,602
66
99
$49,651
$0
$49,651
COI: 5 yrs med, 5 yrs wages, 3% DR,
0
24
$22,331
$0
$22,331
Russell (1998)
25
44
$22,331
$9,033
$31,363
45
54
$22,331
$13,313
$35,644
55
65
$22,331
$76,951
$99,281
66
99
$22,331
$0
$22,331
COI: 5 yrs med, 5 yrs wages, 7% DR,
0
24
$109,474
$0
$109,474
Wittels (1990)
25
44
$109,474
$8,087
$117,561
45
54
$109,474
$11,919
$121,393
55
65
$109,474
$68,894
$178,368
66
99
$109,474
$0
$109,474
COI: 10 yrs med, 5 yrs wages, 7% DR,
0
24
$49,651
$0
$49,651
Eisenstein (2001)
25
44
$49,651
$8,087
$57,738
45
54
$49,651
$11,919
$61,570
55
65
$49,651
$68,894
$118,545
66
99
$49,651
$0
$49,651
COI: 5 yrs med, 5 yrs wages, 7% DR,
0
24
$21,113
$0
$21,113
Russell (1998)
25
44
$21,113
$8,087
$29,200
45
54
$21,113
$11,919
$33,032
55
65
$21,113
$68,894
$90,007
66
99
$21,113
$0
$21,113
sFrom Cropper and Krupnick (1990). Present discounted value of 5 yrs of lost earnings, at 3% and 7% discount rate, adjusted
from 1977$ to 2000$ using CPI-U "all items".
b An average of the 5-year costs estimated by Wittels et al. (1990) and Russell et al. (1998). Note that Wittels et al. appears not
to have used discounting in deriving a 5-year cost of $109,474; Russell et al. estimated first-year direct medical costs and annual
costs thereafter. The resulting 5-year cost is $22,331, using a 3% discount rate, and $21,113, using a 7% discount rate. Medical
costs were inflated to 2000$ using CPI-U for medical care.
H.4 Hospital Admissions & Emergency Room Visits
This section presents the values for avoided hospital admissions, as well as avoided emergency
room visits. We assume that hospital admissions due to acute exposure to air pollution pass through the
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emergency room. However, the value of hospital admissions that we have calculated here does not
account for the cost incurred in the emergency room visit.
H.4.1 Hospital Admissions
As suggested above, the total value to society of an individual's avoidance of a hospital
admission can be thought of as having two components: (1) the cost of illness (COI) to society,
including the total medical costs plus the value of the lost productivity, as well as (2) the WTP of the
individual, as well as that of others, to avoid the pain and suffering resulting from the illness.
In the absence of estimates of social WTP to avoid hospital admissions for specific illnesses
(components 1 plus 2 above), estimates of total COI (component 1) are available for use in BenMAP as
conservative (lower bound) estimates. Because these estimates do not include the value of avoiding the
pain and suffering resulting from the illness (component 2), they are biased downward. Some analyses
adjust COI estimates upward by multiplying by an estimate of the ratio of WTP to COI, to better
approximate total WTP. Other analyses have avoided making this adjustment because of the possibility
of over-adjusting ~ that is, possibly replacing a known downward bias with an upward bias. Based on
Science Advisory Board (SAB) advice, the COI values currently available for use in BenMAP are not
adjusted.
Unit values are based on ICD-code-specific estimated hospital charges and opportunity cost of
time spent in the hospital (based on the average length of a hospital stay for the illness). The opportunity
cost of a day spent in the hospital is estimated as the value of the lost daily wage, regardless of whether
or not the individual is in the workforce.
For all hospital admissions endpoints available in BenMAP, estimates of hospital charges and
lengths of hospital stays were based on discharge statistics provided by the Agency for Healthcare
Research and Quality's Healthcare Utilization Project (2000). The total COI for an ICD-code-specific
hospital stay lasting n days is estimated as the mean hospital charge plus n times the daily lost wage.
Year 2000 county-specific median annual wages194 divided by (52*5) were used to estimate county-
specific median daily wages. Because wage data used in BenMAP are county-specific, the unit value for
a hospital admission varies from one county to another.
Most hospital admissions categories considered in epidemiological studies consisted of sets of
ICD codes. The unit value for the set of ICD codes was estimated as the weighted average of the ICD-
code-specific COI estimates. The weights were the relative frequencies of the ICD codes among hospital
discharges in the United States, as estimated by the National Hospital Discharge Survey (Owings and
Lawrence, 1999, Table 1). The hospital admissions for which unit values are available in BenMAP are
given in Exhibit H-5. Although unit values available for use in BenMAP are county-specific, the
national median daily wage was used to calculate opportunity costs and total costs for the table below, to
give a general idea of the cost of illness estimates for the different hospital admissions endpoints.
The mean hospital charges and mean lengths of stay provided by (AHRQ 2000) are based on a
very large nationally representative sample of about seven million hospital discharges, and are therefore
the best estimates of mean hospital charges and mean lengths of stay available, with negligible standard
errors.
194 Source: U.S. Year 2000 Census, compiled by Geolytics.
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Exhibit H-5. Unit Values Available for Hospital Admissions
EndPoint ICD Codes Age Range Mean Mean Total Cost of
Hospital Length of Illness (Unit
nun.
max.
Charge "
Stay (days) *
Value) b
HA, All Cardiovascular
390-429
65
99
$20,607
5.07
$21,191
HA, All Cardiovascular
390-429
0
99
$20,873
4.71
$21,415
HA, All Cardiovascular
390-429
20
64
$22,300
4.15
$22,778
HA, Congestive Heart Failure
428
65
99
$14,573
5.60
$15,218
HA, E)ysrhythmia
427
0
99
$14,811
3.70
$15,237
HA, Ischemic Heart Disease
410-414
65
99
$25,322
4.81
$25,876
HA, All Respiratory
460-519
65
99
$17,600
6.88
$18,393
HA, All Respiratory
460-519
0
99
$14,999
5.63
$15,647
HA, All Respiratory
460-519
0
2
$7,416
2.97
$7,759
HA, Asthma
493
0
64
$7,448
2.95
$7,788
HA, Asthma
493
65
99
$11,417
4.99
$11,991
HA, Asthma
493
0
99
$8,098
3.30
$8,478
HA, Chronic Lung Disease
490-496
65
99
$12,781
5.59
$13,425
HA, Chronic Lung Disease
490-496
0
99
$10,882
4.59
$11,412
HA, Chronic Lung Disease
490-496
20
64
$10,194
4.04
$10,660
HA, Chronic Lung Disease (less Asthma)
490-492, 494-496
65
99
$12,993
5.69
$13,648
HA, Chronic Lung Disease (less Asthma)
490-492, 494-496
0
99
$12,742
5.45
$13,370
HA, Chronic Lung Disease (less Asthma)
490-492, 494-496
20
64
$11,820
4.48
$11,820
HA, Pneumonia
480-487
65
99
$17,030
7.07
$17,844
HA, Pneumonia
480-487
0
99
$14,693
5.92
$15,375
s Source of hospital charges and lengths of stay: Agency for Healthcare Research and Quality. 2000. HCUPnet, Healthcare Cost
and Utilization Project, http://www.agrq.gov/data/hcup/hcupnet.htm .
b The opportunity cost of a day spent in the hospital was estimated, for this exhibit, at the median daily wage of all workers,
SI 15.20, regardless of age. The median daily wage was calculated by dividing the median weekly wage ($576 in 2000$) by 5.
