United States
Environmental Protection
Agency
Office of Pollution
Prevention and Toxics
Washington. DC 20460
EPA 747-R-97-006
June. 1998
^y EPA Risk Analysis to Support Standards for
Lead in Paint, Dust, and Soil
VOLUME II
Appendices B to G
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EPA 747-R-97-006
June, 1998
RISK ANALYSIS TO SUPPORT STANDARDS
FOR LEAD IN PAINT, DUST, AND SOIL
VOLUME II
APPENDICES B THROUGH G
Prepared
by
Battelle
505 King Avenue
Columbus, Ohio 43201
for
National Program Chemicals Division
Office of Pollution Prevention and Toxics
U.S. Environmental Protection Agency
Washington, D.C. 20460
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DISCLAIMER
Mention of trade names, products, or services does not
convey, and should not be interpreted as conveying, official EPA
approval, endorsement, or recommendation.
This report is copied on recycled paper.
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CONTRIBUTING ORGANIZATIONS
This study was funded and managed by the U.S. Environmental Protection Agency. The
risk analysis was conducted by Battelle Memorial Institute under contract to the Environmental
Protection Agency. Each organization's responsibilities are listed below.
Battelle Memorial Institute (Battelle)
Battelle was responsible for identifying and incorporating the results of relevant studies,
obtaining and managing relevant datasets, developing methodologies for risk assessment and risk
management, carrying out the risk analysis, and preparing the report. The Battelle Task Manager
was Ronald Menton. Robert Lordo, Nancy McMillan, and Nancy Niemuth were key contributors
to preparing the report. Brandon Wood was responsible for the statistical programming.
U.S. Environmental Protection Agency (EPA)
The Environmental Protection Agency was responsible for providing objectives of the
risk analysis, reviewing the developed methodology, contributing to the development of
conclusions, reviewing draft versions of the report, and managing the peer review and
publication of the report. The EPA Work Assignment Manager was Todd Holderman. The
Deputy Work Assignment Managers were Brad Schultz and Karen Lannon. The EPA Project
Officer was Sineta Wooten. Other EPA contributors include Barbara Leczynski, Janet Remmers,
John Schwemberger, Dave Topping, and the EPA/OPPT Risk Assessment Workgroup (chaired
by Lois Dicker).
HI
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APPENDIX B
Health Effects Associated with Exposure to
Lead and Internal Lead Doses in Humans
B-1
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Table B-1. Health Effects Associated with Exposure to Lead and Internal Lead Doses in Humans.
Duration^!
Exposure
< 1 yr (occup)
NS (occup)
•< 3 yr (occup)
NS
2 wk - > 1 yr
(occup)
> 1 yr (occup)
>- 1 yr (occup)
NS
(general population)
NS
(general population)
NS
(general population)
NS
(general population)
-
System
Cardiovascular
Cardiovascular
Cardiovascular
Cardiovascular
Cardiovascular
Cardiovascular
Cardiovascular
Effect
Increase in death due to hypertension,
nephritis, neoplasms
Increase in death due to
cerebrovascular disease, nephritis,
and/or nephrosis
No increase in deaths
Acute encephalopathy resulting in
death in children
Increased blood pressure
No effect on blood pressure
Ischemic electrocardiogram changes
Increased blood pressure
Increased systolic pressure by 1-2
mmHg and increased diastolic pressure
by 1 .4 mmHg with every doubling in
blood-lead level; effect most prominent
in middle-aged white men
No significant correlation between
blood pressure and blood-lead levels
Degenerative changes in myocardium,
electrocardiogram abnormalities in
children
Rood Loadievefe
at which Effect is
Observed fc/g/dLJ
63-80
NS
34-58 (means)
125-750
fc 30- 120
40 (mean)
51 (mean)
44.9 (mean)
7-38
6-13 (median)
orNS
6-20
Reference
Cooper et al., 1 985, 1 988
Fanning 1 988; Malcolm and Barnett
1982; Michaels et al. 1991
Gerhardsson et al. 1 986b
NAS 1972
deKort et al. 1 987; Pollock and Ibels
1 986; Marino et al. 1 989; Weiss et al.
1986, 1988
Parkinson et al. 1 987
Kirkby and Gyntelberg 1 985
Kheraetal. 1980
Coate and Fowles 1 989; Harlan 1 988;
Harlan et al. 1 988; Landis and Flegal
1988; Pirkle et al. 1985; Schwartz 1988
Elwood et al. 1 988; Grandjean et al.
1 989; Neri et al. 1 988; Staessen et al.
1990, 1991
Silver and Rodriguez-Torres 1 968
to
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Table B-1. Health Effects Associated with Exposure to Lead and Internal Lead Doses in Humans. (Continued)
Duration of
ExfXHWft
NS (acute) (occup)
NS (acute)
(general population)
NS (occup)
NS
(general population)
NS (occup)
NS
(general population)
NS
(general population)
NS
(general population)
NS
(general population
NS
(general population)
NS (occup)
System
Gastrointestinal
Gastrointestinal
Hematological
Hematological
Hematological
Hematological
Hematological
Hematological
Hematological
Hematological
Hematological
Effect.
Colic (abdominal pain, constipation,
cramps, nausea, vomiting, anorexia,
weight loss)
Colic in children
Increased ALAS and/or decreased
A LAD
Decreased ALAD
Increased urinary or blood ALA
Increased urinary ALA
Increased FEP
Increased EP
Increased ZPP
Increased urinary coproporphyrin
Decreased hemoglobin with or without
basophilic stippling of erythrocytes
Blood Lead tevefc
at which Effect fa
ObwvadV/g/dU
40-200
60-100
87 or NS
(correlated with
blood-lead level)
3-56 (adult)
No threshold
(children
-c 40-50, 87
(mean) or NS
> 35 (adult)
25-75 children
t 25-35
30-40 (males
20-30 (females)
i 15 (children)
* 35 (children)
t. 40 (adults)
^ 40
Reference
Awad et al. 1986; Baker et al. 1979;
Haenninen et al. 1 979; Holness and
Nethercott 1988; Kumar et al 1987;
Marino et al. 1989; Matte et al. 1989;
Muijser et al. 1987; Pagliuca et al. 1990;
Pollock and Ibels 1 986; Schneitzer et al.
1990
U.S. EPA 1986; N AS 1972
Alessio et al. 1976; Meredith et al. 1978;
Wadaetal. 1973
Chisholm et al. 1985; Lauwerys et al.
1 978; Roels et al. 1 976; Roels and
Lauwerys 1987; Secchi et al. 1974
Lauwerys et al. 1974; Meredith et al.
1 978; Pollock and Ibels 1 986; Selander
and Cramer 1970
NAS 1972; Roels and Lauwerys 1987
Grandjean and Lintrup 1978; Roels et al.
1975
Roels and Lauwerys 1987; Roels et al.
1975, 1976, 1979; Stuick 1974
Hammond et al. 1985; Piomelli et al.
1 982; Rabinowitz et al. 1 986; Roels and
Lauwerys 1987; Roels et al. 1976
U.S. EPA 1986
Awad et al. 1986; Baker et al. 1979;
Grandjean 1979; Lilis et al. 1978;
Pagliuca et al. 1990; Tola et al. 1973;
Wadaetal. 1973
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Table B-1. Health Effects Associated with Exposure to Lead and Internal Lead Doses in Humans. (Continued)
Duration of
: : ixpown*
NS
(general population)
NS
(general population)
NS (occup)
NS
(general population)
NS (acute)
(general population)
NS (chronic) (occup)
1-30 yr (occup)
NS (chronic)
(general population)
NS (acute)
(general population)
0.1 -20 yr (chronic)
(occup)
NS (chronic)
(general population)
NS
(general population
NS (chronic)
(general population)
NS (chronic)
(general population)
.. System
Hematological
Hematological
Hematological
Hematological
Hepatic
Renal
Renal
Renal
Renal
Other
Other
Other
Other
Other
Effect
Decreased hemoglobin
Anemia (hematocrit of < 35%)
Decreased Py-S'-N
Decreased Py-51-N
Decreased mixed function oxidase
activity
Chronic Nephropathy
No effect on renal function
Renal (impairment with gout or
hypertension)
Aminoaciduria; Fancoi syndrome
Decreased thyroxin (T,*)
No effect on thyroid function in
children
Negative correlation between blood
lead and serum 1 ,25-dihydroxyvitamin
D in children
No effect on vitamin D metabolism in
children
Growth retardation in children
Stood Lewi Level*
at wWeh £***<# fe
Observed V/g/dL)
fc 40 (children)
> 20 (children)
NS
7-80 (children)
NS (children)
40 -> 100
40-61
18-26pg/dL
>- 80 (children)
fc 56
2-77 (levels
measured)
12-120
5-24 (levels
measured)
t 30-60; Tooth
lead > 18.7//g/g
Reference
Adebonojo 1974; Betts et at. 1973;
Pueschel et al. 1972; Rosen et al. 1974
Schwartz et al. 1 990
Buc and Kaplan 1978; Paglia et al. 1975,
1977
Angle and Mclntire 1 978; Angle et al.
1982
Alvares et al. 1 975; Saenger et al. 1 984
Biagini et al. 1977; Cramer et al. 1974;
Lilis et al. 1 968; Maranelli and Apostoli
1987; Ong et al. 1987; Pollock and Ibels
1 986; Verschoor et al. 1 987; Wedeen et
al. 1979
Buchet et al. 1 980; Huang et al. 1 988
Batuman et al. 1981, 1983
Chisholm 1 962; Pueschel et al. 1 972
Tuppurainen et al. 1988
Siegel et al. 1 989
Mahaffey et al. 1 982; Rosen et al. 1 980
Kooetal. 1991
Angle and Kuntzelman 1 989; Lauwers et
al. 1986; Lyngbye et al. 1987
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Table B-1. Health Effects Associated with Exposure to Lead and Internal Lead Doses in Humans. (Continued)
- m#$$«f
.; Exposure
NS (chronic)
(general population)
•< 1 8 yr (occup)
NS (acute)
NS
(acute and chronic)
(occup)
NS
(occup)
NS
(occup)
NS
(occup)
NS
(occup)
NS
(general population)
System
Other
Immunological
Neurological
Neurological
Neurological
Neurological
Neurological
Neurological
Neurological
Effect
No association between blood-lead
levels and growth in children
Depression of cellular immune
function, but no effect on humoral
immune function
Encephalopathy (adults)
Neurological signs and symptoms in
adults including malaise, forgetfulness,
irritability, lethargy, headache, fatigue,
impotence, decreased libido, dizziness,
weakness, paresthesia
Neurobehavioral function in adults;
disturbances in oculomotor function,
reaction time, visual motor
performance, hand dexterity, IQ test
and cognitive performance,
nervousness, mood, coping ability,
memory
No effect on neurobehavioral function
in adults
Peripheral nerve function in adults;
decreased nerve conduction velocity
No effect on peripheral nerve function
Neurological signs and symptoms in
children and encephalopathy
Wood Lead Levels
at which Effect is
Observed (pg/dU
10-47 (levels
measured)
21-90
50 - > 300
40-80
40-80
40-60
(levels measured)
30- fc 70
60-80
(levels measured)
60-450 (effects
other than
encephalopathy);
x 80-800
(encephalopathy)
Reference
Greene and Ernhart 1991; Sachs and
Moel 1 989
Alomran and Shleamoon 1 988; Ewers et
al. 1982
Kehoe 1961; Kumar et al. 1987; Smith et
al. 1938
Awad et al. 1986; Baker et al. 1979;
Campara et al. 1 984; Haenninen et al.
1979; Holness and Nethercott 1988;
Marino et al. 1 989; Matte et al. 1 989;
Pagliuca et al. 1 990; Parkinson et al.
1 986; Pasternak et al. 1 989; Pollock and
Ibels 1986; Schneitzer et al. 1990;
Zimmerman-Tansella et al. 1 983
Amvig et al. 1980; Baker et al. 1983;
Baloh et al. 1 979; Campara et al. 1 984;
Glickman et al. 1 984; Haenninen et al.
1 978; Hogstedt et al. 1 983; Mantere et
al. 1 982; Spivey et al. 1 980; Stollery et
al. 1 989; Valciukas et al. 1 978;
Williamson and Too 1 986
Milburn et al. 1976; Ryan et al. 1987
Araki et al.1980; Muijser et al. 1987;
Rosen et al. 1 983; Seppalainen et al.
1983; Triebigetal. 1984
Spivey et al. 1 980
Bradley and Baumgartner 1 958; Bradley
et al. 1956; Chisolm 1962, 1965;
Chisolm and Harrison 1 956; Gant 1 938;
Rummo et al. 1979; Smith et al. 1983
01
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Table B-1. Health Effects Associated with Exposure to Lead and Internal Lead Doses in Humans. (Continued)
Itowrtiwof^iiCf
Exposure -•-I;:
NS
(general population)
NS
(general population)
NS
(general population)
NS
(general population)
NS
(general population)
prenatal
(general population)
prenatal
(general population)
NS
(general population)
^ •
&*: v ^ >•
^ v-i.
5^ g; System
Neurological
Neurological
Neurological
Neurological
Neurological
Developmental
Developmental
Developmental
Effect
Neurobehavioral function in children:
lower IQS and other neuropsychologic
deficits
Neurobehavioral function in children:
slightly decreased performance on IQ
tests and other measures of
neuropsychological function
No con-elation between blood-lead
levels and permanent effects on
neurobehavioral development in
children
Decrease in hearing acuity in children
Alterations in peripheral nerve function
in children
Decreased growth rate
Reduced birth weight and/or reduced
gestational age, and/or increased
incidence of stillbirth and neonatal
death
No association between blood-lead
levels and birth weight, gestational
age, or other neonatal size measures
Blood Lead Levels
at which Effect Is
Observed U/g/dU
40-200
Tooth lead:
6 - >• 30 fJQ/g
Blood lead: 6-60
10-15
4-60
20-30
7.7
12-17
3-55
Reference
dela Burde and Choate 1 972, 1 975;
Ernhart et al. 1981; Kotok 1972; Kotok
et al. 1977; Rummo et al. 1979
Bellinger and Needleman 1 983; Bergomi
et al. 1 989; Fulton et al. 1 987; Hansen
et al. 1989; Hawk et al. 1986;
Needleman et al. 1979, 1985, 1990;
Schroeder et al. 1 985; Schroeder and
Hawk 1987; Silva et al. 1988; Wang et
al. 1989
Cooney et al. 1989; Harvey et al. 1984,
1 988; Lansdown et al. 1 986; McBride et
al. 1 982; Ernhart and Greene, 1 990;
Dietrich et al. 1987a; Bellinger et al.
1 989a; McMichael et al. 1 986; Pocock et
al. 1989; Smith et al. 1983; Winneke et
al. 1984
Schwartz and Otto 1 987
Erenberg et al. 1 974; Landrigan et al.
1 976; Schwartz et al. 1 988; Seto and
Freeman 1964
Shukla et al. 1 989
Bornschein et al. 1 989; McMichael et al.
1986; Moore et al. 1982; Ward et al.
1987; Wibberley etal. 1977
Greene and Ernhart 1991; Factor-Litvak
etal. 1991
o>
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Table B-1. Health Effects Associated with Exposure to Lead and Internal Lead Doses in Humans. (Continued)
Duration o?
Exposure
NS
(general population)
NS
(general population)
NS
(general population
NS
(general population)
NS (occup)
System
Developmental
Developmental
Reproductive
Reproductive
Reproductive
Effect
Impaired mental development in
children
Inverse correlation between blood-lead
levels and ALA and ALAD activity
Increased incidence of miscarriages
and stillbirths in exposed women
No association between blood-lead
levels and the incidence of
spontaneous abortion in exposed
women
Adverse effects on testes
at wttch Effect ts
Observed taj/dLJ
10-15
10-33
(mean)
fc lOorNS
2
40-50
Reference
Baghurst et al. 1987; Bellinger et al.
1984, 1985a, 1985b, 1986a, 19866,
1987a, 1987b; Bomschein et al. 1989;
Dietrich et al. 1986, 1987a, 1987b;
Emhart et al. 1985, 1986, 1987;
McMichael et al. 1 988; Rothenberg et al.
1989; Wigg et al. 1988; Winneke et al.
1985a, 1985b; Wolf et al. 1985;
Vimpani et al. 1985, 1989
Haas et al. 1972; Kuhnert et al. 1977;
Lauwerys et al. 1 978
Baghurst et al. 1987; Hu et al. 1991;
McMichael et al. 1 986; Nordstrom et al.
1979; Wibberley et al. 1977
Murphy et al. 1990
Assennato et al. 1 987; Braunstein et al.
1978; Chowdhury et al. 1986; Cullen et
al. 1 984; Lancranjan et al. 1 975;
Rodamilans et al. 1988; Wildt et al. 1983
ALA = 6-aminotevulinic acid; ALAD = 6-aminolevulinic acid dehydratase; ALAS = 6-aminotevulinic acid synthase; EP = erythrocyte protoporphyrins;
FEP = free erythrocyte protoporphyrins; IQ = intelligence quotient; mmHg = millimeters of mercury; NS = not specified; (occup) = occupational;
Py-S'-N - pyrimidine-5-nucteotidase; wk = week(s); yr = year(s); ZPP - zinc erythrocyte protoporphyrin
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APPENDIX C1
Characterizing Baseline Environmental-Lead
Levels in the Nation's Housing Stock
C1-1
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APPENDIX C1
CHARACTERIZING BASELINE ENVIRONMENTAL-LEAD
LEVELS IN THE NATION'S HOUSING STOCK
As discussed in Section 3.3.1.1, the §403 risk analysis used environmental-lead data from
the National Survey of Lead-Based Paint in Housing ("HUD National Survey") to characterize
baseline environmental-lead levels in the nation's 1997 housing stock. Here, the term "baseline"
refers to conditions prior to implementing interventions in response to §403 rules. Data for 284
privately-owned, occupied housing units included in the HUD National Survey were considered
in the characterization. In total, these units represented the entire U.S. privately-owned, occupied
housing stock built prior to 1980 (USEPA, 1995a). Due to the complex sampling design
employed, the HUD National Survey assigned sampling weights to each unit, which equaled the
number of privately-owned, occupied housing units in the national housing stock built prior to
1980 that were represented by the unit (USEPA, 1995g).
In order to use the information from the HUD National Survey to represent baseline
environmental-lead levels in the 1997 national housing stock, the following steps were taken:
1. Update the sampling weights assigned in the HUD National Survey to reflect the
1997 housing stock (including publicly-owned units).
2. Determine the total number of children residing in the housing units represented by
each sampling weight.
3. Summarize the environmental-lead levels within each surveyed unit.
Methods for conducting each of these steps, and the results from implementing these methods,
are summarized in the following sections.
1.0 UPDATING THE NATIONAL SURVEY SAMPLING WEIGHTS
Characterizing the 1997 national housing stock and its distribution of environmental-lead
levels involved updating the sampling weights assigned hi the HUD National Survey to reflect
the 1997 national housing stock. The tasks performed to update these weights were the
following:
1. Identify demographic variables that served to group the housing units by their
potential for differing environmental-lead levels.
2. Use information within the National Survey weights and the 1993 American Housing
Survey to determine total numbers of 1997 housing units within each of these
housing groups.
C1-2
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3. Allocate these 1997 totals among the National Survey units within the housing
groups.
The methods developed for each of these tasks are presented in the following subsections.
1.1 IDENTIFY SIGNIFICANT FACTORS ASSOCIATED WITH
ENVIRONMENTAL-LEAD LEVELS
In updating the sampling weights of the 284 National Survey units, the units were
classified into housing groups according to a set of demographic factors found to have a
statistically significant influence on environmental-lead levels in the units. Then, the number of
1997 housing units in each group was determined. By grouping the housing units according to
these factors, units within the same group had relatively similar distributions of environmental-
lead levels, while units in different groups had considerably different distributions.
hi determinhig an appropriate housing grouping, a set of candidate factors was identified,
where these factors satisfied three criteria: 1) they would be either important in an economic
analysis for §403 rulemaking, or they were likely to be significantly associated with
environmental-lead levels; 2) their values for National Survey units existed within the National
Survey database; and 3) their values were measured within the 1993 American Housing Survey, a
national survey conducted by the Bureau of the Census and the Department of Housing and
Urban Development (HUD) to characterize the nation's housing stock (Bureau of the Census and
HUD, 1995). Then, a stepwise regression variable selection analysis selected a subset of these
factors which explained the largest proportions of house-to-house variability in the following
four environmental-lead measurements:
• A mass-weighted arithmetic average floor dust-lead concentration* for the unit (i.e.,
each measurement was weighted by the mass of the sample);
• An area-weighted arithmetic average floor dust-lead loading for the unit (i.e., each
measurement was weighted by the square-footage of the sample area);
• A weighted arithmetic average soil-lead concentration for the unit, where results for
samples taken from remote locations were weighted twice as much as results for
dripline and entryway samples.
• Maximum XRF paint-lead level hi the unit (for units containing lead-based paint**).
Prior to calculating the mass-weighted average, dust-lead concentrations were adjusted to reduce bias associated
with underestimated sample weights ("low tap weights") reported in the HUD National Survey for dust samples. The adjustment
procedure is documented in USEPA, 1996c.
**
Lead-based paint was considered present in a unit if its predicted maximum XRF value (as determined by statistical
modeling techniques within the HUD National Survey) in either the ulterior or exterior was greater than or equal to 1.0 mg/cm2.
C1-3
-------
The set of factors included in this analysis are documented in Table Cl-1.
Table C1-1. Demographic Factors Included in the Stepwise Regression Analysis.
Factor
Year the Unit Was Built
Race of Youngest Child
Urbanicity Status
Region of Country
Ownership Status
Number of Units in the Bldg.
Annual Income of Residents
How the Factor Categorized Housing Units
for the Stepwise Regression Analysis
Pre-1940; 1940-1959; 1960-1979
White/Non-Hispanic; Other
City; Suburb/non-metro
Northeast; Midwest; South; West (U.S. Census regions)
Owner-occupied; renter-occupied
One unit; more than one unit
< $30,000; $30,000 or more
The analysis was performed twice on each endpoint: on data for National Survey units
containing lead-based paint (LBP) and for units with no LBP. Table Cl-2 provides the observed
significance levels of each factor considered in the stepwise regression analyses when these
levels were below 0.10. Lower significance levels imply a stronger effect on the measurement.
The columns in Table Cl-2 correspond to separate regression analyses. Across all analyses, the
year in which a unit was built (as categorized by pre-1940,1940-1959, and 1960-1979) had the
strongest and most consistent effect on the environmental-lead level (with floor dust-lead
concentration an exception). Statistical significance levels for the effect of year built were
consistently less than 0.01. While similar significance levels were occasionally observed for
other factors in the table, the extent of significance across the environmental-lead measurements
was not as consistent for any other factor. Therefore, the year in which the unit was built was the
only factor considered in grouping National Survey units for purposes of updating their weights
to 1997.
The stepwise regression analysis assumed that the predicted maximum XRF value is an
accurate indicator of whether or not a unit contains LBP. Also, those units with no predicted
maximum XRF value were assumed not to contain LBP.
1.2 ESTIMATING NUMBERS OF HOUSING UNITS IN 1997 WITHIN
YEAR-BUILT CATEGORIES
In this second task, the number of occupied housing units in 1997, both privately- and
publicly-owned, was estimated for each of four categories denoting when the unit was built: pre-
1940, 1940-1959,1960-1979, and post-1979. These categories are hereafter referred to as "year-
built categories." The results of this task are presented in Table 3-5 within Chapter 3 of this
document.
C1-4
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Table C1-2. Demographic Factors Included in Stepwise Regression Analyses, and
Significance Levels Associated With These Factors When Less Than 0.10.1
Ownographle Factor**
Y«ar tit* Unit Wa»
Bum
Raw of Young»*t
Ch8d
Urbanlcfty Statu*
Ragioft of Country
Ottflwthip State*
*Urtt*int»»ekf0,
: Aimuaf tnconwof :
! ttmktont*
Unit* with pradtetod maximum XRF value
to** titan 1.0 rttg/cm1 or ttftting (n « 4O)
Floor
Dutt-leart
Loadlna
<0.016
0.03
Floor
Dust-Ltarf
Cone.9
SoS-Lwd
Cone.
<0.01
0.04
Unit* with pr*dtet*d maximum XRF vato*
«ora6ov»i4Jn»ojtem*(n-zii)
Floor
OuaMwd
Loading
<0.01
0.01
Floor 0u«t-
Laid Cone**
0.01
Soi-L«»d
Cone.
<0.01
Max.
ObMrv«4
XRFVah»*
<0.01
1 Column headings for this table identify the environmental-lead measurement being considered in the analysis and the
group of National Survey units whose data are included in the analysis. Each column corresponds to a separate regression
analysis. The demographic factors included in the regression analyses are included as rows of the table. As the
significance level for a demographic factor gets closer to zero, the effect of the factor on the given environmental
measurement is considered more highly statistically significant.
2 See Table C1-1 for definitions of these factors.
3 This analysis was performed on unadjusted dust-lead concentrations (i.e., no adjustment was made for bias due to
underestimated sample weights).
4 Regression performed on units where the observed maximum XRF value was at least 1.0 mg/cm*.
5 In the regression analysis of floor dust-lead loading in units without LBP, the effect of the year in which the unit was built
was statistically significant with a p-value of less than 0.01 (i.e., significance can be concluded at the 0.01 level).
The primary data source for determining the number of units within each year-built
category was the 1993 American Housing Survey (AHS) (Bureau of the Census and HUD, 1995).
Data from the 1993 AHS provided estimates of the number of housing units in each year-built
category in 1993. However, it was of interest to obtain estimates for 1997, not 1993. Therefore,
the 1993 estimates were augmented to reflect additions to and removals from the national
housing stock from 1994 to 1997. Once the 1997 estimate of the total within each year-built
category was obtained, the total was distributed among the National Survey units in the group
using information within the National Survey weights. Details on each of these procedures are
now provided.
1.2.1 Characterizing the 1993 National Housing Stock
As hi the National Survey, each unit hi the 1993 AHS was assigned a weight that was
interpreted as the number of units in the national housing stock represented by the given unit.
Therefore, placing the AHS units among the four year-built categories and summing the weights
of the units within each category yielded the estimated number of units in 1993 for each category.
C1-5
-------
Only occupied housing units in the 1993 AHS (either publicly-owned or privately-owned)
were considered in updating to 1997. The definition of an "occupied unit was one which was
occupied by at least one resident who was classified as not having his/her usual residence
elsewhere. Data for 40,931 occupied housing units were available from the 1993 AHS.
1.2.2 Updating the 1993 Housing Stock to 1997
Once the number of housing units in 1993 was determined for each of the four year-built
categories, these totals were updated to reflect the 1997 housing stock. Updating the 1993 totals
to 1997 was done hi the following way:
1. For the post-1979 category, the total number of housing units constructed from
1994 to 1997 and occupied in 1997 was estimated and added to the 1993 total.
2. For all four year-built categories, the total number of housing units occupied in
1993 and lost from the housing stock from 1994 to 1997 was estimated and
subtracted from the 1993 total.
In the first step, numbers of new, privately-owned housing units completed in 1994 and 1995
were obtained from Bureau of the Census and HUD (1996). This publication reported estimates
of 1,346,900 such units completed hi 1994 and 1,311,300 units hi 1995. For this analysis, the
1995 estimate was also used in estimating totals for both 1996 and 1997. Therefore, the 1993
estimate for the post-1979 housing category was incremented by 1,346,900 + 3*1,311,300 =
5,280,800 units. Note that this approach assumes that new housing units are completed and
occupied within the same year. In addition, no provision was considered for adding new
publicly-owned units.
The second step, subtracting the number of housing units occupied in 1993 and lost from
the housing stock from 1994 to 1997 within each of the four year-built categories, was more
complex. Information on losses was not available by considering only the 1993 AHS. To obtain
such information, the 1989 and 1991 AHS databases were obtained. As the AHS retains the
same units from survey to survey, it was possible to determine those units that were occupied in
one survey and lost from the housing stock by the next. Units were considered lost from the
housing stock hi a given survey if they were labeled as a "Type C non-interview" hi the survey,
meaning the unit no longer exists and is dropped from consideration for future surveys. Such
losses include demolition, disaster loss, abandoned permit, or the unit was merged with another
unit. While moving a house or mobile home from the site also labels the unit as a Type C
noninterview, such an instance was not labeled as a loss from the housing stock for this effort, as
it is assumed that the unit remains habitable hi its new location.
As the AHS is conducted every two years, the probability that a unit is lost from the
housing stock over a two-year period was initially estimated from the AHS data. In this
procedure, a dataset of information on occupied housing units present in the 1989 AHS was
created, with each unit identified by its approximate age in 1989 (in years), by its 1989 sample
weight, and by whether or not it was classified as lost from the housing stock hi the 1991 AHS.
C1-6
-------
Similarly, a dataset of information on occupied housing units present in the 1991 AHS was
created, with each unit identified by its approximate age in 1991, by its 1991 sample weight, and
by whether or not it was classified as lost from the housing stock in the 1993 AHS. Both datasets
were combined into a single dataset (without regard to survey year), and a logistic regression
analysis was fitted to the combined data to predict the probability of a loss over a two-year period
as a function of age (in years). Each data point in the regression analysis was weighted by its
sample weight. The resulting prediction model was
Pfloss over a two -year period] =
1
e5.82 - 0.0094 .age
(1)
where "age" is the age of the unit in years. The probability for a one-year period was roughly
one-half of the probability for the two-year period. Table Cl-3 provides the predicted
probabilities of losses over a one-year period for every five years of age.
Table C1-3. Estimated Probability of an Occupied Housing Unit Becoming Lost from the
Housing Stock Over a One-Year Period, Given the Age of Unit.
Aga of Unit (yrs)
5
10
15
20
25
30
35
40
Probability of
to»s
0.0013
0.0014
0.001 5
0.0016
0.0017
0.0018
0.0020
0.0021
Age of Unit
(¥tt)
45
50
55
60
65
70
75
80
Probability of
U>« '^m
0.0023
0.0025
0.0026
0.0028
0.0031
0.0033
0.0036
0.0038
Note: These probabilities were estimated from equation (1) and adjusted to cover a one-year period.
Table Cl-4 illustrates how losses from the housing stock from 1993 to 1997 were
characterized within each of the four year-built categories considered in the risk analysis. First,
an age (in years) associated with each of the four year-built categories was determined for 1993
and 1995. For the 1940-1959, 1960-1979, and post-1979 categories, this age corresponded to the
age of a unit built in the middle year of the category. The single age assigned to all units hi the
pre-1940 category was equal to the age of a unit built hi 1939. Then, the probability of loss from
1993-1995 and from 1995-1997 was determined from equation (1) based on the age of the unit;
these probabilities are labeled hi Table Cl-4 as p^^s and Pi995.97, respectively. The total number
of units hi the category in 1993 was then reduced by multiplying the total by the product (l-
9s)*(l-Pi995-97) (i-e, the last column of Table Cl-4).
C1-7
-------
Table C1-4. Determining Losses from the Housing Stock from 1993-1997.
Year-Built
Category
Pre-1 940
1940-
1959
1960-
1979
Post-1979
Age of
units in
1993
{yr«-»n
54
44
24
7
Prob.of Joss i
* from 1993*
1995
; iPtwwwi*
0.0052
0.0045
0.0034
0.0026
Age of
units in
1995 ,
Cy«M1
56
46
26
9
Prob. of toss
from 1996*
m? (P,w*7>*
0.0054
0.0046
0.0034
0.0027
•f-^. - / ..
- Proportion of - ,,
1993 Total That
Remains in 1 997*
0.989
0.991
0.993
0.995
1 A single age is assigned to all units in a given category according to the approach indicated in the text.
2 Determined from equation (1).
3 Equal to (1-pl9«.8s)*(1-Pi99w>7)
Besides additions and removals, changes in the number of occupied homes in the national
housing stock from 1993 to 1997 are also affected by the number of units that are occupied in
1993 and vacant in 1997, as well as by the number of units that are vacant in 1993 and occupied
in 1997. However, in this approach, it was assumed that the number of occupied units in 1993
that become vacant in 1997 was approximately equal to the number of vacant units in 1993 that
become occupied in 1997, thereby canceling each other out.
1.3 DETERMINING THE NUMBER OF 1997 UNITS REPRESENTED BY EACH
NATIONAL SURVEY UNIT
The procedures outlined in the previous subsection provide a method for estimating total
numbers of housing units hi 1997 within each of the four year-built categories. The results are
displayed in Table 3-5 in Chapter 3 of this report. The housing units were grouped within year-
built categories to facilitate the linking of numbers of units with estimated environmental-lead
levels. The linking process consisted of classifying the National Survey units among the four
categories, then distributing the 1997 total among the National Survey units within each category.
This distribution yielded an updated weight for each National Survey unit, reflecting changes in
the numbers of units hi the year-built category from the time the National Survey was conducted
to 1997. A unit's updated weight represented the number of units in the 1997 housing stock
associated with the National Survey unit (and therefore with its environmental-lead levels).
The 1997 totals include both privately-owned and publicly-owned housing units, while
the 284 National Survey units were privately-owned. Therefore, the revised 1997 weights for the
National Survey units represent publicly-owned as well as privately-owned units.
C1-8
-------
1.3.1 Updating the Weights to Reflect the Pre-1980 Housing Stock
To update the sampling weights for the 284 National Survey units to reflect the pre-1980
housing stock, the units were grouped according to the three pre-1980 year-built categories.
(Recall that all National Survey units were built prior to 1980). For these three categories, the
updated 1997 weight for each unit in the category was calculated as follows:
1997 weight = (National Survey weight) *(Updating factor for the category)
where the updating factor was determined as follows:
# units in the category in 1997
(2)
Updating factor =
Total National Survey weights in the category
(3)
(The sampling weights assigned in the National Survey were determined according to when the
unit was built, whether the unit existed in a single- or multiple-unit building, the Census region
in which the unit was located, and whether or not a child less than aged seven years resided in the
unit).
Table Cl-S contains the updating factors applied to the National Survey units according
to year-built category. As an example, Table Cl-5 indicates that the updated 1997 weight for
each of the 77 National Survey units in the pre-1940 category equaled the weight assigned hi the
National Survey multiplied by 0.936.
Table Cl-5. Number of National Survey Units in the Pre-1980 Year-Built Categories, and
the Multiplicative Factor Used to Update National Survey Weights to 1997.
Year-Built
Category
Pre-1940
1940-1959
1960-1979
# National Survey
Units •
77
87
120
Sum of National
Survey Weights
21,020,019
20,472,997
35,686,004
•s
Uptte&tg Factor
0.936
0.963
0.980
1.3.2 Updating the Weights to Reflect the Post-1979 Housing Stock
Despite the fact that no HUD National Survey units were built after 1979, it was of
interest to use the HUD National Survey data to characterize the entire occupied national housing
stock, including those units built after 1979. Therefore, methods were developed to determine
how to use environmental-lead information from the HUD National Survey to represent the post-
1979 occupied housing stock.
As the post-1979 housing stock was built after the Consumer Product Safety
Commission's 1978 ban on the sale of LBP and its use in residences, the post-1979 housing
C1-9
-------
stock was assumed to be free of LBP. This same assumption was made in the HUD National
Survey and is the reason for not including post-1979 housing in the survey. Therefore, only
National Survey units not containing LBP were considered in representing post-1979 housing.
To determine whether the entire set of National Survey units without LBP should be
considered hi representing post-1979 housing or only a subset of these units, data on dust-lead
and soil-lead concentrations for units having maximum and minimum XRF measurements below
0.7 mg/cm2 were investigated. As the top two plots hi Figure Cl-1 illustrate, a noticeable
relationship exists between lead concentrations and the age of the unit, with higher
concentrations associated with older units, hi contrast, the bottom two plots in Figure Cl-1 show
less of a relationship between concentration and age of unit when only units built from 1960-
1979 were considered. This rinding suggests that older units may be free of LBP, but dust and
soil are more likely to remain contaminated with lead than for newer units, either due to previous
renovation work on the units or from outside contamination.