The median weekly wage was obtained from U.S. Census Bureau, Statistical Abstract of the United States: 2001, Section 12,
Table 621: "Full-Time Wage and Salary Workers - Numbers and Earnings: 1985 to 2000." Actual unit values used in BenMAP
are based on county-specific wages, and are therefore county-specific.
H.4.2 Emergency Room Visits for Asthma
Two unit values are currently available for use in BenMAP for asthma emergency room (ER)
visits. One is $311.55, from Smith et al., 1997, who reported that there were approximately 1.2 million
asthma-related ER visits made in 1987, at atotal cost of $186.5 million, in 1987$. The average cost per
visit was therefore $155 in 1987$, or $311.55 in 2000 $ (using the CPI-U for medical care to adjust to
2000$). The uncertainty surrounding this estimate, based on the uncertainty surrounding the number of
ER visits and the total cost of all visits reported by Smith et al. is characterized by a triangular
distribution centered at $311.55, on the interval [$230.67, $430.93],
A second unit value is $260.67 from Stanford et al. (1999). This study considered asthmatics in
1996-1997, in comparison to the Smith et al. (1997) study, which used 1987 National Medical
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Expenditure Survey (NMES) data). In comparing their study, the authors note that the 1987 NMES,
used by Smith et al., "may not reflect changes in treatment patterns during the 1990s." In addition, its
costs are the costs to the hospital (or ER) for treating asthma rather than charges or payments by the
patient and/or third party payer. Costs to the ER are probably a better measure of the value of the
medical resources used up on an asthma ER visit (see above for a discussion of costs versus charges).
The unit values and the corresponding distributions available in BenMAP for asthma-related ER
visits are summarized in Exhibit H-6.
Exhibit H-6. Unit Values Available for Asthma-Related ER Visits
Basis for Estimate
Age Range
Unit
Distribution of Unit
Parameters of Distribution
Value
Value
mm.
max.
PI
P2
COI: Smith etal. (1997)
0
99
$312
triangular
$231
$431
COI: Standford etal. (1999)
0
99
$261
normal
5.22
-
H.5 Acute Symptoms and Illness Not Requiring Hospitalization
Several acute symptoms and illnesses have been associated with air pollution, including acute
bronchitis in children, upper and lower respiratory symptoms, and exacerbation of asthma (as indicated
by one of several symptoms whose occurrence in an asthmatic generally suggests the onset of an asthma
episode). In addition, several more general health endpoints which are associated with one or more of
these acute symptoms and illnesses, such as minor restricted activity days, school loss days, and work
loss days, have also been associated with air pollution. We briefly discuss the derivation of the unit
values for each of these acute symptoms and illnesses, and then present all of these unit values in
exhibits H-9 and H-10 at the end of this section.
For several of the acute symptoms and illnesses for which more than one unit value is available
in BenMAP, one of these is the value that EPA used in several recent benefits analyses. These
"original" unit values were all based on a set of three CV studies, in which respondents were asked their
WTP to avoid a day of specific symptoms. These study- and symptom-specific WTP estimates, along
with the recommended midrange estimates derived by IEc (1993) on which the original unit values were
based, are presented in Exhibit H-7 below.
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Exhibit H-7. Median WTP Estimates and Derived Midrange Estimates (in 1999 $)
Symptom a
Dickie et al. (1987)
Tolley et al. (1986)
Loehman et al.
(1979)
Mid-Range
Estimate
Throat congestion
4.81
20.84
-
12.75
Head/sinus congestion
5.61
22.45
10.45
12.75
Coughing
1.61
17.65
6.35
8.93
Eye irritation
-
20.03
-
20.03
Headache
1.61
32.07
-
12.75
Shortness of breath
0.00
-
13.47
6.37
Pain upon deep inhalation (PDI)
5.63
-
-
5.63
Wheeze
3.21
-
-
3.21
Coughing up phlegm
3.51b
-
-
3.51
Chest tightness
8.03
-
-
8.03
s All estimates are WTP to avoid one day of symptom. Midrange estimates were derived by IEc (1993).
b 10% trimmed mean.
H.5.1 Acute Bronchitis in Children
Estimating WTP to avoid a case of acute bronchitis is difficult for several reasons. First, WTP
to avoid acute bronchitis itself has not been estimated. Estimation of WTP to avoid this health endpoint
therefore must be based on estimates of WTP to avoid symptoms that occur with this illness. Second, a
case of acute bronchitis may last more than one day, whereas it is a day of avoided symptoms that is
typically valued. Finally, the C-R function used in the benefit analysis for acute bronchitis was
estimated for children, whereas WTP estimates for those symptoms associated with acute bronchitis
were obtained from adults.
Three unit values are available in BenMAP for acute bronchitis in children. In previous benefits
analyses, EPA used a unit value of $59.31. This is the midpoint between a low estimate and a high
estimate. The low estimate is the sum of the midrange values recommended by IEc (1994) for two
symptoms believed to be associated with acute bronchitis: coughing and chest tightness. The high
estimate was taken to be twice the value of a minor respiratory restricted activity day. For a more
complete description of the derivation of this estimate, see Abt Associates (2000, p. 4-30).
The above unit value assumes that an episode of acute bronchitis lasts only one day. However,
this is generally not the case. More typically, it can last for 6 or 7 days. A simple adjustment, then,
would be to multiply the original unit value of $59.31 by 6 or 7. A second unit value of $356 (=$59.31 x
6) was therefore derived.
Finally, as noted above, the epidemiological study relating air pollution to the incidence of acute
bronchitis referred to children specifically. The value of an avoided case should therefore be WTP to
avoid a case in a child, which may be different from WTP to avoid a case in an adult. Recent work by
Dickie and Ulery (2002) suggests, in fact, that parents are generally willing to pay about twice as much
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to avoid sickness in their children as in themselves.195 In one of several models they estimated, the
natural logarithm of parents' WTP was related both to the number of symptom-days avoided and to
whether it was their child or themselves at issue. Dickie and Ulery noted that "experiencing all of the
symptoms [considered in their study - cough and phlegm, shortness of breath/wheezing, chest pain, and
fever] for 7 days, or 28 symptom-days altogether, is roughly equivalent to a case of acute bronchitis ..."
Using this model, and assuming that a case of acute bronchitis can be reasonably modeled as consisting
of 28 symptom-days, we estimated parents' WTP to avoid a case of acute bronchitis in a child to be
$374.196 This is the third unit value available in BenMAP.
H.5.2 Upper Respiratory Symptoms (URS) in Children
In past benefits analyses, EPA based willingness to pay to avoid a day of URS on symptom-
specific WTPs to avoid those symptoms identified as part of the URS complex of symptoms. Pope et al.
(1991) defined a day of URS as consisting of one or more of the following symptoms: runny or stuffy
nose; wet cough; and burning, aching, or red eyes. The three contingent valuation (CV) studies shown in
Exhibit H-7 above have estimated WTP to avoid various morbidity symptoms that are either within the
URS symptom complex defined by Pope et al., or are similar to those symptoms. The three individual
symptoms that were identified as most closely matching those listed by Pope et al. for URS are cough,
head/sinus congestion, and eye irritation, corresponding to "wet cough," "runny or stuffy nose," and
"burning, aching or red eyes," respectively. A day of URS could consist of any one of the seven
possible "symptom complexes" consisting of at least one of these three symptoms. The original unit
value for URS was based on the assumption that each of these seven URS complexes is equally likely.
This unit value for URS, $24.64, is just an average of the seven estimates of mean WTP for the different
URS complexes.
The WTP estimates on which the first unit value is based were elicited from adults, whereas the
health endpoint associated with air pollution in the epidemiological study is in children. As noted above,
recent research by Dickie and Ulery (2002) suggests that parental WTP to avoid symptoms and illnesses
in their children is about twice what it is to avoid those symptoms and illnesses in themselves. We
therefore derived a second unit value of $49.28 (=2 x $24.64) from the first unit value.
A third unit value was derived by using Model 1, Table III in Dickie and Ulery (2002) (the same
model used for acute bronchitis), assuming that a day of URS consists of 2 symptoms. As noted above,
this model relates parental WTP to the number of symptom-days avoided and to whether it is the parent
or the child at issue. The unit value derived from this model is $187.197
195 This is, to our knowledge, the only estimate, based on empirical data, of parental WTP for their children versus
themselves.
196 The mean household income among participants in the Dickie and Ulery CV survey was slightly higher than the
national average. We therefore adjusted all WTP estimates that resulted from their models downward slightly, using an income
elasticity of WTP of 0.147, the average of the income elasticities estimated in the four models in the study. The adjustment factor
thus derived was 0.9738.
197 A WTP estimate elicited from parents concerning their WTP to avoid symptoms in their children may well include
some calculation of lost earnings resulting from having to lose a day of work. Estimates from the Dickie and Ulery model therefore
(appropriately) probably include not only their WTP to have their children avoid the pain and suffering associated with their illness,
but also the opportunity cost of a parent having to stay home with a sick child.
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H.5.3 Lower Respiratory Symptoms (LRS) in Children
The three unit values for LRS in children currently available in BenMAP follow the same
pattern as those for URS in children. In past benefits analyses, EPA based willingness to pay to avoid a
day of LRS on symptom-specific WTPs to avoid those symptoms identified as part of the LRS complex
of symptoms. Schwartz et al. (1994) defined a day of LRS as consisting of at least two of the following
symptoms: cough, chest tightness, coughing up phlegm, and wheeze. Of the symptoms for which WTP
estimates are available (listed in Exhibit H-7), those that most closely match the symptoms listed by
Schwartz et al. are coughing, chest tightness, coughing up phlegm, and wheeze. A day of LRS, as
defined by Schwartz et al., could consist of any one of 11 possible combinations of at least two of these
four symptoms. In the absence of any further information, each of the 11 possible "symptom clusters"
was considered equally likely. The original unit value for LRS, $15.57, is just an average of the eleven
estimates of mean WTP for the different LRS symptom clusters.
A second unit value is twice the original unit value, or $31.15, based on the evidence from
Dickie and Ulery (2002) that parents are willing to pay about twice as much to avoid symptoms and
illness in their children as in themselves. The third unit value is based on Model 1, Table III in Dickie
and Ulery, assuming that, as for URS, a day of LRS consists of 2 symptoms. As noted above, this
model relates parental WTP to the number of symptom-days avoided and to whether it is the parent or
the child at issue. The unit value derived from this model is $187.
H.5.4 "Any of 19 Respiratory Symptoms"
The presence of "any of 19 acute respiratory symptoms" is a somewhat subjective health effect
used by Krupnick et al. (1990). Moreover, not all 19 symptoms are listed in the Krupnick et al. study. It
is therefore not clear exactly what symptoms were included in the study. Even if all 19 symptoms were
known, it is unlikely that WTP estimates could be obtained for all of the symptoms. Finally, even if all
19 symptoms were known and WTP estimates could be obtained for all 19 symptoms, the assumption of
additivity of WTPs becomes tenuous with such a large number of symptoms. The likelihood that all 19
symptoms would occur simultaneously, moreover, is very small.
Acute respiratory symptoms must be either upper respiratory symptoms or lower respiratory
symptoms. In the absence of further knowledge about which of the two types of symptoms is more
likely to occur among the "any of 19 acute respiratory symptoms," we assumed that they occur with
equal probability. Because this health endpoint may also consist of combinations of symptoms, it was
also assumed that there is some (smaller) probability that upper and lower respiratory symptoms occur
together. To value avoidance of a day of "the presence of any of 19 acute respiratory symptoms" we
therefore assumed that this health endpoint consists either of URS, or LRS, or both. We also assumed
that it is as likely to be URS as LRS and that it is half as likely to be both together. That is, it was
assumed that "the presence of any of 19 acute respiratory symptoms" is a day of URS with 40 percent
probability, a day of LRS with 40 percent probability, and a day of both URS and LRS with 20 percent
probability. Using the point estimates of WTP to avoid a day of URS and LRS derived above, the point
estimate of WTP to avoid a day of "the presence of any of 19 acute respiratory symptoms" is:
(0.40)($24.64) + (0.40)($15.57) + (0.20)($24.64 + $15.57) = $24.12.
Because this health endpoint is only vaguely defined, and because of the lack of information on the
relative frequencies of the different combinations of acute respiratory symptoms that might qualify as
"any of 19 acute respiratory symptoms," the unit dollar value derived for this health endpoint must be
considered only a rough approximation.
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H.5.5 Work Loss Days (WLDs)
Work loss days are valued at a day's wage. BenMAP calculates county-specific median daily
wages from county-specific annual wages by dividing by (52*5), on the theory that a worker's vacation
days are valued at the same daily rate as work days.
H.5.6 Minor Restricted Activity Days (MRADs)
Two unit values are currently available in BenMAP for MRADs. No studies are reported to
have estimated WTP to avoid a minor restricted activity day (MRAD). However, IEc (1993) derived an
estimate of WTP to avoid a minor respiratory restricted activity day (MRRAD), using WTP estimates
from Tolley et al. (1986) for avoiding a three-symptom combination of coughing, throat congestion, and
sinusitis. This estimate of WTP to avoid a MRRAD, so defined, is $38.37 (1990 $). Although Ostro
and Rothschild (1989) estimated the relationship between PM2 5 and MRADs, rather than MRRADs (a
component of MRADs), it is likely that most of the MRADs associated with exposure to PM2 5 are in fact
MRRADs. The original unit value, then, assumes that MRADs associated with PM exposure may be
more specifically defined as MRRADs, and uses the estimate of mean WTP to avoid a MRRAD.
Any estimate of mean WTP to avoid a MRRAD (or any other type of restricted activity day
other than WLD) will be somewhat arbitrary because the endpoint itself is not precisely defined. Many
different combinations of symptoms could presumably result in some minor or less minor restriction in
activity. Krupnick and Kopp (1988) argued that mild symptoms will not be sufficient to result in a
MRRAD, so that WTP to avoid a MRRAD should exceed WTP to avoid any single mild symptom. A
single severe symptom or a combination of symptoms could, however, be sufficient to restrict activity.