As a result of the conclusions made from Figure Cl-1, only the 28 National Survey units
built between 1960 and 1979 and containing no LBP (predicted maximum XRF measurement
less than 1.0 mg/cm2) were selected to represent the post-1979 housing stock. As a result, it was
assumed that the environmental-lead levels for these 28 units represented levels that exist in the
post-1979 housing stock. These units also were included among those representing the 1960-
1979 housing stock. Therefore, the total 1997 sampling weight for these 28 units consisted of
two parts: that representing the 1960-1979 housing stock, and that representing the post-1979
housing stock, 1997 weight = (1960-1979 housing stock weight) + (post-1979 housing stock
weight), where the 1960-1979 housing stock weight was calculated as described above. The
portion representing the post-1979 housing stock was determined by dividing the total number of
post-1979 units in 1997 by 28,
post-1979 housing stock weight = (total # of post-1979 units) / 28. (4)
2.0 POPULATING HOUSING UNITS WITH CHILDREN
To characterize risk reduction that may result from performing interventions in response
to §403 rules, it was necessary to estimate numbers of children of specific age groups who reside
within the national housing stock. This section documents the methods for populating the 1997
national housing stock with children.
Section 1.0 of this appendix presented methods to revising the sampling weights for HUD
National Survey units to reflect the 1997 national housing stock of occupied units. Therefore,
each weight represents a subset of the national housing stock. It was desired to link numbers of
children with each weight. Two age groups of children were of interest:
• Children aged 12 to 35 months (1 to 2 years)
• Children aged 12 to 71 months (1 to 5 years)
C1-10
-------
10000
1000
100
10
1900 1920 1940 1960
Year Built
1980
100000
10000
1000
100
10
1900 1920 1940 1960
Year Built
1980
10000
1000
100
10
1960 1965 1970 1975
Year Built
1980
100000
10000
1000
100
10
1960 1965 1970 1975
Year Built
1980
Figure C1-1. Plots of Dust- and Soil-Lead Concentration (f/g/g) Versus Age of Unit, for
HUD National Survey Units With Maximum XRF Value Less Than 0.7
mg/cm2
C1-11
-------
The 1-2 year age group was the primary group of interest in this risk analysis, while the 1-5 year
age group was considered in the sensitivity analysis within Chapter 5 (Section 5.4.1).
For a given age group of children, the estimated number of children associated with the
units represented within a 1997 sampling weight was the product of three statistics:
# children = (1997 weight) *(Average # residents per unit) *(# children per person) (5)
As the 1997 weight was determined for each National Survey unit using the methods hi Section
1.0 of this appendix, it was necessary to obtain estimates for the latter two statistics in equation
(5).
The factor "average # residents per unit" in equation (5) was calculated for the housing
group based on information obtained in the 1993 AHS. The 1993 AHS database provided
information on up to 15 residents within each housing unit in the AHS. Once these units were
placed within the four year-built categories, the average number of people residing in a unit
(regardless of age) was calculated for each group. This average ranged from 2.5 to 2.7 across the
four year-built categories. A common average of 2.7 residents per unit was used for all units in
the national housing stock. While this average was based on 1993 data, it is assumed to also
hold for the 1997 housing stock.
The third factor in equation (5), "# children per person," represented the average number
of children (of the given age group) per person residing in units within the housing group. This
factor was calculated from information presented hi Day (1993). This document provided two
types of information necessary to calculate average number of children per person:
1. Predicted numbers of births per 1,000 people hi the general population within
selected years from 1993 to 2050
2. Predicted numbers of people hi the general population of specific ages for these
selected years.
For 1997, Day (1993) predicted a total of 14.8 births predicted per 1,000 people in the U.S.*
Therefore, it was assumed that in any subset of occupied housing hi 1997, the units within this
subset will contain 14.8 children less than one year of age for every 1000 residents.
Day (1993) also provided a predicted number of children of various age groups hi the
nation in 1997. A total of 3,907,000 children aged 0-11 months, 7,835,000 children aged 12 to
This is a "middle series assumption" birth rate, indicating the level at which assumptions are placed on fertility, life
expectancy, and yearly net immigration.
C1-12
-------
35 months, and 20,066,000 children aged 12 to 71 months were predicted. By dividing each of
these latter two statistics by 3,907,000, approximately 2.01 children aged 12 to 35 months and
5.14 children aged 12 to 71 months are predicted in 1997 for every child aged 0-11 months.
Thus, using the birth rate in the previous paragraph, a total of 2.01 x 14.8 = 29.7 children aged 12
to 35 months, and 5.14 x 14.8 = 76.1 children aged 12 to 71 months, are predicted in 1997 per
1000 people in the U.S.
Table Cl-6 contains estimates of average number of children per unit in the 1997 national
housing stock, according to age group. These numbers are the product of the final two factors in
equation (5). Therefore, these numbers are multiplied by the 1997 sampling weights for each
National Survey unit to obtain an estimated number of children residing in units represented
within the weight By summing the estimates across National Survey units, the total number of
children aged 12-35 months and 12-71 months residing within the 1997 national housing stock is
obtained by year-built category and for the nation. These results are presented in Table 3-35 in
Chapter 3 of this report.
Table C1-6. Estimated Average Number of Children Per Unit in the 1997 National
Housing Stock, by Age of Child.
Age Group
1 2-35 months
12-71 months
Estimated Average Number of
Children Per Unit
2.7*0.0297 = 0.080
2.7*0.0761 = 0.205
3.0 SUMMARIZING ENVIRONMENTAL-LEAD LEVELS WITHIN THE HUD
NATIONAL SURVEY UNITS
The methods of Sections 1.0 and 2.0 of this appendix were used to link each of the 284
units hi the HUD National Survey with an estimated number of units in the 1997 national
housing stock and an estimated number of children residing within these units. In this final step,
it is necessary to summarize the environmental-lead levels within each National Survey unit.
The following statistics were calculated for each National Survey unit, summarizing the
unit's dust-lead loadings and dust-lead concentrations from floors and window sills, and soil-lead
concentrations:
C1-13
-------
• A mass-weighted arithmetic average floor dust-lead concentration* for the unit (i.e.,
each measurement is weighted by the mass of the sample);
• An area-weighted arithmetic average floor dust-lead loading for the unit (i.e., each
measurement is weighted by the square-footage of the sample area);
• A mass-weighted arithmetic average window sill dust-lead concentration* for the
unit (i.e., each measurement is weighted by the mass of the sample);
• An area-weighted arithmetic average window sill dust-lead loading for the unit (i.e.,
each measurement is weighted by the square-footage of the sample area);
• A weighted arithmetic average soil-lead concentration for the unit, where results for
samples taken from remote locations were weighted twice as much as results for
dripline and entryway samples. If a unit has no soil-lead results for a particular
location, the arithmetic average was unweighted (i.e., results for the remaining
locations were not weighted).
• An unweighted arithmetic average soil-lead concentration, considering only the
dripline and entryway samples for the unit.
• The maximum paint-lead concentration in the ulterior and the exterior of the unit, as
measured by XRF techniques in selected rooms and on selected components within
these rooms.
• The amount of damaged lead-based paint measured in the interior and the exterior
of the unit.
These summary values were used hi the statistical models to represent environmental-lead levels
hi the national housing stock, in determining health benefits associated with intervention.
In the HUD National Survey database, some units have unrecorded (or "missing") values
for dust-lead loadings or concentrations, or soil-lead concentrations, preventing values for one or
more of the first six summary statistics above from being calculated. As the values of certain
statistics were used as input to the IEUBK and empirical models to predict any risk reductions
that may result from performing interventions in response to §403 rules, it was necessary that
every housing unit have values for these statistics, even if no data existed for a particular unit.
Therefore, an imputation scheme was devised to obtain summary values for units having no data
hi the National Survey database for the given parameter. In this approach, if a unit did not have
data to allow the value of a summary statistic from being calculated, the value assigned to the
unit equaled the weighted arithmetic average of those values for units within the same year-built
' Prior to calculating the mass-weighted average, dust-lead concentrations on floors and window sills were adjusted to
reduce bias associated with underestimated sample weights ("low tap weights") reported in the National Survey for dust
samples.
C1-14
-------
category and having the same indicator for the presence of LBP, with each value weighted by the
1997 weight for the respective unit. For example, a total of eight National Survey units were
built prior to 1940 and contained no LBP. If one of these units had no floor dust-lead loadings,
then the summary value of floor-dust-lead loading for this unit would equal the weighted average
of the summary values across the other seven units. The inputed values are documented in Table
3-14 of Chapter 3.
Table Cl-7 contains a listing of National Survey units within the three year-built
categories in which they are classified. Also note that the 28 National Survey units built from
1960-1979 and containing no LBP were listed within a fourth category within Table Cl-7,
representing the national housing stock built after 1979. The dust-lead concentrations
summarized in Table Cl-7 were initially adjusted for underestimated sample weights (USEPA,
1996c). Also, dust-lead loadings summarized in Table Cl-7 were initially adjusted to reflect
loadings that would be obtained if wipe collection techniques were used, rather than the Blue
Nozzle vacuum method employed in the HUD National Survey. The method to converting from
Blue Nozzle vacuum to wipe loadings is presented hi Chapter 4.
Table Cl-7 also contains the updated 1997 sampling weights for each unit (as calculated
in Section 1.0 of this appendix) and the estimated numbers of children aged 12-35 months and
12-71 months that reside within the units (as calculated hi Section 2.0 of this appendix). For the
28 units listed hi both the 1960-1979 and post-1979 categories, the sampling weights and
numbers of children are only that portion representing units within the category.
C1-15
-------
Table C1-7. Estimated Environmental Lead Levels in the 1997 Housing Stock, As Determined from National Survey Units
o
_*
•
o>
Year
Built
<1940
national
Survey
ID
0320408
0320507
1210806
1921709
1932300
1942606
1953009
2022507
0211102
0221101
0221507
0310102
0310607
0310706
0311100
0320705
0350801
0411207
0520106
0520403
0520700
0520908
0711002
0720300
0720706
0721001
0730606
0820506
0911800
0920900
0941005
0950402
0951004
1010909
1011303
1011501
1011600
1041607
1221902
1250406
1251107
1251404
1352608
1353705
1411909
1531201
1531300
1631209
1631308
1740901
1751304
1820802
1830801
1830900
1840503
1851104
1931906
1951904
19S2506
2121507
2240406
LBP
Present?
NO
No
No
Mo
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Wipe Floor
Dust- Lead
Loading
(ug/ft2)
8.43
17.2
23.1
23.5
106.
31.4
0.99
93.3
17.3
2.09
26.7
13.2
2.83
2.83
96.6
6.40
22.6
236.
4.61
130.
75.7
12.2
24.6
13.3
16.1
31.0
49.3
6.83
2.83
4.73
4.84
17.7
7.52
23.2
44.2
19.0
46.2 *
2.85
100.
32.8
74.1
11.0
173.
4.85
197.
134.
16.8
12.9
6.28
81.1
14.8
3.96
9.48
375.
114.
32.8
17.0
44.9
12.6
27.2
225.
Vac. Floor
Dust -Lead
Loading
(ug/ft2)
1.72
4.19
6.28
5.86
40.0
9.10
0.13
34.0
4.64
0.32
6.95
3.08
0.46
0.48
41.7
1.28
6.55
118.
0.81
51.8
27.2
2.93
7.08
3.07
3.80
8.56
14.8
1.32
0.43
0.84
0.86
4.26
1.57
6.63
13.3
4.51
17.9 *
0.45
41.4
9.01
27.2
2.40
78.1
0.86
102.
53.4
4.29
3.09
1.15
27.7
3.54
0.69
1.90
194.
47.3
10.3
4.19
13.1
2.76
7.68
97.7
BN Floor
Dust -Lead
Cone, (ug/g)
320.
338.
970.
448.
412.
246.
103.
589.
778.
148.
975.
297.
63.8
197.
1600.
406.
2110.
1810.
86.6
299.
938.
631.
537.
340.
526.
326.
527.
130.
92.2
187.
244.
641.
522.
1240.
1100.
616.
451.
0.09
6320.
2260.
1760.
638.
2070.
451.
4340.
831.
303.
215.
122.
860.
198.
105.
271.
3630.
1970.
316.
193.
625.
328.
281.
781.
Wipe U. Silt
Dust -Lead
Loading
(ug/ft2)
1.83
35.6
17.6
35.7
1220.
2250.
1.36
176.
0.14
0.80
449.
2.58
440.
59.6
3.03
0.86
29.6
14.6
4.92
246.
6190.
108.
8.32
2540.
298.
2300. *
43700.
13.3
97.2
1.28
896.
2310.
101.
24.4
2300. *
48.3
2300. *
1.12
14600.
96.4
85.7
36.3
2300. *
7.54
7.05
542.
35.0
210.
229.
2300. *
0.02
0.81
3.07
8.85
22.1
414.
1030.
303.
0.38
2300. *
28400.
Vac. W. Sill Yardwlde
Oust -Lead
Loading
(ug/ft2)
0.62
7.78
4.55
8.28
166.
277.
0.52
31.9
0.08
0.33
65.1
0.89
68.3
12.8
1.02
0.35
6.47
3.88
1.54
41.8
592.
21.2
2.41
307.
46.3
207. *
3150.
3.59
19.3
0.49
127.
262.
18.5
5.84
207. *
9.95
207. *
0.44
1200.
19.1
17.4
8.08
207. *
2.17
2.06
83.0
8.11
37.1
40.0
207. *
0.01
0.32
1.03
2.36
5.17
66.0
132.
50.2
0.17
207. *
2190.
Avg.
Soil -Lead
Cone, (ug/g)
36.5
113.
279.
305.
279.
259.
279.
326.
84.2
394.
2020.
138.
1240.
534.
711.
274.
25.9
805.
59.6
102.
258.
17.4
642.
1460.
841.
80.4
372.
835.
49.8
162.
1620.
2000.
1170.
851.
717.
4620.
392.
39.5
444.
628.
1030.
569.
679.
109.
586.
251.
105.
841.
539.
137.
358.
1430.
841.
841.
841.
383.
841.
841.
841.
860.
335.
Obs. Max.
Interior XRF
(Bfl/C«2)
0.60
..
..
..
..
0.60
0.60
0.60
2.8
0.60
10.
0.60
3.4
7.1
5.3
0.70
..
0.40
0.60
0.70
0.60
0.70
0.20
12.
8.0
3.3
10.
0.70
0.60
0.60
0.80
0.30
0.60
10.
0.80
0.40
0.30
0.30
6.4
6.2
5.0
20.
7.0
13.
0.60
0.90
3.3
1.4
1.2
9.4
2.9
0.60
6.6
4.7
1.2
0.60
4.4
6.0
1.9
1.7
0.60
Obs. Max.
Exterior XRF
(•0/CB2)
..
..
0.00
..
8.7
5.1
6.0
0.60
..
14.
5.8
27.
..
0.40
0.40
1.8
2.8
0.60
13.
0.60
5.0
0.60
8.8
3.6
0.80
54.
3.8
0.30
6.5
51.
..
38.
29.
0.30
11.
4.9
0.00
4.0
10.
1.8
7.9
14.
4.4
1.6
1.6
15.
9.5
..
..
-.
..
4.6
2.7
-.
2.4
7.1
3.5
Daaaged
Interior
LBP (ft2)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
9.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
11.5
0.0
0.0
0.0
0.0
0.0
89.8
17.6
0.0
18.7
0.0
0.0
0.0
0.8
0.0
0.0
6.2
0.0
Damaged
Exterior
LBP (ft2)
0.0
0.0
..
0.0
0.0
0.0
0.0
0.0
0.0
4.8
0.0
0.0
57.6
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
24.6
0.0
28.0
226.8
0.0
0.0
0.0
0.0
457.3
0.0
..
0.0
182.0
0.0
8.4
0.0
0.0
0.0
141.4
0.0
0.0
585.7
112.0
0.0
0.0
0.0
0.0
0.0
--
--
..
0.0
0.0
0.0
0.0
25.1
604.8
1997
Height
183.864
183,864
121.752
199.528
199.528
199.528
199.528
1.140,935
183,864
95,766
183,864
183,864
183,864
95,766
183,864
183,864
95,766
244,799
244,799
114,632
199.528
114.632
111,365
111.365
111,365
60.761
111.365
111.365
111.365
111.365
773.094
773.094
773.094
244.799
244,799
114,632
244.799
244.799
1.140.935
121.752
121.752
1.140.935
111.365
111.365
95,766
773,094
111.365
199.528
199.528
121,752
121.752
60.761
60.761
199.528
60,761
121.752
199,528
60.761
60.761
199,528
244.799
* Children
12-35 10.
14,744
14.744
9,763
16.000
16,000
16,000
16,000
91,492
14.744
7.679
14,744
14.744
14,744
7.679
14,744
14,744
7.679
19.630
19,630
9.192
16.000
9.192
8,930
8.930
8.930
4,872
8.930
8,930
8.930
8.930
61.994
61,994
61.994
19,630
19,630
9.192
19.630
19.630
91.492
9.763
9,763
91.492
8.930
8,930
7.679
61,994
8.930
16.000
16,000
9,763
9,763
4,872
4,872
16.000
4.872
9,763
16.000
4,872
4,872
16,000
19,630
* Children
12-71 mo.
37,779
37,779
25,016
40.997
40.997
40,997
40,997
234,428
37.779
19,677
37,779
37,779
37,779
19,677
37,779
37,779
19.677
50,299
50,299
23,553
40,997
23,553
22,882
22,882
22.882
12,485
22.882
22.882
22,882
22,882
158,848
158,848
158,848
50.299
50,299
23,553
50.299
50,299
234,428
25.016
25.016
234,428
22,882
22,882
19.677
158,848
22,882
40.997
40,997
25.016
25.016
12.485
12.485
40.997
12.485
25,016
40.997
12.485
12,485
40.997
50,299
-------
Table C1-7. Estimated Environmental Lead Levels in the 1997 Housing Stock, As Determined from National Survey Units. (Continued)
o
1
— *
••J
National
Year Survey
Built ID
<1940 2311108
(cont.) 2343002
2410801
2441608
2521300
2541209
2542009
2550309
2551802
2651800
2710101
2721009
2931608
3011103
3011905
3020401
1940-1959 0340406
0341107
1312701
1722206
2230100
2611101
2731503
3040706
0120105
0131102
0131201
0251900
0310201
0320101
0321307
0351205
0410100
0411306
0411603
0520809
0531301
0612002
0651901
0710103
0750406
0821009
0911503
0920801
0921304
1010503
1030204
1051200
1120401
1121300
1130806
1140508
1332402
1333806
1352806
1410406
1440205
1450907
LBP
Present?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
NO
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Wipe Floor
Oust -Lead
Loading
(ug/ft2)
76.3
6.35
8.95
5.11
15.3
32.8
11.1
1.32
12.2
25.1
8.47
17.0
80.6
79.7
8.84
8.94
2.80
3.96
0.51
42.9
5.17
0.73
8.12
2.43
11.0
72.0
8.88
5.40
4.50
7.47
4.01
28.9
13.2
171.
7.99
53.5
33.1
6.29
1.25
5.64
51.6
2.25
37.6
1.90
2.21
136.
3.00
1.37
39.6
2.15
10.0
15.5
8.32
22.4
3.68
4.67
16.7
29.8
Vac. Floor
Dust-Lead
Loading
(ug/ft2)
26.4
1.19
1.85
0.98
3.51
10.5
2.31
0.17
3.19
6.46
1.69
3.93
31.3
27.8
1.98
1.79
0.53
0.83
0.07
15.5
1.24
0.10
1.99
0.43
2.99
36.8
2.37
1.23
1.12
1.81
0.97
9.93
3.62
94.4
2.10
24.5
11.8
1.62
0.19
1.24
23.2
0.40
13.7
0.34
0.39
71.0
0.57
0.21
15.0
0.39
2.75
S.S8
2.26
7.57
0.73
0.98
5.44
11.0
BN Floor
Oust -Lead
Cone, (ug/g)
1280.
277.
612.
342.
150.
161.
277.
57.5
142.
399.
261.
316.
813.
1310.
764.
327.
60.6
44.7
62.0
373.
32.2
52.9
137.
186.
116.
813.
144.
269.
120.
333.
161.
706.
18.6
1240.
215.
543.
241.
705.
78. 0
232.
667.
97.5
259.
80.1
131.
1560.
101.
112.
248.
60.0
258.
775.
275.
318.
94.2
166.
236.
73.5
Wipe U. S111
Dust-Lead
Loading
(ug/ft2)
1850.
85.6
67.1
469.
1.13
254.
442.
21.8
16.7
5.37
1.11
1020.
401.
808.
1130.
198.
1.45
5.66
2.40
8.63
1.21
5.22
113.
17.4 *
53.8
42.5
80.9
13.6
8.46
3.57
0.01
1400.
16100.
6540.
41.0
3390.
21.7
12.4
105.
309. *
11.3
31.5
37.3
0.07
309. *
113.
309. *
5.65
8.52
1.46
1.82
26.2
6.75
7.76
2.83
6.96
54.7
0.23
Vac. W. Sill Yardwldi
Dust-Lead
Loading
(ug/ft2)
216.
16.0
14.1
67.5
0.42
42.7
68.6
5.29
4.02
1.66
0.44
142.
64.3
114.
129.
31.9
0.53
1.63
0.80
2.48
0.46
1.62
21.9
3.73*
11.6
9.59
16.4
3.47
2.44
1.08
0.01
173.
1330.
618.
9.31
353.
5.43
3.13
19.7
34.5 *
3.02
7.44
7.85
0.04
34.5 *
21.0
34.5 *
1.57
2.28
0.5S
0.63
5.77
1.98
2.14
0.88
1.53
11.9
0.12
Avg.
Soll-Leai
Cone, (ug,
841.
256.
290.
609.
35.0
28.6
125.
76.4
159.
47.4
613.
110.
1160.
1500.
2750.
1390.
25.2
47.6
36.3
39.3
42.8
75.1
5.40
43.5
34.6
60.4
109.
198.
214.
209.
146.
81.4
43.2
122.
115.
347.
160.
135.
70.9
217.
52.4
90.5
21.7
9.26
75.8
7030.
65.7
142.
99.0
144.
81.0
90.0
182.
61.1
71.3
130.
24.9
26.0
0.70
5.7
7.6
3.9
0.60
0.50
0.90
6.6
0.50
0.30
5.0
0.50
7.7
6.9
3.3
5.3
21.9
0.5
238.6
0.0
0.0
7.0
139.9
0.0
0.0
0.0
0.0
0.0
28.8
0.9
6.6
0.0
0.0
1.7
77.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
16.5
1.140.935
121.752
121,752
121.752
244.799
114,632
114.632
244.799
244,799
244,799
244.799
244.799
183.864
111.365
773.094
773,094
91.492
9.763
9.763
9.763
19.630
9.192
9.192
19.630
19.630
19.630
19.630
19.630
14,744
8.930
61.994
61.994
234,428
25,016
25.016
25.016
50.299
23,553
23.553
50,299
50,299
50.299
50,299
50.299
37,779
22,882
158.848
158,848
Obs. Max. Obs. Max. Oanaged Danaged
Interior XRF Exterior XRF Interior Exterior
(•g/cii2) (ng/ci2) LBP (ft2) LBP (ft2)
8.6
2.3
5.9
9.4
0.50
1.5
8.2
0.60
1.3
0.60
2.6
2.9
3.9
12.
10.
0.60
0.60
0.60
0.60
0.30
0.20
1.6
1.5
0.60
0.60
0.60
1.0
3.2
2.9
0.50
7.0
0.40
0.40
0.50
0.90
0.60
0.70
1.1
0.40
0.50
0.50
11.
0.50
0.30
0.90
0.70
7.3
1.1
0.60
0.60
1.9
0.60
1.4
0.60
1997 # Children # Children
Weight 12-35 BO. 12-71 mo.
0.60
0.00
0.60
0.30
0.20
0.60
3.7
1.8
1.9
0.60
0.60
3.1
8.4
3.3
1.4
7.8
0.60
0.60
10.
0.60
0.60
1.4
0.30
0.30
0.00
30.
0.50
0.40
2.6
17.
8.3
4.8
0.60
2.2
0.50
1.9
2.2
0.50
19.676.320 1.577.844 4.042,893
0.0
0.0
0.0
0.0
--
0.0
0.0
.-
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
..
0.0
0.0
0.0
0.0
0.0
0.0
10.3
0.0
0.0
0.0
0.0
33.7
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
5.1
0.0
0.0
6.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
258.519
273,941
227.108
108.151
213,598
181.223
181.223
227.108
273.941
273.941
108.151
273.941
273,941
273.941
273.941
258.519
108.151
213.598
213.598
108.151
181,223
213.598
108.151
227,108
227.108
227.108
227,108
227.108
227.108
213,598
213.598
213,598
181,223
213.598
213.598
181.223
291.118
227.108
227.108
273.941
273.941
258.519
20.731
21.967
18,212
8,673
17,128
14,532
14,532
18.212
21,967
21,967
8,673
21,967
21.967
21.967
21.967
20.731
8.673
17.128
17.128
8.673
14.532
17.128
8.673
18.212
18.212
18.212
18.212
18.212
18,212
17.128
17.128
17.128
14,532
17.128
17.128
14.532
23.345
18.212
18.212
21.967
21.967
20.731
53.118
56,287
46,664
22.222
43.888
37.236
37.236
46,664
56.287
56,287
22,222
56,287
56.287
56.287
56,287
53.118
22.222
43.888
43.888
22.222
37.236
43.888
22.222
46,664
46.664
46,664
46,664
46.664
46.664
43.888
43.888
43.888
37.236
43.888
43.888
37.236
59.816
46.664
46,664
56.287
56.287
53.118
-------
Table C1-7. Estimated Environmental Lead Levels in the 1997 Housing Stock, As Determined from National Survey Units. (Continued)
Wipe Floor vac. Floor
National
Year Survey
Built ID
1940-1959 1521400
(eont.) 1521509
1530500
1550102
1550607
1551704
1730407
1730704
1730803
1731603
1750108
1831106
1831304
1840305
1841105
2022705
2030302
2110906
2141505
2142107
2211902
2332005
2343606
2421709
_. 2441509
2 2451805
i 2520906
£ 2540102
" 2540201
2541407
2541902
2610103
2651206
2652303
2711505
2730703
2731800
2812204
2840403
2841203
2841500
2910107
2931202
2940708
3011509
1960-1979 0130708
0131003
0150201
0330308
0350306
0420901
0430108
0440305
0440602
0541201
0940700
0940809
1020205
LBP
Present?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
NO
NO
No
No
No
NO
NO
No
NO
Dust-Lead
Loading
(ug/ft2)
25.0
22.5
3.51
10.0
17.6
27.8
12.2
5.18
6.40
0.63
5.32
26.4
14.8
13.8
17.1
13.5
4.07
158.
0.62
5.79
17.9
27.4
4.20
7.81
36.6
3.14
40.3
78.8
4.97
56.2
1.25
7.48
4.48
4.38
18.6
2.13
19.9
10.2
15.2
37.3
4.84
10.1
16.9
4.68
4.35
3.35
6.35
12.2
1.97
2.65
9.30
3.89
12.1
5.52
1.72
1.79
6.32
2.30
Dust -Lead
Loading
(ug/ft2)
8.44
7.13
0.69
2.78
5.29
9.63
3.62
1.18
1.50
0.09
1.32
9.79
4.31
3.99
5.37
3.73
0.89
90.2
0.08
1.35
5.58
9.06
0.90
2.14
13.7
0.63
14.6
34.0
1.09
26.5
0.19
1.85
1.00
0.98
5.73
0.39
6.70
3.08
5.31
15.0
1.16
2.68
5.21
0.98
0.89
0.83
2.01
5.99
0.47
0.57
3.54
1.08
5.43
1.72
0.33
0.34
1.93
0.51
BN Floi
Dust -Lei
Cone, (ui
173.
394.
160.
287.
419.
314.
162.
210.
88.4
17.4
316.
836.
444.
244.
284.
94.4
102.
1680.
32.0
93.6
61.7
761.
136.
169.
1690.
193.
321.
254.
266.
378.
61.0
283.
16.8
273.
210.
84.7
114.
483.
1070.
1270.
118.
230.
316.
218.
330.
87.9
111.
68.8
54.8
112.
20.2
68.8
245.
144.
21.5
47.0
429.
171.
U1pe U. Sill Vac. W. Sill Yardwlde
Dust-Lead Dust-Lead Avg. Obs. Max. Obs. Hax. Daaaged Gauged
Loading Loading Soil-Lead Interior XRF Exterior XRF Interior Exterior
(ug/ft2) (ug/ft2) Cone, (ug/g) (Bg/c«2) («g/c«2) LBP (ft2) LBP (ft2)
1997 * Children « Children
Weight 12-35 mo. 12-71 mo.
47
130.
24.2
256.
2
309. *
58.9
299.
7.43
62.3
309. *
6.47
173.
475.
177.
188.
15.3
5.45
475.
0.13
309. *
9.66
59.9
1.73
107.
50.7
335.
45.3
234.
27.0
19.1
98.4
16.9
39.7
309. *
642.
9.28
258.
15.1
9.29
1290.
0.66
3.53
40.0
6.77
11.8
32.7
7.53
11.7
1.68
4.35
1590.
12.7
3.11
8.69
6.48
81.5 *
1.00
15.0
24.5
5.95
39.7
0.81
34.5 *
11.7
50.1
2.19
13.3
34.5 *
1.74
31.5
74.0
31.4
33.8
3.98
1.68
71.3
0.07
34.5 *
2.73
12.0
0.64
20.4
11.1
54.1
9.90
40.6
6.34
4.65
19.5
4.38
8.88
34.5 *
95.8
2.64
44.2
3.96
2.60
159.
0.28
1.15
9.10
2.00
3.24
7.31
2.21
3.22
0.62
1.31
206.
3.44
1.03
2.85
1.51
12.2 *
0.40
3.97
145.
132.
264.
209.
145.
136.
63.9
77.3
77.3
171.
53.8
1410.
1410.
313.
313.
60.1
33.7
372.
58.9
123.
22.0
313.
225.
52.4
4320.
34.1
55.8
102.
33.0
485.
116.
43.5
26.3
49.0
218.
119.
12.1
162.
52.1
61.9
41.4
51.8
220.
44.3
346.
29.7
5.35
6.16
61.6
14.2
21.0
21.3
97.4
79.3
17.9
7.23
17.7
49.2
2.4
1.5
1.8
3.5
1.2
2.9
1.8
2.1
1.8
1.5
1.2
2.0
0.60
20.
1.0
0.70
0.60
0.60
1.7
1.2
0.70
8.0
0.80
0.60
0.60
0.60
0.80
2.7
0.60
0.60
0.70
0.20
0.60
0.50
1.7
0.40
0.40
2.8
6.1
9.6
1.0
1.4
0.80
1.7
0.60
0.60
0.60
0.60
0.60
0.40
0.30
0.50
0.60
0.30
0.30
0.30
2.8
13.
3.7
2.1
2.0
2.6
2.3
1.5
1.5
1.4
1.8
1.5
0.60
6.3
1.5
0.90
5.0
2.5
1.4
3.9
0.60
0.70
1.5
1.2
0.50
0.50
0.20
0.30
0.30
7.6
0.20
1.0
0.60
8.7
13.
1.8
0.50
0.50
1.5
1.4
0.60
0.00
0.50
0.60
0.60
0.60
0.60
0.60
0.30
0.30
0.50
6.3
0.0
0.0
12.5
73.5
0.0
4.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
201.9
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
278.5
56.0
3.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
..
..
..
.-
0.0
0.0
7.3
2.5
..
0.0
77.1
0.0
0.0
118.3
0.0
0.0
20.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
227.108
227,108
227.108
227.108
227,108
227.108
108.151
108.151
108.151
108,151
433.850
111.336
108.151
108,151
111.336
433.850
433,850
108.151
291.118
227.108
213.598
433.850
433,850
433.850
411.982
433.850
213.598
213.598
213.598
181.223
213,598
213.598
213.598
213.598
181.223
213.598
213.598
213.598
213.598
213.598
213.598
273,941
108,151
•273.941
227.108
19.717.970
658,726
291.351
291.351
291.351
658.726
291.351
116,364
116,364
316,764
116,364
291.351
291.351
316.764
18.212
18,212
18,212
18,212
18,212
18.212
8.673
8.673
8,673
8.673
34.790
8.928
8,673
8,673
8,928
34,790
34,790
8,673
23,345
18,212
17,128
34,790
34,790
34,790
33,037
34,790
17,128
17.128
17,128
14,532
17,128
17.128
17.128
17.128
14.532
17.128
17.128
17.128
17.128
17.128
17,128
21.967
8.673
21.967
18,212
1,581.184
52.823
23.363
23,363
23.363
52.823
23,363
9,331
9,331
25,401
9.331
23.363
23,363
25.401
46.664
46,664
46.664
46,664
46.664
46.664
22,222
22.222
22,222
22.222
89,143
22.876
22,222
22.222
22.876
89.143
89.143
22.222
59.816
46.664
43.888
89.143
89.143
89,143
84.650
89.143
43.888
43.888
43.888
37.236
43.888
43.888
43.888
43,888
37,236
43,888
43.888
43.888
43.888
43,888
43,888
56.287
22.222
56,287
46,664
4.051,451
135.348
59.864
59.864
59.864
135.348
59.B64
23,909
23.909
65.085
23.909
59.864
59.864
65.085
-------
Table C1-7. Estimated Environmental Lead Levels in the 1997 Housing Stock, As Determined from National Survey Units. (Continued)
o
National
Year Survey
Built ID
1960-1979 1020502
(cent.) 1021005
1040500
1323609
1441302
2220507
2230209
2511806
2521201
2551000
2552107
2822005
2831006
2831709
3050101
0130906
0150102
0250902
0252404
0311209
0331009
0340505
0340802
0341404
0410605
0421206
0430207
0430306
0430702
0440107
0441105
0441204
0530105
0530600
0531400
0540203
0541300
0621607
0631408
0840702
0911404
0930701
1011709
1020304
1020403
1020700
1020809
1050509
1050608
1051408
1150200
1150705
1241801
1311505
1312800
1322601
1353309
1441005
1510403
1510908
1520204
LBP
Wipe Floor Vac. Floor
Dust-Lead Dust-Lead
Loading Loading
Present? (ug/ft2)
No
No
No
NO
NO
NO
No
No
No
NO
NO
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
3.30
1.74
3.46
1.37
1.06
5.81
2.00
1.85
12.9
1.29
1.47
2.68
1.21
3.01
3.81
5.38
7.59
3.61
8.08
5.95
3.08
6.94
11.5
2.92
6.39
41.7
13.2
13.5
12.5
15.7
4.40
19.4
7.27
4.18
32.3
8.59
7.59
2.37
3.46
3.23
1.71
3.58
3.19
2.25
2.34
0.75
2.65
1.02
1.09
1.50
3.17
3.62
2.48
1.37
12.3
1.37
0.66
1.93
4.40
7.86
4.44
(ug/ft2)
0.78
0.33
0.91
0.27
0.18
1.85
0.39
0.37
5.58
0.22
0.25
0.58
0.19
0.73
0.98
1.56
2.72
0.97
3.11
1.80
0.78
2.76
6.33
0.74
2.07
31.7
5.38
6.81
6.50
7.85
1.19
9.48
2.35
1.15
20.0
3.31
2.62
0.49
0.93
0.77
0.30
1.00
0.78
0.47
0.47
0.09
0.57
0.15
0.20
0.27
0.97
0.92
0.51
0.25
6.71
0.22
0.09
0.36
1.19
3.15
1.50
BN Floor
Dust- Lead
Wipe W. S111
Dust-Lead
Loading
Cone, (ug/g) (ug/ft2)
160.
198.
208.
102.
85.2
123.
68.6
52.2
183.
52.1
40.5
65. B
33.8
64.3
458.
68.2
188.
206.
225.
330.
27.5
15.8
652.
34.1
60.9
643.
87.3
7.04
318.
319.
75.4
177.
246.
193.
143.
59.9
184.
63.2
221.
82.4
98.6
378.
366.
150.
104.
51.5
263.
44.1
124.
127.
241.
185.
112.
81.8
250.
101.
15.8
46.9
249.
188.
227.
19.5
4.60
9.64
81.5 *
0.02
81.5 *
4.60
0.83
127.
2.05
0.52
124.
0.12
6.10
81.5 *
5.40
2.64
4.29
329.
885.
8.63
0.51
6.86
28.0
605.
665.
15.8
6.96
217. *
130.
10.7
326.
38.2
217. *
103.
217. *
160.
0.45
26.2
1.20
1.76
1.53
0.45
217. *
0.81
0.19
9.64
217. *
0.12
217. *
60.6
450.