Therefore WTP to avoid a MRRAD should, these authors argue, not necessarily exceed WTP to avoid a
single severe symptom or a combination of symptoms. The "severity" of a symptom, however, is
similarly not precisely defined; moreover, one level of severity of a symptom could induce restriction of
activity for one individual while not doing so for another. The same is true for any particular
combination of symptoms.
Given that there is inherently a substantial degree of arbitrariness in any point estimate of WTP
to avoid a MRRAD (or other kinds of restricted activity days), the reasonable bounds on such an
estimate must be considered. By definition, a MRRAD does not result in loss of work. WTP to avoid a
MRRAD should therefore be less than WTP to avoid a WLD. At the other extreme, WTP to avoid a
MRRAD should exceed WTP to avoid a single mild symptom. The highest IEc midrange estimate of
WTP to avoid a single symptom is $20.03 (1999 $), for eye irritation. The point estimate of WTP to
avoid a WLD in the benefit analysis is $83 (1990 $). If all the single symptoms evaluated by the studies
are not severe, then the estimate of WTP to avoid a MRRAD should be somewhere between $16 and
$83. Because the IEc estimate of $38 falls within this range (and acknowledging the degree of
arbitrariness associated with any estimate within this range), the IEc estimate is used as the mean of a
triangular distribution centered at $38, ranging from $16 to $61. Adjusting to 2000 $, this is a triangular
distribution centered at $50.55, ranging from $21 to $80.
A second unit value is based on Model 1, Table III in Dickie and Ulery (2002). This model
estimates the natural logarithm of parents' WTP to avoid symptoms as a linear function of the natural
logarithm of the number of symptom-days avoided and whether or not the person avoiding the
symptoms is the parent or the child. The unit value derived from this model, assuming that an MRAD
consists of one day of 3 symptoms in an adult, is $98.
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Appendix H. Economic Valuation of Health Effects
H.5.7 Asthma Exacerbation
Several respiratory symptoms in asthmatics or characterizations of an asthma episode have been
associated with exposure to air pollutants. All of these can generally be taken as indications of an
asthma exacerbation ("asthma attack") when they occur in an asthmatic. BenMAP therefore uses the
same set of unit values for all of the variations of "asthma exacerbation" that appear in the
epidemiological literature.
Two unit values are currently available in BenMAP for asthma exacerbation in adults, and three
are currently available for asthma exacerbation in children. In past benefits analyses, EPA based
willingness to pay to avoid an asthma exacerbation on four WTP estimates from Rowe and Chestnut
(1986) for avoiding a "bad asthma day." The mean of the four average WTPs is $32 (1990 $), or $43 in
2000$. The uncertainty surrounding this estimate was characterized by a continuous uniform
distribution on the range defined by the lowest and highest of the four average WTP estimates from
Rowe and Chestnut, [$12, $54] in 1990$, or [$16, $71] in 2000 $. This unit value is available for both
adults and children.
A second unit value for adults was derived by using Model 1, Table III in Dickie and Ulery
(2002) (the same model used for acute bronchitis, LRS, and URS), assuming that an asthma exacerbation
consists of 1 symptom-day. As noted above, this model relates parental WTP to the number of
symptom-days avoided and to whether it is the parent or the child at issue. The unit value derived from
this model for adults is $74.
Two additional unit values are available for children. One of these is twice the original unit
value, or $86, based on the evidence from Dickie and Ulery (2002) that parents are willing to pay about
twice as much to avoid symptoms and illness in their children as in themselves. The third unit value is
based on Model 1, Table III in Dickie and Ulery (the same model used for asthma exacerbation in adults,
only now with the "adult or child" variable set to 1 rather than 0). The unit value derived from this
model is $156.
H.5.8 School Loss Days
There is currently one unit value available in BenMAP for school loss days, based on (1) the
probability that, if a school child stays home from school, a parent will have to stay home from work to
care for the child, and (2) the value of the parent's lost productivity. We first estimated the proportion of
families with school-age children in which both parents work, and then valued a school loss day as the
probability of a work loss day resulting from a school loss day (i.e., the proportion of households with
school-age children in which both parents work) times a measure of lost wages.
From the U.S. Bureau of the Census (2002) we obtained (1) the numbers of single, married, and
"other" (i.e., widowed, divorced, or separated) women with children in the workforce, and (2) the rates
of participation in the workforce of single, married, and "other" women with children. From these two
sets of statistics, we calculated a weighted average participation rate of 72.85 percent, as shown in
Exhibit H-8.
Our estimated daily lost wage (if a mother must stay at home with a sick child) is based on the
median weekly wage among women age 25 and older in 2000 (U.S. Bureau of the Census, 2002, Table
621). This median weekly wage is $551. Dividing by 5 gives an estimated median daily wage of $103.
The expected loss in wages due to a day of school absence in which the mother would have to stay home
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Appendix H. Economic Valuation of Health Effects
with her child is estimated as the probability that the mother is in the workforce times the daily wage she
would lose if she missed a day = 72.85% of $103, or $75. We currently have insufficient information to
characterize the uncertainty surrounding this estimate.
Exhibit H-8. Women with Children: Number and Percent in the Labor Force, 2000, and Weighted
Average Participation Rate
Category
Women in Labor
Force
(millions) a
(1)
Participation Rate
(%) a
(2)
Implied Total
Number in
Population (in
millions)
(3)=(l)/(2)
Implied Percent in
Population
(4)
Population-
Weighted Average
Participation Rate
[=sum (2) *(4) over
rows]
Single
3.1
73.9%
4.19
11.84%
-
Married
18.2
70.6%
25.78
72.79%
-
Otherb
4.5
82.7%
5.44
15.36%
--
Total
__
__
35.42
__
72.85%
1 Source: U.S. Bureau of the Census (2002, Table 577).
b Widowed, divorced, or separated.
A unit value based on the approach described above is likely to understate the value of a school
loss day in two ways. First, it omits WTP to avoid the symptoms/illness which resulted in the school
absence. Second, it effectively gives zero value to school absences which do not result in a work loss
day. The unit value of $75 is therefore considered an "interim" value until such time as alternative
means of estimating this unit value become available.
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Appendix H. Economic Valuation of Health Effects
Exhibit H-9. Unit Values Available for Acute Symptoms and Illnesses
. _ Parameters of
_ ... „ . ,. 111 "e Unit Distribution Distribution
Health Endpoint Basis for Estimate ... ,... . uistriDunon
Value ol Unit Value
min.
max.
PI
P2
Acute Bronchitis
WTP: 1 day illness, CV studies
0
17
$59
uniform
17.5099
101.107
WTP: 6 day illness, CV studies
0
17
$356
uniform
105.059
606.639
WTP: 28 symptom-days, Dickie and
Ulery (2002)
0
17
$374
lognormal
5.9470
0.0907
Any of 19
Respiratory
Symptoms
WTP: 1 day illness, CV studies
18
65
$24
uniform
0
48.2476
Minor Restricted
Activity Days
WTP: 1 day, CV studies
WTP: 3 symptoms 1 day, Dickie and
Ulery (2002).
18
18
99
99
$51
$98
triangular
lognormal
20.7114
4.60884
80.3688
0.06486
Lower
Respiratory
Symptoms
WTP: 1 day, CV studies
WTP: 2 symptoms 1 day, Dickie and
Ulery (2002).