3440.
1.73
0.50
0.74
0.28
0.83
217. *
1.87
7.31
Vac. W. $111
Dust -Lead
Loading
(ug/ft2)
4.52
1.46
2.73
12.2 *
0.01
12.2 *
1.38
0.34
24.2
0.73
0.23
23.7
0.07
1.85
12.2 *
1.67
0.91
1.28
51.9
126.
2.48
0.22
2.03
6.73
91.1
98.7
4.14
2.07
28.3 *
24.1
2.98
45.9
8.68
28.3 *
19.9
28.3 *
26.8
0.20
6.36
0.47
0.61
0.57
0.20
28.3 *
0.34
0.10
2.73
28.3 *
0.07
28.3 *
12.9
70.8
377.
0.62
0.20
0.31
0.12
0.34
28.3 *
0.66
2.16
Yardwlde
Avg.
Soil -Lead
Cone, (ug/g)
58.3
25.5
24.5
20.4
13.0
14.1
5.58
11.6
73.4
22.6
27.2
82.5
21.1
40.8
6.68
39.5
4.79
180.
604.
186.
15.3
23.7
31.8
20.0
127.
22.8
35.2
27.2
26.4
34.7
5.22
87.4
50.9
215.
56.1
14.8
7.52
39.4
85.4
30.6
29.8
19.7
996.
26.6
25.0
23.8
25.4
116.
57.5
143.
35.3
81.6
196.
20.8
13.8
33.3
51.6
18.8
4.63
14.8
35.9
Obs. Max.
Interior XRF
(mg/cm2)
0.30
0.50
0.40
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.80
0.60
1.0
0.80
0.60
0.60
0.90
1.0
1.4
0.50
0.50
0.40
0.40
0.60
0.50
0.40
1.4
1.0
0.70
0.80
0.90
0.70
0.40
0.80
0.30
0.60
11.
0.80
0.70
0.60
0.40
3.0
0.30
0.30
1.0
1.6
0.60
0.60
0.90
0.60
0.60
1.5
0.50
0.30
0.30
Obs. Max.
Exterior XRF
dug/en?)
0.30
-.
..
0.50
0.60
0.60
0.50
0.10
0.50
0.50
0.00
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.00
1.7
0.80
0.70
0.40
0.50
0.60
0.60
0.70
0.60
1.7
0.70
0.60
0.30
--
1.2
0.30
0.30
0.40
0.70
0.30
0.70
--
0.60
0.30
1.7
9.1
0.40
1.4
0.00
--
--
0.00
0.50
0.60
0.20
10.
Damaged Damaged
Interior Exterior
LBP (ft2) LBP (ft2)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
28.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
..
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
5.9
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
--
0.0
0.0
0.0
0.0
0.0
1997 # Children #
Weight 12-35 mo.
316.764
316.764
116.364
312.998
658.726
316.764
316.764
116.364
316.764
316.764
316.764
316.764
316,764
116.364
312.998
126.372
658.726
352.318
291.351
352.318
352.318
658.726
352.318
658.726
291.351
291.351
316.764
316.764
116.364
316.764
116.364
316.764
116.364
291.351
116.364
316.764
316.764
126,372
126.372
291.351
173.719
312.998
116.364
316.764
316.764
316.764
316.764
316.764
316.764
116.364
291.351
291.351
451.561
173.719
312.998
312.998
291.351
658.726
173.719
312.998
312.998
25.401
25,401
9.331
25.099
52.823
25.401
25.401
9.331
25,401
25.401
25.401
25,401
25.401
9.331
25,099
10.134
52,823
28,252
23.363
28.252
28,252
52.823
28.252
52,823
23.363
23.363
25,401
25,401
9.331
25.401
9.331
25.401
9,331
23.363
9.331
25.401
25,401
10.134
10,134
23.363
13.931
25.099
9.331
25.401
25.401
25.401
25.401
25.401
25,401
9.331
23,363
23.363
36.211
13.931
25.099
25,099
23,363
52.823
13.931
25.099
25,099
Children
12-71 mo.
65,085
65.085
23.909
64,312
135,348
65.085
65.085
23.909
65.085
65.085
65.085
65,085
65.085
23.909
64,312
25.966
135.348
72.391
59.864
72.391
72.391
135.348
72.391
135,348
59.864
59.864
65,085
65.085
23.909
65.085
23,909
65.085
23.909
59.864
23.909
65.085
65.085
25.966
25.966
59.864
35,694
64.312
23.909
65.085
65.085
65.085
65.085
65.085
65,085
23,909
59,864
59.864
92.782
35,694
64,312
64.312
59.864
135.348
35.694
64.312
64.312
-------
Table C1-7. Estimated Environmental Lead Levels in the 1997 Housing Stock, As Determined from National Survey Units. (Continued)
o
^^
1
ro
o
National
Year Survey
Built ID
1960-1979 1530104
(cont.) 1530302
1S30B07
1531607
1531706
1540202
1540400
1540806
1541200
1741701
1741800
1743103
2040301
2122000
2130706
2131902
2141604
2151207
2211308
2230506
2351500
2352201
2430403
2431807
2452605
2520609
2521102
2531804
2541506
2620508
2621704
2622603
2623007
2650208
2711109
2751402
2810307
2812105
2830602
2832004
2832103
2840106
2840205
2841401
2940401
3051000
LBP
Present?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Wipe Floor
Oust -Lead
Loading
(ug/ft2>
7.38
6.81
11.0
12.5
6.26
2.26
8.48
13.1
3.28
40.0
10.5
1.21
5.81
23.1
9.68
2.60
9.93
8.75
4.67
2.83
5.26
3.14
4.76
4.69
4.79
6.30
4.29
1.31
35.7
2.24
4.53
1.28
1.19
2.56
7.60
106.
3.33
3.39
5.12
6.16
1.74
7.67*
7.67*
2.57
1.38
1.95
Vac. Floor
Dust -Lead
Loading
(ug/ft2)
2.40
2.11
4.49
5.19
2.07
0.49
3.47
5.97
0.82
31.9
4.15
0.19
1.68
14.2
3.49
0.57
3.72
3.48
1.32
0.64
1.56
0.88
1.47
1.70
1.40
2.55
1.35
0.21
26.0
0.45
1.33
0.21
0.19
0.60
2.68
124.
0.78
0.79
1.72
1.95
0.31
4.25*
4.25*
0.60
0.22
0.37
1
BN Floor
Dust -Lead
Cone, (ug/g)
204.
328.
238.
289.
159.
139.
159.
175.
180.
141.
143.
29.1
126.
395.
127.
76.4
87.0
324.
89.4
77.3
135.
180.
457.
215.
315.
803.
117.
60.0
2200.
133.
191.
2.01
130.
93.0
128.
50400.
137.
137.
170.
283.
87.5
740. *
740. *
59.8
66.4
152.
<1pe W. Sill
Dust-Lead
Loading
(ug/ft2)
51.3
448.
48.3
5790.
545.
217. *
16.6
217. *
217. *
217. *
217. *
0.07
22.8
132.
9.59
50.1
3.70
42.3
503.
12.2
305.
217. *
4.19
6.17
217. *
0.22
149.
0.42
315.
217. *
1.40
3.01
1.76
14.9
32.0
19.9
217. *
217. *
11.4
0.34
217. *
217. *
217. *
228.
1.31
217. *
Vac. H. S111
Dust-Lead
Loading
(ug/ft2)
11.3
66.2
9.95
618.
75.7
28.3 *
4.32
28.3 *
28.3 *
28.3 *
28.3 *
0.04
5.53
22.9
2.72
11.0
1.21
8.63
75.4
3.14
45.8
28.3 *
1.22
1.86
28.3 *
0.11
27.7
0.19
50.2
28.3 *
0.53
1.02
0.64
3.90
7.54
4.66
28.3 *
28.3 *
3.16
0.15
28.3 *
28.3 *
28.3 *
35.9
0.50
28.3 *
1 Yardwlde
Avg.
Soil -Lead :
Cone, (ug/g)
78.7
68.4
40.5
105.
23.4
15.9
49.9
30.1
17.1
54.7
95.7
28.6
14.8
355.
13.7
21.1
39.2
17.5
20.4
6.11
115.
42.5
69.7
41.1
121.
15.7
26.8
66.4
45.2
46.1
68.5
54.6
26.0
52.7
32.0
35.0
23.2
91.3
32.1
20.8
75.6
63.4
63.4
35.6
27.2
31.1
Obs. Max.
Interior XRF
0.10
1.5
2.5
11.
1.3
0.70
0.20
0.30
0.70
0.80
0.90
3.3
3.6
0.60
1.3
1.6
0.60
0.50
1.3
..
0.10
0.10
3.4
5.1
0.60
0.50
1.0
0.50
0.50
0.60
8.8
1.1
0.60
3.0
0.80
0.60
0.00
1.5
1.5
0.60
0.20
5.1
2.0
1.6
..
0.60
Damaged
: Interior
LBP (ft2)
0.0
0.0
0.0
12.5
0.0
0.0
0.0
0.0
0.0
0.0
9.5
.0.0
0.0
0.0
57.3
0.0
0.0
0.0
0.0
0.0
1.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
12.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Damaged
Exterior
LBP (ft2)
0.0
0.0
0.0
27.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.6
0.0
0.0
8.0
0.0
0.0
0.0
72.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
20.7
25.7
0.0
-.
0.0
1997 i
Weight
312.998
312.998
312.998
173,719
312,998
173,719
312,998
312.998
173,719
243.025
451.561
451.561
451.561
291.351
173,719
312,998
173,719
312.998
316.764
316.764
243.025
243,025
451,561
451,561
451.561
116.364
316,764
316,764
116,364
126,372
126.372
291.351
126,372
116,364
316.764
291.351
291.351
291.351
116.364
116.364
316,764
126.372
316.764
116.364
658.726
312.998
t Children
12-35 no.
25.099
25.099
25,099
13,931
25,099
13,931
25,099
25,099
13,931
19,488
36,211
36,211
36,211
23,363
13,931
25.099
13,931
25,099
25,401
25.401
19,488
19,488
36.211
36,211
36,211
9,331
25.401
25,401
9,331
10,134
10,134
23,363
10,134
9,331
25,401
23,363
23.363
23.363
9,331
9.331
25.401
10,134
25.401
9,331
52,823
25,099
n Children
12-71 no.
64,312
64,312
64.312
35.694
64,312
35.694
64.312
64,312
35.694
49,934
92,782
92.782
92,782
59,864
35,694
64,312
35,694
64.312
65.085
65,085
49,934
49,934
92.782
92.782
92,782
23,909
65,085
65,085
23,909
25,966
25,966
59,864
25.966
23,909
65,085
59.864
59.864
59.864
23,909
23,909
65,085
25.966
65.085
23.909
135,348
64,312
>1979
34,984.547 2.805.411 7.188.275
0130708
0131003
0150201
0330308
0350306
0420901
0430108
0440305
0440602
0541201
0940700
0940809
No
No
No
No
No
No
No
No
NO
No
No
NO
3.35
6.35
12.2
1.97
2.65
9.30
3.89
12.1
5.52
1.72
1.79
6.32
0.83
2.01
5.99
0.47
0.57
3.54
1.08
5.43
1.72
0.33
0.34
1.93
87.9
111.
68.8
54.8
112.
20.2
68.8
245.
144.
21.5
47.0
429.
32.7
7.53
11.7
1.68
4.35
1590.
12.7
3.11
8.69
6.48
83.0 *
1.00
7.31
2.21
3.22
0.62
1.31
206.
3.44
1.03
2.85
1.51
12.3 *
0.40
29.7
5.35
6.16
61.6
14.2
21.0
21.3
97.4
79.3
17.9
7.23
17.7
0.60
0.60
0.60
0.60
--
0.40
0.30
0.50
--
0.60
0.30
0.30
0.60
0.00
0.50
0.60
0.60
0.60
0.60
0.60
0.30
0.30
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
889,038
889,038
889,038
889,038
889,038
889,038
889,038
889,038
889,038
889,038
889.038
889,038
71,292
71,292
71,292
71,292
71,292
71.292
71.292
71,292
71,292
71,292
71,292
71.292
182,671
182,671
182,671
182.671
182.671
182.671
182.671
182,671
182,671
182,671
182,671
182.671
-------
Tabie C1-7. Estimated Environmental Lead Levels in the 1997 Housing Stock, As Determined from National Survey Units. (Continued)
Year
Built
>1979
(cont.)
National
Survey
ID
1020205
1020S02
1021005
1040500
1323609
1441302
2220507
2230209
2511806
2521201
2551000
2552107
2822005
2831006
2831709
3050101
LBP
Present?
No
No
NO
No
No
NO
No
No
No
NO
NO
No
No
No
No
NO
Wipe Floor
Oust- Lead
Loading
(ug/ft2)
2.30
3.30
1.74
3.46
1.37
1.06
5.81
2.00
1.85
12.9
1.29
1.47
2.68
1.21
3.01
3.81
Vac. Floor
Dust-Lead
Loading
(ug/ft2)
0.51
0.78
0.33
0.91
0.27
0.18
1.85
0.39
0.37
5.58
0.22
0.25
0.58
0.19
0.73
0.98
BN Floi
Dust -Lei
Cone, (u
171.
160.
198.
208.
102.
85.2
123.
68.6
52.2
183.
52.1
40.5
65.8
33.8
64.3
458.
Wipe U. Sill Vac. W. Sill Yardwlde
Dust-Lead Dust-Lead Avg. Obs. Max. Obs. Max. Danaged Damaged
Loading Loading Soil-Lead Interior XRF Exterior XRF Interior
(ug/ft2) (ug/ft2) Cone, (ug/g) (ng/cn2) («g/cm2)
0.50
0.30
0.50
0.60
0.60
0.50
0.10
0.50
0.50
0.00
0.60
0.60
15.0
19.5
4.60
9.64
83.0 *
0.02
83.0 *
4.60
0.83
127.
2.05
0.52
124.
0.12
6.10
83.0 *
3.97
4.52
1.46
2.73
12.3 *
0.01
12.3 *
1.38
0.34
24.2
0.73
0.23
23.7
0.07
1.85
12.3 *
49.2
58.3
25.5
24.5
20.4
13.0
14.1
5.58
11.6
73.4
22.6
27.2
82.5
21.1
40.8
6.68
0.30
0.30
0.50
0.40
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
irlor Exterior
(ft2) LBP (ft2)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
--
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1997 n Children #
Weight 12-35 «o.
889.038
889.038
889,038
889,038
889.038
889,038
889.038
889,038
889,038
889.038
889.038
889,038
889.038
889.038
889.038
889.038
71.292
71.292
71.292
71.292
71.292
71.292
71.292
71.292
71.292
71.292
71.292
71,292
71.292
71.292
71.292
71,292
Children
12-71 BO.
182.671
182.671
182.671
182.671
182,671
182,671
182,671
182,671
182.671
182,671
182.671
182.671
182.671
182.671
182.671
182.671
24.893.064 1,996,175 5,114.778
TOTAL ACROSS ALL UNITS: 99.271,901 7,960.614 20.397.397
> *
Note:
As no data for this parameter existed in the National Survey database for the given housing unit, this value is the average
of the values across all units in the same year-built category and having the same value for the LBP indicator that had
reported data (see Table 3-14 in Chapter 3). The average is weighted using the 1997 weights.
Dust-lead loadings are area-weighted arithmetic averages for the unit. "Wipe" loadings are converted from Blue Nozzle
("Vac.") vacuum loadings (see Chapter 4). Dust-lead concentrations are mass-weighted arithmetic averages of individual
sample concentrations for the unit that have been adjusted for low tap weights (USEPA, 1996c). Soil-lead concentration
represents a weighted arithmetic yardwide average for the unit, with remote sample results weighted twice that of
entryway and dripline samples.
-------
This page intentionally blank.
-------
APPENDIX C2
Method for Computing Confidence Intervals
Associated with Estimates in the
Exposure Assessment and Risk Characterization
C2-1
-------
APPENDIX C2
METHOD FOR COMPUTING CONFIDENCE INTERVALS
ASSOCIATED WITH ESTIMATES IN THE
EXPOSURE ASSESSMENT AND RISK CHARACTERIZATION
In Chapters 3 and 5, approximate 95% confidence intervals were calculated for selected
exposure and risk estimates to provide a measure of precision for these estimates. These risk
estimates included children's geometric mean blood-lead concentrations in the nation's housing
stock (Tables 3-36, 3-38, 3-39, and 3-40), the percentage of children's blood-lead concentrations
greater than or equal to specified thresholds (10 or 20 ug/dL) (Tables 3-37, 3-38, 3-39, 3-40, 5-1,
and 5-9), the percentage of children experiencing IQ decrements greater than or equal to 1, 2, or
3, as a result of lead exposure (Tables 5-1 and 5-9), and average IQ decrement due to childhood
lead exposure. Confidence intervals were also computed for lead levels in dust which, when
assuming fixed lead levels in other media, control the percentage of children with blood-lead
concentrations greater than or equal to 10 |ig/dL to specified levels (Tables 5-6 and 5-7). This
appendix presents the methodology used to compute these intervals.
For endpoints estimated from the NHANES ni data, the method for computing a
confidence interval needs to account for the complex survey design associated with NHANES ffl.
To do this, Software for Survey Data Analysis (SUDAAN) was used to compute standard errors
for NHANES IE distribution parameters. These standard errors were then used to compute
standard errors for the estimated exposure and risk endpoints. These methods are presented in
the following subsections, according to the type of baseline risk estimate.
1.0 GEOMETRIC MEAN BLOOD-LEAD CONCENTRATION
Data from Phase 2 of NHANES HI were used to construct estimates of geometric mean
blood-lead concentration for specified subgroups of the nation's children (e.g., 1-2 year old
children, 1-2 year old children living in pre-1946 housing). For some confidence level a (from 0
to 1), a (l-cc)*100% confidence interval for the geometric mean was calculated as
, o-w* g+w*) (1)
where GM is the estimated geometric mean blood-lead concentration of the subgroup of interest,
s is the standard error of the arithmetic mean of the log-transformed blood-lead concentrations in
this subgroup (computed using SUDAAN), n is the sample size for the subgroup, and t^.,>B) is the
(l-a)*100th percentile of the Student t-distribution with n-1 degrees of freedom. In the risk
analysis, a=0.05 (i.e., 95% confidence intervals were calculated). Note that this approach to
calculating a confidence interval assumes that blood-lead concentrations are lognormally
distributed. While the estimate of s accounted for the complex survey design, the degrees of
C2-2
-------
freedom for the t-statistic were not adjusted. However, not adjusting the degrees of freedom is
anticipated to have little effect because of the large sample size (987).
2.0 PERCENTAGE OF CHILDREN'S BLOOD-LEAD CONCENTRATIONS GREATER
THAN OR EQUAL TO A SPECIFIED THRESHOLD
Data from Phase 2 of NHANES HI were used to compute estimates of the percentage of
children's blood-lead concentrations greater than or equal to a specified threshold for specified
subgroups of the nation's children. In the risk analysis, two methods for characterizing the
distribution of blood-lead concentrations were used:
Method 1 : The distribution was characterized empirically from the observed NHANES HI data.
Under this method, which produced the estimates presented in Section 3.4.1 of
Chapter 3, the estimated percentage equaled the observed percentage of children in
the survey who were at or above the threshold, with each child weighted by his/her
assigned sampling weight.
Method 2: The percentages were computed using the geometric mean and geometric standard
deviation estimated in Method 1 assuming that the distribution of blood-lead
concentrations is lognormal. This method was used to compute the estimates
presented in Section 5.1.1 of Chapter 5.
Standard errors of the percentages estimated under Method 1 were calculated using
SUDAAN to account for the complex survey design in NHANES ffl. If px is the estimated
percentage of children with blood-lead concentration at or above X ng/dL (for some threshold X)
and SECpJ is the estimated standard error of this percentage, then (asymmetric) approximate (1-
oc)*100% confidence intervals associated with px were calculated as
(2)
where t^, a) is the (l-a)*100th percentile of the Student t-distribution with n degrees of freedom
(Kleinbaum etal., 1982).
Under Method 2, the value of px is estimated as
mn IAA *( \n(X)-LGM
px = 100 - 100* — v ' —
( JLGV
where LGM and LGV are the weighted arithmetic mean and variance, respectively, of the log-
transformed blood-lead concentrations. Assuming independence between LGM and LGV, and
using the first order Taylor series approximation of equation (3), an estimate of variability
associated with px is
C2-3
-------
]n(X)-LGMr /r^,. \n(X)-LGM /T~1Ki
v ' — [var(LGM)+\ — ^ - var(LGVj]
LGV
The variance of LGM, var(LGM), was estimated in SUDAAN to account for the complex survey
design employed in NHANES ffl. The variability associated with LGV, var(LGV) was estimated
based on the chi-squared distribution and the "design effect" for LGV (DE^y):
(5)
n-
where n is the sample size for the subgroup of interest. The design effect for a given statistic
quantifies the information lost due to the survey design employed and is calculated as the
variance of the statistic assuming the complex survey design was employed in data collection,
divided by the variance assuming simple random sampling was employed. Because a design
effect for LGV was not easily available, the design effect for LGM was used. Although not the
optimal solution, this was deemed more appropriate than not accounting for the complex survey
design at all.
Because many of the percentage estimates were small, asymmetric confidence intervals
were also calculated for model-based estimates using the logarithmic transformation, and the
t-distribution with n-1 degrees of freedom (see Equation 2).
3.0 PERCENTAGE OF CHILDREN WITH IQ DECREMENTS
GREATER THAN OR EQUAL TO 1, 2, OR 3
Data from Phase 2 of NHANES HI were combined with an estimate of the relationship
between blood-lead concentration and IQ decrements based on Schwartz, 1994 (Section 4.4 and
Appendix D2) to construct estimates of percentage of children with IQ decrements greater than
or equal to 1, 2, or 3 that results from lead exposure. Using notation from Section 2.0 above,
estimates of this population characteristic were constructed assuming that blood-lead
concentrations are lognoimally distributed and that the relationship between blood-lead
concentration and IQ score decrements is linear:
= Pxlm = 100 - 100** ^jff*0 («)
where X is the specified IQ decrement, m is the slope of the assumed linear relationship between
blood-lead concentration and IQ score decrements, GM is the geometric mean blood-lead
concentration for the subgroup, and GSD is the geometric standard deviation of blood-lead
concentrations.
C2-4
-------
The standard error of the percentage in equation (6), necessary for calculating a
confidence interval for this percentage, was calculated using a first order Taylor series
approximation, using estimates of the variability associated with the values of GM, GSD, and the
slope factor m. Thus, the confidence interval considers sampling variability from NHANES HI
data, as well as variability associated with the blood-lead concentration-IQ decrement
relationship.
The function for computing the percentage of children with IQ decrements greater than 1,
2, or 3 was expanded in an alternative parameterization to simplify the procedure:
Percent[IQ Decrements^X\=lOQ-lOO^
where LGM and LGV are the arithmetic mean and variance of the log-transformed blood-lead
concentrations. Assuming independence between LGM, LGV, and m and using the first order
Taylor series approximation to equation (7), the variability associated with estimated percentage
of children with IQ decrements greater than X is
var(Percent[IQ
\ ,. ,,,,,. ( ]n(X/m)-LGM\2 /r^r/vl
— var(m)+var(LGM)+\ ^ ' - var(LGV)]
\ 2LGV )
The variance of LGM was estimated in SUDAAN to account for the complex survey design
employed in NHANES ffl. The variability associated with LGV was estimated as described in
Section 2.0 of this appendix. The variability associated with m was assumed to be 0.041, based
on the meta-analysis described in Schwartz, 1994 (Appendix D2).
Because many of the percentage estimates were small, asymmetric confidence intervals
were calculated using the logarithmic transformation (Kleinbaum, et al., 1982) as described hi
Section 2.0.
4.0 AVERAGE IQ DECREMENT
Data from Phase 2 of NHANES m were combined with an estimate of the relationship
between blood-lead concentration and IQ decrements based on Schwartz, 1994 (Section 4.4 and
Appendix D2) to construct estimates of average IQ decrement. Estimates of this population
characteristic were constructed assuming that blood-lead concentrations are lognormally
distributed and that the relationship between blood-lead concentration and IQ score decrements is
linear:
Average IQ Decrement = m*e(MM+u;vn.) (9)
C2-5
-------
where m is the slope of the assumed linear relationship between blood-lead concentration and IQ
score decrements and LGM and LGV are the weighted arithmetic mean and variance of the log-
transformed blood-lead concentrations, respectively.
The standard error of average IQ decrement, necessary to calculate a confidence interval,
was calculated using a first order Taylor series approximation and estimates of the variability
associated with the values of GM, GSD, and the slope factor m. Thus, confidence intervals
presented include sampling variability from NHANES HI data, as well as variability associated
with the blood-lead concentration-IQ decrement relationship.
Assuming independence between LGM, LGV, and m and using the first order Taylor
series approximation to equation (9), the variability associated with estimated average IQ
decrement is
var(Average IQ Decrement) =e ^WM^v(yar(rn) +m 2 *var(LGM) +— *var(LGV)) (10)
4
The variance of LGM was estimated in SUDAAN to account for the complex survey design
employed in NHANES HI. The variability associated with LGV was estimated as described in
Section 2.0 of this appendix. The variability associated with m was assumed to be 0.041, based
on the meta-analysis described hi Schwartz 1994 (Appendix D2).
Confidence intervals were constructed using the t-distribution with degrees of freedom
approximated by one less than the sample size.
5.0 INDIVIDUAL RISKS
Upper confidence bounds on the dust-lead loading which, assuming fixed lead levels in
other media, controls the percentage of children with blood-lead concentrations greater than or
equal to 10 ng/dL due to exposure at these levels, were calculated and presented in Section 5.3
(Tables 5-6 and 5-7) of the risk analysis. The method used to calculate these upper confidence
bounds accounts for the variability associated with estimating the parameters of the Rochester
multimedia model, which was used to estimate the dust-lead loading.
The method is presented for the example of predicting the floor dust-lead loading which,
assuming fixed lead levels in soil and window sill dust, controls the percentage of children with
blood-lead concentrations greater than or equal to 10 (ig/dL to no higher than a%. This floor
dust-lead loading was estimated as
PbF=e
where $'' is the inverse normal transformation, PbF is the floor dust-lead loading, PbS is the
soil-lead concentration, PbWS is the window sill dust-lead loading and the P's are estimates of
C2-6
-------
the coefficients for the Rochester multimedia model (Section 4.2.3). The variance of PbF was
calculated using a first order Taylor Series approximation, considering the covariance between
the parameter estimates from the Rochester multimedia model:
var(PbF) =PbF2[—var(y) -2 *^- *cov(y,z)+^- *var(z)] (12)
f9 « ._ J —*\
where
y = Po + to(PbS)*Vsoil + \*(PbWS)*VwiMl (13)
z = Pfloor, PbS is the soil-lead concentration, and PbWS is the window sill dust-lead loading.
Approximate 95% upper confidence bounds for PbF were then computed as
PbF+l .65 *Jvar(PbF) (14)
In the same manner, this approach was used to calculate upper confidence bounds for the window
sill dust-lead loading which controls the percentage of children's blood-lead concentrations
greater than or equal to 10 ug/dL, assuming fixed soil-lead concentrations and floor dust-lead
loadings.
C2-7
-------
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-------
APPENDIX D1
Assumptions and Scientific Evidence to Account
for the Effect of Pica for Paint
D1-1
-------
APPENDIX D1
ASSUMPTIONS AND SCIENTIFIC EVIDENCE TO ACCOUNT
FOR THE EFFECT OF PICA FOR PAINT
The scientific evidence on paint chip ingestion is scant and can be contradictory. It is
well known that pica for paint and plaster is associated with lead poisoning. However, survey
data and blood-lead concentrations collected in the Rochester Lead-in-Dust Study (USHUD,
199Sa) indicated that children whose parents responded that they have a tendency to eat paint
chips had blood-lead levels only slightly more elevated, on average, than those who do not
exhibit pica. The scientific evidence and assumptions required to estimate the percentage of
children who exhibit pica for paint and their blood-lead levels are summarized in this section.
PERCENTAGE OF CHILDREN WHO INGEST PAINT CHIPS
In a study involving 2,402 children attending the Child Development Center of the
University of Virginia, de la Burde and Reames (1973) reported that 9% of mothers of children
between eight months and seven years of age responded that their child exhibited pica for paint
or plaster. A similar estimate (10%) was reported for 205 children ages 1 to 2 years in the
Rochester study (USHUD, 1995a). For this risk analysis, the incidence of paint pica is assumed
to be 9% of children living in homes with damaged lead-based paint (defined as greater than 0 ft2
of interior or exterior deteriorated lead-based paint). Both children with recent paint chip
ingestion and those who ingested paint chips at some time are included in the 9%.
Although detailed information on the condition of homes was not available, children in
the University of Virginia study were generally from low income families and lived in
substandard housing, where flaking paint or falling plaster were likely to be accessible.
However, it is not clear whether the homes of all children with pica contained paint chips. Of the
children reported to have a history of pica for paint or plaster, 83% lived hi urban neighborhoods
with old and dilapidated housing and 9% lived in newer urban or suburban homes. The
remaining children lived in rural areas, or the type of housing was unknown. It was reported that
some children with a history of pica were known to have eaten paint chips or plaster in the home
of a relative or babysitter, where they spent a large part of the day. Thus it is possible that
children living in homes without damaged lead-based paint may ingest paint chips. It is also
possible that children may not be observed eating paint chips, or may ingest paint chips by
chewing on intact paint. Because blood-lead concentrations are adjusted only for the incidence
of observed pica, only in homes with damaged lead-based paint, the effect of pica on childhood
blood-lead levels may be underestimated in the risk analysis. However, it is assumed that the
impact is minimal, because estimated blood-lead concentrations are adjusted for pica even in
homes with small amounts of damaged lead-based paint.
For HUD National Survey homes where no damaged lead-based paint is present, the
EEUBK model and the empirical model (with paint/pica = 0) predicted values are used to
D1-2
-------
estimate blood-lead concentrations for all children represented by the home. When damaged
lead-based paint is present, the same predicted values are used to estimate blood-lead
concentrations under each model for 91% of the children, who are assumed not to ingest paint
chips. The modeling approaches differ for the remaining 9% of children, who are assumed to
ingest paint chips. Because the empirical model incorporates the effect of pica for paint, the
model predicted values are used to estimate blood-lead concentrations for children who ingest
paint chips. The IEUBK model does not include a direct mechanism for estimating the effect of
pica for paint. Thus, adjustments are made to the BEUBK model estimates after the model is
applied. The assumptions utilized hi this risk analysis, to account for the effect of paint pica
under the IEUBK model, are described in the sections that follow.
BLOOD-LEAD CONCENTRATION FOR CHILDREN WITH RECENT PAINT CHIP INGESTION
(IEUBK MODEL)
When the IEUBK model is used, the blood-lead concentration is set equal to 63 |4.g/dL for
children who have recently ingested paint chips. The basis underlying this blood-lead
concentration and the percentage of children assumed to have recently ingested paint chips are
discussed hi this section.
The effect of pica for paint will be applied only for HUD National Survey homes where
damaged lead-based paint is present. Fifty-five of the 284 homes in the HUD National Survey
have damaged lead-based paint. These homes represent 15.2% of U.S. housing, based on 1997-
projected weights used hi the risk analysis.
Of the 924 children ages 1-2 years in the NHANES m Survey (Brody, et al., 1994), just
one child had a blood-lead level greater than 40 u£/dL. The percentage of children ages 1-2 with
blood lead greater than 40 ng/dL, adjusted for sampling weights, is 0.03%.
Information on condition of housing was not available for NHANES ffl participants. It is
assumed that blood-lead levels greater than 40 ug/dL are extremely rare in homes with no
damaged lead-based paint. Thus the entire 0.03% of children nationwide with blood lead greater
than 40 ug/dL are assumed to reside in the 15.2% of homes with damaged lead-based paint.
Combining these figures, we estimate that 0.20% of children hi homes with damaged lead-based
paint have blood-lead levels greater than 40 ng/dL.
A St. Louis study (McElvaine, et al., 1992) found that 13 of 90 (14.4%) children less than
age 3 years with blood-lead levels greater than 40 ng/dL, or less than age 7 years with blood lead
levels greater than 50 ng/dL, had radiographic evidence of recent paint chip ingestion. This
information, combined with the preceding estimate, leads us to conclude that 0.03% of children
in homes with damaged lead-based paint have blood lead greater than 40 |ig/dL due to recent
paint chip ingestion. Table Dl-1 shows step by step the methodology for computing the
percentage of children living in homes with damaged lead-based paint who have blood-lead
levels greater than 40 (ig/dL and have recently ingested paint chips. The underlying assumptions
of this approach are that 1) blood-lead concentrations are greater than equal to 40 for children
who have recently ingested paint chips containing lead and 2) only children who reside hi homes
D1-3
-------
with damaged lead based paint ingest paint chips containing lead. The 1 3 children in the
St. Louis study, who were confirmed to have ingested paint chips, had a mean blood-lead level of
63 ug/dL. The blood lead levels of children with recent pica (0.03% of children in homes with
damaged lead-based paint) will be mapped to 63 ug/dL.
Table D1-1.
Calculation of Percentage of Children Who Have Recently Ingested Paint
Chips.
VaritbtoNam*
PC_EAT
(PbBi40|/a/dL|
Damaged LBP)
Damaged LBP
PbBi40//g/dL
(PC EAT | PbB 2
40j/g/dL)
. . .,, VaHabte DrtnitkMt . .;.,. .
Percentage of children with blood lead
concentration 2 40 i/g/dL, living in homes
with damaged lead-based paint, who have
recently ingested paint chips containing lead.
Percentage of children with blood-lead
concentration 2 40 A/g/dL, living in homes
with damaged lead based paint.
Percent of US housing units with damaged
lead based paint.
Percentage of children aged 1 -2 with blood-
lead concentration 2 40 //g/dL.
Percentage of children with blood-lead
concentration 2 40 pg/dL who have recently
ingested paint chips.
Mrtho4ofC«k«riatioo
(PbB 2 40|/g/dL| Damaged LBP)
• (PC_EAT | PbB * 40 //g/dL)
(PbB * 40 i/a/dL)
(Damaged LBP)
Percentage of housing units with
damaged lead-based paint,
estimated in the HUD National
Survey.
Taken from NHANES III for
children 1-2 years of age.
Taken from McElvaine's St.
Louis study.
_ Vatu»
. 197% x. 144 -
.03%
0.03%
0.152 - 0.197%
15.2%
0.03%
13/90 = 14.4%
BLOOD-LEAD CONCENTRATION FOR CHILDREN WHO INGESTED PAINT CHIPS AT SOME
TIME (IEUBK)
For HUD National Survey homes with damaged lead-based paint, 9% of the children
represented by those homes are assumed to ingest paint chips, with 0.03% of children assumed to
have recent paint chip ingestion, as described above. The remaining 8.97% of children are
assumed to have ingested paint chips at some time, but not recently. The geometric mean blood-
lead concentration for the 8.97% of children in homes with damaged lead-based paint, who have
ingested paint chips at some time, is estimated to be 3 ug/dL greater than the IEUBK predicted
value for children who do not eat paint chips. The basis for this adjustment is presented in this
section.
Although the University of Virginia study was used to estimate the percentage of children
who ingest paint chips, children in this study would have been exposed to lead from sources,
such as automobile exhaust, no longer present in the environment. Thus their blood-lead levels;
if available, would not be comparable to those of present-day children. A current estimate of the
effect of pica for paint may be derived from Rochester Lead-in-Dust study (USHUD, 1995a). In
that study, 20 of 205 children (10%) were reported to exhibit pica for paint. The geometric mean
D1-4
-------
blood lead for children who were reported to have ingested paint chips was 9.1 fig/dL, while the
geometric mean blood lead for children who were reported to have never ingested paint chips
was 6.1 |ig/dL. Thus, the geometric mean blood-lead concentration for children who ingested
paint chips at some time is assumed to be 3.0 ng/dL greater than the EEUBK model predicted
geometric mean for children who do not ingest paint chips.
D1-5
-------
This page intentionally blank.