0
0
17
17
$16
$187
uniform
lognormal
6.94334
5.2556
24.4664
0.07048
WTP: 2 x 1 day, CV studies
0
17
$31
uniform
13.8867
48.9327
School Loss Days
0
0
17
$75
none
N/A
N/A
Upper Respiratory
WTP: 1 day, CV studies
0
17
$25
uniform
9.22265
43.1093
Symptoms
WTP: 2 symptoms 1 day, Dickie and
Ulery (2002)
0
17
$187
lognormal
5.2556
0.07048
WTP: 2 x 1 day, CV studies
0
17
$49
uniform
18.4453
86.2186
Work Loss Daysb
Median daily wage, county-specific
18
65
$115
none
N/A
N/A
1 All unit values pulled from a lognormal distribution from Model 1, Table III in Dickie and Ulery (2002) are multiplied by
0.973811 to adjust for a difference in mean household income between the study participants and the general population. The
unit values shown here have already been adjusted.
bUnit values for work loss days are county-specific, based on county-specific median wages. The unit value shown here is the
national median daily wage, given for illustrative purposes only.
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Appendix H. Economic Valuation of Health Effects
Exhibit H-10. Unit Values Available for Asthma-related Acute Symptoms and Illnesses
Health
Endpoint
Basis for Estimate*
Age Range
min. max.
Unit
Value
Unit Value
Distribution
Parameters of
Distribution
PI P2
Asthma
WTP: bad asthma day, Rowe and Chestnut (1986)
18
99
$43
uniform
15.5599
70.8826
Exacerbation,
Asthma
WTP: 1 symptom-day, Dickie and Ulery (2002)
18
99
$74
lognormal
4.321
0.09569
Attacks
WTP: bad asthma day, Rowe and Chestnut (1986)
0
17
$43
uniform
15.5599
70.8826
WTP: 2 x bad asthma day, Rowe and Chestnut
0
17
$86
uniform
31.1198
141.765
(1986)
WTP: 1 symptom-day, Dickie and Ulery (2002)
0
17
$156
lognormal
5.074
0.09253
Asthma
WTP: bad asthma day, Rowe and Chestnut (1986)
18
99
$43
uniform
15.5599
70.8826
Exacerbation,
Cough
WTP: 1 symptom-day, Dickie and Ulery (2002)
18
99
$74
lognormal
4.321
0.09569
WTP: bad asthma day, Rowe and Chestnut (1986)
0
17
$43
uniform
15.5599
70.8826
WTP: 2 x bad asthma day, Rowe and Chestnut
0
17
$86
uniform
31.1198
141.765
(1986)
WTP: 1 symptom-day, Dickie and Ulery (2002)
0
17
$156
lognormal
5.074
0.09253
Asthma
WTP: bad asthma day, Rowe and Chestnut (1986)
18
99
$43
uniform
15.5599
70.8826
Exacerbation,
Moderate or
WTP: 1 symptom-day, Dickie and Ulery (2002)
18
99
$74
lognormal
4.321
0.09569
Worse
WTP: bad asthma day, Rowe and Chestnut (1986)
0
17
$43
uniform
15.5599
70.8826
WTP: 2 x bad asthma day, Rowe and Chestnut
0
17
$86
uniform
31.1198
141.765
(1986)
WTP: 1 symptom-day, Dickie and Ulery (2002)
0
17
$156
lognormal
5.074
0.09253
Asthma
WTP: bad asthma day, Rowe and Chestnut (1986)
18
99
$43
uniform
15.5599
70.8826
Exacerbation,
One or More
WTP: 1 symptom-day, Dickie and Ulery (2002)
18
99
$74
lognormal
4.321
0.09569
Symptoms
WTP: bad asthma day, Rowe and Chestnut (1986)
0
17
$43
uniform
15.5599
70.8826
WTP: 2 x bad asthma day, Rowe and Chestnut
0
17
$86
uniform
31.1198
141.765
(1986)
WTP: 1 symptom-day, Dickie and Ulery (2002)
0
17
$156
lognormal
5.074
0.09253
Asthma
WTP: bad asthma day, Rowe and Chestnut (1986)
18
99
$43
uniform
15.5599
70.8826
Exacerbation,
Shortness of
WTP: 1 symptom-day, Dickie and Ulery (2002)
18
99
$74
lognormal
4.321
0.09569
Breath
WTP: bad asthma day, Rowe and Chestnut (1986)
0
17
$43
uniform
15.5599
70.8826
WTP: 2 x bad asthma day, Rowe and Chestnut
0
17
$86
uniform
31.1198
141.765
(1986)
WTP: 1 symptom-day, Dickie and Ulery (2002)
0
17
$156
lognormal
5.074
0.09253
Asthma
WTP: bad asthma day, Rowe and Chestnut (1986)
18
99
$43
uniform
15.5599
70.8826
Exacerbation,
Wheeze
WTP: 1 symptom-day, Dickie and Ulery (2002)
18
99
$74
lognormal
4.321
0.09569
WTP: bad asthma day, Rowe and Chestnut (1986)
0
17
$43
uniform
15.5599
70.8826
WTP: 2 x bad asthma day, Rowe and Chestnut
0
17
$86
uniform
31.1198
141.765
(1986)
WTP: 1 symptom-day, Dickie and Ulery (2002)
0
17
$156
lognormal
5.074
0.09253
*A11 unit values pulled from a lognormal distribution from Model 1, Table III in Dickie and Ulery, 2002, are multiplied by
0.973811 to adjust for a difference in mean household income between the study participants and the general population. The
unit values shown here have already been adjusted.
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Exhibit H-ll. Unit Value Uncertainty Distributions and Their Parameters
Distribution a
Parameter 1 (PI)
Parameter 2 (P2)
Normal
standard deviation
-
Triangular
minimum value
maximum value
Lognormalb
mean of corresponding normal
distribution
standard deviation of corresponding
normal distribution
Uniform
minimum value
maximum vaue
Weibullc
a
P
s In all cases, BenMAP calculates the mean of the distribution, which is used as the "point estimate" of the unit value.
b If Y is a normal random variable, and Y = logeX, then X is lognormally distributed. Equivalently, X is lognormally
distributed if X = eY, where Y is normally distributed.
1)
a)
: The Weibull distribution has the following probability density function: t ^
a
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Appendix I. Uncertainty & Pooling
Appendix I: Uncertainty & Pooling
This Appendix discusses the treatment of uncertainty in BenMAP, both for incidence changes
and associated dollar benefits. Some background is then given on pooling methodology. Finally, the
mechanics of the various Pooling Methods available in BenMAP are discussed in detail, including
Subjective Weight based pooling, Fixed Effects pooling, Random / Fixed Effects pooling, and
independent and dependent Sum and Subtraction.
1.1 Uncertainty
Although there are several sources of uncertainty affecting estimates of incidence changes and
associated benefits, the sources of uncertainty that are most readily quantifiable in benefits analyses are
uncertainty surrounding the C-R relationships and uncertainty surrounding unit dollar values. The total
dollar benefit associated with a given endpoint group depends on how much the endpoint group will
change in the control scenario (e.g., how many premature deaths will be avoided) and how much each
unit of change is worth (e.g., how much a statistical death avoided is worth).