-------
APPENDIX D2
Results of Three Published Meta-Analyses on the Relationship
Between IQ Point Loss and Childhood Blood-Lead Levels
D2-1
-------
APPENDIX D2
RESULTS OF THREE PUBLISHED META-ANALYSES ON THE RELATIONSHIP
BETWEEN IQ POINT LOSS AND CHILDHOOD BLOOD-LEAD LEVELS
INTRODUCTION
The association between blood-lead levels and low IQ scores has been consistently
reported in the scientific literature. The estimates of the dose-response relationship published in
the literature have been combined via meta-analysis and reported in the three articles listed
below. This appendix provides a summary of each article and a discussion of the key results,
relative to this risk analysis. The studies cited in these articles are summarized in Tables D2-1
and D2-2 at the end of this appendix.
PRIMARY REFERENCES
Schwartz, J., 1993, Beyond LOEL's, p Values, and Vote Counting: Methods for Looking
at the Shapes and Strengths of Associations, Neuro Toxicology 14(2-3):237-246.
Schwartz, J., 1994, Low-Level Lead Exposure and Children's IQ: A Meta-analysis and
Search for a Threshold, Environmental Research 65:42-55.
Pocock, S. J., Smith, M., and Baghurst, P., 1994, Environmental Lead and Children's
Intelligence: A Systematic Review of the Epidemiological Evidence, BMJ 309:1189-
1197.
SUMMARY OF SCHWARTZ. J.. 1993
This paper uses examples from the lead literature to illustrate statistical methods for
determining the shape of dose-response relationships, including the possible existence of
thresholds, and for assessing the strengths of associations within a study and for the literature as a
whole. Of interest to this risk analysis is a meta-analysis of the results from 7 studies that
estimated a slope for the relationship between children's blood-lead levels and IQ scores. These
studies used linear, or log-linear, regression models to fit the relationship between IQ scores and
PbB in children. Up to 17 additional covariates were included in the models. The weighted
mean regression slope over the 7 studies, weighted by the inverse of the estimated variance, was -
0.245 (±0.039). That is, a 1 ug/dL increase in PbB was associated with a 0.245 decrease in IQ
score.
SUMMARY OF SCHWARTZ. J.. 1994
This article focuses on the relationship between blood lead and IQ scores, while the
earlier paper by Schwartz used this relationship to illustrate a statistical method. The 1994 paper
D2-2
-------
presents a meta-analysis of 7 studies, some of which had been cited in the earlier paper, that
estimated a slope for the relationship between children's blood-lead levels and IQ scores. Three
longitudinal and four cross-sectional studies were included in the analysis. The studies used
linear, or log-linear, regression models to fit the relationship between IQ scores and PbB in
children. Additional covariates were included in the models. A random effects model was
employed in the meta-analysis, using the method of Dersimonian and Laird (1986). The
weighted mean regression slope over the 7 studies, weighted by the inverse of the estimated
variance, was -0.257 (±0.041). That is, a 1 |ig/dL increase in PbB was associated with a 0.257
decrease hi IQ score.
0>
a
£
en
o
1.5
1.2
0.9
0.6
0.3
fl ft-
0.3-
Cross-Sectional Studies
Longitudinal Studies
Hawk
Hatzakls
Fulton
Yule
Bellinger Dietrich Baghurst
Study
Figure D2-1. Estimated Slopes from the Seven Studies Used in the
Schwartz (1994) Meta-analysis, with 95% Confidence
Intervals.
SENSITIVITY ANALYSIS
Schwartz conducted a sensitivity analysis to measure the robustness of the meta-analysis
and to determine the influence of differences in study design and study populations. The results
of the sensitivity analysis are summarized in the following table.
D2-3
-------
Revised Analysis
Study with Largest Effect Size Removed:
Study with Most Significant Effect Removed:
Add 8 Studies with No Effect (each with
average weight of the 7 studies):
Longitudinal vs. Cross-sectional:
Disadvantaged vs. Nondisadvantaged Lifestyle:
Add 2 Studies that Included Younger Children:
ResuJtfog Slope
( ± 1 standard error of the mean}
-0.243 (±0.034)
-0.252 (±0.058)
Association still significant, but slope reduced
to about half of original estimate
-0.296 (±0.1 25) vs. -0.269 (±0.051)
-0.1 85 (±0.092) vs. -0.289 (±0.050)
-0.239 (±0.031)
Three analyses were used to examine the robustness of the meta-analysis. First, the study
with the largest effect size (Bellinger et al., 1992) was removed. Next, the study with the most
significant effect (Hatzakis et al., 1987) was removed. Based on these results, Schwartz
concluded that the meta-analysis was not dominated by any individual study. The third analysis
added eight hypothetical studies that reported no association between blood-lead levels and IQ
scores. Each study was assigned the average weight of the seven original studies. In this
analysis, the association between blood-lead levels and IQ scores was still highly significant
(p<0.01), but the estimated slope was reduced.
Additional analyses were conducted to determine the effect of differences in study design
(longitudinal vs. cross-sectional) and study populations (advantaged vs. disadvantaged, age of
child). Schwartz concluded that there was little evidence of a difference in effect size between
longitudinal and cross-sectional studies. It did appear that estimates of IQ loss were lower in
studies of disadvantaged children. Schwartz suggested that this result may be due to the greater
influence of confounding variables in a disadvantaged population. Finally, the addition of two
studies that examine younger children did not have a great impact on the estimated slope.
THRESHOLD ANALYSIS
The question of whether a threshold exists in the relationship between IQ scores and
PbBs was examined through a meta-analysis that compared studies with different mean blood
lead levels. In studies with mean blood lead levels of 15 ug/dL or lower, the estimated slope was
-0.323 (±0.126) compared to -0.232 (±0.040) for studies with means above 15 ug/dL. Thus, if
anything, a trend toward a higher slope at lower concentrations was observed. This result
suggests that the log-linear model may be more appropriate than the linear model, for this
relationship.
An alternative approach to the threshold issue examined the data from the Boston study
(Bellinger, 1992) more thoroughly. The Boston study was chosen because it had the lowest mean
PbB. For this analysis, separate regression models for IQ score and PbB were fit using the same
D2-4
-------
set of covariates. A nonparametric smoothed curve (LOESS) was fit to the relationship between
the two sets of residuals. Based on this analysis, Schwartz concluded that the relationship
between blood lead and IQ continues at PbB below 5 ug/dL in this study, i.e., no threshold was
evident.
SUMMARY OF POCOCK. S. J.. SMITH. M.. AND BAGHURST. P.. 1994
This paper presents a meta-analysis of 26 epidemiological studies: 5 prospective studies,
14 cross-sectional studies of blood-lead, and 7 cross-sectional studies of tooth-lead. The three
types of studies are considered in separate meta-analyses. The results are summarized as follows:
-,, 'V '"
•• Ana!y«i8
Prospective Studies, PbB at Birth:
Prospective Studies, PbB around 2 Years:
Prospective Studies, Postnatal Mean PbB:
Cross-Sectional Blood-Lead Studies:
Cross-Sectional Blood-Lead Studies, Excluding Shanghai:
Cross-Sectional Tooth-Lead Studies:
Resulting Slope
f ± 1 standard error of the
mean)
0.018 (±0.062)
-0.185 (±0.051)
-0.088 (±0.058)
-0.253 (±0.041)
-0.1 74 (±0.043)
-0.095 (±0.025)
Only the analysis of cross-sectional blood-lead studies had a statistically significant slope.
DISCUSSION
There was considerable overlap hi the studies cited by the three meta-analysis papers.
Two studies, Fulton et al. (1987) and Yule et al. (1981), were cited in all three papers, while
several others were cited in two of the three papers. In addition, some studies cited by Schwartz
(1993) or Pocock were used by Schwartz (1994) in the sensitivity analysis.
The three papers are directly comparable hi that a common endpoint was used for all
meta-analyses. For the meta-analysis endpoint, the regression coefficients and standard errors
calculated by the original authors were used to estimate the change in IQ for an increase hi
blood-lead from 10 to 20 u,g/dL. This was necessary, because some of the original authors
worked with log-transformed data, while others did not transform the data. In most cases, the
regression coefficients were adjusted for other covariates included in the model. The other
covariates varied from study to study. For this risk analysis, we have converted the estimated
change hi IQ back to a slope for untransformed blood-lead concentrations.
The Schwartz (1993) paper focuses on introducing the statistical methods to a non-
technical audience. The Schwartz (1994) and Pocock papers focus on the relationship between
D2-5
-------
IQ and blood-lead levels. The Schwartz (1994) paper includes a sensitivity analysis and search
for threshold in the relationship. These topics are not covered in the Schwartz (1993) and
Pocock papers. However, in the meta-analysis of prospective studies, the Pocock paper does
include separate analyses for blood-lead measures at three ages. Also, one of the studies
(Schroeder, 1985) used in the Schwartz (1993) paper included approximately 50 children under
30 months of age. This study and another (Emhart, 1989) with younger children were included
in the sensitivity analysis in Schwartz (1994).
The Pocock paper analyzes longitudinal and cross-sectional studies separately, while the
Schwartz papers include both types of studies in the same meta-analysis. The Schwartz (1994)
paper considers the study designs separately in the sensitivity analysis. It is important to point
out that the measures of blood-lead concentration are different between longitudinal and cross-
sectional studies. Cross-sectional studies generally have a single blood lead measurement, taken
when the IQ test is administered to school age children. Longitudinal studies generally have
several blood-lead measurements available, which may be taken years prior to the IQ testing. In
some longitudinal studies (Dietrich et al, 1993; Baghurst et al, 1992), the lifetime average blood-
lead concentration is related to IQ. In others (Bellinger et al, 1992; Emhart et al, 1989), blood-
lead concentration at a specified age is related to IQ. The interpretation of the modeled
relationships should take into account the differing blood-lead measurements employed. While
each author attempts to take this into account, by modeling longitudinal and cross-sectional
studies separately, neither distinguishes between the differing measures of blood-lead
concentration in longitudinal studies.
In the analysis of prospective studies, Pocock includes an analysis of how PbB at
approximately age 2 affects IQ measured at school age. The slope for this analysis (-0.185) is
less than the values (approximately -0.25) from Schwartz (1993 and 1994) and the Pocock cross-
sectional studies analysis.
Both Schwartz (1994) and Pocock included "full scale IQ score" in school-age children as
a selection criteria for studies used in the meta-analysis. Most of the studies cited used the
Wechsler Intelligence Scale for Children - Revised (WISC-R) test. The 1993 Schwartz paper
includes one study, Schroeder (1985), that uses the Bayley Scales of Infant Development (BSID),
for children less than 30 months of age. The BSID score is not directly comparable with the IQ
scores, as this test measures developmental endpoints as well as cognitive ability.
D2-6
-------
Table D2-1. Design Information for Studies that Investigate the Relationship Between Child's IQ and Blood-Lead Level.
' (MMMNMNM
! th»t
-------
Table D2-1.
Design Information for Studies that Investigate the Relationship Between Child's IQ and Blood-Lead
Level. (Continued)
Wrowy
IftlWWNWSW^
TtttkCMtttiw
Sfcdv
Schwartz (1993)
Schwartz (1994)
Pocock
Schwartz (1993)
Pocock
Pocock
Schwartz(1994)
Pocock
Pocock
Pocock
Pocock
Schwartz (1993)
Schwartz (1994)
Pocock
'SOW
Yule et al.
(1981)
Lansdown et al.
(1986)
Winneke et al
(1990)
Silva(1988)
Harvey et al
(1988)
Wang et al
(1989)
Winneke et al
(1985a)
Fulton et al.
(1987)
Type Of Study
Pilot Study
Replication of
Yule Study
Multi-Center,
Cross - Sectional
Study
Cross - Sectional
Cross - Sectional
Cross - Sectional
Cross - Sectional
Cross - Sectional
f
t-J.
... > Y*ar(tt) of
Study
Summer 1980
(PbB taken 9-
1 2 months
earlier)
1972-1973
Late 1979-
early1981
1983-1985
taatkrti of study
Paiti$ipiints
Outer London,
England
Within 1 km of a
factory in London,
England
Bucharest
Budapest
Moden
Sofia
Dusseldorf
Ousseldorf
Dunedin, New
Zealand
Birmingham,
England
Shanghai, China
Nordenham,
Germany
Edinburgh, Scotland
*g»
-------
Table D2-2. Summary of Results from Studies that Investigate the Relationship Between Child's IQ and Blood-Lead Level.
J2HLM
IwfflHMIftMR
ThatCit. ti*
Study i
Schwartz
(1993)
Schwartz
(1994)
Pocock
Schwartz
(1993)
Schwartz
(1994)
Pocock
Schwartz
(1994)
Pocock
Pocock
Pocock
A
.%
Study
Hatzakis
etal.
(1987)
Hatzakis
etal.
(1989)
Bellinger
etal.
(1991)
Bellinger
etal
(1992)
Baghurst
et al
(1992)
Ernhart et
al (1989)
Cooney et
al(1991)
PbSo? Study
P*rtfrbt**rf*m fittt/HI Y
fi^B^ff
7.4-
63.9
7.4-
63.9
0.0-
23.3
Sort*****
tJttrtlftfew
AM = 23.7
STD = 9.2
10%ile = 13.9
50%ile = 21 .5
90%ile = 36.0
AM = 23.7
STD =9.2
AM = 6.4
STD = 4.1
19% were
>10//g/dL
4% were
> 1 5//g/dL
AM = 6.5
STD = 4.9
AM = 20
AM = 16.7
STD = 6.45
AM = 14.2
tQofSHi
Ebdp4bit
t«W
WISC-R
GCI
WISC-R
WISC-R
WPPSI
WISC-R
Range/Summary
StnKftfe*
AM = 87.7
STD =14.8
80-150
AM = 115.5
STD = 14.5
71-147
AM=119.1
STD = 14.8
AM = 104.7
AM = 87. 5
STD = 16.6
Maa&tm
l*~»»
-0.270 change in IQ
per unit increase in
PbB
(-0.403, -0.137)
-2.7 change in IQ
for increase from
10-20 //g/dL in PbB
-2.28 change in IQ
per unit increase in
Log(PbB)
(-6.0, 1 .4)
-0.250 change in IQ
per unit increase in
PbB from 5- 15
//g/dL PbB
-5.8 change in IQ
for increase from
10 to 20 //g/dL in
PbB
-3.3 change in IQ
for an increase from
10-20 //g/dL in PbB
-1.1 change in IQ
for an increase from
1 0-20 //g/dL in PbB
0.39 change in IQ
for an increase from
10-20 //g/dL in PbB
P-V(*»
<0.001
<0.001
0.23
0.007
0.04
<0.01
CoyartatM
1 7 potential
confounders or IQ
correlates'41
(called the
"optimal" model)
Up to 24,
including mother's
IQ
1 3 covariates'51
HOME mother's
IQ,
8 other
covariates181
HOME, mother's
IQ, 1 1 others m
HOME , mothers
IQ, and 1 1
others11"
HOME ,mothers
IQ, and 4
others l121
Blood-Uttd LftVttte™
' . ¥
Qth^r (nfaffitiitiQR
Dose-response investigation
showed no PbB effect on IQ
when PbB < 25 //g/dL.
Dose-reponse curve showed
evidence of a threshold at the
level of about 25 //g/dL PbB
Regression diagnostics were
used to check the robustness ol
estimates. These results reflect
only PbB data at age 57
months.
Slightly elevated blood lead
levels around the age of 24
months are associated with
intellectual and academic
performance deficits at age 10
years.
Found low-level exposure to
lead during early childhood is
inversely associated with
neuropsychological
development through first
seven years of life.
o
N>
-------
Table D2-2. Summary of Results from Studies that Investigate the Relationship Between Child's IQ and Blood-Lead
Level. (Continued)
Primary
TbatCto tfw
Study
Schwartz
(1993)
Schwartz
(1993)
Schwartz
(1994)
Schwartz
(1994)
Pocock
Schwartz
(1993)
Schwartz
(1994)
Pocock
Schwartz
(1993)
Pocock
- -
%Mv
O 1* 1Qra/dL
4.8% were
>20//fl/dL
AM = 12.75
STD = 3.07
77% were
>10//g/dL
1 .5% were
>20(igldL
IQofSt«
Endpolnt
^-Typ*
BSID
«30
mo.)
SBIS
(230
mo.)
SBIS
WISC-R
WISC-R
WISC-R
WISC-R
ltotg«/$MrfMnary
^...^..-^M-. .
SnMMHMM-
45-140
59-118
AM = 86.9
STD = 11.3
AM = 98.21
STD = 13.44
AM = 105.24
STD = 14.20
Measure pf AsKXtla^oO Between IQ and Wood-Lead Levels01
•MWUM9W
-0.199 change in IQ
per unit increase in
PbB
-0.255 change in IQ
per unit increase in
PbB
(-0.554, 0.043)
1 .3 esimated loss in
IQ for an increase
from 10 to 20
//g/dL in PbB
-8.08 change in IQ
per unit increase in
Log(PbB) (4.63)
-0.560 change in IQ
per unit increase in
PbB from 10-20
//g/dL
2.15 change in IQ
per unit increase in
Log(PbB)
0.1 49 change in IQ
per unit increase in
PbB from 10-20
A/g/dL
P-Vafcw
<0.01
<0.05
<0.10
0.084
0.63
CoVWifctM
7 covariates161 plus
interaction with
PbB. Quadratic
and cubic
components of
PbB also
considered.
Gender, HOME
score, maternal IQ
HOME score.
maternal IQ, birth
weight, birth
length, child sex,
cigarette
consumption
during pregnancy
Age, social class
Age, social class
0«h«r Information
Unforced stepwise regression.
SES was only other significant
covariate.
Postnatal PbB concentrations
were inversely associated with
Full Scale IQ.
Social class was considered a
crude measure.
N = 86 for regression analysis.
Social class was also a
significant factor.
o
to
-------
Table D2-2. Summary of Results from Studies that Investigate the Relationship Between Child's IQ and Blood-Lead
Level. (Continued)
TbatCto th*
Study
Pocock
Schwartz
(1994) Pocock
Pocock
Study
Winneke
etal
(1990)
Bucharest
Winneke
etal
(1990)
Budapest
Winneke
etal
(1990)
Moden
Winneke
etal
(1990)
Sofia
Winneke
etal
(1990)
Dusseldorf
Winneke
etal
(1990)
Dusseldorf
Silva
(1988)
Harvey et
al (1988)
PbB of Study
PW"
ft««*
4-50
0.2-
1.4
mol/L
JVPUP"1 VwrvM
Summary
JtlaiUittet
GM = 18.9
STD=1.3
GM = 18.2
STD = 1.7
GM = 11.0
STD = 1.3
GM = 18.2
STD = 1.6
GM = 8.3
STD = 1.4
AM = 7.4
STD = 1.3
AM = 11.1
STD =4.91
AM = 12.3
STD -0.2
KltrfStu
Type
WISC-
Short
Form
WISC-
Short
Form
WISC-
Short
Form
WISC-
Short
Form
WISC-
Short
Form
WISC-
Short
Form
WISC-R
WPPSI
Statistic.
AM = 116
AM = 108.9
STD = 15.12
AM = 105.9
STD=10.6
Measure of ****)*** B*tW*n Ifc »d BfaKKtUfttf. i«y*fi^.J
M^o
Loss of 1.51 inlQ
for an increase in
PbB of 10-20/i8/dL
p-v«hw
<0.1
<0. 1
<0. 1
<0,
<0,
<0,
ClOVMFHitM
Gender, age,
social class,
mother's
education
Gender, age,
social class
Gender, age,
social class,
mother's
education
Gender, age,
social class,
mother's
education
Gender, age,
social class,
mother's
education
Gender, age,
social class,
mother's
education
None
None
OtH^,™^
No significant relationship was
found between overall IQ and
PbB
o
K>
-------
Table D2-2. Summary of Results from Studies that Investigate the Relationship Between Child's IQ and Blood-Lead
Level. (Continued)
¥famt "1
isssrsL^
Study \
Pocock
Pocock
Schwartz
(1993)
Schwartz
( 1 994)
Pocock
«, ^
*%5
iudt\
Wanget
aid 989)
Winneke
et al
(1985a)
Fulton et
al. (1987)
PbB of Study
' PWWVW* WtfvU
fel»9»
4.5-
52.8
1/g/dL
4.4-
23.8
pg/dL
3.3-
34
AM = 21.1
STD= 10.11
AM =8.2
STD = 1.4
GM = 11.5
1 .2% were
>25M/dL
; ^A>«»
(Q-Hf #wq||!^01|MV||$
Eminnlnf
**f Wf)|WfM»
wise
WISC-R
BASC
AM = 89
AM = 120.2
STD=10.3
AM = 112
STD = 13.4
•
MaaitJJtt
-------
Notes for Table D2-2:
i11 "Range" indicates the observed range of PbB levels among the study participants. Among the summary statistics, AM
= arithmetic mean; GM = geometric mean; STD = standard deviation; x%ile = x percentile of observed distribution.
121 "Type" indicates the type of IQ endpoint measured in the study. WISC-R = Wechsler Intelligence Scale for Children -
Revised (full-scale IQ measurement); GCI = McCarthy Scales of Children's Abilities: General Cognitive Index; BSID =
Bayley Scales of Infant Development; SBIS = Stanford-Binet Intelligence Scale; BASC = British Ability Scales:
Combined Score. Among the summary statistics, AM = arithmetic mean; STD = standard deviation.
131 Results are the outcome of a regression analysis to predict IQ endpoint based on PbB level and other covariates.
"Measure" is the estimated slope parameter indicating the change in IQ measurement associated with a unit change in
the (possibly transformed) PbB level. If the PbB level is transformed, the change in IQ measurement over a given range
of the untransformed PbB level is also given. When available, a 95% confidence interval associated with the slope
estimate is given, or a standard error associated with the estimate. "P-value" is for the test that the slope parameter is
equal to zero versus an alternative that it is not zero. "Adjusted covariates" indicates the number of covariates included
in the regression model; these covariates are named if the number is small. "Other information" indicates specifics
associated with the regression fit (e.g., method used, whether a log-transformation was taken on the PbB level prior to
analysis, information on the covariates).
141 Covariates include parental IQ, birth order, family size, father's age, parental education, alcoholic mother, age,
bilingualism, birth weight, length of child's hospital stay after birth, walking age, history of CNS disease, history of head
trauma, illness affecting sensory function, parent's divorce.
'» Covariates include family social class, material IQ, preschool attendance, HOME total score, # hours per week of "out-
of-home" care, # changes in family residence since birth, medication use in preceding month, # adults in household,
gender, race, birth weight, material marital status, birth order.
181 HOME score, maternal IQ, child's age, child's sex, SES of parents, type of IQ test, presence of father in home, number
of siblings.
171 Parent's vocabulary and matrices tests, child's interest score, age, father's qualifications, length of gestation, parental
involvement with school score, class year, ft days absent from school, sex, standardized height, car/telephone
ownership, employment status of father.
181 Child stress, maternal age, race, SES, sex, birth order, martial status, number of residence changes prior to age 57
months
191 Sex, parents' level of education, maternal age at delivery, parents' smoking status, socio-economic status, quality of
the home environment, birth weight, birth order, feeding method (breast feeding, bottle, or both), duration of breast -
feeding, and whether the child's natural parents were living together
1101 Age, sex, father's education, father's occupation, father's daily smoking quantity
1111 Sex, race, birth weight, birth order, gestational age at birth, parental education, maternal variables like PPVT-R, API,
MAST SCORE, AA/day in pregnancy, cigarettes per day, and use of marijuana and other drugs in pregnancy, medical
problems and psychosocial problems.
"" Gestational age, education of the mother, education and occupational status of the father.
D2-13
-------
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-------
APPENDIX E2
Generating Distribution of Blood-Lead Concentrations
Based on Model-Predicted Geometric Mean and Geometric
Standard Deviation
E2-1
-------
APPENDIX E2
GENERATING DISTRIBUTION OF BLOOD-LEAD CONCENTRATIONS
BASED ON MODEL-PREDICTED GEOMETRIC MEAN AND GEOMETRIC
STANDARD DEVIATION
This section discusses how the geometric mean blood-lead concentrations predicted by
either model at each housing condition were combined to characterize the national distribution of
children's blood-lead concentrations for children aged 1-2. This approach was used for
characterizing both pre- and post-intervention distributions predicted with the models.
Historical data suggest that blood-lead concentrations usually follow a lognormal
distribution. A lognormal distribution can be characterized using two parameters, the geometric
mean which is a measure of the "center" of the distribution, and the geometric standard deviation
(GSD) which is a measure of the spread of the distribution. The empirical and IEUBK models
both predict a geometric mean blood-lead concentration for a population of children exposed to
specific levels of environmental lead. However, a population of children exposed to the same
levels of environmental lead would not all have the same blood-lead concentration represented
by the predicted geometric mean. Their blood-lead concentrations will vary about the predicted
geometric mean because of the many other factors that contribute to children's blood-lead
concentrations. These factors include differences in children's activity patterns, tendency to
ingest dust or soil, parental supervision, dietary lead, other lead exposures, and amount of lead
absorbed due to various biological factors.
Extant data from various studies indicate that the inherent variability in blood-lead
concentration among children exposed to similar environmental-lead levels corresponds to a
GSD of 1.6, the default GSD recommended in the IEUBK guidance manual (USEPA, 1994a).
Under the assumption that blood-lead concentrations have a lognormal distribution with a
geometric mean, GM, and GSD of 1.6, the logarithms of the blood-lead concentrations have a
normal distribution with mean \i = ln(GM) and standard deviation s = ln(1.6)=0.47.
The predicted national distribution of children's blood-lead concentrations was also
assumed to follow a lognormal distribution. The predicted geometric mean of the national
distribution of children's blood-lead concentrations is calculated by taking a weighted geometric
mean of the empirical or IEUBK model-predicted blood-lead concentrations associated with each
home in the HUD National Survey, using the HUD National Survey weights adjusted for 1997
population totals.
The predicted national GSD is calculated by taking the square root of the sum of the
predicted between-house variability and the assumed within-house variability. Between-house
variability represents the variability among the predicted blood-lead concentrations for homes in
the HUD National Survey and is computed as the weighted geometric variance of the model
predicted blood-lead concentrations for each home hi the HUD National Survey, using the
E2-2
-------
adjusted weights for 1997. Within-house variability, variability in blood-lead concentrations of
children exposed to the same levels of environmental lead, is calculated as the weighted mean of
the log variances assigned to each HUD National Survey home. This variability is assumed to be
characterized by a GSD of 1.6 (log variance = In (1.6)2) for all HUD National Survey homes.
There is one exception where the child is assumed to have a blood-lead level of 63 ug/dL in
.«rt*«s>Vi />aca tVio /~JGT~l ic dCCiimoH tn Vto 1
which case the GSD is assumed to be 1.
The methodology for characterizing the national blood-lead distribution is slightly
different for the EEUBK and empirical models because of the different ways the two models
incorporate paint pica. For the empirical model, the national distribution of blood-lead
concentrations is characterized as follows. For each house hi the HUD National Survey, let Nf
be the number of children aged 1-2 years associated with the housing unit, GMlj denote the
model-predicted geometric mean blood-lead concentration for children without pica tendencies,
and GM2j denote the model-predicted geometric mean blood-lead concentration for children
with pica tendencies. Recall that GM2( is calculated only for units containing deteriorated or
damaged lead-based paint.
The distribution of children's blood-lead concentrations hi homes with no deteriorated
lead-based paint was assumed to have a lognormal distribution with geometric mean GM1{ and a
GSD of 1 .6. Children hi housing units with damaged or deteriorated lead-based paint in either
the interior or exterior, were partitioned into two groups:
Group #1: Assumed to contain 91% of the children, representing children who show
no tendency toward paint pica. The blood-lead concentration distribution
of this group is assumed to be lognormal with geometric mean GM1; and
a GSD of 1.6.
Group #2: Assumed to contain 9% of the children representing children who have
exhibited some tendency towards paint pica. The distribution of blood-lead
concentrations for this group is assumed to be lognormal with geometric
meanGMlj and a GSD of 1.6.
Let N be the sum of Nj across all homes represented hi the HUD National survey (i.e., the
total number of children aged 1-2 years in the 1997 housing stock). Furthermore, let A denote all
housing units in the section containing no deteriorated lead-based paint, and let B denote the
housing units that have some deteriorated lead-based paint. Then the aggregated log-transformed
geometric mean blood-lead concentration, denoted by \i, is calculated as:
N j+KGMlj)) + ( £ N s*(0.91 *ln(GMli)+0.09*ln(GM2i))>|
) V J6B _ I
N
The aggregated log-transformed GSD, denoted by s, is calculated as:
E2-3
-------
s =
f E KO + ( E (°-91 *K1i
I!!* - / \*»
N-l
where Kl{ = N;*(n - ln(GMlj))2 and K2S = N;*(n - ln(GM2j))2. The resulting national
distribution of blood-lead concentrations is assumed to be lognormally distributed with
geometric mean equal to e*1 and GSD equal to es .
For the IEUBK model, let GMj be the model-predicted geometric mean blood-lead
concentration for the 1th housing unit. For units without any damaged or deteriorated lead-based
paint then the distribution of blood-lead concentrations is assumed to be lognonnal with
geometric mean GMj and a GSD of 1 .6. Children in housing units with damaged or deteriorated
lead-based paint in either the interior or exterior, were partitioned into three groups:
i
Group #1: Assumed to contain 91% of the children, representing those children who
show no tendency toward paint pica. The blood-lead concentration
distribution of this group is assumed to be lognonnal with geometric mean
and a GSD of 1.6.
Group #2: Assumed to contain 8.97% of the children, representing those children who
exhibit paint pica, but have not recently ingested Lead-based paint. The
distribution of blood-lead concentrations for this group is assumed to be
lognonnal with geometric mean GMj + 3 and a GSD of 1 .6.
Group #3: Assumed to contain 0.03% of the children, representing those children who
have recently ingested lead-based paint. The distribution of blood-lead
concentrations for this group is assumed to be lognonnal with geometric mean
63 ug/dL and a GSD of 1 .
The national log-transformed geometric mean blood-lead concentration is:
ieA
N
N t*(0.91 *ln(GMi)+0.0897*ln(GMi+3)+0.0003 *ln(63))>|
N
The national log-transformed GSD is:
E2-4
-------
s =
f
V i
E(0.91*Klj + 0.0897 *K2j + 0.0003
J6B
N-l
where
V =
f £ N; *ln(l .
_ UA
Ni *0.9997 *ln(l .
N
where Kl{ = Ni*(^ - ln(GMi))2, K2( = Ns*(n - ln(GMj + 3))2 and K3; = Nf*(n - ln(63))2. The
resulting national distribution of blood-lead concentrations predicted by the IEUBK model is
assumed to be lognormally distributed with geometric mean equal to e*1 and GSD equal to es.
E2-5
-------
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-------
APPENDIX F1
Methodology for Estimating Post-Intervention Distribution
of Children's Blood-Lead Concentrations Resulting
from Proposed §403 Rules
F1-1
-------
APPENDIX F1
METHODOLOGY FOR ESTIMATING POST-INTERVENTION DISTRIBUTION OF
CHILDREN'S BLOOD-LEAD CONCENTRATIONS RESULTING FROM PROPOSED
§403 RULES
This appendix details the procedures used to estimate the national distribution of blood-
lead (PbB) concentrations in children aged 1-2 years in 1997 immediately after performing the
relevant intervention strategies on the nation's housing stock under the proposed §403 rules.
Outline of the Methodology
This methodology characterizes the pre-§403 blood-lead distribution for children aged
1-2 years using reported information from NHANES HI. A model-based procedure (either the
empirical or IEUBK model) is used to characterize the distribution of blood-lead concentrations
at both pre-§403 and post-§403, and the observed differences between the two distributions are
identified. Then, a post-§403 distribution that is comparable to the pre-§403 NHANES HI
distribution is derived based on the differences between the two model-based estimates and the
pre-§403 NHANES m distribution.
The methodology consists of the following four steps:
#1. Use blood-lead concentration data reported in the NHANES HI to estimate the
geometric mean (GM) and the geometric standard deviation (GSD) associated with
the baseline (i.e., pre-6403) distribution of blood-lead concentration for children
aged 1-2 years.
#2. Use the environmental-lead levels for HUD National Survey units as input to either
the IEUBK or Empirical model to obtain a model-based estimate of the geometric
mean and the geometric standard deviation (GSD) associated with the baseline
distribution of blood-lead concentration for children aged 1-2 years.
#3. Use adjusted (post-§403) environmental-lead levels for HUD National Survey units
as input to the model used in Step #2 to estimate the geometric mean and the
geometric standard deviation (GSD) associated with the post-$403 distribution of
blood-lead concentration for children aged 1-2 years.
M. Combine the parameters of the three distributions described in #1,2, and 3 to
estimate the geometric mean and GSD of a post-S403 blood-lead distribution that is
consistent with the pre-§403 NHANES in distribution determined hi Step #1 and
the changes in the blood-lead distributions estimated in Steps #2 and #3.
F1-2
-------
Details of the Methodology
A key assumption in this methodology is that blood-lead concentrations are assumed to
be lognormally distributed, regardless of whether they represent pre- or post-§403 concentrations
or whether the distribution is based on NHANES IE data or is model-based. With this
assumption and by estimating the geometric mean and GSD of the distribution, the entire
distribution is characterized.
All four steps of the methodology are now discussed in detail.
#1. Use NHANES in to characterize the pre-6403 distribution.
A weighted geometric mean and weighted geometric standard deviation of the blood-lead
concentrations are calculated for 1-2 year old children based on NHANES ffl. The weights are
those discussed in Section 3.4.1. Call these variables GM, and GSD,, respectively. These values
were calculated as geometric mean ( GM,) = 3.14 u.g/dL and geometric standard deviation
(GSD,) = 2.09.
#2. Derive a model-based characterization of the pre-S403 distribution.
Because interventions under §403 have not yet occurred, precluding post-§403 blood-lead
concentrations from being directly measured, the blood-lead distribution resulting from the
proposed §403 rules must be estimated. For this reason, this methodology characterizes pre- and
post-§403 blood-lead distributions that are model-based (i.e., predicted blood-lead concentrations
as a function of environmental-lead levels are obtained using either the EEUBK or empirical
model).
Environmental-lead levels hi the HUD National Survey database are used as input to the
model to characterize the pre-§403 distribution of blood-lead in children aged 1-2 years. The
model-based pre-§403 blood-lead distribution is assumed to be lognormally distributed. A
weighted geometric mean and weighted geometric standard deviation of these concentrations are
calculated, where the weights correspond to the number of children associated with each
concentration. Call these variables GM2 and GSD2, respectively.
#3. Derive a model-based characterization of the post-§403 distribution.
The same method used hi Step #2 is used to characterize a model-based post-§403
distribution (Step #3). Step #3 differs from Step #2 hi that the environmental-lead levels from
the HUD National Survey are adjusted to reflect the effects of intervention. This adjustment is
documented hi Table 6-2 of Volume I. Let GM3 and GSD3 be the weighted geometric mean and
geometric standard deviation, respectively, of the predicted post-§403 blood-lead concentrations.
Thus, the model-based post-§403 blood-lead distribution is characterized as lognormally
distributed with geometric mean GM3 and geometric standard deviation GSD3.
F1-3
-------
#4. Derive a post-S403 distribution from NHANES HI and Steps #2 and #3.
The three distributions calculated in Steps #1 through #3 are used to characterize a post
§403 blood-lead distribution that is directly comparable with the pre-§403 distribution
determined in Step #1 . This distribution is assumed to be lognormal with geometric mean
and geometric standard deviation GSD4 calculated by the following formulas:
= GM,*(GM3/GM2) (1)
GSD4 = GSD, * (GSD3 / GSD^ (2)
F1-4
-------
APPENDIX F2
Estimation of Primary Prevention Efficacy
Using Model of Bone-Lead Mobilization
F2-1
-------
APPENDIX F2
ESTIMATION OF PRIMARY PREVENTION EFFICACY
USING MODEL OF BONE-LEAD MOBILIZATION
Though the scientific literature documents the effectiveness of a range of behavioral and
environmental intervention strategies on their ability to reduce childhood lead exposure, efficacy
is measured only among already exposed children (USEPA, 1995b). Specifically, declines in
children's blood-lead concentration on the order of 25% as measured 6 to 12 months following a
variety of intervention strategies were reported (Copley, 1983; Charney, et al., 1983; Amitai, et
al., 1991; Weitzman, et al., 1993; Staes, et al., 1994; Kimbrough, et al., 1994). This secondary
prevention intervention effectiveness is likely not representative of the effectiveness being sought
from the promulgation of §403. The §403 standards for lead in dust, soil, and paint are mostly
intended to prevent childhood lead exposure before it occurs and, therefore, their effectiveness
will be assessed by measures of primary prevention efficacy.
Secondary prevention efficacy results are not necessarily representative of those expected
from primary prevention because lead present in blood is a combination of current environmental
exposure and internal sources of lead. A significant internal source of lead is bone tissue. After
prolonged exposure to lead, bone tissue retains much more lead than the other body tissues
(Schroeder and Tipton, 1968; Barry and Mossman, 1970; Barry, 1975; Barry, 1981; Leggett, et
al., 1982). Nordberg, et al. suggest that bone can become an internal source of lead during
periods of reduced external exposure to lead; see also (Rabinowitz, et al., 1976; Barry, 1981;
Hyrhorczuk, et al., 1985; Rabinowitz, 1991). The reported declines in blood-lead concentration,
therefore, may underestimate the primary prevention effectiveness of the associated intervention
strategy.
Unfortunately, there is limited empirical evidence regarding the extent to which bone-lead
stores are able to keep blood-lead levels elevated following an intervention, especially
concerning children. One study (Markowitz, et al., 1993) measured bone-lead levels in children
before and after an intervention, but found no significant decline in the levels over a period of six
weeks. Despite the lack of studies concerning children, Nordberg, et al. claim that "skeletal
turnover is highest among children under 10 years of age." Several studies have been conducted
to study bone-lead mobilization in adults (Rabinowitz, et al., 1976; Hyrhorczuk, et al., 1985;
Wrenn, et al., 1972; Cohen, et al., 1973; Rabinowitz, et al., 1973; Batschelet, et al., 1979; Heard,
et al., 1984; Marcus, 1985; Christofferson, et al., 1986; Cristy, et al., 1986; Schutz, et al., 1987;
Bert, et al., 1989; Nilsson, et al. 1991; Gulson, et al., 1995). For example, Gulson, et al. show
that 45% to 70% of lead hi the blood of adult women comes from long-term tissue stores,
primarily the bone tissue. A similar result was observed hi another study on five adult subjects
undergoing knee and hip replacement (Smith, et al., 1996).
If the contribution of mobilized bone-lead stores can be characterized, however, it would
be possible to translate the documented secondary prevention results into estimated primary
prevention results. An approach is presented here for estimating the efficacy of a primary
prevention intervention given an observed effectiveness for a secondary prevention intervention.
F2-2
-------
The approach is based on a bone-lead mobilization model developed to estimate the degree to
which bone-lead stores could mask the full effectiveness of an intervention by mobilizing into
the child's blood. This model is extensively discussed and its basis documented elsewhere (Rust,
et al., 1996), though a summary is provided below.
A Model for Bone-Lead Mobilization
To evaluate the potential for continuing elevated blood-lead levels due to bone-lead
mobilization, a two-compartment model (see Figure F2-1) was adopted for the transfer of lead
between the blood and bone tissues within the body and elimination of lead from the body.
BONE
Uptake
BLOOD
Elimination
Figure F2-1. Two Compartment Model of Bone-Lead Mobilization.
In this model, lead is taken into the body (from the gastrointestinal tract and lungs) via the blood,
transfers between the blood and bone tissue, and is eliminated from the body via the blood. It is
assumed that the transfer of lead between the blood and bone tissues, and elimination of lead
from the blood follows a first-order kinetic relationship.
While the adopted model is most certainly an oversimplification, model results will
approximate those of other more complicated models involving additional tissue compartments
for two reasons:
• While lead does mobilize from non-bone tissues following a decrease in
environmental lead uptake, the effects are believed to be limited to a period of days or
weeks due to the lower concentrations of lead amassed in these tissues, and
• While all lead elimination from the body does not occur via a direct pathway from the
blood, the kinetic parameters used hi the model properly include these other pathways
(endogenous fecal and via other soft tissues) as if they were directly from the blood.
F2-3
-------
Based on the model illustrated in Figure F2-1, blood-lead concentrations (PbB) after
intervention would follow the relationship illustrated in Figure F2-2. More specifically,
immediately after intervention there would be an initial drop from the pre-intervention PbB level
(PbBpjJ to achieve an immediate post-intervention PbB level (PbB,,,^,^. PbE^^,,,, represents
the blood-lead concentration that can be supported by the amount of lead being transferred from
the bone. After this initial drop, blood-lead concentrations would follow an exponential decline
toward the long-term post-intervention PbB level (PhE^T,,™). PhE^y^,,, is the blood-lead level
that can be supported by the post-intervention exposure level, with no additional lead from the
bone. At any a particular length of time following the intervention, illustrated by the symbol "T"
on the horizontal axis hi Figure F2-2, a target post-intervention PbB level (PbBofce,^ will be
observed. The original analysis using this model (Rust, et al., 1996) estimated the maximum
length of time (T) the bone-lead stores would be capable of keeping the blood-lead concentration
above the targeted observed level (PbBofc,^ for a given value of PbBL^e,,,,. For the purposes
of the sensitivity analysis for §403, the maximum long-term effectiveness is estimated instead.
As the long-term percent decline reflects the post-intervention PbB that can be support by the
post-intervention exposure level, it is assumed this decline is equal to the primary prevention
effectiveness of the intervention.
P re-Intervention
PbB Level
Immediate
Post-Intervention
PbB Level
Target
Post-Intervention
PbB Level
Long-Term
Post-Intervention
PbB Level
T Time (days)
Figure F2-2. Blood-Lead Concentration Versus Time Following a Reduction
in Lead Uptake.
The child's blood-lead concentration at t days post-intervention is given by the equation
PbB =
(1)
F2-4
-------
where KBONEBL^ is the net rate of lead flow from bone to blood to elimination. This rate is a
function of the blood-lead level following the initial drop (PbBj,,,^,^ as well as other kinetic
parameters (e.g., the lead mass ratio of bone to blood and the elimination rate of lead from the
blood) which can be estimated from existing scientific literature (Rust, et al., 1996). As
portrayed in Figure ¥2-2, the blood-lead concentration follows an exponential decline toward
PbBLongTen,,. Setting PbB in Equation (1) equal to PhBo^e^ and solving for the long-term percent
decline hi blood-lead concentration (RumgTeim) results in the following equation:
R _ PbBLongTcnn _ s^ve
IxmgTcnn j _ exp( -t . ( '
PbBObsefved PbBIimnPost
where
T,,T>
Pit PbBPre
The maximum efficacy of an intervention, then, may be calculated given two parameters:
1 . the observed percent decline (Robs«ved) m an exposed child's blood-lead concentration
following an intervention (i.e., the observed secondary prevention efficacy); and
2. the length of time (t) following the intervention when the decline was observed.
Note that this process estimates the maximum value of R^Teim that might have yielded the
inputted values of PbBobj^^ and t based on Equation (1). The specific value may lie between
Rotted and R^giem- The estimated primary prevention efficacy is a maximum hi that R^ap,^,
and therefore KECNEE!^, cannot be estimated from available data (Rust, et al., 1996). It is
necessary to estimate the maximum efficacy over a range of possible values for R^ap,^.
Results of Modeling Bone-Lead Mobilization
To illustrate the efficacy of primary prevention, values of 25%, 50%, and 75% are
considered for the observed secondary prevention efficacy and values of 6, 12, 18, and 24 months
are considered for the lengths of time. Table F2-1 presents the maximum primary prevention
efficacy for these scenarios for children 1 to 7 years of age. The standard error of the estimated
efficacy — calculated by propagating, through the model, the standard errors of the underlying
model parameters — is enclosed in parentheses.
As an example of the results in Table F2-1, note that if the observed effectiveness of a
secondary intervention is assumed to be 25% (i.e., PbB decline to 75% percent of the pre-
intervention level) at 6 months post-intervention for a 2 year old, then the implied effectiveness
of primary prevention will be at most 47%. The scientific literature reports secondary prevention
efficacy of approximately 25% declines in blood-lead concentration 12 months following dust
F2-5
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abatements, lead-based paint abatements, elevated soil lead abatements, and intensive
educational efforts (USEPA, 1995b). Depending upon the age of the child benefitting from the
intervention, the results in Table F2-1 would suggest these interventions would prompt primary
prevention efficacy of between 30% and 59% (column: "Length of Time, 12 Months"; row:
"Observed Efficacy of Secondary Prevention, 25%").
Empty cells in Table F2-1 indicate that those scenarios cannot possibly occur based on
Equation (1). For example, for a 7 year old, the impact of mobilized bone-lead stores would
result in less than a 25% decline in blood-lead concentration at 6 months, even for a 100%
effective intervention. Estimates of primary prevention efficacy under these "impossible"
scenarios are not meaningful and are therefore not shown.
Consistent with the limited data available on bone-lead mobilization, the standard errors
in Table F2-1 are quite large. By incorporating the 95% upper confidence bounds on the
maximum primary prevention efficacy, the resulting bounded estimates are 1.2 to 1.9 times larger
than the mean estimates reported hi the table.
As described above, this analysis estimates the maximum efficacy of primary prevention
interventions. Consideration was also given to obtaining the minimum efficacy. It was
determined that the present model can provide a meaningful solution for the maximum case only,
and that additional empirical data and extensive model enhancement are required to solve the
minimum case. Only the maximum efficacy, therefore, is reported.
F2-6
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Table F2-1. Maximum Efficacy of Primary Prevention For Blood-Lead Levels (PbB)
Observed at 25%, 50%, and 75% of Pre-lntervention Levels at 6, 12, 18,
and 24 Months.
Observed
Efficacy of
Secondary
prevention"
25%
50%
75%
Child's Age
(year*)
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Length of Time"*
(months J
0
0.39(0.16)
0.47(0.18)
0.56(0.21)
0.67 (0.25)
0.79 (0.27)
0.91 (0.32)
0.78 (0.32)
0.94 (0.36)
:: : ..:. '•. ta ;
0.30 (0.05)
0.33 (0.08)
0.36 (0.14)
0.41 (0.19)
0.47 (0.19)
0.53 (0.21)
0.59 (0.22)
0.60 (0.09)
0.65 (0.16)
0.73 (0.27)
0.83 (0.37)
0.93 (0.38)
0.90(0.14)
0.98 (0.25)
18
0.28 (0.03)
0.30 (0.04)
0.31 (0.07)
0.34(0.10)
0.37 (0.14)
0.40(0.19)
0.44(0.19)
0.56 (0.05)
0.59 (0.08)
0.63 (0.13)
0.68(0.21)
0.73 (0.29)
0.81 (0.37)
0.89 (0.37)
0.84 (0.08)
0.89(0.13)
0.94 (0.20)
24
0.27 (0.02)
0.28 (0.03)
0.29 (0.04)
0.31 (0.06)
0.33 (0.08)
0.35 (0.12)
0.37(0.15)
0.55 (0.04)
0.56 (0.06)
0.59 (0.08)
0.62(0.13)
0.66(0.17)
0.70 (0.24)
0.75 (0.31)
0.82 (0.05)
0.85 (0.09)
0.88 (0.13)
0.93 (0.19)
0.98 (0.25)
Note: An empty cell means that the scenario is not possible according to model predictions.
'" This is equivalent to the observed percent decline in an exposed child's blood-lead levels at a specified
time point following the intervention.
Ib)
This is equivalent to the length of time following the intervention when the decline was observed.
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APPENDIX G
Multi-Media Model (Empirical Model) for Use in the
Section 403 Risk Assessment
G-1
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APPENDIX G
MULTI-MEDIA MODEL (EMPIRICAL MODEL) FOR USE IN THE
SECTION 403 RISK ASSESSMENT
EXECUTIVE SUMMARY
Purpose Of The Appendix
This appendix documents development and evaluation of an empirical regression model
relating measures of lead in a residential environment to geometric mean children's blood-lead
concentrations. The model is used as one tool in the Section 403 risk assessment to estimate
blood-lead concentrations of children exposed to lead in paint, dust and soil as measured in the
HUD National Survey. This model is also employed to evaluate various options for risk
management for the Section 403 standards. In this analysis, EPA estimated a national
distribution of blood-lead levels (and, ultimately, estimated health effects) before enactment of
the Section 403 standards, and then employed models to relate environmental levels of lead to
children's blood-lead levels to estimate a national distribution of blood-lead levels (and health
effects) after enactment of specific 403 standards. Environmental measures of lead from the
HUD National Survey are used as inputs to the empirical model to predict the national
distribution of blood-lead concentrations. Therefore, the model development was constrained to
variables in the HUD National Survey data set. The goal was to develop a model that could be
used to give an approximation of expected blood-lead concentrations related to residential
environmental lead based on a single source of data.
In this appendix the empirical model is presented and its prediction of a national
distribution of blood-lead concentrations is compared to the results of Phase 2 of the Third
National Health and Nutrition Examination Survey (NHANES m).
Model Development Issues
The choice and construction of variables, the mathematical form of the empirical model,
assessment of goodness-of-fit and influential points, and the treatment of measurement error in
predictor variables were all given consideration during the development of the empirical model.
One particular difficulty was that the empirical model was constructed using dust lead
results collected from wipe sampling in the Rochester study, whereas dust lead results in the
HUD National Survey were collected from blue nozzle vacuum sampling. Similarly, the
empirical model was constructed using soil lead concentrations observed from drip-line sample
locations in the Rochester study, whereas soil lead results in the HUD National Survey were
based on an average concentration of lead in soil from drip-line, entryway and remote locations.
A statistical method was developed to account for both systematic differences as well as
differences in error structures between the sampling methods employed in the Rochester study
and the HUD National Survey.
G-2
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The Empirical Model
The form of the empirical model is:
ln(PbB) = P0 + p, • ln(PbFBN) + P2 • ln(PbWBN) + 03 - ln(PbS) + P4 • PbP + e
where PbB represents the blood-lead concentration, PbFBN and PbWBN correspond to dust-lead
loading from interior floors and window sills respectively (on a Blue Nozzle Vacuum Scale), PbS
represents soil-lead concentration, PbP represents paint/pica hazard, and e represents the residual
error left unexplained by the model.
Results Of The Comparison With NHANES III
The predicted distribution of blood-lead concentrations for children aged 1-2 years
obtained by applying the empirical model to the HUD National Survey Data was compared to
Phase 2 of NHANES HI. Results of this comparison indicate:
• The national geometric mean blood-lead concentration (pre-intervention) was
properly calibrated to the geometric mean reported in NHANES HI.
• The variability in the national distribution of blood-lead concentrations predicted by
the empirical model using the HUD National Survey is approximately 1.71 (GSD), in
contrast to a GSD of 2.09 for Phase 2 of NHANES m.
• The estimated proportions of blood-lead concentrations exceeding 10,20 or 30 (ig/dL
using the empirical model predictions are much lower than the corresponding
proportions estimated by NHANES IE. For example, the percentage of children aged
1-2 years estimated to have blood-lead concentrations above 10 ug/dL using the
empirical model was 1.54% hi comparison to 5.75% estimated in Phase 2 of
NHANES m.
Differences between the Rochester study population and the national population represent
the primary limitation when using the empirical model based on data from the Rochester Study to
predict a national distribution of blood-lead concentrations.
Use Of The Empirical Model
The empirical model is used in the Section 403 risk assessment and economic analyses to
predict a distribution of childhood blood-lead concentrations based on measures of lead hi paint,
dust and soil at the child's primary residence. This information is used to evaluate various
options for risk management for the proposed Section 403 Standards. In these analyses, the
model is used to predict national distributions of children's blood-lead concentrations both
before and after the rule is proposed. Estimates of environmental levels of lead before and after
enactment of the Section 403 standards and after interventions resulting from the standards will
be used as inputs to the model. The empirical model should only be used to predict a distribution
G-3
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of blood-lead levels when environmental levels for all media are known or estimated. It is not
intended as a general dose-response model, but rather as a predictive model developed
specifically for use in the Section 403 Risk Assessment and specifically to predict blood-lead
concentrations from estimates of environmental lead as measured in the HUD National Survey or
as measured by a standard Section 402 risk assessment.
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G1.0 INTRODUCTION
In order to better inform risk managers as they consider various options for the Section
403 standards, EPA estimated the range of risk reductions that are expected to result from a
variety of potential standards. In order to do this, EPA estimated a national distribution of blood-
lead levels (and, ultimately, potential health effects) before enactment of the Section 403
standards, and then relied on models relating environmental levels of lead to children's blood-
lead levels to estimate a national distribution of blood-lead levels (and potential health effects)
after enactment of specific 403 standards. The empirical model is used in the Section 403 risk
assessment and economic analysis to predict a distribution of blood-lead concentrations related
(jointly) to measures of lead in three media at the child's primary residence: paint, dust, and soil.
Environmental measures of lead from the HUD National Survey were used as inputs to the
empirical model to predict the national distribution of blood-lead concentrations. Therefore, the
model development was constrained to variables in the HUD National Survey data set. Given
time and budget constraints the goal for the empirical model development could not include
construction of the best possible model based on multiple data sources. Rather, the goal was to
develop a model that could be used to give an approximation of expected blood-lead
concentrations related to residential environmental lead based on a single source of data. This
model has not undergone formal validation and is based on only one data set. It is not intended
as a general dose-response model, but rather as a predictive model developed specifically for use
in the Section 403 Risk Assessment and specifically to predict blood-lead concentrations from
estimates of environmental lead as measured in the HUD National Survey or as measured by a
standard Section 402 risk assessment. The model was used to estimate the benefits of the 403
rule in the post-403 situation by estimating the reduction in children's blood lead concentrations
resulting from application of various options for the 403 standards via risk assessments in
residential housing.
In this appendix the empirical model is presented and its prediction of a national
distribution of blood-lead concentrations is compared to the results of the NHANES ffl Survey as
follows:
A national distribution of housing and population characteristics was estimated
using the HUD National Survey of environmental levels of lead in paint, dust, and
soil in residential housing along with pertinent Census information. The Census
information and the HUD National Survey measurements of environmental lead
(after appropriate conversions) were used as inputs to the model to predict a
national distribution of children's blood-lead levels before enactment of the
Section 403 standards. This pre-rulemaking distribution was compared to the
national distribution of children's blood-lead concentrations estimated by the
NHANES HI survey to assess the adequacy of the model and its applicability on a
national level.
The empirical model is also used to predict the national distribution of children's blood-
lead levels after enactment of the Section 403 standards. Estimates of environmental levels of
lead after the conduct of interventions performed in response to various options for the Section
G-5
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403 standards are used as inputs to the model. Comparison of the pre- and post-rulemaking
distributions allow estimation of the benefits associated with the rulemaking.
The empirical model is not intended to be used to estimate the effect of a single media on
blood-lead levels. The model should only be used to predict a distribution of blood-lead levels
when environmental levels for all media are known or estimated. Individual parameter estimates
should not be interpreted in isolation.
The choice and construction of variables, the mathematical form of the empirical model,
assessment of goodness of fit and influential points, and the treatment of measurement error in
predictor variables were all given consideration during the development of the empirical model,
and are described in detail in this document.
GA
-6
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G2.0 DESCRIPTION OF DATA
The purpose of the statistical analysis was to provide a predictive model which relates
childhood blood-lead concentration to measures of lead exposure from paint, dust and soil.
Variables which represent lead exposure in environmental media were based on data that was
available in both the HUD National Survey, and in the Rochester Lead-in-Dust study. Data from
the HUD National Survey and from NHANES in are based on surveys that were designed to be
nationally representative of the housing stock and the population of children, respectively. The
HUD National Survey was a survey of pre-1980 housing that was adjusted using data from the
1993 American Housing Survey to represent the 1997 housing stock as described in the Section
403 Risk Assessment document. The Rochester Study was based on a targeted sample limited to
a single geographic area as were other candidate epidemiological (epi) studies. It is unclear as to
whether inferences drawn from any particular epi-study can be generalized to the national
population of children and/or housing. Following is a brief discussion of each individual source
of data, as well as a rationale and description of the variables that were included in the statistical
analyses.
G2.1 SOURCES OF DATA
G2.1.1 Rochester Lead-in-Dust Study
The Rochester Lead-in-Dust Study is a cross sectional study which recruited 205 children
from live births at three local hospitals using a stratified sampling scheme. The sampling scheme
was designed to recruit a high proportion of low income families living in older (pre 1940)
housing. Blood-lead and hand-lead sample collection from recruited children occurred between
August 31 and November 20,1993. A detailed questionnaire was also completed at the time of
blood sample collection. Environmental assessment of the primary residence of each recruited
child was generally completed within three weeks of the date of blood sample collection, and
included samples of dust from floors, window sills and wells, samples of soil from the dripline
adjacent to the foundation and the child's play area, and measurements of painted interior and
exterior surfaces (condition of paint and XRF paint lead loading).
G2.1.2 HUD National Survey
The HUD National Survey collected environmental samples of paint, dust, and soil from
284 private homes between 1989 and 1990. The objective of the study was to obtain data for
estimating the prevalence of lead-based paint and lead-contaminated dust and soil in the nation.
The presence or absence of children with elevated blood-lead was not part of the sampling
design. One floor-dust sample was collected from each of three rooms, and one window sill and
window well sample was collected from each of two rooms using a blue nozzle vacuum sampler.
Three soil samples were collected from the dripline, entryway and remote locations. Paint
sampling included XRF measures of paint-lead loading and condition of paint from generally two
interior rooms and one side on the exterior of each residential unit.
G-7
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In the HUD National Survey, each unit was assigned a sampling weight equal to the
number of pre-1980 privately-owned, occupied units in the national housing stock that were
represented by the given unit in the survey. The total of all 284 sampling weights equaled the
number of pre-1980 privately-owned, occupied units in the national housing stock at the time of
the survey. Sampling weights in the National Survey were determined according to four
demographic variables associated with the units:
• Age category of unit
• Number of units in the building
• Census region
• Presence of a child under age 7 years
Since EPA's Risk Assessment uses 1997 as a base year for Section 403 activities, it was
desirable to use the environmental-lead levels from the National Survey to characterize
environmental-lead levels in the 1997 national housing stock. Therefore the sampling weights of
National Survey units were revised to represent the 1997 occupied housing stock. The revised
weights indicate the number of units in the 1997 national housing stock that are associated with
the given National Survey unit, and therefore, with its distribution of environmental-lead levels.
G2.1.3 National Health and Nutritional Educational Survey (NHANES) III
The Third National Health and Nutrition Examination Survey (NHANES HI), conducted
from 1988 to 1994, was the seventh hi a series of national examination studies conducted by
CDC's National Center for Health Statistics (NCHS) to trace the health and nutritional status of
the non-institutionalized, civilian U. S. population. The target population for NHANES HI
included the civilian non-institutionalized population 2 months of age and older.
To provide for a nationally representative sample and sufficient precision in
characterizing key subgroups, a complex survey design was employed in NHANES HI.
Approximately 40,000 persons were sampled in NHANES HI, including approximately 3,000
children aged 1 to 2 years. Although estimates of national population health and nutrition
parameters were the primary objectives of the survey, suitably precise estimates for certain age
and race groups were obtained through over sampling. As a result, the NHANES in provides a
solid basis for obtaining national estimates of the distribution of childhood blood-lead
concentrations. Details on the study design and how the survey was conducted are available
from CDC, 1992 and CDC, 1994.
G2.1.4 Other Candidate Epi Studies Considered
There are various other epi studies that were potential data sources on which to base the
empirical model. Given time and budget constraints the goal for the empirical model
development could not include construction of the best possible model based on multiple data
sources. Rather the goal was to develop a model that could be used to give an approximation of
expected blood-lead concentrations related to residential lead based on a single source of data.
The Rochester Study was chosen because of the following advantages:
G-8
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1. All media, locations, and surfaces that are being considered for Section 403 standards
were measured for lead in the Rochester Study.
2. The Rochester Study includes dust-lead loadings from wipe sampling and the Section
403 dust standard is expected to be based on dust-lead loading from wipe sampling.
3. The selection of homes and children in the Rochester Study, although targeted, was
more random and more representative of a general population than is the case with
most recent epidemiological studies of lead exposure in non-smelter communities.
4. The Rochester Study is recent.
The primary limitation associated with the Rochester Study is concern over the degree to
which the Rochester Study may be considered representative of the nation as a whole. The
limitations of the Rochester Study are discussed in more detail in Section G8.
Other data sets considered for use in constructing the empirical model included:
1. Pre-intervention data from the Baltimore Repair and Maintenance (R&M) Study. The
R&M Study is a prospective longitudinal study which was designed to investigate the
potential health and environmental benefits associated with performing R&M
interventions on urban housing with lead-paint hazards. The pre-intervention sample
included 115 children living hi 87 homes. Samples of blood were collected from each
participating child, and samples of dust, soil and water were collected from each
house during the pre-intervention campaign. Due to the fact that the housing stock in
this study consisted primarily of Baltimore City rowhouses, only 42 children living in
29 homes had soil samples. The absence of measures of lead in soil would have
limited the use of this data in the development of an empirical model focused on all
three media: paint, dust and soil.
2. Pre-intervention data from the Boston Soil Lead Abatement Demonstration Project.
The Boston 3-City Study recruited 152 children living in 101 houses from four
different urban neighborhoods during the pre-intervention campaign. The main
restrictions for recruitment into the study were that the children had to be under the
age of 5 and have an initial blood-lead concentration between 7 and 24 ug/dL. For
each household recruited into the study, a detailed environmental assessment was
conducted concurrently with the blood-sampling. This environmental assessment
included the collection of samples from paint, dust, soil and water. All dust samples
from the Boston 3-City Study were collected using the Sirchee-Spitler Method. This
method entails the use of a modified Black & Decker Dustbuster vacuum, and its
properties with respect to other sampling methods are not well understood at the
current time. Collection of a handwipe sample from each participating child and the
completion of a questionnaire was also conducted with each blood sample.
G-9
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The restricted range of blood-lead concentrations recruited into this study was likely
to have a large impact on parameter estimates of the relationships under investigation,
and therefore, this source of data was not considered optimal for use in developing the
empirical model.
3. Pre-intervention data from the Baltimore Soil Lead Abatement Demonstration
Project. The Baltimore 3-City Study recruited 402 children living in 204 houses from
two different urban neighborhoods during three rounds of pre-intervention sampling.
There were no restrictions on the blood-lead concentration of children recruited into
the study, however children had to be under the age of seven. For each household
recruited into the study, a detailed environmental assessment was conducted once
during the pre-intervention campaign. This environmental assessment included the
collection of samples from dust, soil, exterior paint, and water. The Baltimore 3-City
Study did not include samples of lead in paint or dust from window sills or window
wells. Samples of interior paint were collected after the soil abatement intervention
took place. In addition, all dust samples from the Baltimore 3-City Study were
collected using the Sirchee-Spitler Method, and its properties with respect to other
sampling methods are not well understood at the current time. Therefore, this source
of data was not considered optimal for use in developing the empirical model.
4. Pre-intervention data from the Cincinnati Soil Lead Abatement Demonstration
Project. The Cincinnati 3-City Study included 201 children living in 129 houses from
six different urban neighborhoods in the first (pre-intervention) phase of the study.
The households recruited into the study were mostly single family residential units
within multi-unit apartment buildings. It was believed that lead-based paint was
removed from participating residential units in the early 1970's as part of a housing
rehabilitation project. The pre-intervention environmental assessment consisted of the
collection of interior and exterior dust and paint from each participating residential
unit, and samples of soil from neighborhood recreation areas such as parks and
playgrounds. Dust samples were collected using the DVM sampling method. Soil
abatement was performed on a neighborhood scale, in parks, play areas, and other
common grounds. Exterior dust was also removed from the neighborhood streets,
alleys, and sidewalks as part of the intervention. Since soil samples could not be
related to individual residences, this source of data was not considered optimal for use
in developing the empirical model.
5. Data from the Cincinnati Longitudinal Study. The Cincinnati Longitudinal Study is a
prospective study which followed a cohort of several hundred children from birth to
five years of age. It was designed to assess the impact of urban lead exposure on
children's blood-lead concentrations. Once a year, blood-lead and hand lead samples
were collected from each participating child. Progress in social, behavioral and
cognitive development for each child was also measured over the course of the study.
Environmental samples which included interior surface dust, XRF paint and exterior
surface scrapings were collected from the residences of each participating child at
approximately the same time as blood sample collection. There was also a qualitative
G-10
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housing evaluation that was conducted for each residence included in the study. The
Cincinnati Longitudinal Study provides data on the relationship between blood-lead
and environmental lead over .time. Although it is uncertain as to whether the exterior
surface scrapings are representative of exterior dust or soil (or both), it appeared as
though the Cincinnati Longitudinal Study was a good potential source of data for the
empirical model; however these data have not yet been publicly released by the
University of Cincinnati.
6. Data from the HUD Lead-Based Paint Hazard Control Grant Program in Private
Housing (HUD Grantee data). HUD has provided grants to states and units of general
local government (Grantees) for environmental interventions in privately owned low-
and moderate-income housing. HUD requires Grantees to conduct dust-wipe testing
and blood testing prior to environmental intervention. Paint and soil sampling are
optional. Data from this program was not available for analysis at the time of
preparation of the empirical model.
G2.2 VARIABLES UNDER CONSIDERATION
Following is a rationale and description of the variables that were most closely examined
for inclusion hi the empirical model. These variables represent a subset of all the variables
originally considered. They were selected based on several properties, including strength of
association with blood-lead concentration in bivariate models, predictive power when included
into a model with competing sources of lead exposure, interpretation, ability to construct the
variable across different sources of data, and applicability to data collected by a standard Section
402 risk assessment.
The criteria used for the selection of variables hi the empirical model emphasized use of
measures of environmental lead and other factors observed hi both the Rochester Lead-in-Dust
Study and the HUD National Survey. Variables whose definition provided a convenient
translation when applied to the National Survey, whose predictive power in Rochester were high,
and whose spread in the National Survey populations covered a wide enough range of values,
were used in the empirical model.
The first group of variables are subject specific, constructed from measurements on each
child recruited into the empirical studies. The second group of variables are property specific,
representing observations from the primary residences of each of the subjects. Because the
Rochester Study included only one child per household, all of the variables measured in this
statistical analysis can be organized using an identifier for household, represented by the
subscript, i, throughout this document.
G2.2.1 Subject Specific Variables
Table G-l gives descriptions of the subject-specific variables: blood-lead concentration,
age, pica and race.
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Table G-1. Subject-Specific Variable Descriptions
Variable
Description
Blood-
Lead
Blood lead concentration on a venous sample is reported in units of micrograms of lead per
deciliter d/g/dL). Because the distribution of blood-lead concentration is usually skewed, a
natural log transformation was applied to blood lead concentration for use as a response variable
in the statistical models. The natural log transformation helps the distribution of observed blood-
lead levels meet normality assumptions required by the statistical models.
LPbB, = Natural log of the blood lead concentration measured from the ith child.
Pica
It has been hypothesized that sources of lead exposure in environmental media influence blood-
lead concentration as a function of the hand-to-mouth activity or mouthing behavior of the child.
A child who exhibits "strong" mouthing behavior or pica may be at higher risk for attaining an
elevated blood-lead concentration. The following two questions were included in the Rochester
Lead-in-Dust study as part of the questionnaire, and were designed to measure mouthing
behavior or pica tendencies in children: (1) How often does the child put paint chips in his/her
mouth?, and (2) How often does the child put dirt or sand into his/her mouth? The following
choices were given as a possible response to these questions.
0 Never
1 Rarely
2 Sometimes
3 Often
4 Always
The following Pica variables were constructed based on the parental/guardian responses to the
above two questions:
Paint Pica, = Tendency of the ith child to put paint chips in the mouth (on a scale of
0 to 4).
Soil Pica, = Tendency of the ith child to put dirt or sand in the mouth (on a scale of
0 to 4).
Age
Age has been documented as having a nonlinear effect on blood lead concentration when
children are young (CDC, 1991). Therefore the age of each subject (in years) measured at the
time of blood sampling was considered as a potential covariate in the statistical analysis.
Age, = Age (continuous measure in years) of the ith child.
Race
It is quite possible that there are biological, cultural and/or behavioral differences among children
recruited into the Rochester study that cannot be explained by any of the other measured
variables barring race. Indicator variables representing race were therefore explored as
covariates for the statistical analyses:
White, = 1 if the ith child is Caucasian.
= 0 Otherwise
Black, = 1 if the ith child is of African American descent.
= 0 Otherwise
Other, = 1 if the ith child is not Caucasian or not African American.
= 0 Otherwise
G2.2.2 Property Specific Variables
The property specific variables that were investigated in this statistical analysis
correspond to measures of lead exposure from paint, dust and soil. There are many different
ways of constructing lead exposure variables from the various different samples that were
collected from each environmental media. The variables discussed below represent one way of
characterizing lead levels in environmental media.
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Table G-2. Property-Specific (Dust and Soil) Variable Descriptions
ixpoaure
Description
Paint
(75th
Percentile)
Interior and exterior paint lead loading was measured on multiple different painted surfaces
within each residential unit using portable XRF instruments. Usually the condition of the paint
was also measured for each painted surface that was sampled. Several variables were
constructed using a combination of observed paint lead loadings and condition of the paint
from both the interior and exterior of each residential unit. Two variables were chosen for the
statistical analyses, which represent the presence and severity of deteriorated interior and
exterior lead-based paint. The following formula describes the construction of the paint-lead
variables, and was applied separately for interior and exterior paint samples within each
residential unit:
Let XRF,, represent the observed paint lead loading (mg/cm2) from the jth component within
the ith residential unit, if the XRF value was greater than or equal to 1 mg/cm2. An observed
XRF paint-lead loading greater than or equal to one is considered lead-based paint. If the
observed paint lead loading was less than 1 mg/cm2, XRF,, is equal to zero.
Condition of the paint is characterized as Good whenever less than 5% of the surface is
deteriorated; Fair whenever 5% to 15% of the surface is deteriorated; and Poor whenever
more than 15% of the surface is deteriorated. By combining categories, let Cond,, represent
the condition of the paint on the jth component within the ith residential unit; Cond,, is equal
to one if the surface was rated Fair or Poor, and is equal to zero if it was rated Good. Then
we have a measure of deteriorated LBP, which is given by DETLBP,, = XRF,, • Cond,,
Paint, is defined as the 75th percentile of the j observed levels of DETLBP,,. It is a variable
which represents the presence and severity of deteriorated lead-based paint within a
residential unit. Residential units in which less than 25% of the sampled painted surfaces had
deteriorated lead-based paint result in a DETLBP,, value that is equal to zero. Residential units
with 25% or more of the sampled painted surfaces having deteriorated lead-based paint result
in DETLBP,, values that are greater than or equal to one.
Intjsnt, = Paint, based on interior painted surfaces.
Ext_pnt, = Paint, based on exterior painted surfaces.
Paint/Pica
Hazard
An additional paint variable combined paint condition, lead-based paint and pica. An indicator
variable which was nonzero whenever each of the following conditions existed in a residential
unit: presence of deteriorated or damaged interior paint in the household; and presence of
interior lead-based paint in the household; and presence of a child with paint pica in the
household.
The paint variable had values of:
0 No LBP (XRF reading < 1), or condition is Good, or child does not exhibit paint pica;
1 LBP (XRF reading * 1), condition is Fair or Poor, and child exhibits paint pica rarely;
2 LBP (XRF reading * 1), condition is Fair or Poor, and child exhibits paint pica at least
sometimes.
In the Rochester Study, a child's tendency towards paint pica was characterized as:
0 = Never, 1 = Barely, 2 = Sometimes, 3 = Often and 4=Always.
Because of limited sample size in each category. Paint pica was collapsed for this modeling to
have values: 0 = No paint pica, 1 = Child exhibits paint pica rarely, and
2 = Child exhibits paint pica at least sometimes.
A value of 1.5 was chosen as the input value for those children exhibiting pica at least rarely
in applying the empirical model to the HUD National Survey. The average value of this pica
variable for children who exhibited any pica in the Rochester Study was 1.25
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Table G-2. Property-Specific (Dust and Soil) Variable Descriptions (Continued)
Floor Dust
Combined
With
Proportion of
Carpeted/
Uncarpeted
Surfaces
There were residential units in which all floor surfaces that were sampled were either carpeted
or uncarpeted, resulting in missing values for the variables Floor_C, or FloorJJ,. A second set
of floor-dust exposure variables were therefore pursued in an effort to recapture residential
units with missing values.