Both the uncertainty about the incidence changes and uncertainty about unit dollar values can be
characterized by distributions. Each "uncertainty distribution" characterizes our beliefs about what the
true value of an unknown (e.g., the true change in incidence of a given health effect) is likely to be,
based on the available information from relevant studies.198 Unlike a sampling distribution (which
describes the possible values that an estimator of an unknown value might take on), this uncertainty
distribution describes our beliefs about what values the unknown value itself might be. Such uncertainty
distributions can be constructed for each underlying unknown (such as a particular pollutant coefficient
for a particular location) or for a function of several underlying unknowns (such as the total dollar
benefit of a regulation). In either case, an uncertainty distribution is a characterization of our beliefs
about what the unknown (or the function of unknowns) is likely to be, based on all the available relevant
information. Uncertainty statements based on such distributions are typically expressed as 90 percent
credible intervals. This is the interval from the fifth percentile point of the uncertainty distribution to the
ninety-fifth percentile point. The 90 percent credible interval is a "credible range" within which,
according to the available information (embodied in the uncertainty distribution of possible values), we
believe the true value to lie with 90 percent probability. The uncertainty surrounding both incidence
estimates and dollar benefits estimates can be characterized quantitatively in BenMAP. Each is
described separately below.
1.1.1 Characterization of Uncertainty Surrounding Incidence Changes
To calculate point estimates of the changes in incidence of a given adverse health effect
associated with a given set of air quality changes, BenMAP performs a series of calculations at each
grid-cell. First, it accesses the C-R functions needed for the analysis, and then it accesses any data
needed by the C-R functions. Typically, these include the grid-cell population, the change in population
exposure at the grid-cell, and the appropriate baseline incidence rate. BenMAP then calculates the
change in incidence of adverse health effects for each selected C-R function. This is described more
198 Although such an "uncertainty distribution" is not formally a Bayesian posterior distribution, it is very similar in
concept and function (see, for example, the discussion of the Bayesian approach in Kennedy 1990, pp. 168-172).
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Appendix I. Uncertainty & Pooling
fully in Chapter 5. The resulting incidence change is stored, and BenMAP proceeds to the next grid-
cell, where the above process is repeated.
In Latin Hypercube mode (see Chapter 5), BenMAP reflects the uncertainty surrounding
estimated incidence changes (resulting from the sampling uncertainty surrounding the pollutant
coefficients in the C-R functions used) by producing a distribution of possible incidence changes rather
than a single point estimate. To do this, it uses the distribution (Dist Beta) associated with the pollutant
coefficient (Beta, or P), and potentially the point estimate (Beta) and two parameters (PIBeta, P2Beta).
Typically, pollutant coefficients are normally distributed, with mean Beta and standard deviation
PIBeta. See Chapter 8 for more information on these C-R Function variables.
BenMAP uses an N-point Latin Hypercube199 to represent the underlying distribution of P and to
create a corresponding distribution of incidence changes in each population grid cell, where N is
specified by you (as Latin Hypercube Points - see Chapter 5). The Latin Hypercube method represents
an underlying distribution by N percentile points of the distribution, where the percentile point is
equal to:
, . 100 100
in-1> +
N 2N
Suppose, for example, that you elect to use a 20-point Latin Hypercube. BenMAP would then represent
the distribution of P by 20 percentile points, specifically the 2.5th, 7.5th, ..., 97.5th. To do this, the inverse
cumulative distribution function specified by the distribution of P is called with the input probability
equal to each the 20 percentile points. BenMAP then generates an estimate of the incidence change in a
grid-cell for each of these values of p, resulting in a distribution of N incidence changes. This
distribution is stored, and BenMAP proceeds to the next population grid-cell, where the process is
repeated.
1.1.2 Characterization of Uncertainty Surrounding Dollar Benefits
The uncertainty distribution of the dollar benefits associated with a given health or welfare effect
is derived from the two underlying uncertainty distributions - the distribution of the change in incidence
of the effect (number of cases avoided) and the distribution of the value of a case avoided (the "unit
value"). The derivation of the uncertainty distribution for incidence change is described above. The
distributions used to characterize the uncertainty surrounding unit values are described in detail in
Appendix H. As noted in that Appendix, a variety of distributions have been used to characterize the
uncertainty of unit values, including uniform, triangular, normal, and Weibull.
To represent the underlying distribution of uncertainty surrounding unit values, a 100-point
Latin Hypercube is generated in the same way described in the previous section for the distribution of p.
That is, the unit value distribution is represented using the 0.5th, 1.5th, ..., and 99.5th percentile values of
its distribution.
199The Latin Hypercube method is used to enhance computer processing efficiency. It is a sampling method that divides a
probability distribution into intervals of equal probability, with an assumption value for each interval assigned according to the
interval's probability distribution. Compared with conventional Monte Carlo sampling, the Latin Hypercube approach is more
precise over a fewer number of trials because the distribution is sampled in a more even, consistent manner (Decisioneering, 1996,
pp. 104-105).
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A distribution of the uncertainty surrounding the dollar benefits associated with a given endpoint
is then derived from latin hypercube values generated to represent the change in incidence and the latin
hypercube values generated to represent the unit value distribution. To derive this new distribution, each
of the 100 unit values is multiplied by each of the N incidence change values, yielding a set of 100 * N
dollar benefits. These values are sorted low to high and binned down to a final distribution of N dollar
benefit values.
1.2 Pooling
There is often more than one study that has estimated a C-R function for a given pollutant-health
endpoint combination. Each study provides an estimate of the pollutant coefficient, p, in the C-R
function, along with a measure of the uncertainty of the estimate. Because uncertainty decreases as
sample size increases, combining data sets is expected to yield more reliable estimates of p, and therefore
more reliable estimates of the incidence change predicted using p. Combining data from several
comparable studies in order to analyze them together is often referred to as meta-analysis.
For a number of reasons, including data confidentiality, it is often impractical or impossible to
combine the original data sets. Combining the results of studies in order to produce better estimates of p
provides a second-best but still valuable way to synthesize information (DerSimonian and Laird, 1986).
This is referred to as pooling. Pooling P's requires that all of the studies contributing estimates of p use
the same functional form for the concentration-response function. That is, the P's must be measuring the
same thing.
It is also possible to pool the study-specific estimates of incidence change derived from the C-R
functions, instead of pooling the underlying P's themselves. For a variety of reasons, this is often
possible when it is not feasible to pool the underlying P's. For example, if one study is log-linear and
another is linear, we could not pool the P's because they are not different estimates of a coefficient in the
same C-R function, but are instead estimates of coefficients in different C-R functions. We can,
however, calculate the incidence change predicted by each C-R function (for a given change in pollutant
concentration and, for the log-linear function, a given baseline incidence rate), and pool these incidence
changes. BenMAP allows the pooling of incidence changes predicted by several studies for the same
pollutant-health endpoint group combination. It also allows the pooling of the corresponding study-
specific estimates of monetary benefits.
As with estimates based on only a single study, BenMAP allows you to characterize the
uncertainty surrounding pooled estimates of incidence change and/or monetary benefit. To do this,
BenMAP pools the study-specific distributions of incidence changes (or monetary benefit) to derive a
pooled distribution. This pooled distribution incorporates information from all the studies used in the
pooling procedure.
1.2.1 Weights Used for Pooling
The relative contribution of any one study in the pooling process depends on the weight assigned
to that study. A key component of the pooling process, then, is the determination of the weight given to
each study. There are various methods that can be used to assign weights to studies (these are three of
the Pooling Methods - see Chapter 6 for more information). Below we discuss the possible weighting
schemes that are available in BenMAP.
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Subjective (User-specified) Weights
BenMAP allows you the option of specifying the weights to be used. Suppose, for example, you
want to simply average all study-specific results. You would then assign a weight of 1/N to each of the
N study-specific distributions that are to be pooled. Note that subjective weights are limited to two
decimal places, and are normalized if they do not sum to one.
Automatically Generated Weights
A simple average has the advantage of simplicity but the disadvantage of not taking into account
the uncertainty of each of the estimates. Estimates with great uncertainty surrounding them are given the
same weight as estimates with very little uncertainty. A common method for weighting estimates
involves using their variances. Variance takes into account both the consistency of data and the sample
size used to obtain the estimate, two key factors that influence the reliability of results. BenMAP has two
methods of automatically generating pooling weights using the variances of the input distributions -
Fixed Effects Pooling and Random /Fixed Effects Pooling.
The discussion of these two weighting schemes is first presented in terms of pooling the
pollutant coefficients (the P's), because that most closely matches the discussion of the method for
pooling study results as it was originally presented by DerSimonian and Laird (1986). We then give an
overview of the analogous weighting process used within BenMAP to generate weights for incidence
changes rather than P's.
Fixed Effects Weights
The fixed effects model assumes that there is a single true concentration-response relationship
and therefore a single true value for the parameter p that applies everywhere. Differences among P's
reported by different studies are therefore simply the result of sampling error. That is, each reported P is
an estimate of the same underlying parameter. The certainty of an estimate is reflected in its variance
(the larger the variance, the less certain the estimate). Fixed effects pooling therefore weights each
estimate under consideration in proportion to the inverse of its variance.
Suppose there are n studies, with the ith study providing an estimate P, with variance v, (1=1,
..., n). Let
denote the sum of the inverse variances. Then the weight, w;, given to the ith estimate, p,, is
1 /v,
w. =
S
This means that estimates with small variances (i.e., estimates with relatively little uncertainty
surrounding them) receive large weights, and those with large variances receive small weights.
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The estimate produced by pooling based on a fixed effects model, then, is just a weighted
average of the estimates from the studies being considered, with the weights as defined above. That is,
p/e = E w. * [3f. .
The variance associated with this pooled estimate is the inverse of the sum of the inverse variances:
i
Exhibit 1-2 shows the relevant calculations for this pooling for three sample studies.
Exhibit 1-2. Example of Fixed Effects Model Calculations
Study
Pi
Vj
1/v,
Wj
Wj*Pi
1
0.75
0.1225
8.16
0.016
0.012
2
1.25
0.0025
400
0.787
0.984
3
1.00
0.0100
100
0.197
0.197
Sum
£ = 508.16
£=1.000
£=1.193
The sum of weighted contributions in the last column is the pooled estimate of p based on the
fixed effects model. This estimate (1.193) is considerably closer to the estimate from study 2 (1.25) than
is the estimate (1.0) that simply averages the study estimates. This reflects the fact that the estimate from
study 2 has a much smaller variance than the estimates from the other two studies and is therefore more
heavily weighted in the pooling.
The variance of the pooled estimate, vfe, is the inverse of the sum of the variances, or 0.00197.
(The sums of the P and v, are not shown, since they are of no importance. The sum of the 1 / v, is S, used
to calculate the weights. The sum of the weights, w;, i=l, ..., n, is 1.0, as expected.)
Random / Fixed Effects Weights
An alternative to the fixed effects model is the random effects model, which allows the
possibility that the estimates P, from the different studies may in fact be estimates of different
parameters, rather than just different estimates of a single underlying parameter. In studies of the effects
of PM10 on mortality, for example, if the composition of PM10 varies among study locations the
underlying relationship between mortality and PM10 may be different from one study location to another.
For example, fine particles make up a greater fraction of PM10 in Philadelphia than in El Paso. If fine
particles are disproportionately responsible for mortality relative to coarse particles, then one would
expect the true value of p in Philadelphia to be greater than the true value of p in El Paso. This would
violate the assumption of the fixed effects model.
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The following procedure can test whether it is appropriate to base the pooling on the random
effects model (vs. the fixed effects model):
A test statistic, Qw , the weighted sum of squared differences of the separate study estimates
from the pooled estimate based on the fixed effects model, is calculated as:
ft„ = Er -
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Appendix I. Uncertainty & Pooling
The estimate produced by pooling based on the random effects model, then, is just a weighted
average of the estimates from the studies being considered, with the weights as defined above. That is,
B , = t w;' * .
The variance associated with this random effects pooled estimate is, as it was for the fixed
effects pooled estimate, the inverse of the sum of the inverse variances:
i
^rand
2 1/v/
The weighting scheme used in a pooling based on the random effects model is basically the
same as that used if a fixed effects model is assumed, but the variances used in the calculations are
different. This is because a fixed effects model assumes that the variability among the estimates from
different studies is due only to sampling error (i.e., each study is thought of as representing just another
sample from the same underlying population), while the random effects model assumes that there is not
only sampling error associated with each study, but that there is also between-study variability ~ each
study is estimating a different underlying p. Therefore, the sum of the within-study variance and the
between-study variance yields an overall variance estimate.
Fixed Effects and Random / Fixed Effects Weighting to Pool Incidence Change Distributions and
Dollar Benefit Distributions
Weights can be derived for pooling incidence changes predicted by different studies, using either
the fixed effects or the fixed / random effects model, in a way that is analogous to the derivation of
weights for pooling the P's in the C-R functions. As described above, BenMAP generates a latin
hypercube representation of the distribution of incidence change corresponding to each C-R Function
selected. The means of those study-specific latin hypercube distributions of incidence change are used
in exactly the same way as the reported P's are used in the calculation of fixed effects and random effects
weights described above. The variances of incidence change are used in the same way as the variances
of the P's. The formulas above for calculating fixed effects weights, for testing the fixed effects
hypothesis, and for calculating random effects weights can all be used by substituting the mean
incidence change for the ith C-R Function for P, and the variance of incidence change for the ith C-R
Function for vr200
Similarly, weights can be derived for dollar benefit distributions. As described above, BenMAP
generates a latin hypercube representation of the distribution of dollar benefits . The means of those
latin hypercube distributions are used in exactly the same way as the reported P's are used in the
calculation of fixed effects and random effects weights described above. The variances of dollar benefits
are used in the same way as the variances of the P's. The formulas above for calculating fixed effects
weights, for testing the fixed effects hypothesis, and for calculating random effects weights can all be
200 There may be a problem with transferring the fixed effects hypothesis test to "incidence change space." The test
statistic to test the fixed effects model is a chi-squared random variable. In the original paper on this pooling method, DerSimonian
and Laird, 1986, were discussing the pooling of estimates of parameters, which are generally normally distributed. The incidence
changes predicted from a C-R function will not be normally distributed if the C-R function is not a linear function of the pollutant
coefficient, which, in most cases it is not. (Most C-R functions are log-linear.) In that case, the test statistic may not be chi-square
distributed. However, most log-linear C-R functions are nearly linear because their coefficients are very small. In that case the test
statistic is likely to be nearly chi-square distributed.