Let PC,, represent the proportion of floor dust samples collected from carpeted surfaces
within the ith house: PC, = [Number of carpeted floor surfaces], / [Total number of floor
surfaces sampled],
Then Carp fir, = Floor_C, * PC,, and
Barejflr, = Floor_U, • (1-PC,) where
Carp_flr, represents the area weighted arithmetic average dust-lead loading from
carpeted floors multiplied by the proportion of floor dust samples that
were collected from carpeted surfaces in the ith residential unit. Note that
Carp_flr, is equal to zero for residential units that had no carpeted surfaces
sampled.
Bare_flr, represents the area weighted arithmetic average dust-lead loading from
uncarpeted floors multiplied by the proportion of floor dust samples that
were collected from uncarpeted surfaces in the ith residential unit. Note
that Bare_flr, is equal to zero for residential units that had no uncarpeted
surfaces sampled.
Dust
(Window
Trough,
Window Sill
and Floor)
Samples of interior household dust were collected from floors, window sills and window wells
from residential units in the Rochester Study. Dust samples were collected using both wipe
and vacuum samples, thus measures of dust-lead loading were available for all dust samples,
and measures of dust-lead concentration are available for those dust samples that were
collected using vacuum samples. Variables were constructed which represent the area
weighted arithmetic average dust-lead loading and the mass weighted arithmetic average dust-
lead concentration for each component type tested within each residential unit. Due to a lack
of understanding of potential differences between the exposure mechanism between carpeted
and uncarpeted surfaces, floor dust samples collected from carpeted and uncarpeted surfaces
were treated as separate component types in the construction of variables. An initial
assessment comparing dust-lead loading variables to dust-lead concentration variables (for
samples collected using vacuum sampling) in the Rochester Lead-in-Dust Study demonstrated
that the lead-loading variables were consistently stronger predictors of blood-lead
concentrations. In addition, it is expected that dust standards will be specified in terms of
dust-lead loading from wipe samples. Therefore, the following measures of wipe dust-lead
loading were considered as potential variables in the predictive model:
Floor_A, represents the area weighted arithmetic average dust-lead loading from all
surface (carpeted or uncarpeted) floors in the ith residential unit.
Floor_C| represents the area weighted arithmetic average dust-lead loading from
carpeted floors in the ith residential unit.
FlooMJ, represents the area weighted arithmetic nv«raf« duet-tad loading from
uncarpeted floors in the ith residential unit.
W_Sill, represents the area weighted arithmetic average dust-lead loading from
window sills in the ith residential unit.
W_Well, represents the area weighted arithmetic average dust-lead loading from
window wells in the ith residential.
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Table G-2. Property-Specific (Dust and Soil) Variable Descriptions (Continued)
Exposure
Description
Soil
Composite samples of soil were collected using a coring tool from several different locations
within the yard of each residential unit. In the Rochester Lead-in-Dust Study, the laboratory
analysis of the composite soil samples resulted in measures of soil-lead concentration U/g/g)
for a fine soil fraction and a coarse soil fraction. An initial assessment of the soil-lead data
from the Rochester Lead-in-Dust Study Data showed no statistically significant difference in
predictive power between the fine and coarse soil fractions. Soil samples usually undergo
some degree of sieving (note the HUD Guidelines protocol for soil sampling. Appendix 13.3,
page App 13.3-3). Historically, the fine soil fraction has been used as a predictor variable in
lead exposure studies, because it was thought that the fine-soil fraction is more bioavailable to
children. We therefore considered only the fine-soil fraction in the statistical analyses. The
following soil-lead exposure variables were considered as potential predictor variables in the
statistical models:
Drip_Soil, represents the observed lead concentration in a composite soil sample
collected from the dripline (adjacent to the foundation) of the ith home.
Play_Soil, represents the observed lead concentration in a composite soil sample
collected from the play area of the ith home. Note that Play_Soil, could be
considered a subject specific variable.
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G3.0 FORMS OF THE STATISTICAL MODELS
This section contains a discussion of the different forms of mathematical models
considered for characterizing the relationship between blood-lead and measures of lead exposure
that were considered as part of the modeling effort. The following five mathematical model
forms were investigated for the development of a multi-exposure predictive model for childhood
blood-lead concentrations. Each model is individually discussed in terms of statistical
assumptions, biological/physical assumptions, and mathematical ease of use. Although
biological/physical plausibility is an important issue, the objective of the empirical Model was to
predict a rational distribution of blood-lead concentrations. Thus, the primary basis for choosing
a model was based on predictive ability. It should be noted that there is currently no definitive
model accepted by the scientific community for the relationship between childhood blood-lead
and environmental-lead. The final form of the empirical model is presented hi Section G6.
G3.1 LOG-LINEAR MODEL
The log-linear model expresses natural-log transformed blood-lead concentration as a
linear combination of natural-log transformed exposure variables and select covariates. A
multimedia exposure log-linear model for blood-lead concentrations (in generic form) would
appear as follows:
ln(PbBj) = p0 + P, • hXDustj) + P2 • ln(Soilj) + P3 • ln(Paint.) + y ' Covariatej
where e; (the residual error) is assumed to follow a normal distribution with mean zero and
variance
One main advantage of the log-linear model is its mathematical convenience. The log-
linear model is easily fitted using standard linear regression methods (although in the
development of a multiple-exposure model it may be necessary to fit the log-linear model using a
numerical approximation method while constraining parameter estimates for exposure variables
to positive values; i.e. P,, P2, and P3 £ 0). Another mathematical convenience of the log-linear
model is the fact that calculation of tolerance intervals and exceedance proportions, and adjusting
for the effects of measurement error in predictor variables is relatively straight-forward.
With respect to biological/physical assumptions, the log-linear model when translated
back into the original scale of observed blood-lead concentrations, results in a multiplicative
relationship for environmental-lead:
PbBj = exp(p0) • DustjPl • Soilj Pz • Paint) Ps • Covariatej Y • exp^)
Thus, the effect of dust-lead on blood-lead is dependant on the combined effects of all of
the other variables included hi the model. Furthermore, the difference in predicted blood-lead
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concentration for children exposed to dust-lead loadings of 5 and 50 ug/ft2 is the same as the
difference in predicted blood-lead concentration for children exposed to dust-lead loadings of
500 and 5000 jig/ft2. Although the multiplicative interpretation of the log-linear model is not
considered biologically/physically plausible, it often fits the data better than statistical models
with a more plausible, biological/physical basis for data with low to moderately exposed children
(Rust, etal., 1996).
G3.2 LOG-ADDITIVE MODEL
Whereas the log-linear model when translated back to the original scale of measurement
results in an assumed multiplicative relationship, the log-additive model results hi an assumption
of additivity among the exposure variables. The log-additive model expresses natural-log
transformed blood-lead concentration as the natural-log of a linear combination of exposure
variables and select covariates. A multimedia exposure log-additive model for blood-lead
concentrations (in generic form) would appear as follows:
ln(PbBj) = In(p0 + p, • Dustj + P2 • Soil; + p3 • Paintj + y • CovariatCj) + e{
where ef (the residual error) is assumed to follow a normal distribution with mean zero and
variance
Since the response variable in the log-additive model is expressed as a non-linear
function of the exposure variables, it must be fitted using a non-linear regression algorithm.
Thus, the mathematical conveniences of the log-linear model do not apply to the log-additive
model.
With respect to biological/physical assumptions, the log-linear model when translated
back into the original scale of observed blood-lead concentrations, results in an additive
relationship for environmental-lead:
PbB; = (p0 + Pj • Dustj + p2 • Soilj + P3 • Paintj + y • Covariate;) • exrfe,)
Thus, the effect of each measure of environmental lead on blood-lead is not dependant on
the combined effects of all of the other variables that were included in the model. The model is
attractive in that it is reasonable and biologically plausible that the relationship between blood-
lead and environmental lead would be additive at low levels of environmental exposure.
However, there is also evidence that saturation of the effect of environmental lead on blood-lead
concentration occurs at higher levels of lead exposure, in which case additivity may no longer
hold.
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G3.3 ALTERNATE LOG-ADDITIVE MODEL
Although the additive interpretation of the log-additive model is more biologically
plausible than the multiplicative interpretation of the log-linear model, the tendency of the log-
additive model to over predict blood-lead at higher levels of environmental lead exposure may
present a problem. One method for solving the problem is to use mathematically transformed
measures of environmental-lead (such as the natural-log transformation) in the log-additive
model. This "Alternate Log-Additive Model" would preserve the additivity property associated
with the log-additive model, while also accounting for a saturation of the effect of environmental
lead on blood-lead concentration at higher levels of lead exposure. A multimedia exposure
version of an alternate log-additive model for blood-lead concentrations (in generic form) would
appear as follows:
ln(PbBj) = In[p0 + Pj • In^ust;) + P2 • ln(Soilj) + P3 • ln(Paintj)
where e{ (the residual error) is assumed to follow a normal distribution with mean zero and
variance
The alternate log-additive model must also be fitted using non-linear regression, and
therefore the alternate log-additive model does not have the same mathematical conveniences
that are associated with the log-linear model. When using the alternate log-additive model,
particular attention should be paid to the mathematical transformation that is applied to the
environmental lead exposure variables. A transformation that is too strong may result in a model
in which the effect of saturation at high environmental-lead levels is over-predicted, resulting in a
model which under-predicts blood lead.
G3.4 ACTIVE/PASSIVE UPTAKE MODEL
Another method of adjusting the log-additive model to compensate for saturation of the
response at high levels of environmental lead is to parameterize the saturation effect itself. The
following "Active/Passive Uptake" Model demonstrates one method for parameterizing the
saturation effect:
Let Exposurej represent a linear combination of the exposure variables (on the original
scale) similar to the linear combination that appears inside the natural-log function in the log-
additive model;
Exposure; = PO + Pr Du^ + ?2 ' Soils + p3 • Paintj + y * CovariatCj
The Active/Passive Uptake Model is then expressed as:
G-18
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;) = InOExposure,) + In fftsslvt
+ Expoture,
8
where O^FP,«iw <. 1 and 0<6
Passive
Figure G-l provides a plot of blood-lead concentration as a function of Exposure^
assuming that 0=10 ug/dL and that FPassive takes on values of 0,0.05,0.1,0.5 and 1. The plot
shows that when FPassive is equal to zero, 6 =10 ug/dL provides an asymptote for the maximum
blood-lead concentration that is predicted as a function of Exposure^ In the Active/Passive
Uptake Model, Fpassive represents the portion of ExposurCj which has a linear effect on blood-lead
concentration beyond the saturation point of 0(1- FPassive). When F,,.^ equals 1, the
Active/Passive Uptake Model is identical to the log-additive model, and therefore does not
compensate for saturation of the response at high levels of exposure.
Advantages include biological/physical plausibility, goodness of fit relative to other
candidate models (as is seen in the tables of Section G13) and the fact that this model is similar
in nature to the relationship modeled within the EEUBK model. Disadvantages include the fact
that this model may overparameterize the relationship between blood-lead and environmental
lead in these data. Also, the active/passive uptake model does not have the same mathematical
conveniences associated with the log-linear model.
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50
45
40
35
30
25
20
15
0-10
5
0
A
1.00 (Log-Additive) /'
/ X
X' -" F - 0.15
„„—--'~7- F - 0.10
F - 0.00 (Active Uptake)
20
40 GO
Exposure^
80
100
Figure G-1. Plot of Blood-Lead Concentration as a Function of Lead
Exposure Using the Active/Passive Uptake Model with
6= 10 /ig/dL and Fp^h, Ranging from Zero to One.
G3.5 ACTIVE UPTAKE MODEL
The Active Uptake Model is simply a reduced form of the Active/Passive Uptake model
in which the parameter FPassive is held fixed at zero. This model includes properties similar to the
Active/Passive Uptake model, and may hi some cases provide more interpretable parameter
estimates for situations hi which the Active/Passive Uptake Model is overparameterized.
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G4.0 MEASUREMENT ERROR
The fact that the lead predictor variables for paint, dust and soil are subject to
measurement error raises issues about the need to account for this measurement error in the
model building process. In addition, the fact that different sampling methods were used in the
Rochester Study and the HUD National Survey also raises issues about similar adjustments for
different sampling methods when applying the empirical model to the HUD National Survey
Data. Choosing an appropriate statistical methodology for adjustment is dependant on several
factors including use of the model, interpretation of the predictor variables, the definition of the
components of measurement error in the predictor variables, and the mathematical form of the
model relating blood-lead to environmental lead.
Sections G4.1, G4.2, and G4.3 of this appendix discuss, respectively, the questions of:
1. what is being measured (and modeled) hi the empirical model;
2. what adjustment for the effects of measurement error hi predictor variables or
differences hi sampling methods is appropriate (with respect to Section 403
rulemaking activities);
3. the definition and characterization of measurement error associated with dust
predictor variable.
G4.1 WHAT IS BEING MEASURED (AND MODELED)
The purpose of the empirical model is to assess the changes hi the distribution of blood-
lead levels of children one to two years old that are likely to result from the application of the
403 Rule standards. The vehicle for application of the 403 Rule standards is a risk assessment
conducted in accordance with the work practice standards in the 402 Rule and following the
detailed approach for risk assessments in the 1995 HUD Guidelines. Accordingly, the multi-
media model defined hi this document seeks to establish a relationship between children's blood-
lead levels and environmental-lead levels as would be measured hi a risk assessment.
Environmental and blood-lead data from the Rochester Lead-in-Dust Study provided the means
to develop the multi-media model. The relationship between blood-lead and environmental-lead
observed in the Rochester Study was to be applied to environmental inputs from the HUD
National Survey (with weights adjusted to represent housing hi 1997). In most cases,
environmental variables included hi the multi-media model based on the Rochester data were
constructed similarly using environmental-lead levels observed hi the HUD National Survey.
However, dust and soil measures were sufficiently different between these two studies, and a
statistical adjustment procedure had to be developed to allow dust-lead and soil-lead measures
from the HUD National Survey to be properly used as inputs to the model. This adjusted
relationship between blood-lead and environmental-lead as observed hi the HUD National
Survey results hi what this document refers to as the empirical model. For development of 403
Ride standards, the empirical model will be used to assess different options for the standards, and
the resulting changes in the children's blood-lead distribution will be assessed to estimate the
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benefits of the various options. Proper development of the empirical model requires attention to
and balancing of three key features: 1) how environmental lead measurements are made in a risk
assessment, 2) how environmental measurements were made in the Rochester Study and hi the
HUD National Survey, and 3) in the Rochester Study, what environmental measures are strong
predictors of children's blood-lead levels.
The lead exposure variables used in the statistical model(s) were constructed from
measured levels of lead in various different samples of paint, dust, or soil from the primary
residence of each subject child. Protocols for environmental sampling were used in each study
to assure that the measures of lead hi environmental media were consistent across the various
different houses recruited into that particular study. These protocols required detailed sampling
in an effort to characterize the levels of lead in paint, dust, and/or soil at the time of sampling.
The collection of environmental samples from a child's primary residence usually occurred
within a few weeks of the collection of that child's blood-sample.
In the variable selection phase of the statistical analysis, various different ways of
combining the lead-loading (or lead concentration) of same media samples within a residence
into a lead exposure variable were investigated hi terms of (1) then- association with blood-lead
hi bivariate model(s), (2) then- association with blood-lead hi multimedia exposure model(s), and
(3) ease of interpretation. In each case, the resulting variable was designed to characterize the
child's exposure to lead in paint, dust, or soil from the primary residence.
Although a child's blood-lead concentration is a product of cumulative exposure to lead,
most of the available data from the lead exposure studies only provide information on the lead
levels in environmental media at one point hi time. Thus, the lead exposure variables that were
constructed for use hi the statistical models represent an estimate of the child's exposure to lead
from paint, dust or soil from the primary residence at the time of sampling. The exposure
variables (environmental lead) characterize current exposure to lead, rather than cumulative
exposure to lead, whereas the response variable (blood-lead) is a measure of cumulative
exposure. These exposure variables, including dust-wipe lead loadings, are similar to the
measures that would be collected in a standard Section 402 risk assessment.
Therefore, the empirical model provides an estimate of the relationship between
childhood blood-lead concentrations (indicative of a child's cumulative exposure to lead) and
sampled measurements of lead from paint, dust, or soil from the primary residence at the time
of sampling. Further discussion of the decision to focus on exposure from the primary residence
at the time of sampling is provided hi Section G4.3 below hi the sections on spatial and temporal
variability.
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G4.2 WHAT ADJUSTMENT FOR MEASUREMENT ERROR IS APPROPRIATE
The first question to be asked when addressing measurement error is: Is an adjustment
for measurement error necessary? The appropriateness of an adjustment for measurement error
is dependent on the use of the statistical model.
G4.2.1 Errors-ln-Variables Adjustment To Model "True" Lead Exposure
A primary differentiation in model use concerns whether the model is being used to
characterize the relationship between observed blood-lead levels in children and "true" lead
exposures or whether the model is being used to predict blood-lead concentrations based on
measured levels of environmental lead. The former case is the classic measurement error
problem (Carroll, et al., 1995). Although this case may be of interest to EPA in documenting the
extent of the lead problem, the primary use of the empirical model in the Section 403 rulemaking
is for the latter case, prediction.
Therefore, because the empirical model is not intended to be used as a dose-response
model, but rather is intended to be used to predict blood-lead levels based on measured levels
of environmental lead, a classic errors-in-variables approach that would model the
relationship between "true" lead exposure and children's blood lead concentrations was
considered inappropriate for this analysis.
G4.2.2 Adjustment To Account For Differences In Measurement Error Between Dust
Sampling Methods Used In The Rochester Study And Those Used In The HUD
National Survey
In order to predict the national distribution of childhood blood-lead concentrations (prior
to, and following implementation of Section 403 rules), the empirical model based on the
Rochester Study must be combined with environmental data observed in a nationally
representative sample (the HUD National Survey). As mentioned earlier, the dust and soil
sampling methods were different between these two studies and therefore an adjustment for both
systematic differences and differences in measurement error between the Rochester dust-lead and
soil-lead predictor variables and the HUD National Survey dust-lead and soil-lead predictor
variables must be considered.
An empirical model unadjusted for the effects of differences in the lead exposure
predictor variables would be appropriate for prediction of the national distribution of blood-lead
concentrations (prior to, and following Section 403 interventions) if the following four
assumptions are met:
1. The sampling scheme for environmental lead implemented in the Rochester Lead-in-
Dust Study (or other studies used for model building) is similar to the sampling
scheme implemented in the HUD National Survey.
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2. The sampling collection devices and instruments used to measure lead have similar
properties with respect to measurement error between the Rochester Study and the
HUD National Survey.
3. The distribution of observed environmental lead levels is similar between the
Rochester Lead-in-Dust Study and the HUD National Survey.
4. The characteristics of the relationship between blood-lead and environmental lead in
Rochester is the same as in the U.S. as a whole.
If either of the first two assumptions are not met, it would be necessary to adjust the
model for differences in measurement error between variables constructed using the Rochester
data and variables constructed using the HUD National Survey data. Although this can be
considered an adjustment for "measurement error," the resulting model would not be interpreted
as the relationship between blood-lead and "true" environmental lead levels (measured without
error). Rather, this adjustment will account for differences in variability related to the different
sampling methods to facilitate a more accurate prediction of the national distribution of
childhood blood-lead concentrations.
If the third or fourth assumptions are not met, it raises the question as to whether the data
from the Rochester Lead-in-Dust Study is an appropriate source of data for informing decisions
concerning lead exposures nationwide.
Initial investigation of the data suggested that the first two assumptions were not met by
the observed data in the two studies; and therefore, an adjustment for the differences between
dust-lead and soil-lead predictor variables used in the model building process and dust-lead
and soil-lead input variables from the HUD National Survey used in the prediction process is
warranted.
A related issue concerns the degree to which equation error (or an incorrect mathematical
form of the model) can affect the accuracy and precision of model predictions. Measurement
error and the form of the model are directly related in that the specific methodology for a
measurement error adjustment is dependent on the form of the model.
G4.3 DEFINITION AND CHARACTERIZATION OF MEASUREMENT ERROR ASSOCIATED
WITH EACH PREDICTOR VARIABLE
While it was determined that a classic adjustment for measurement error (Carroll, et al.,
1995) was not appropriate for this particular use of the model, the statistical adjustment to the
model for differences in sampling methods requires estimates of the variability associated with
measuring the dust-lead and soil-lead exposure predictor variables. The following equation
represents the three sources of variability that contribute to an estimate of measurement error in a
dust-lead (or soil-lead) sample from the primary residence at the time of sampling and that are
taken into account in the statistical adjustment to the model for differences in sampling methods:
G-24
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2 222
° Measurement Emor ~ & Spatial & Sampling ° Laboratory
Another potential component of variability was temporal variability, o2^,,,,,,,,,,, but this
component of variability was not included in any measurement error adjustments for reasons that
are discussed below. The question of whether or not it is appropriate to consider any particular
component of variation as part of the estimated measurement error for an exposure variable is
dependant on the interpretation of the exposure variable and the way it is being used in the
statistical model. Each component, including temporal variability, is discussed in the following
subsections with respect to characterizing measurement error in the lead exposure predictor
variables.
Details concerning the estimation of variability associated with measurement error in the
dust-lead predictor variables are provided in Section G10.
G4.3.1 Spatial Variability
Spatial variability (o2Spat]al) represents variability in environmental lead levels among all
possible locations on the surface(s) being tested as part of the sampling scheme. Although an
ideal lead exposure variable would characterize lead-levels from all the surfaces which are
related to a child's lead exposure (both inside and outside of the primary residence), the
environmental data corresponding to a subject's lead exposure is usually limited to the sampling
schemes implemented during a study. (For residential risk assessments, it is limited to the
sampling schemes specified by the Section 402 rule.) It is an assumption that the sampling
schemes that were implemented in these studies provide a sample of environmental lead as
would be obtained in a risk assessment.
Lead measures outside the primary residence are unlikely to be taken in a risk assessment.
There appear to be two ways of viewing lead exposures that occur outside the primary residence
(such as in a day care center):
1. Lead exposure that occurs outside the primary residence is not captured by the
observed lead exposure variables. Outside exposure represents a group of covariates
that are not included in the statistical models, and therefore, o2Spatia, would be limited
to the variability of environmental lead that occurs among all possible locations
within the primary residence.
2. Lead exposure that occurs outside the primary residence is captured by the observed
lead exposure variables (measured within the primary residence), based on an
assumption that levels of environmental lead inside the primary residence are similar
to levels of lead found outside the primary residence. Under this assumption, the
definition of o2Spatia) would be expanded to include the variability of environmental
lead that occurs among all possible locations to which a child has been exposed (both
inside and outside the primary residence).
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We accepted the first viewpoint of spatial variability (o2Spatiaj) based on the following
three facts:
1. There is no known information that can be used to verify the assumption that lead-
levels in paint, dust, or soil within the primary residence are representative of lead-
levels that occur outside the home.
2. There is no known information that can be used to estimate o2^,,) under an expanded
definition which includes all surfaces to which a child is exposed (both inside and
outside of the primary residence). However, there is information that can be used to
estimate spatial variability in environmental lead levels that occur within a primary
residence.
3. Environmental interventions that will occur under Section 403 will likely be focussed
on reducing residential exposure to lead. It may therefore be inappropriate to develop
a model in which the predictor variables are interpreted in a way which represents
exposure that occurs outside of the primary residence.
Spatial variability was taken into account in the statistical adjustments to the model for
differences in dust and soil sampling methods.
G4.3.2 Sampling Variability
Sampling variability o^s^p,^ represents variability introduced during the physical
collection of environmental samples, and is a typical source of measurement error associated
with the lead exposure predictor variables. Examples of variability that may be classified as
sampling variability when collecting dust samples include:
• variability associated with sampling methods, e.g. wipe versus vacuum sampling
• variability associated with sampled surfaces, e.g. carpeted versus uncarpeted floors
• variability associated with properties of the given sample, e.g. particle size and dust-
loading.
Examples of variability that may be classified as sampling variability when collecting soil
samples include:
• variability associated with sampling methods, e.g. coring tool versus grab sample
• variability associated with sampled surfaces, e.g. bare soil versus covered soil
• variability associated with properties of the given sample, e.g. fraction of soil sample
that is fine (versus coarse).
Sampling variability was taken into account in the statistical adjustments to the model for
differences in dust and soil sampling methods.
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G4.3.3 Laboratory Variability
Laboratory variability (o2^,,^) represents variability in the laboratory analysis of an
environmental sample, and includes error in sample preparation and analytical error. It is often
the case that laboratory error is a very small component of the total measurement error associated
with a sample result.
Laboratory variability was taken into account in the statistical adjustments to the model
for differences in laboratory methods for measuring lead in dust and soil samples.
G4.3.4 Temporal Variability
Temporal variability (^aapo^) represents the variability over time in environmental lead
levels on the locations(s) selected to be part of the sample. Although lead levels in paint may not
be subject to substantial temporal variability, it is documented that lead levels in dust and soil
vary over time.
Since we are interpreting the lead exposure variables as being representative of current
lead exposure (as would be measured in a Section 402 Risk Assessment) rather than cumulative
lead exposure, temporal variability in environmental lead levels was not taken into account in the
statistical adjustments to the model for differences in dust and soil sampling methods.
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G5.0 MODEL BUILDING BASED ON DATA FROM THE ROCHESTER STUDY
This chapter describes the steps involved in the development of a multi-media predictive
model based on data observed in the Rochester Lead-in-Dust Study. First, single media models
of the Rochester data were investigated, then the variables identified from them were used to
explore joint media models. Diagnostic analyses are described which were used to validate
assumptions made during model development. Finally, information from these efforts was used
to develop a multi-media predictive model based on data observed in the Rochester Study.
G5.1 USE OF SINGLE MEDIA MODELS
(Bivariate Relationships Between Blood-Lead and Each Potential Variable)
Statistical modeling of the data from the Rochester Lead-in-Dust Study began with an
initial evaluation of the bivariate relationship between blood-lead concentration and each
individual exposure variable or select covariate. This evaluation included an assessment of all
five candidate statistical models discussed in Section G3.
Section Gl 1 contains for each potential exposure variable constructed from the Rochester
Lead-in-Dust Study Data, a figure which displays the estimated regression curve for each
candidate statistical model plotted along with the observed data, as well as a table which
summarizes parameter estimates and associated standard errors for each candidate model. Note
that parameter estimates and associated standard errors for the active/passive uptake model are
not included in the tables in Section Gl 1, because in most cases, the FPusive parameter was
estimated as zero in the bivariate models, and thus, the active/passive uptake model reduces hi
form to the active uptake model. Candidate models and the strength of the relationship between
blood-lead and each variable were compared using measures of R2 and estimated likelihood
ratios. R2 (also called the coefficient of determination) is a measure of the proportion of the
variability in childhood blood-lead concentrations that is explained by a model. Estimated
likelihood ratios were calculated using parameter estimates from each model and the observed
data. Use of the likelihood ratio as a diagnostic tool is discussed in Section G5.3 on regression
diagnostics.
Results of the bivariate statistical analysis of the relationship between blood-lead
concentration and each potential exposure variable from the Rochester Lead-in-Dust Study Data
demonstrated the following:
1. The variables representing the presence and severity of ulterior deteriorating lead-
based paint were significant predictors of blood-lead. The variables representing the
presence and severity of exterior deteriorating lead-based paint were only borderline
significant at the 0.05 level.
2. Measures of floor dust-lead loading from uncarpeted surfaces were better predictors
of blood-lead than measures of floor dust-lead loading from carpeted surfaces.
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3. Measures of dust-lead loading from window wells were better predictors of blood-
lead than measures of dust-lead loading from window sills.
4. Both measures of soil-lead concentration (Dripline & Play-Area) were strong
predictors of children's blood-lead concentration. Using Dripline soil Pb
concentration (n=186) allowed more children/houses to enter the model versus Play-
area (n=87).
5. Pica for paint chips was a significant predictor of blood-lead. Pica for soil was
borderline significant.
6. The indicator variable representing race (black) was the strongest single predictor of
blood-lead concentrations.
7. Age was not significantly associated with blood-lead in the Rochester data.
G5.2 DESCRIPTION OF JOINT MEDIA MODELS
(Development of a Multimedia Exposure Statistical Model)
After assessing the bivariate relationships with each variable under consideration, the
variables were systematically evaluated in an effort to develop a parsimonious multimedia
exposure model for each source of data. There were a number of technical issues involved in the
fitting of these models, including variable selection, collinearity among environmental exposure
variables, and details concerning the use of non-linear regression:
G5.2.1 Variable Selection and Collinearity
Variable selection for the multimedia exposure model was based on several properties,
including strength of relationship with blood-lead concentration as estimated using the bivariate
statistical models, predictive power of each variable when included into a model with competing
sources of lead exposure, and interpretability of the parameter estimates. Another goal related to
variable selection was to develop a predictive model that was based on lead exposure from the
three environmental media; paint, dust and soil. Thus, measures of lead exposure from paint,
dust, and soil were considered as primary variables hi the statistical analyses, and all other
variables were considered as secondary variables. If a secondary variable was competing with a
primary exposure variable in the multimedia exposure model (in terms of explaining variability
hi childhood blood-lead concentration), the secondary variable was excluded from the model in
its final form.
Another issue hi variable selection is the fact that the multimedia exposure models
included variables which represent lead-levels in paint, dust, and soil from each residential unit.
These measures tend to be correlated, and may result in meaningless parameter estimates when
jointly added to the same statistical model (i.e. the association between blood-lead and
environmental-lead might be estimated as negative for one or more sources of exposure hi the
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joint model). To avoid negative parameter estimates for lead exposure predictor variables, all
five candidate models were originally fitted using non-linear regression models with constraints
on the parameter estimates associated with exposure variables (the parameter estimates for these
variables were constrained to be greater than or equal to zero). Log-linear models with positive
parameter estimates for lead exposure predictor variables were later fitted using standard linear
regression models. The models occasionally converged to local maximums rather than the global
maximum likelihood solution, however, this problem was resolved by identifying improved
starting values for each model. Further discussion of collinearity diagnostics is presented in
Section G5.3 and Section G12.
G5.2.2 Multimedia Exposure Model Development
As discussed above, many combinations of variables were considered for the multi-media
exposure model. Section G13 presents details of statistical model fittings for four sets of
variables which met the variable selection criteria discussed above. The variable selection and
model development work resulted in the following general conclusions:
1. Measures of soil-lead concentration from the dripline, dust-lead loading from floors,
dust-lead loading from window sills, interior deteriorated lead based paint, pica for
paint, and race were consistent predictors of blood-lead concentrations. Window sill
lead loading appeared to compete with interior deteriorated lead-based paint as a
predictor of blood-lead concentration.
2. A reduced set of variables (including measures of lead in paint, dust and soil, race
and pica for paint) resulted hi statistical models which were able to explain roughly
40% of the variability hi children's blood-lead concentrations.
3. The log-additive model was outperformed by the other candidate models, as
indicated by log likelihood statistics presented in Section G13, largely due to a
saturation of the response at higher levels of environmental lead.
4. The Fpusre parameter in the Passive/Active Uptake model was consistently estimated
at or very close to zero. The Active Uptake model may therefore be a more
appropriate model (since it won't be over-parameterized).
5. The log-linear model consistently outperformed all other candidate models (with
the same variables) based on an evaluation of log likelihoods, as can be seen hi
Section G13.
Parameter estimates and associated standard errors of a series of four different multi-media
exposure models (each of which included a different set of predictor variables) are provided hi
Section G13. Each table in Section G13 contains the results of fitting all five candidate statistical
model forms to data from the Rochester Lead-in-Dust Study.
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G5.3 REGRESSION DIAGNOSTICS
This section describes the diagnostic analyses performed as part of development of the
multi-media predictive model using data from the Rochester Lead-in-Dust Study. Through the
use of regression diagnostics the adequacy of fit of the various candidate models developed to the
data observed can be determined, and model assumptions can be verified. For these models, the
following regression diagnostic procedures were performed:
1. A normal quantile plot of the residuals was created. The normal quantile plot
approximated a straight line indicating that residuals (errors) were approximately
normally distributed, as assumed.
2. Residual values were plotted versus predicted values. This scatterplot did not
indicate signs of nonconstant variance (if points spread out or tighten up as you
move from left to right) or nonlinearity (if points look quadratic or bow-shaped).
The scatterplot exhibited no pattern, indicating no such problems. Similarly, plots of
residuals versus predictors indicated no discernible pattern.
3. Cook's distance and DFFITS (both measures of influence) were plotted versus
studentized residuals (a measure of how far an observation deviates from the
modeled relationship) to indicate potential outliers - points with undue influence and
points lying far outside the model's prediction. These plots of Cook's distance and
DFFITS were produced only for the log-linear models, which were implemented
using standard linear regression, and identified no obvious outliers or influential
points.
4. For a closer examination of how points influence model parameter estimates, the
models were fit while excluding a single point at a time. Analysis of the coefficients
adjusted for their standard error (intercept, and coefficients of PbS, PbF, PbW and
PbP), including plots, again identified no major problems with influential data
points.
5. Partial regression leverage plots were created for the environmental measures of lead
exposure: dripline soil, floor dust from carpeted and uncarpeted floors, paint/pica
hazard, and window sill dust. A partial regression leverage plot that exhibits a strong
linear relationship between blood-lead and the variable under consideration is
indicative of a strong linear relationship between blood lead and the environmental
measure of lead exposure while controlling for all the other variables hi the model.
Partial regression leverage plots were produced only for the log-linear models, which
were implemented using standard linear regression, and indicated an adjusted
positive relationship for each lead exposure variable included hi the multi-media
predictive model.
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6. Partial R2 comparisons between predictor variables included in the model were
calculated. A high partial R2 indicates greater importance in predicting blopd-lead
concentration.
7. Estimated log-likelihoods were calculated using parameter estimates from each
model and the observed Rochester data, and the likelihood ratios between different
models were then assessed. The likelihood ratio (LR) is equivalent to the ratio of the
data's probability under one model compared to its probability under a second
model. The likelihood ratio evaluation consistently indicated that the log-linear
model provided the best fit to the data.
8. An analysis into the effects of collinearity using several methods was conducted
during the development of the multi-media predictive model. Estimates of the
tolerance statistic and the variance inflation factor associated with each predictor
variable in the model were calculated, along with a single value decomposition for
the design matrix of observed predictor variables hi the model. These analyses
suggested that the model did not suffer from a problem with collinearity.
The above regression diagnostics and tests of collinearity among explanatory variables for
the multi-media predictive model are provided hi detail in Section G12. Based on the regression
diagnostics on the multi-media predictive model it was concluded that:
• no influential or outlying points should be deleted from the analysis,
• the model developed fits the data observed,
• model assumptions are verified, and
• the model does not appear to suffer from a severe problem with collinearity.
G5.4 THE MULTI-MEDIA PREDICTIVE MODEL BASED ON ROCHESTER DATA
The criteria used for the selection of variables in the multi-media predictive model
emphasized use of measures of environmental lead and other factors observed hi both the
Rochester Lead-in-Dust Study and the HUD National Survey. Variables whose definition
provided a convenient translation when applied to the National Survey, whose predictive power
in Rochester were high, and whose spread in the National Survey populations covered a wide
enough range of values, were used in the empirical model. For example, the paint/pica variable
was chosen for use in the multi-media predictive model because it was a better predictor and
because application of the paint (75th percentile) variable in the HUD National Survey data
resulted hi a variable that provided very little discrimination between houses in the survey.
Another example is that although the variable Bare_flr was a stronger predictor of blood-lead
than the variable Floor_A hi the Rochester Study, Floor_A was a more appropriate choice for
construction hi the HUD National Survey, and was therefore selected for use in the multi-media
predictive model. Therefore, measures of lead hi soil, floor dust, window sill dust and the
paint/pica variable were chosen for use in the multi-media predictive model. The final
mathematical form of this model was:
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ln(PbB) =
ln(PbF)
ln(PbW)
ln(PbS)
PbP
where PbB represents the blood-lead concentration, PbF corresponds to measurements from
interior floor dust, PbW represents environmental lead from window sills, PbS represents soil-
lead, PbP represents paint hazard, and e represents the residual error left unexplained by the
model. Parameter estimates and associated standard errors, and measures of R-squared and the
residual standard deviation for the empirical model are provided in Table G-3. Note that the
parameter estimate associated with floor dust-lead loading was only borderline statistically
significant when considered jointly with the effect of window sill dust-lead loading (and other
exposure variables) in the multi-media predictive model.