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Appendix I. Uncertainty & Pooling
used by substituting the mean dollar benefit change for the ith valuation for p, and the variance of dollar
benefits for the ith valuation for vr
BenMAP always derives Fixed Effects and Random /Fixed Effects weights using nationally
aggregated results, and uses those weights for pooling at each grid cell (or county, etc. if you choose to
aggregate results prior to pooling). This is done because BenMAP does not include any regionally based
uncertainty - that is, all uncertainty is at the national level in BenMAP, and all regional differences
(population, for example) are treated as certain.
1.2.2 The Mechanics of Pooling in BenMAP
Once weights are generated for each input distribution, BenMAP has three options for using
these weights to combine the input distributions into a single new distribution. These options are
referred to as Advanced Pooling Methods (see Chapter 6 for more details).
Round Weights to Two Digits
This is BenMAP's default Advanced Pooling Method, and is always the method used when
Subjective Weights are used. The first step is converting the weights to two digit integers by multiplying
them by 100 and rounding to the nearest integer. If all the integral weights thus generated are divisible
by the smallest weight, they are each divided by that smallest weight. For example, if the original
weights were 0.1, 0.2, 0.3, and 0.4, the resulting integral weights would be 10/10, 20/10, 30/10, and
40/10 (or 1, 2, 3, and 4).
BenMAP then creates a new distribution by sampling each entire input distribution according to
its weight. That is, in the above example the first distribution would be sampled once, the second
distribution twice, and so forth. The advantage of sampling whole distributions is that it preserves the
characteristics (i.e., the moments - the mean, the variance, etc.) of the underlying distributions.
Assuming n latin hypercube points, the resulting distribution will contain a maximum of 100 * n values,
which are then sorted low to high and binned down to n values, which will represent the new, pooled
distribution.
Round Weights to Three Digits
This Advanced Pooling Method is essentially the same as rounding weights to two digits, except
that the weights are converted to three digit integers, and so forth. That is, the weights are multiplied by
1000 and rounded to the nearest integer. Again, if all the integral weights thus generated are divisible by
the smallest weight, they are each divided by that smallest weight. Assuming n latin hypercube points,
the resulting distribution with this Advanced Pooling Method can contain a maximum of 1000 * n
values, which are sorted low to high and binned down to n values, which represent the new, pooled
distribution.
Exact Weights for Monte Carlo
This Advanced Pooling Method uses a Monte Carlo method to combine the input distributions.
Using this method, on each of many iterations, (1) an input distribution is selected (with the probability
of selection equal to the weight assigned to the distribution), and (2) a value is randomly drawn from that
distribution. Values chosen in this way are placed into a temporary pooled distribution, which will have
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Appendix I. Uncertainty & Pooling
one point per iteration of the Monte Carlo method. The number of iterations is specified by the user (see
Chapter 6), and defaults to 5,000. After the temporary distribution is fully generated, it is sorted low to
high and binned down to n values (where n is the number of Latin Hypercube Points chosen for the
analysis - see Chapter 5).
1.2.3 Summing Distributions
Sometimes rather than pooling distributions we want to add them. For example, some studies
have estimated a C-R function for hospital admissions for COPD and another C-R function for hospital
admissions for pneumonia. From each of these C-R functions, BenMAP can derive the corresponding
distributions for incidence change. Hospital admissions for COPD and pneumonia are two of the most
important components of respiratory hospital admissions, and we may want to estimate the number of
cases of "respiratory hospital admissions," as characterized by being either COPD or pneumonia. To do
this we would add the two distributions.
Summing across distributions can be done in one of two ways: We can assume the two
distributions are independent of each other or dependent. Which is the more reasonable assumption
depends on the particulars of the distributions being summed.
Assuming Independence
This is the Sum (Independent) Pooling Method (see Chapter 6 for details). To sum two
distributions that are independent, on each of many iterations of a Monte Carlo procedure, BenMAP (1)
randomly selects a value from the first input distribution, (2) randomly selects a value from the second
input distribution, and (3) adds the two values together. To sum N distributions that are independent,
BenMAP follows an analogous procedure in which, on each iteration it makes a random selection from
each of the input distributions and then adds the results together. When the Monte Carlo procedure is
completed, all such generated results are sorted low to high and binned down to the appropriate number
of latin hypercube points. The number of iterations is determined by the Monte Carlo Iterations setting
(see Chapter 6).
Assuming Dependence
This is the Sum (Dependent) Pooling Method (see Chapter 6 for details). Recall that the
uncertainty distributions in BenMAP are latin hypercube representations, consisting of N percentile
points. To sum two distributions assumed to be dependent, BenMAP simply generates a new N point
latin hypercube where each point is the sum of the corresponding points from the input latin hypercubes.
That is, the first point in the new latin hypercube is the sum of the first points in the two input latin
hypercubes, and so forth. To sum n distributions that are assumed to be dependent, BenMAP follows an
analogous procedure in which each point in the new latin hypercube is the sum of the corresponding
points from each of the input latin hypercubes.
1.2.4 Subtracting Distributions
In some cases, you may want to subtract one or more distribution(s) from another. For example,
one study may have estimated a C-R function for minor restricted activity days (MRADs), and another
study may have estimated a C-R function for asthma "episodes." You may want to subtract the change
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in incidence of asthma episodes from the change in incidence from MRADs before estimating the
monetary value of the MRADs, so that the monetary value of asthma episodes avoided will not be
included.
Subtracting across distributions can be done in one of two ways: we can assume the two
distributions are independent of each other or dependent. Which is the more reasonable assumption
depends on the particulars of the distributions being subtracted.
Assuming Independence
This is the Subtraction (Independent) Pooling Method. To subtract one distribution from
another, assuming independence, on each of many iterations of a Monte Carlo procedure, BenMAP (1)
randomly selects a value from the first input distribution, (2) randomly selects a value from the second
input distribution, and (3) subtracts the second value from the first. To subtract N distributions from
another distribution, assuming independence, BenMAP follows an analogous procedure in which, on
each iteration it makes a random selection from each of the input distributions and then subtracts the
second through the Nth from the first. When the Monte Carlo procedure is completed, all such
generated results are sorted low to high and binned down to the appropriate number of latin hypercube
points. The number of iterations is determined by the Monte Carlo Iterations setting (see Chapter 6).
Assuming Dependence
This is the Subtraction (Dependent) Pooling Method (see Chapter 6 for details). Recall that the
uncertainty distributions in BenMAP are latin hypercube representations, consisting of N percentile
points. To subtract one distribution from another, assuming them to be dependent, BenMAP simply
generates a new N point latin hypercube where each point is the result of subtracting the corresponding
point of the second input latin hypercube from the corresponding point of the first input latin hypercube.
That is, the first point in the new latin hypercube is the result of subtracting the first point in the second
latin hypercube from the first point of the first latin hypercube, and so forth. To subtract n distributions
from another distribution, assuming dependence, BenMAP follows an analogous procedure in which
each point in the new latin hypercube is the result of subtracting the corresponding points of the second
through the Nth input latin hypercubes from the corresponding point of the first.
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