Table G-3. Parameter Estimates and (Associated Standard Errors) for the Multi-Media
Predictive Model Based on Data from the Rochester Lead-in-Dust Study
Parameter :
Po
Pi
P2
Pa
P*
R2
o
Variable Description
Intercept
log (PbF): Area-Weighted Arithmetic Mean (Wipe) Dust-Lead
Loading from Any Floor (Carpeted or Uncarpeted)
log (PbW): Area-weighted Arithmetic Mean (Wipe) Dust-
Lead Loading from Window Sills
log (PbS): Dripline Soil-Lead Concentration (fine soil fraction)
PbP: Indicator of Interior Paint/Pica Hazard
Coefficient of Determination
Root Mean-Square Error (Residual Error)
E»dlllBEti|||l|p|
0.418
(0.240)
0.066
(0.040)
0.087
(0.036)
0.114
(0.035)
0.248
(0.100)
21.67%
0.56188
The above multi-media predictive model is used in the Section 403 Risk Assessment to
determine the probability that a child in the Rochester Study exposed to specific levels of lead in
paint, dust and soil will have a blood-lead concentration exceeding 10 ug/dL.
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G6.0 THE EMPIRICAL MODEL
The goal of the empirical model is to provide a relationship between blood-lead
concentration and various environmental lead exposures as measured in the HUD National
Survey for use in the Section 403 risk assessment. Unfortunately, the HUD National Survey
contains no information about blood-lead concentration. However, data from the Rochester
Lead-in-Dust Study (i.e. the multi-media predictive model) can provide a basis for the empirical
model. At issue is how to use the multi-media predictive model based on the Rochester data set
to develop an empirical model applicable to the data observed in the HUD National Survey.
Matters are complicated by the fact that the sampling methodology used to measure lead
exposures in HUD is different from that used in Rochester. Thus, some variables have a
different interpretation in each of these two studies. Specifically, two of the lead exposure
measurements in HUD are blue nozzle floor dust lead loading and blue nozzle window sill dust
lead loading, compared to floor wipe dust lead loading and window sill wipe dust lead loading in
Rochester. Another example is that the soil variable in Rochester was based on a composite
sample from the dripline area adjacent to the house, whereas in the HUD National Survey, the
soil variable was based on a weighted average of samples collected from dripline, entryway and
remote locations (with weights of 25%, 25% and 50%, respectively). Also the paint/pica hazard
predictor variable was constructed differently between the Rochester Study and the HUD
National Survey data. The primary difference was that the paint/pica hazard input variable from
the HUD National Survey data was based on the measures of paint on both interior and exterior
surfaces, whereas the variable used in Rochester for estimation of the effect of paint/pica hazard
was based on measure of paint on only interior surfaces. Lead based paint on deteriorated
exterior surfaces was not considered in the estimation of the paint/pica model parameter based on
Rochester data because approximately 84 percent of houses in the Rochester Study were built
prior to 1940 and as a result virtually every home surveyed in the Rochester Study had lead based
paint on exterior surfaces. Therefore, a paint/pica hazard variable which included presence of
exterior lead based paint in Rochester lost its statistical significance and its predictive power.
The differences in paint/pica variable construction between the Rochester and HUD National
Survey is considered minor in comparison to the differences in dust and soil sampling
methodologies. Table G-4 provides details comparing the construction and interpretation of
variables in both the Rochester Lead-in-Dust Study and the HUD National Survey.
The following statistical method was used to account for differences in dust and soil
sample collection methods between the Rochester Study and the HUD National Survey when
assessing the impact of 403 rulemaking on children's blood-lead levels. The method involves
establishing a relationship between blood-lead and environmental variables as measured by
methods used in the Rochester Study (i.e. the multi-media predictive model based on Rochester
Data), and then adjusting this relationship to use dust-lead and soil-lead variables as measured in
the HUD National Survey. The adjustment takes into account both systematic differences and
differences hi error structures between the Rochester wipe dust-lead and drip-line soil-lead
predictor variables versus the HUD National Survey Blue Nozzle dust-lead and averaged soil-
lead predictor variables. The method provides a relationship between blood-lead concentration,
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Table G-4. Variable Construction in the Rochester Lead-in-Dust Study and the HUD
National Survey
Predictor
Variable
Rochester Study
HUD National Survey Input Variables
Soil
Natural log transformation of
dripline soil-lead concentration (fine
soil fraction).
The natural log transformation of the weighted
average of dripline, entryway and remote soil-lead
concentrations, with weights of 25%, 25% and 50%
respectively when all three soil samples were
collected. If these values were missing, an imputed
value1 was used.
Floor Dust
The natural logarithm of the area
weighted arithmetic average (wipe)
dust-lead loading from carpeted
and uncarpeted floors.
The natural logarithm of the area-weighted arithmetic
average dust-lead loading (Blue Nozzle Vacuum) from
3 sample locations (wet, dry and entry rooms) was
used as the measure of lead in dust. If the dust-lead
loadings from all of the 3 sample locations were
missing, an imputed value1 was used.
Window Sill
Dust
The natural logarithm of the area-
weighted arithmetic average (wipe)
dust-lead loading from window
sills.
The natural logarithm of the area-weighted arithmetic
average dust-lead loadings (Blue Nozzle Vacuum) from
window sills from 2 sample locations (wet and dry
rooms). If the window sill dust-lead loadings from
both sample locations were missing, an imputed
value1 was used.
Interior
Pica/Paint
An indicator variable which was
nonzero when the following
conditions each existed in a
residential unit: presence of
deteriorated or damaged interior
paint; presence of interior lead-
based paint; and presence of a
child with paint pica. The paint
variable had values of:
0 No LBP (XRF reading < 1),
or condition* is Good, or
child does not exhibit pica;
1 LBP (XRF reading * 1),
condition is Fair or Poor, and
child exhibits pica rarely;
2 LBP (XRF reading * 1),
condition is Fair or Poor, and
child exhibits pica at least
sometimes.
HUD National Survey homes were determined to have
deteriorated LBP whenever there is any deterioration
in interior or exterior lead-based paint, as measured
by square footage (that is, square footage of
deteriorated LBP surface > 0). That is, the LBP
indicator was defined as
1 Whenever square footage of surface exhibiting
deteriorated LBP (interior and exterior) > 0
0 Otherwise
The pica factor was only considered for houses with
deteriorated LBP. In these houses, it was assumed
that 9% of U.S. children aged 1-2 years have pica for
paint. For the children with pica for paint, the pica
value was defined to be 1.5".
1 Imputed values for dust and soil were based on a presence of LBP indicator variable and on a house age-
specific indicator. The presence of LBP indicator was defined as:
0 Predicted maximum XRF < 1 for both interior and exterior samples
1 Predicted maximum XRF 2 1 for either interior or exterior samples.
The house age-specific indicator had categories: Pre-1940, 1940-1960, 1960-1979, Post-1979. The
imputed values for dust and soil were constructed by taking the means for the associated subsets formed by
crossing the paint and age of house categories.
* Condition of the paint in the Rochester Lead-in-Dust Study is described in Table G-2.
b The Paint/Pica Hazard Variable was described in Table G-2. A value of 1.5 was chosen as the input value
for those children exhibiting pica in applying the empirical model to the HUD National Survey.
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floor and window sill dust-lead loadings, soil-lead concentrations, and other covariates as
observed in the HUD National Survey. An errors in variables measurement error adjustment is
applied as an intermediate step in reaching this goal. The method for adjusting the multi-media
predictive model may be described as follows, and is provided with complete detail in
Appendix Gl.
The first step involves fitting an errors in variables measurement error adjusted multi-
media exposure model that assumes blood-lead concentration is a function of true unobserved
floor and window sill dust-lead loadings and dripline soil-lead concentrations along with other
covariates (paint/pica hazard) used in the model. While the dependence of blood-lead
concentration on true dust-lead loadings, dripline soil-lead concentrations, and other covariates
can not be observed, they can be estimated via equations (2.2.12) and (2.2.16) hi Fuller, 1987.
In order to use these equations for estimating this relationship, the measurement error associated
with each particular dust-lead loading and soil-lead concentration must be obtained. This is
achieved by taking individual measurements of dust-lead loadings and soil-lead concentrations
within households and calculating their variability. The average of all within household
variances is then used as an estimate of the true measurement error associated with each
particular dust-lead loading and soil-lead concentration. The estimated measurement errors are
then used to calculate parameter estimates for a model based on Rochester data that relates
blood-lead concentration to true dust-lead loadings, dripline soil-lead concentrations, and other
covariates (paint/pica hazard). Keep in mind that the model must be developed using Rochester
data because there is no blood-lead concentration variable in the HUD data set.
If the goal had been to identify the nature of the dependence of blood-lead concentration
on true floor and window sill dust-lead loadings, dripline soil-lead concentrations, and the other
covariates, then the adjustment described above would have been all that was required.
However, the relationship of interest is blood-lead concentration as a function of floor and
window sill dust-lead loadings, average soil-lead concentrations, and other covariates (paint/pica
hazard) as observed in the HUD National Survey. Therefore, adjusting for measurement error is
only the first step toward a final solution to this problem.
The next step in this process is to define the relationship between blood-lead
concentrations, observed dust-lead and soil-lead predictor variables as measured hi both
Rochester and HUD, dust-lead and soil-lead predictor variables measured without error on the
scale of measure used hi Rochester, and any other covariates (paint/pica hazard) hi the
multimedia exposure model. It is assumed that these random variables jointly follow a
multivariate normal distribution. Standard statistical theory then allows for deriving the
distribution of blood-lead concentration conditioned on floor and window sill dust lead loadings,
average soil lead concentrations, and other covariates as measured in HUD. Estimates of the
parameters for a multimedia exposure model that relates blood-lead concentration to lead
exposures as measured hi the HUD National Survey are obtained from this conditional
distribution.
The final step in developing the empirical model was to derive an estimate for the
intercept. The empirical model intercept was designed to calibrate the model so that the
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predicted national (pre-403) geometric mean blood-lead concentration obtained from applying
the empirical model to data observed in the HUD National Survey equals the geometric mean
blood-lead concentration estimated in Phase 2 of NHANES ffl.
The empirical model involves an adjustment to the multi-media predictive model based
on the Rochester Study to allow use of Blue-Nozzle dust-lead loadings rather than wipe dust-lead
loadings and average soil-lead concentration rather than dripline soil-lead concentration. The
final mathematical form of this model is:
ln(PbB) =
ln(PbFBN)
ln(PbWBN)
ln(PbS)
PbP
where PbB represents the blood-lead concentration, PbFBN and PbWBN correspond to dust-lead
loading from interior floors and window sills respectively (for samples collected in the HUD
National Survey with the blue nozzle vacuum), PbS represents average soil-lead concentration,
PbP represents paint/pica hazard, and e represents the residual error left unexplained by the
model. Table G-5 provides parameter estimates and associated standard errors for the empirical
Model developed to predict the national distribution of children's blood-lead concentrations
using data as observed in the HUD National Survey. The standard errors provided in Table G-5
were estimated using a Bootstrap Algorithm which is detailed in Section G10.4.
Table G-5. Parameter Estimates and Associated Standard Errors for the Empirical Model
used to Predict the National Distribution of Children's Blood-Lead
Concentration Based on Data from the HUD National Survey
.::::::::::, :'.-,,:",, /Variable
Intercept
Floor Dust-Lead Loading
(Blue Nozzle Vacuum)
Window Sill Dust-Lead Loading
(Blue Nozzle Vacuum)
Average Soil-Lead Concentration
Paint/Pica Hazard
Error
Parameter
3o
P,
P2
P3
P*
OSmx
Estimate
(Standard Error)
0.650
(0.154)
0.032
(0.044)
0.050
(0.031)
0.094
(0.043)
0.256
(0.098)
0.313
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G7.0 ESTIMATING THE NATIONAL DISTRIBUTION OF BLOOD-LEAD USING THE
EMPIRICAL MODEL
As stated previously, the empirical model will be used in the Risk Assessment to predict a
national distribution of children's blood-lead concentrations both before and after interventions
resulting from the Section 403 standards. A nationally representative sample of environmental
conditions in housing is required as input to the empirical model to predict a national distribution
of children's blood-lead concentrations. The HUD National Survey is a nationally representative
study which assessed environmental lead-levels in paint, dust and soil in residential housing.
Environmental conditions observed in the HUD National Survey were used as input to the EPI
model for predicting blood-lead levels in children 1-2 years old. A population of children aged
1-2 years is both the target age group for EPA's Risk Assessment, and the age group that was
recruited in the Rochester Lead-in-Dust Study (thus the empirical model is representative of
children in this age group). The empirical model is used to estimate an average log-transformed
childhood blood-lead concentration associated with each home in the HUD National Survey.
As noted in Table G-5, the variables used for prediction are average soil-lead
concentration, blue-nozzle vacuum dust-lead loading on floors (carpeted or uncarpeted), blue-
nozzle vacuum dust-lead loading on window sills, and an indicator of paint/pica hazard. These
variables, constructed from observed levels of lead in each HUD National Survey residential
unit, are used as input to the empirical model for predicting the pre-403 national distribution of
children's blood-lead concentrations.
To predict a post-403 national distribution of children's blood-lead concentrations, the
following method was used to prepare the HUD National Survey Data for input into the
empirical model:
[1] Observed levels of lead in environmental variables in the HUD National Survey
were compared to proposed section 403 standards. Blue-nozzle vacuum floor and
window sill dust-lead loadings were converted to wipe dust-lead loadings before
comparison to the 403 standards.
[2] Section 403 interventions were triggered in HUD National Survey residential
units that had levels of lead in environmental variables that were above the
proposed standard. If an intervention was triggered, assumed post-intervention
lead levels in environmental variables were substituted for observed levels
according to the Section 403 risk assessment assumptions. Post intervention dust-
lead levels that were specified in terms of wipe dust-lead loadings were converted
to a blue nozzle vacuum scale for use in the prediction.
The distribution of blood-lead concentrations associated with each home was
characterized by assigning a geometric mean (predicted by the empirical model) and a geometric
standard deviation. A geometric standard deviation of 1.6 was assumed for the distribution of
blood-lead concentrations associated with each home. The default geometric standard deviation
of blood-lead concentrations for children at similar environmental-lead levels for the IEUBK
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model is 1.6 and the estimated variability from the multi-media predictive model based on the
Rochester Data was 1.76 as measured by the exponentiation of the root mean square error. Thus,
a population of children (aged 1-2 years) associated with environmental lead levels found at each
home in the HUD National Survey was constructed using the geometric mean blood-lead
concentration predicted by the empirical model, an assumed geometric standard deviation of 1.6,
and population weights based on the 1993 American Housing Survey adjusted to 1997.
The predicted national distribution of blood-lead concentrations can be characterized
using a geometric mean and a geometric standard deviation. The predicted national geometric
mean is calculated by taking a weighted geometric mean of the empirical Model predicted blood-
lead concentration associated with each home in the HUD National Survey, using the adjusted
weights for 1997. The predicted national geometric standard deviation is calculated by taking the
square root of the sum of the predicted between-house variability and the assumed within-house
variability. The predicted between-house variability is estimated as a weighted geometric
variance among the empirical Model predicted blood-lead concentration associated with each
home in the HUD National Survey, using the adjusted weights for 1997. Thus, the between-
house variability represents the variability among the predicted blood-lead concentrations
associated with the environmental conditions observed in each home in the HUD National
Survey. The assumed within-house variability was (1.6)2, and represents the expected variability
among children who are exposed to similar environmental conditions. The predicted national
geometric standard deviation relies on an assumption that the between-homes distribution of
blood-lead concentration is log-normally distributed.
The predicted national distribution of children's blood-lead concentrations can also be
characterized using exceedance percentiles (i.e. the percentage of children estimated to have
blood-lead concentrations above a specified level, such as 10,20 and 30 |ig/dL). These
exceedance proportions were calculated in two ways, first by using normal probability theory
combined with the estimated national geometric mean and standard deviation, and second by
empirical evaluation of a national population built by summing discretized populations of
children associated with each home.
The second approach is robust to deviations from the assumed log-normal distribution of
blood-lead concentrations between homes, and can be described as follows:
A distribution of blood-lead concentrations is constructed for each home using the
empirical Model predicted geometric mean and the assumed within house geometric standard
deviation of 1.6. Each of these distributions are then partitioned into seven discrete blood-lead
intervals. Table G-6 provides the specific method for partitioning a distribution of log blood-
lead concentrations into the seven intervals about the log of the geometric mean (predicted from
the empirical model). Figure G-2 graphically illustrates this partitioning. The two tails of the
distribution represent log blood-lead concentrations below or above 2.5 standard deviations from
the mean, respectively. The percentage of the distribution assigned to each of these intervals,
0.62%, is based on the area under a standard normal curve for z-values less than -2.5 hi the
lower tail or greater than 2.5 hi the upper tail. The assigned log blood-lead concentration for the
lower tail is the expected value of a standard normal random deviate lying hi the interval from - °°
G-39
-------
to -2.5; the assigned log blood-lead concentration was similarly chosen for the upper tail, and
mid-points were used for the finite-length intervals. The assigned blood-lead concentration for
each interval was obtained by exponentiating the assigned log blood-lead for the interval. For
example, for the lower tail,
-2.82x0
-2.82=.
GM
GSD282
Table G-6. Allocation of Blood-Lead Distribution to Seven Intervals
Log Blood-Lead Concentrations ^
Interval for tog Hood Lead'
l-~, u - 2.5 * 0]
U/-2.5 * a,u- 1.5 *o]
fy-1.5 *0,Af-0.5 * 0]
[//-0.5 * o.fj + 0.5 • o]
[// + 0.5 • a.u + 1.5 * a]
U/ + 1.5 • o,/j + 2.5 * o]
U/ + 2.5 * 0, + -]
Percentage of
Distribution in interval
0.0062
0.0606
0.2417
0.3830
0.2417
0.0606
0.0062
Assigned tog Hood
Lead for interval
H - 2.82 • 0 b
U - 2.00 • 0
// - 1 .00 • 0
V
U + 1 .00 • 0
fj + 2.00 • o
U + 2.82 • 0 c
-.
Awigntd Hood-L«ad
Concentration for
interval
GM/IGSD2-82]
GM/[GSD2-°°]
GM/IGSD1-00]
GM
GM'IGSD100]
GM"[GSD200]
GM*[GSD2-82]
' Blood-lead concentrations were assumed to have a log-normal distribution with the geometric mean (GM)
predicted by the empirical model and a geometric standard deviation (GSD) of 1.6 (the default geometric
standard deviation for the IEUBK model). The distribution of log blood-lead concentrations was assumed to
be normal with mean fj given by log(GM) and standard deviation o given by log(GSD = 1.6).
b The expected value of a normal random deviate known to lie in the interval [-*>, -2.5] is -2.82.
c The expected value of a normal random deviate known to lie in the interval [2.5,+ °°] is +2.82.
For this lower tail, if N children were associated with the specific housing condition (according
to weights in the 1993 American Housing Survey adjusted to 1997) then 0.62 percent of the N
children were assigned a blood-lead concentration of GM/GSD282. The remaining 99.28 percent
were similarly assigned to the other blood-lead concentrations presented in Table G-S using the
percentages given in the second column of the table. In this manner, the distribution of blood-
lead concentrations of the N children were allocated to a distribution of blood-lead
concentrations centered around the GM predicted by the empirical model with a GSD of 1.6.
The predicted distributions at each housing condition were men combined to generate a
distribution of childhood blood-lead levels over all of the housing conditions present hi the HUD
National Survey.
G-40
-------
y •* •< "* •< "*•»•< ^ ^
Distribution of Log(Blood-lead levels)
Figure G-2. Distribution of Blood-Lead Levels About Geometric Mean on
Logarithmic Scale.
The exceedance percentiles can then be assessed by empirically tabulating the proportion
of children hi this constructed distribution who are above the target blood-lead concentrations of
10,20 and 30 ug/dL.
G7.1 RESULTS OF THE COMPARISON WITH NHANES III
The predicted distribution of blood-lead concentrations obtained by applying the
empirical model to the HUD National Survey Data was compared to NHANES m as a check on
how well the empirical model performed. Table G-7 contains characteristics of the predicted
blood-lead distribution for the empirical model, including estimates of exceedance proportions
(the estimated proportion of blood-lead concentration exceeding 10,20 or 30 ug/dL), the
geometric mean, and the geometric standard deviation. Results in Table G-7 for the NHANES
HI distribution, the distribution of children recruited into the Rochester Lead-in-Dust Study, and
the predicted national distribution based on applying the empirical model to data from the HUD
National Survey (both before and after Section 403 interventions take place) are presented first
with exceedance proportions calculated from the discretized distribution and second for
exceedance proportions calculated assuming a log-normal distribution with the calculated
geometric mean and geometric standard deviation.
G-41
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Table G-7. Predicted National Distribution Characteristics for Empirical Model Compared
to Rochester and NHANES III
Predicted
Model Results
National Geometric Mean
National Geometric
Standard Deviation
Discretized Distribution
Exceedance Percentiles
(% of Population *
10, 20&30/yg/dL)
Log-Normal Distribution
Exceedance Percentiles
(% of Population *
10, 20&30*/g/dL)
: Parameter
fp
Op
% k10//g/dL
% *20 /yg/dL
% *30//g/dL
% *10//g/dL
% *20;/g/dL
% 2 30 /yg/dL
Pre-lnterventtan
: Blood-lead Levate
NHANES
IB
3.14
2.09
5.88%
0.43%
0.07%
5.75%
0.59%
0.11%
Rochester
Study
6.36
1.85
22.90%
2.90%
1.00%
23.10%
3.13%
0.01%
Empirical
Modal
3.14
1.71
0.00%
0.00%
0.00%
1.54%
0.03%
0.0013%
Post-Intervention
BJood-lead Levels1
Empirical
Model
3.03
1.67
0.00%
0.00%
0.00%
1.00%
0.01%
0.0004%
1 For illustration of a calculation of a post-intervention blood-lead distribution, standards were set at: 100/ig/ft2 for floor
dust-lead loading (wipe), 500 jig/ft2 for window sill dust-lead loading (wipe), 2000 fjg/g for soil removal, 5 ft2 damaged
LBP for paint repair, and 20 ft2 damaged LBP for paint abatement. Post-403 lead levels for homes that were above the
standard were adjusted to 401/g/ft2 for floor dust-lead loading (wipe), 100|/g/ft2 for window sill dust-lead loading
(wipe), 150 t/g/g for soil removal, and 0 ft2 damaged LBP for paint repair or abatement.
The results of the comparison with NHANES HI for the revised empirical model indicate:
• The national geometric mean blood-lead concentration (pre-intervention) was
calibrated to the geometric mean reported in NHANES HI.
• The variability in the national distribution of blood-lead concentration predicted by
the empirical model using the HUD National Survey (pre-403) is estimated at 1.71
(GSD), in contrast to a GSD of 2.09 for NHANES m.
• The estimated proportions of blood-lead concentrations of at least 10,20, or 30
ug/dL using the empirical model predictions are much lower than the corresponding
proportions estimated by NHANES HI.
It should also be noted that NHANES in itself is only an estimate of the true national distribution
of blood-lead concentrations (pre-403), and that an "exact" match of NHANES HI does not mean
an exact match of the true national distribution, nor does it guarantee that the model is
appropriate for predicting a post-403 national distribution.
G-42
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G8.0 DISCUSSION
The primary limitation associated with the Rochester Study is concern over the' degree to
which the Rochester Study may be considered representative of the nation as a whole.
Differences between the Rochester Study population and the national population include the
following:
a. Almost one-quarter (22.9%) of the Rochester children had observed blood-lead
concentrations above 10 jig/dL, whereas only 5.9% of children aged 1-2 years
nationwide were estimated to have blood-lead concentrations above 10 (ig/dL by
Phase 2 of NHANES m.
b. The geometric mean blood-lead concentration in Rochester is 6.4, whereas the
geometric mean blood-lead concentration nationwide as estimated by NHANES m is
3.1. The GSD for Rochester is 1.9, compared to 2.1 for NHANES m.
c. Approximately 84 percent of the housing included in the Rochester Study was built
prior to 1940, and there is a well documented relationship between age of housing
and presence of lead-based paint. Only approximately 20% of housing nationwide
was built prior to 1940.
d. Approximately 40% of the sample of children in the Rochester Study were African
Americans, compared to an estimated 13% of the population of children nationwide
(from 1997 US Census Projections), and compared to approximately 7% in the HUD
National Survey.
e. Environmental levels of lead in soil in the Rochester Study were higher than would
be expected in the HUD National Survey. For example, the geometric mean dripline
soil-lead concentration in the HUD National Survey was approximately 75 ppm
whereas the Rochester geometric mean was approximately 730 ppm.
f. Subjects recruited into the Rochester Study represent children whose primary
exposure to lead was from dust, soil and paint at the primary residence. Children
whose parents had lead exposure, who spent time away from the home, or whose
homes underwent renovation or remodeling were excluded from the study. Only 376
of 1,536 families were eligible to participate in the study after the initial telephone
screening. The selection criteria utilized in the Rochester Study may have resulted hi
a biased sample of children, since children who had potential lead exposure outside
of the primary residence were excluded.
The difference hi the observed blood-lead distributions between the Rochester Study and
NHANES HI is illustrated in Figure G-3. Although there are limitations associated with the
Rochester Study, there are also positive aspects of the study that recommend its use:
G-43
-------
100.0-
KXO-
1.0 -
0.1
NHANES III
White
and Other
Rochester
White
and Other
NHANESI
Black
Rochester
Black
Figure G-3. Box Plot of Blood-lead Concentrations for Children Aged 1-2 Years for
Phase II of NHANES III versus Rochester Data Sets.
a. all media, locations, and surfaces that are being considered for Section 403 standards
were measured for lead in the Rochester Study.
b. the Rochester Study includes dust-lead loadings from wipe sampling and the Section
403 dust standard is expected to be based on dust-lead loading from wipe sampling.
c. the selection of homes and children in the Rochester Study, although targeted, was
more random and more representative of a general population than is the case with
most recent epidemiological studies of lead exposure in non-smelter communities.
The ability of an empirical model to predict the national distribution of blood-lead
concentrations following Section 403 lead hazard reduction activities may be most severely
limited by factors that are not included in the model. Reflecting its use in the Section 403 Risk
Assessment, the empirical model accounts only for factors related to environmental lead
G-44
-------
exposures at the residence, and does not account for other factors that might affect childhood
blood lead. Such factors that may affect children's blood-lead concentration but may not be able
to be controlled by the Section 403 rule include:
(1) home and personal cleaning habits,
(2) diet and nutritional status,
(3) bio-availability of the lead found in residential environmental media,
(4) non-residential exposures,
(5) inhalation exposure,
(6) children's behavior,
(7) socio-economic factors,
(8) renovation and remodeling (R&R) activity,
(9) hobbies,
(10) occupation.
Finally, it should be noted that the empirical model contains variables that differ from
variables created for a best-fit of the Rochester data, because the goal of the empirical model was
to provide a basis for using measures of lead from the HUD National Survey to predict a national
distribution of childhood blood-lead concentrations. In particular, the empirical model differs
from the multimedia regression model used to characterize the dose-response relationship
between environmental-lead and blood-lead.
G-45
-------
G9.0 REFERENCES
See Chapter 7 of Volume I for references cited within this appendix.
G-46
-------
G10: Appendix on Methodology for Adjusting for
Different Sampling Methods
G-47
-------
Statistical Details
Section G10 of Appendix G is comprised of four sections that describe the statistical
details associated with the Empirical Model. Section G10.1 explains statistical methodology
used to account for differences in sample collection methods used in the Rochester Lead-in-Dust
Study and the HUD National Survey. Section G10.2. describes the classic errors hi variables
regression model. Section G10.3 provides details on the estimation of variance components used
as input to the above two statistical models. Finally, Section G10.4 explains the bootstrap
algorithm used for approximating the standard errors associated with parameter estimates of the
model that accounts for differences in sampling methods.
G10.1 STATISTICAL ADJUSTMENTS TO ACCOUNT FOR DIFFERENCES IN
SAMPLE COLLECTION METHODS USED IN THE ROCHESTER LEAD-IN-
DUST STUDY AND THE HUD NATIONAL SURVEY
The goal of this section is to provide a statistical methodology for adjusting the multi-
media predictive model to appropriately use environmental lead levels observed in the HUD
National Survey as inputs to the model. The adjustment takes into account both systematic
differences and differences hi error structures between the Rochester predictor variables and the
HUD National Survey predictor variables. The method provides a relationship between blood-
lead concentration and a set of lead exposure variables and other covariates as they were
measured in the HUD National Survey. As an initial overview the method may be described as
follows. Assume:
Y represents children's blood-lead levels,
R represents wipe dust lead loading observed in the Rochester Study,
H represents blue nozzle dust lead loading observed hi the HUD National Survey,
and
C represents covariates of interest which appear both in the Rochester Study and
in the HUD National Survey.
The density of interest is children's blood lead levels as a function of lead exposures
measured hi the HUD National Survey, namely
Fmc(y|h,C)= J Fyp^Cylr&C) •FR|HtC(r|h,C) .
Given that we do not have a source of data with Y,R,H and C observed simultaneously,
the method used for estimating Fmc(y|h,C) is:
= / Fy|x,c(ylx»c) •Fxp.cCxIkQ where x is a latent variable that
represents dust lead loading
measured without error.
G-48
-------
This method assumes that Y can be modeled as a function of X using an errors-in-variables
approach.
Details of the method are provided in the following subsections. Section Gl 0.1.1
presents the methodology for the specific case of an errors-in-variables adjustment of a single
covariate. This section is provided to aid in the understanding of the theoretical development of
the model parameters. Section G10.1.2 presents the methodology for the general case of an
errors-in-variables adjustment of one or more covariates. The Empirical model involves an
errors-in-variables adjustment of three covariates: floor wipe dust lead loading, window sill wipe
dust lead loading, and drip-line soil lead concentration. Thus, the Empirical model parameter
development follows the methodology detailed in Section G10.1.2.
G10.1.1 MODELING BLOOD-LEAD AS A FUNCTION OF ONE VARIABLE MEASURED
WITH ERROR AND OTHER SELECT COVARIATES.
The following theoretical development of the Empirical model parameters is specific to
an errors-in-variables adjustment of a single covariate. Details are given for this specific case for
two reasons:
1. The original theory was developed in this context.
2. The theoretical development is easiest to follow for a single variable adjustment.
In general, the theory applies to errors-in-variables adjustments for any number of covariates in
the model. Section Gl0.1.2 below uses matrix notation to present the general theoretical details,
which includes as a special case the errors-in-variables adjustment of a single covariate.
Definitions and Assumptions
Define the following variables:
Y = The response variable, log of blood-lead concentration.
R = Log of the area weighted arithmetic mean of the floor wipe dust lead loading as
observed and measured in the Rochester Lead-in-Dust Study.
H = Log of the area weighted arithmetic mean of the blue nozzle floor dust lead
loading as observed and measured in the HUD National Survey.
X = Log of the "true" unobserved area weighted arithmetic mean floor wipe dust lead
loading (measured without error).
C = A vector (or scalar) of remaining covariates used as independent variables. For
the model detailed in this section, which adjusts for the measurement error in
floor wipe dust lead loading only, C is a vector consisting of the variables drip-
line soil lead concentration and paint/pica hazard. These covariates are assumed
to be measured using identical methods hi the Rochester Lead-in-Dust Study and
the HUD National Survey.
The model assumes
G-49
-------
(A)
Mr
Me
J VY v u/-
sc
°x axc
(B)
> °»vir,c)
and all errors are independent of one another.
The parameters cc^c, Pypc(C)» an<^ Pvicpo represent the intercept and slopes, respectively,
associated with a regression of Y on X(unobserved) and C; and o^c is the variability in Y
unexplained by X and C. o2^ is the measurement error associated with wipe floor dust lead
loading in the Rochester Study, o2^ is the measurement error associated with blue nozzle
vacuum floor dust lead loading in the HUD National Survey, cc^ represents a location shift in
the distribution of H relative to the distribution of X. Similarly, P^ represents a scale shift in
the distribution of H relative to the distribution of X. a^ and P^ are the intercepts and slopes,
respectively, associated with a regression of X on the covariates hi C. o2^ represents the
variability hi X unexplained by the covariates in C.
In addition, the calculations that follow rely heavily on the assumption that the
conditional distribution of X given C(X\C)is the same hi the Rochester Lead-in-Dust Study and
the HUD National Survey. This assumption will be referred to as an assumption of
transportability.
Parameter Development
Using assumption (A) of Section Gl 0. 1 . 1 , normal distribution theory implies that Y
conditioned on H and C is normally distributed with the following parameters:
G-50
-------
2 2
HC
-1
'Y\H,C~VY
2 2
OH OHC
-i
Qyf
Qw
Solving the inverse matrix above and using assumption (B) of Section Gl 0.1.1 for
substitutions yields:
"7 9
2 2
2 _ 2
x\c+aH\x
Using (B), observe that
(Q
where the left-hand side of (C) represents the portion of o^ that remains after conditioning on C.
From (C),
P
Y\H(Q
v
1-
G-51
-------
0
'y\c(X)
jqc
and
°Y\H,C ~ °y\x,c'
2 2
°H\X °A)
2 «2
°nrc + Pywn
Zp\,l^ I /|/\^^«^
2 2
"fllAT °A]C
k °WIC >
The equations above provide formulas for the slope parameters and the variance of the
model. The remaining model parameter to be considered is the intercept, a^c, which can be
expressed as a function of the slope parameters derived above and the mean of the variables Y,
H, and C. The formula for the model's intercept is as follows:
G10.1.2 MODELING BLOOD-LEAD AS A FUNCTION OF ONE OR MORE VARIABLES
MEASURED WITH ERROR AND OTHER SELECT COVARIATES.
Definitions and Assumptions
In the notation that follows, matrices are indicated by bold capital letters and vectors are
indicated by underlined letters. Also, squares and square roots of the elements of diagonal
matrices are written as the matrix raised to a power(e.g., A2 or A1/2).
Define the following variables:
Y = The response variable, log of blood-lead concentration.
R = A vector (or scalar) of observed Rochester Lead-in-Dust Study covariates
measured with error (for the Empirical model this vector consists of the log of
the area weighted arithmetic mean of floor wipe dust lead loading, the log of the
area weighted arithmetic mean of window sill wipe dust lead loading, and the log
of the drip-line soil lead concentration).
G-52
-------
(A)
H = A vector (or scalar) of observed HUD National Survey covariates measured with
error (for the Empirical model this vector consists of the log of the area weighted
arithmetic mean of floor blue nozzle vacuum dust lead loading, the log of the
area weighted arithmetic mean of window sill blue nozzle vacuum dust lead
loading, and the log of the average soil lead concentration).
X = A vector (or scalar) of unobserved covariates measured without error (for the
Empirical model this vector consists of the "true" unobserved log of the area
weighted arithmetic mean of floor wipe dust lead loading, the "true" unobserved
log of the area weighted arithmetic mean of window sill wipe dust lead loading,
and the "true" unobserved log of the drip-line soil lead concentration).
C = A vector (or scalar) of remaining covariates (for the Empirical model this
variable is the scalar paint/pica hazard). These covariates are assumed to be
measured using identical methods in the Rochester Lead-in-Dust Study and the
HUD National Survey.
The model assumes
4
N
-
YX
(B)
For a random sample of size N generated from the distribution in (A):
2
Vc -
H[X
and all errors are independent of one another.
G-53
-------
The parameters a^^c, ^ypc(c)>an<^ fivicpg represent the intercept and slopes, respectively,
associated with a regression of Y on X(unobserved) and C; and o^c is the variability in Y
unexplained by X and C. A^ is a p, by p, diagonal matrix with ith diagonal element equal to
o^Ripci' the measurement error associated with the ith covariate in Rochester measured with error.
AHJX is defined analogously for HUD. The ith element of the p, by 1 vector o^ represents a
location shift in the distribution of the ith variable in H relative to the distribution of the ith
variable in X. Similarly, B^ is a p, by p, diagonal matrix with ith diagonal element representing
a scale shift hi the distribution of the ith variable in H relative to the distribution of the ith
variable hi X. The p, by 1 vector o^ and the p2 by p, matrix B^ are the intercepts and slopes,
respectively, associated with a regression of X on the covariates hi C. A^ is a diagonal matrix
with ith diagonal element equal to the variability hi the ith element of X unexplained by the
covariates hi C.
In addition, the calculations that follow rely heavily on the assumption that the
conditional distribution of X given C (X\Q is the same in the Rochester Lead-in-Dust Study and
the HUD National Survey. This assumption will be referred to as an assumption of
transportability.
Parameter Development
Using assumption (A) of Section Gl 0.2.1,normal distribution theory gives the following
result for the conditional distribution of Y given H and C:
r,C ' °F|/f,c) ; Wnere>
HH
CC
-1
cJ
and
-1
2
S//c Sc
Solving for the inverse above and using (B) for substitutions gives:
V +
*A]C
V)"1 (V
H
1CJ
and
-1
G-54
-------
Upon substituting the equality A = RJ^ Ac + A into the equation above,
assumptions (A) and (B) yield the following slope and variance estimates for the Empirical
model:
and
= °Y\X,C +
Finally, the formula used to estimate the Empirical model's intercept is given by:
G10.1.3 PARAMETER ESTIMATION
Sections G10.1 and G10.2 above provide equations for the model parameters after
adjusting for differences between sample collection methods in the Rochester Lead-in-Dust
Study and the HUD National Survey. Each variable appearing in the above equations first must
be estimated hi order to obtain the final estimates of the Empirical model parameters. The
following text describes the methodology used to estimate the variables that appear in the final
Empirical model formulas of Section Gl 0.2.2. Note that all the variance components described
below are provided hi Table Gl 0. 1 .
In the discussion that follows, all estimates for parameters from the HUD National
Survey are weighted estimates. The weights correspond to the 1993 American Housing Survey
adjusted to 1997. Weights are used because the HUD National Survey is designed to be
nationally representative and each observation hi HUD is weighted with respect to the population
it represents.
Estimation of Parameters Used in Deriving the Empirical Model Slopes and Variance
For estimating the parameters fiypc(C)» &YIC(X)> an<^ °2Ypc,c» a classic errors-in-variables
model is applied to the Rochester data. The application of this model requires an estimate of the
true measurement errors associated with the elements of R(i.e., A^. For further detail on the
errors-in-variables model and the estimation of measurement errors associated with both R and H
(i.e., ARJX and A, see Sections 2 and 3 below.
G-55
-------
The ith diagonal element of A^ and A^ is estimated by the mean squared error from a
least squares regression of the ith element of R on the covariate vector C hi Rochester and the
mean squared error from a weighted least squares regression of the ith element of H on the
covariate vector C in HUD, respectively. For example, in the Empirical model, the first diagonal
element of A^ is estimated by the mean squared error from the least squares regression of log
floor wipe dust lead loading on paint/pica hazard in the Rochester data set.
Using assumption (B) from Section 1.2.1 along with the assumption that all errors are
independently distributed yields
The estimate of A^ is derived easily from the second equality given above. Using both
equalities above, B^ is estimated as
VKV- VXV- V)"1]"2-
Since X is a latent variable, the parameter B^ cannot be observed. However, from
assumption (A) in Section 1.2.1,
So, Bjqc is estimated by B^, which is obtained from a least squares regression of R on the
covariate vector C hi Rochester.
Estimation of Parameters Used in Deriving the Empirical Model Intercept
Estimates of the slope parameters, ^YIHCQ an(^ £YIC follow from Section Gl- 1.3.1 above.
The mean parameters, u^ and u^, are estimated by weighted means of H and C, respectively, as
observed hi the HUD National Survey. Unfortunately, Y is not measured hi the HUD National
Survey; therefore, UY can not be estimated directly from HUD data. As a result, using the
intercept formula given hi Section G10.1.2 requires an alternative estimate of UY.
Given the intent of the Empirical model, the alternative estimate that is used for uy is the
mean of the log of blood-lead concentration hi the NHANES in data set. This decision was
arrived at for the following reasons:
(1) NHANES ID data provide a perfectly legitimate estimate of UY, the national mean of
log(blood-lead concentration), with the added appeal of guaranteeing the model's
predicted national mean equals the targeted national mean.
G-56
-------
(2) The only other sensible estimate of |aY, the sample mean from the Rochester study,
may be a poor estimator since the distribution of covariates in Rochester is different
from the distribution of covariates in HUD. Subsequently, mean blood-lead
concentrations(being a function of the covariates) can be expected to differ across
studies as well.
G10.2 REGRESSION PARAMETER ESTIMATION IN THE PRESENCE OF
MEASUREMENT ERROR
Let
Y = Xp + e (1)
where,
Y = an nxl vector containing the n values of the dependent variable,
X = an nxp matrix where each column contains the n values of one independent
variable in the regression model (in a model with an intercept term, one of the
columns would be a column of ones),
P = a pxl vector of regression coefficients, and
e = an nxl vector of random error terms.
In a standard regression model it is assumed that X is a matrix of fixed and known
constants, P is a vector of fixed and unknown constants, and € is distributed as MVN^o2!)
where MVN(n,S) represents a multivariate normal distribution with mean vector n and
covariance matrix S. Estimates of regression parameters for this standard regression model are
obtained as follows:
=(X1X)'1XTY
d2 =YT[I-X(XTX)-1XT]Y/(n-p) (2)
Cov (p1) = d2
In the presence of measurement error, it is assumed that
Y = Rp + e (3)
where,
X = an nxp matrix of fixed but unknown constants representing the values of the
independent variables if measured without error;
G-57
-------
R = X + A is an nxp matrix representing the values of the independent variables
observed with measurement error, and
A = an nxp matrix of the random measurement errors associated with each of the
observed values of the independent variables.
Y and € are as defined above. It is assumed that A is distributed as MVN^IsSa) where SA is
known and A is stochastically independent of 6. Under this measurement error model, estimates
of regression parameters are obtained as follows:
=(RTR-nEA)-1RTY
= YT[I-R(RTR)-1RT]Y/(n-p) (4)
Cov (fl) = MSEyp (RTR - nSa)'1 RTR (RTR -
These estimators are equivalent to those recommended in Equations (2.2.1 1) and (2.2.12) by
Fuller (Measurement Error Models. 1987).
It can be shown that
la. The difference between [(RTR - nS^ / n] and [X1^ / n] converges in probability to
zero as n-~;
Ib. The difference between [(RTR - (n-p^a) / (n-p)] and [X?X / (n-p)] converges in
probability to zero as n-°°; and
2. The difference between [RTY / n] and P^Y / n] converges in probability to zero as
n-*°°.
Additionally, it is assumed that
3. X is distributed as MVNQ. u^IsZ,) and is stochastically independent of both A and
e,
and hence all inferences are based on the conditional distribution of Y given X.
G10.3 DETAILS ON MEASUREMENT ERROR ESTIMATION
The statistical models that account for differences in sample collection methods used in
the Rochester Lead-in-Dust Study and the HUD National Survey require estimates of variance
components associated with the dust-lead and soil-lead predictor variables in each study. In the
G-58
-------
notation that follows, a subscript off represents floor dust lead loadings, a subscript of "w"
represents window sill dust lead loadings, and a subscript of "s" represents soil lead
concentrations. Specifically, we need to obtain the following estimates:
1. The "between homes" variance of observed values of the dust-lead and soil-lead
predictor variables for Rochester (o2^, a2Rw, and o2^ corresponding to the diagonal
elements of 5^ from Section G10.1.2 above) and for HUD (o2^, o2^ and o2^,
corresponding to the diagonal elements of SHH from Section G10.1.2 above),
2. After adjusting for the effects of covariates included in the Empirical model, the
"between homes" variance of observed values of the dust-lead and soil-lead predictor
variables for Rochester (o2^, a2^^, and o2^ corresponding to the diagonal
elements of A^ from Section G10.1.3 above) and for HUD ( o2^, o^p, and o2^
corresponding to the diagonal elements of A^ from Section G10.1.3 above), and
3. The "within homes" variance attributable to measurement error associated with the
dust-lead and soil-lead predictor variables for Rochester (o2^, o2,^^ and o2^^
corresponding to the diagonal elements of A^ from Section G10.1.2 above) and for
HUD (rffifjcf
-------
Between home variances of log(blue nozzle floor dust lead loading), log(blue nozzle
window sill dust lead loading), and log(average soil lead concentration) from the HUD Survey
are represented by o2^, o2^ and o2^, respectively. In contrast to the Rochester between home
variance estimates described above, HUD Survey between home variance estimates are weighted.
Each observation is weighted using weights from the 1993 American Housing Survey adjusted to
1997. Weights are used because the HUD Survey is designed to be nationally representative and
each observation in HUD is weighted with respect to the population it represents. Specifically,
N _ N _ N _
E WjCHfj -Hf)2 E Wi(HWj-Hw)2 E Wj(HSj -Hs)2
- - - .2 _ i=l
N
where w{ represents the population weight for the ith home in the HUD National Survey, Hf),
and Hs4 represent the floor and window sill dust-lead predictor variables and soil-lead
_
predictor variable associated with each house in the HUD National Survey, E wj =N , and Hf ,
_ _ i=1
Hw , and Hs are weighted means calculated as follows:
_ EW.HW,
, and
N ' N N
G10.3.2 COVARIATE ADJUSTED "BETWEEN HOMES" VARIANCE OF DUST-LEAD AND
SOIL-LEAD PREDICTOR VARIABLES
represent the portion of between home variance
and o2^, respectively) that remams after adjusting for the other
covariates included in the Empirical model. An estimate of these quantities can be obtained from
the mean squared error of a least squares regression of the variables (Rf, Rw, Rs, Hf, Hw, or Hs)
on the other covariates in the Empirical model. The least squares regression model treats the
covariates as fixed; and the resulting mean squared error estimates the remaining variability of
the variable in the presence of the fixed covariates.
The covariate adjusted between home variances from the Rochester Lead-in-Dust Study,
^Rflo ^Rwp and o2,^, are estimated using mean squared errors obtained from ordinary least
squares regressions of log(floor wipe dust lead loading), log(window sill wipe dust lead loading),
and log(drip-line soil lead concentration) on the remaining model covariates, respectively.
Similarly, the covariate adjusted between home variances from the HUD Survey, o^* o2Hwjc.
and o^tyc, are estimated using mean squared errors obtained from weighted least squares
regressions of log(floor wipe dust lead loading), log(window sill wipe dust lead loading), and
log(average soil lead concentration) on the remaining model covariates, respectively. Again,
G-60
-------
least squares regressions involving HUD data are weighted because the HUD Survey is designed
to be nationally representative.
G10.3.3 MEASUREMENT ERROR ASSOCIATED WITH PREDICTOR VARIABLES
The dust-lead predictor variables in the statistical models represent area-weighted
arithmetic average individual sample dust-lead loadings from floors and window sills. The
following equation represents the three sources of variability that must be accounted for in an
estimate of measurement error for these dust-lead predictor variables:
° Measurement Error ~ O" Spatial ° Sampling ^ Laboratory »
where o2Spatia, represents the variability in dust-lead levels among all possible locations on the
surface being tested, o2^,,,^ represents variability hi the collection of dust from the surface, and
^Laboratory represents variability in the chemical analysis of the sample. This definition of
measurement error is consistent with the interpretation of each predictor variable as exposure to
lead from floor or window sill dust found at the primary residence at the time of sampling. Thus
there was no attempt to estimate a component of variation associated with temporal variability.
The following two subsections contain details on estimating the measurement associated with
dust-lead and soil-lead predictor variables.
G10.3.3.1 Measurement Error Associated with Dust-Lead Predictor Variables
Several sources of data were considered for providing information about the variability hi
dust sample results due to measurement error, including field duplicate data and data that
included multiple dust samples (of a given component type) collected from within the same
house. Since the predictor variables included in the statistical models represented area weighted
averages of multiple dust sample results collected within a house, the individual sample lead
loading results from the Rochester Lead-in-Dust Study and the HUD National Survey were used
to assess the measurement error. Specifically, let
Dustjjk represent the dust-lead loading from the kth component type (floor or window
sill) from the jth location within the ith residential unit,
represent the area of the sample from the kth component type from the jth
location within the ith residential unit, and
The following model was then fitted separately for floors and window sills from each
study to estimate the within house variability in dust-lead loadings between individual dust
samples:
+ Hik + Eijk,
G-61
-------
where uk is the geometric mean of Dustyk among all samples of component k, H^ is the random
effect associated with the ith House, and Eijk is the random within-house error term associated
with Dustjjk. Hfc is assumed to follow a normal distribution with mean zero and variance 0^8^^,,
is assumed to follow a normal distribution with mean zero and variance a2^^,, Houses.
characterizes the variability between houses. o^^,, Houses characterizes the
variability within a house; attributed to a combination of spatial, sampling, and laboratory
variability. The following two subsections describe how weights were used with the above
model to calculate the measurement error variance components o2Rflxf and o2Rw(Xw corresponding
to the Rochester Lead-in-Dust Study, and o2,^ and o2^^,, corresponding to the HUD National
Survey.
Rochester Lead-in-Dust Study
Since area weighted (arithmetic) mean floor and window sill dust-lead loadings were
used to characterize the dust-lead levels in each house in the Rochester Lead-in-Dust Study, the
above model was fitted using weights corresponding to the percent of total area that was
associated with each sample:
where % is the number of samples collected from component k within the ith house.
Values of o2wjthinHouses calculated hi this weighted analysis are used as estimates of o2
and o2RwpCw in the statistical models described hi Sections 1 and 2 of this appendix. In actuality,
these estimates of o2,^ and o2Rw(Xw correspond more closely to measurement error in area
weighted geometric mean dust-lead loadings from floors and window sills within each house.
Table G10-1 provides estimates of o2,^ and o^,^ as calculated from the Rochester Lead-in-
Dust Study data.
HUD National Survey
Since area weighted (arithmetic) mean floor and window sill dust-lead loadings were
used to characterize the dust-lead levels hi each house in the HUD National Survey, the above
model was fitted using a combination of weights corresponding to the percent of total area that
was associated with each sample, and the survey weight associated with each home sampled:
Arealtk HSW.
'
where % is the number of samples collected from component k within the ith house, n is the
number of homes included in the HUD National Survey, and HSW; is the survey weight
associated with the ith home in the HUD National Survey.
G-62
-------
Table G10-1. Components of Variation Used to Implement an Adjustment of the
Rochester Multi-Media Predictive Model for Use with Environmental Lead
Levels as Measured in the HUD National Survey.
Sttidy
Rochester
Lead-in-Dust
HUD
National
Survey
-'^;:"',-lf^^ip|eir;::.. v;:
° Rf|Xf
° nw|Xw
O^talX.
02R,|c
02RW|C
02R,|C
02M
o2^
o2*
C' Hf|Xf
° Hw|Xw
° Ht|X«
° Hf|C
02Hw|C
02H,|C
°*Hf
02Hw
o2*
Final Empirical Model
0.2082
0.5708
0.3898
1 .3323
1.8505
1 .6497
1.3410
1.8592
1 .6640
0.6125
1 .6937
0.3016
2.3589
5.2881
2.2125
2.3767
5.3225
2.2434
Values of t^within Houses calculated in this weighted analysis are used as estimates of o2
and o^p^ in the statistical models described in Sections 1 and 2 of this appendix. In actuality,
these estimates of 0^^ and o^p^ correspond more closely to measurement error in area
weighted geometric mean dust-lead loadings from floors and window sills within each house.
G-63
-------
Table G10-1 provides estimates of o2^^ and o^p^ as calculated from the HUD National
Survey data.
G10.3.3.2 Measurement Error Associated with Soil-Lead Predictor Variables
Due to the fact that there was analytical information available from only one composite
drip-line soil sample collected from each home in Rochester, we were unable to derive an
estimate of measurement error (o2^^ using data observed in the Rochester Lead-in-Dust Study.
We therefore derived estimates of measurement error associated with soil-lead predictor
variables in both the Rochester Study (O^R,,^ and the HUD National Survey (o2^,^ using data
collected in the HUD National Survey.
Up to three different soil samples were collected from each home hi the HUD National
Survey: an entryway soil sample, a drip-line soil sample, and a remote soil sample. The soil-lead
predictor variables used hi the Empirical Model can be regarded as weighted averages of these
multiple soil sample results collected within each HUD National Survey home. Specifically, we
considered the Rochester soil-lead predictor variable to be representative of the average between
entryway and drip-line soil samples collected hi the HUD National Survey (each sample
receiving weight of 0.5). The HUD National Survey predictor variable was constructed as the
average between the remote soil sample and the average between entryway and drip-line soil
samples (remote sample receiving weight of 0.5, and drip-line and entryway samples each
receiving weight of 0.25). The individual soil-lead concentration results from the HUD National
Survey were used to assess the measurement error variance components as follows:
Let Soiljj represent the soil-lead concentration from the jth location within the ith residential unit.
The following model was then fitted to estimate the within house variability in soil-lead
concentration between individual soil samples:
ln(Soiljj) = ln(u) + Hj + Esj,
where uk is the geometric mean of Soiljj among all samples, Hj is the random effect associated
with the ith House, and E;j is the random within-house error term associated with Soiljj. Hj is
assumed to follow a normal distribution with mean zero and variance o2BetweenHouses, and Ey is
assumed to follow a normal distribution with mean zero and variance o2
^Between Houses characterizes the variability between houses. O^^H,,,^ characterizes the
variability within a house; attributed to a combination of spatial, sampling, and laboratory
variability. Weights were used with the above model to calculate the measurement error variance
components o2!^ corresponding to the Rochester Lead-in-Dust Study, and o^x, corresponding
to the HUD National Survey as follows:
G-64
-------
where n is the number of homes included in the HUD National Survey, HSWf is the survey
weight associated with the ith home in the HUD National Survey, and Wy is the weight
corresponding to each individual sample being averaged:
Soil Sample
location
Drip-line
Entryway
Remote
Value of W, when Estimating
<*ii»t*»
0.5
0.5
0.0
O^fX. :-
0.25
0.25
0.5
Values of c^wwiin Houses calculated in this weighted analysis are used as estimates of o
and o2H5(xsm me statistical models described in Sections 1 and 2 of this appendix. Table G10-1
provides estimates of o2Rjpb and o2Hsp{s as calculated from the HUD National Survey data.
G10.3.4 EFFECT OF IMPUTING BLUE NOZZLE WINDOW SILL DUST LEAD LOADINGS
IN THE HUD PATASET ON ESTIMATED VARIANCE COMPONENTS
The floor and window sill dust-lead loading predictor variable was imputed for several of
the homes in the HUD National Survey (for homes that did not include any dust samples from
window sills) in an effort to keep as many homes in the analysis as possible, and thus maintain its
property of being nationally representative (with appropriate survey weights).
The HUD sample used for calculating o2^ o2^ and o2^ includes imputed values, and is
the same for the preliminary and final Empirical models; therefore the estimate of o2^ is
consistent across the rows in Table G10-1. The HUD sample used for calculating o^
and o^ also includes imputed values.
HflC> °Hw|C>
In contrast, a2
wfsxf)
and a2^^ can only be estimated using those houses in which
floor and window sill dust samples and soil samples were collected. Values for o2Hflxf
therefore calculated separately for each version of the empirical model.
were
G10.3.5 ESTIMATED COMPONENTS OF VARIATION
The following table provides the components of variation used to implement an
adjustment of the Rochester multi-media predictive model for use with environmental lead levels
as measured hi the HUD National Survey.
G10.4 BOOTSTRAP ESTIMATION OF STANDARD ERRORS
In ordinary least squares regression, formulas are readily available for calculating
standard errors associated with the model's parameter estimates. For the parameter estimates of
G-65
-------
the model that accounts for differences in sample collection methods used in the Rochester Lead-
in-Dust Study and the HUD National Survey, no such simple formulas exist. As a result, 48
standard errors can only be approximated. The method of approximation used for estimating the
standard errors corresponding to the parameters of the adjusted model is a basic bootstrap
algorithm, which is described below. Note that the following definitions and algorithm are taken
directly from Efron and Tibshirani, "An Introduction to the Bootstrap," 1993 pp. 45-47.
Let Jc = (x1,x2,...,xn) represent a sample dataset.
Let d(x) be an estimator of a parameter of interest 6, where 0(x) is such that its standard error is
not easily obtained.
Define F to be the empirical distribution that assigns probability 1/n to each of the n
observations in the sample dataset.
Define a bootstrap sample, x ^ , as a random sample of size n drawn with replacement from F .
A bootstrap estimate of the standard error of §(x) is obtained as follows:
1. Collect B independent bootstrap samples, x, ,Jc2 ,.. .,XB
2. For each bootstrap sample, calculate ^(x^ , i=l,2,..., B.
3. Estimate the standard error of Q(x) as:
1/2 _ B
= JVMA/v^ _ a W| / m-i\( «rkara 0^=^
seD = w JO(XS") - u~| / (B-l)^ , where 6lj =
i=l
\=i
The above algorithm is used to estimate the standard errors of the estimators described in
Section 1 ( $Ywa»jXs,cy ^Y\Hw(HfMj,Q' $v\H*(tifJfo,Q' $r\c(H/ji»ji*)> and "viHf.Hw.Hs.c)- Because the
adjustment procedure is based on data from die Rochester Lead-in-Dust Study, the Rochester
dataset is treated as the sample dataset, x . Data from the HUD National Survey are held fixed
in the implementation of the algorithm. In essence, the adjusted model parameters are viewed as
functions of sample data(Rochester dataset) that are calibrated to correspond to population
values(HUD dataset). Thus, their variability is assumed, in this preliminary assessment, to stem
from the Rochester dataset only.
Finally, observe that,
lun seB =
That is, as the number of bootstrap replications increases, the estimated standard error
approaches the population standard error; where the population distribution is estimated by F.
Efron and Tibshirani (1993) recommend between 25 and 200 bootstrap replications for adequate
approximations. 200 bootstrap replications were used in the application of the bootstrap
algorithm to approximate the standard errors of parameters in the adjusted model.
G-66
-------
G11: Appendix on Bivariate Relationships Between Blood Lead
and Potential Lead Exposure Predictor Variables
G-67
-------
Statistical
Modal
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
s.a. (B0)
1.99
(0.0545)
5.93
(0.2722)
7.37
(0.4378)
5.93
(0.2721)
P,
s.e.
-------
Statistical
Modal
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Error*)
Po
t.e. (ft,)
1.89
(0.0459)
6.04
(0.3015)
6.62
(0.3140)
6.04
(29.1731)
Pi
a.a. (B,J
0.03
(0.0167)
0.08
(0.0410)
0.21
(0.1125)
0.08
(0.8766)
ew
a.e. (9W)
-
-
-
6.8E8
(3.7E15)
o*
0.3733
0.3722
0.3733
0.3759
R2
0.0187
0.0215
0.0186
0.0215
Estimated
Log-
Likelihood
-188.88
-188.58
-188.89
-188.59
Number of
Observations
205
205
205
205
50
40
30
20
10
• -OtMaivad Value*
PradfcMd (Atamrta Log-AddMve)
Pradtattd (Log-AddWve)
Predded (Log-Linear)
PmdfcMd (AcUw Uptake Model)
0.01 0.10 1.00 10.00
75% of Deteriorated Exterior Lead-Based Paint ( mg/cm. x )
100.00
• -ObMived Valun
Predated (Alternate Log-AddUve)
-•--PiBdMed (Loo-AddWvo)
Pndk^ad (Log-UnMi)
PrecSoted (Active Uptake ModaO
-3-2-10 1 2 3 4
ln(75% of Deteriorated Exterior Lead-Based Paint)
Figure G11-2. Bivariate Relationship Between Blood-Lead Concentration and the 75th
Percentile of Deteriorated Exterior Lead-Based Paint.
G-69
-------
Statistical
Modal
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimate* and (Associated
Standard Errors)
Po
s.e. (Po)
1.38
(0.1130)
6.37
(0.2807)
3.60
(0.6354)
6.58
(1.3665)
P,
s.e. (B,)
0.17
(0.0365)
0.00
(0.0006)
1.02
(0.2343)
0.31
(0.1902)
"H»
s.e. (8,0,)
-
--
~
13.22
(3.5208)
o1
0.3433
0.3741
0.3452
0.3407
R1
0.0959
0.0148
0.0909
0.1119
Estimated
Lofl-
LikeUhood
-173.22
-181.68
-173.76
-171.47
Number of
Observations
197
197
197
197
50
40
30
20
10
- •Observed VWuee
Predicted (Alternate Log-Additive)
---Predicted (Log-Addmve)
Prsdfctod (LoQ *~ LJnsiw)
Predicted (Active Uptake Model)
0.1 1.0 10.0 100.0 1000.0 10000.0 100000.0
Floor Oust-Pb Loading from Uncaipeted Surfaces (Wipe) ( ^g/ft2 )
•Obeemd VWuee
- Pradtottd (ABemete Log-AdoWve)
- Predated (Log-AdoWn)
-Predcted (Log-Uneej)
-Predotad (Aottxe Uptato ModeQ
-10 1 23456789 10
ln(Rcor Dust-Pb Loading from Uncaipeted Surfaces (Wipe))
Figure G11-3. Bivariate Relationship Between Blood-Lead Concentration and Floor Dust-
Lead Loading from Uncarpeted Surfaces (Wipe Samples).
G-70
-------
Statistical Modal
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
S.e. (Po)
1.63
(0.0636)
6.23
(0.2751)
5.40
(0.3133)
7.40
(1.2816)
Pi
s.e. (p,)
0.12
(0.0254)
0.01
(0.0031)
0.55
(0.1350)
0.60
(0.3635)
ew
s.e. OH,,)
-
-
-
12.68
(2.8613)
o2
0.3451
0.3708
0.3515
0.3351
R2
0.0928
0.0252
0.0760
0.1277
Estimated
Log-
UkeOhood
-180.83
-188.20
-182.71
-176.81
Number of
Observations
205
205
205
205
£
50
40
30
20
10
• • Observed Value*
Predicted (Alternate Log-Additive)
- Pradtotad (Log-Additive)
- — Predicted (Log-Unoai)
Predicted (Active Uptake Model)
0.01 0.10 1.00 10.00 100.00 1000.00 10000.00
(Prop, of Uncarp. Roore)*(Ftoor Dust—Pb Loading from Uncarp. Floors) (Wipe) (
•Obeecved Velue*
-Pradoted (Alterrate Log-Additive)
* Predicted (Log~AddMve)
•Predated (Log-Unew)
-PmoTcted (Acdve Uptato ModaQ
-3-2-10123456789
in((Prop. of Uncarp. Fkxx«)*(Fkx3r Dust—Pb Loading from Uncarp. Floors) (Wipe))
Figure G11-4. Bivariate Relationship Between Blood-Lead Concentration and (Proportion
of Uncarpeted Floors Samples)*(Floor Dust-Lead Loading from Uncarpeted
Floors) (Wipe Samples).
G-71
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
s.e. (Bo)
1.56
(0.1066)
6.16
(0.2734)
4.29
(0.6156)
15.00
(0.0000)
P,
s.e. (B,)
0.10
(0.0385)
0.00
(0.0002)
0.76
(0.2481)
0.00
(0.0012)
ew
s.e. (GHJ,)
-
-
-
10.44
(0.7862)
0*
0.3363
0.3492
0.3334
0.3532
R2
0.0368
0.00
0.0453
0.00
Estimated
Log-
Likelihood
-155.47
-158.82
-154.67
-158.83
Number of
Observations
179
179
179
179
50
40
30
20
10
- -Obeorvnd VWUM
Predicted (Alternate Log-Addttto)
Predicted (Log-AddMv*)
Predctod (Log—Unoflf)
Predicted (Acttw Upteto Model)
0.1 1.0 10.0 100.0 1000.0 10000.0 100000.0
Floor Dust—Pb Loading from Carpeted Surfaces (Wipe) (
•Obeerved VWue*
-Pradtotod (AJtem«le Log-AddWve)
• PredMad (Log-AddKM)
-Predtoted (Log-LJnew)
-Predtated (Acttvo Uptafea Model)
-101 23456789
ln(Floor Dust—Pb Loading from Carpeted Surfaces (Wipe))
10
Figure G11-5. Bivariate Relationship Between Blood-Lead Concentration and Floor Dust-
Lead Loading from Carpeted Surfaces (Wipe Samples).
G-72
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimate* and (Associated
Standard Errors)
Po
«.«. (Po)
1.85
(0.0511)
6.38
(0.2764)
6.38
(0.3262)
16.22
(0.0000)
Pi
s.e. (p,)
0.00
(0.0217)
0.00
(0.0004)
0.00
(0.1384)
0.00
(0.0028)
&»»
s.e. (0H.,)
-
-
-
10.52
(0.7520)
0*
0.3804
0.3804
0.3804
0.3842
R2
0.00
0.00
0.00
0.00
Estimated
Log-
Likelihood
-190.81
-190.81
-190.81
-190.82
Number of
Observations
205
205
205
205
50
40
30
20
10
• • Obntvod VUun
Pradcttd (Alternate Log-AddWw)
Predated (Log-AddUw)
Predicted (Log-UnMf)
PmdfcMd CAOtv* Uptake Mod*))
0.01 0.10 1.00 10.00 100.00 1000.00 10000.00
(Prop, of Carp. Roor8)*(F1oor Dust—Pb Loading from Caip. Floors) (Wipe) (
4
(Mtomaw Log-AddWva)
(Loo-AddMve)
(Log-Uneefl
(taHve Uptake Model)
-3-2-101 2 3 4 5 6 7 8 9 10
ln((Prop. of Carp. Flooi8)*(Floor Dust—Pb Loading from Carp. Floors) (Wipe))
Figure G11-6. Bivariate Relationship Between Blood-Lead Concentration and (Proportion
of Carpeted Floors Sampled)*(Floor Dust Lead-Loading from Carpeted
Floors (Wipe Samples).
G-73
-------
Statistical Mode!
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimate* and (Associated
Standard Errors)
Po
*... (Po)
1.04
(0.1658)
5.58
(0.2956)
2.36
(0.8614*
7.42
(1.2696)
Pi
s.e. (P,)
0.15
(0.0304)
0.00
(0.0005)
0.77
(0.1731)
0.02
(0.0144)
OHW
s.e. (6,0,)
-
-
-
12.63
(3.0407)
o2
0.3409
0.3525
0.3476
0.3369
R*
0.1144
0.0845
0.0971
0.1339
Estimated
Log-
Ukelihood
-171.65
-174.91
-173.56
-169.48
Number of
Observations
196
196
196
196
50
40
30
20
10
Log-Add**}
-Predlc«ed (Log-Addlft*)
Prodtetod (Log—Unoci)
PrtKfcted (Acttw UpWca Modd)
10 100 1000
Window SIM Dust-Pb Loading (Wipe) (
10000 100000
- -ObMivBd \Murn
Pradtotad (Alternate Log-AddMvg)
•-•-PmdMKl (Log-AddHw)
— PradMKl (Log-Un««)
• — PradtolKl
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
s.e. (Po)
1.17
(0.1600)
5.85
(0.2927)
2.45
(0.8881)
11.69
(2.6346)
P,
s.e. (P,)
0.08
(0.0183)
0.00
(0.0000)
0.47
(0.1123)
0.00
(0.0014)
0HfF
«.e. (6,0,)
-
-
-
8.89
(1.1742)
o1
0.3533
0.3676
0.3550
0.3568
tf
0.0929
0.0561
0.0884
0.0938
Estimated
Log-
Ukefihood
-168.85
-172.61
-169.31
-168.77
Number of
Observations
189
189
189
189
50
40
30
20
10
— Predated (Alternate Log-AddMve)
-•Predated (Log-Addftw)
~" Pnxflctod (Log•*Lfcw)
Pradctod (Acttv* Uptata Model)
10
100 1000 10000 100000 1000000
Window Dough Dust-Pb Loacfing (Wipe) ( MO/ft* )
PraddKi (Mtan«M Log-AddHve)
-PradoM (Log-Add*»)
PraddKi (Log-LkiMi)
I (AeHve UpW« McxtoQ
5 6 7 8 9 10 11 12 13
InOMndow Dough Dust-Pb Loading (Wipe))
14
Figure G11-8. Bivariate Relationship Between Blood-Lead Concentration and Window Well
Dust-Lead Loading (Wipe Samples).
G-75
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
».e. (W
1.56
(0.0726)
6.32
(0.2830)
4.59
(0.3635)
7.58
(2.3187)
Pi
s.e. (B,)
0.10
(0.0205)
0.00
(0.0002)
0.68
(0.1285)
1.38
(0.8114)
OHW
s.e. (6^)
-
-
-
8.63
(0.8053)
o1
0.3383
0.3769
0.3375
0.3417
R1
0.1186
0.0182
0.1207
0.1190
Estimated
Log-
LikeHhood
-168.27
-178.68
-168.04
-168.23
Number of
Observations
193
193
193
193
50
40
30
20
10
• ObMnwd Vriuw
Predated (*WmeJo Log-AddHwa)
Pradk**d (Log-AddMM)
Predated (AoUva Uptata ModaO
0.01 0.10 1.00 10.00 100.OO 1000.00 WOOO.OO 100000.X
Floor Dust-Pb Loading from Uncarpotad Surfaces (BRM) (
Log-AddWw»)
(Log-AddMv.)
Predated (Aobvv Uptaka Modal)
-4-20 2 4 6 8 10
ln(Ftoor Oust—Pb Loading from Uncarpeted Surfaces (BRM))
12
Figure G11-9. Bivariate Relationship Between Blood-Lead Concentration and Roor Dust-
Lead Loading from Uncarpeted Surfaces (BRM Samples).
G-76
-------
Statistical Modal
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
«.e. (Po)
1.71
(0.0508)
6.18
(0.2713)
5.68
(0.2715)
10.90
(2.4049)
Pi
s.e. (PO
0.08
(0.0164)
0.00
(0.0009)
0.44
(0.1007)
1.58
(1.1784)
ew
s.e. (8^)
-
-
-
8.93
(0.9558)
o*
0.3435
0.3651
0.3467
0.3455
R*
0.0970
0.0402
0.0886
0.1008
Estimated
Log-
Ukelihood
-180.35
-186.61
-181.30
-179.93
Number of
Observations
205
205
205
205
50
40
30
20
10
- •ObMrvod WUM
Pradtetad (Alternate LoQ-AddMve)
---Rredtted (Log-AddRto)
Pradtotad (Loo—Unaav)
Pradtetad (Aedvv Upt*a Modal)
•-. -I- .-
'*•'•'•> •= :A^^=^=i=i
, . . ,1 « • , i . .
O.O1 0.10 1.00 10.00 100.00 10OO.OO 10000.00 100000.00
(Prop, of Uncarp. Roof8)*(Hoor Dust—Pb Loading from Uncarp. Floors) (BRM) ( MO"t2 )
•ObMivad \Mua*
-PradWwJ (MMnrwto Log-AddUv«)
• Pradtatod (Log-AddHva)
-Predtatad (Log-Unan)
-Pmdtotad (Active UpHto ModaQ
-3-2-101 2 3 4 5 6 7 8 9 10
ln((Prop. of Uncarp. Fk>ore)*(Floor Dust—Pb Loading from Uncarp. Roore) (BRM))
Figure G11-10. Bivariate Relationship Between Blood-Lead Concentration and (Proportion
of Uncarpeted Floors Samples) *(Roor Dust-Lead Loading from
Uncarpeted Floors)(BRM Samples).
G-77
-------
Statistical Mod*!
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
St
Po
s.e. (BJ
1.20
(0.1530)
6.06
(0.2848)
2.46
(0.8656)
9.11
(2.0871)
itimates and (Associated
andard Errors)
P,
s.e. (B,)
0.11
(0.0265)
0.00
(0.0001)
0.69
(0.1658)
0.03
(0.0259)
BH*
s.e. (S^)
-
-
-
9.34
(1.4739)
o2
0.3203
0.3498
0.3204
0.3197
R*
0.0923
0.0085
0.0920
0.1042
Estimated
Loo-
Likelihood
-151.08
-158.99
-151.11
-149.91
Number of
Observations
179
179
179
179
£
50
40
30
20
10
•Obeeiwd VWuee
-Praddad (Monde Log-AddMve)
- Predtotad (Log-AddMve)
-PradMad (Log-l>Mef)
-PiedWed (Adlv* Uptake Model)
1 10 100 1000 10000 100000
ROOT Oust—Pb Loading from Carpeted Surfaces (BRM) ( /iff/ft.2 )
(Mtemete Log-AddWvw)
(U»g-Ad»V»)
-Pradfctad (Active UpleJta Model)
• ' . • •*•. 1
. . •• •
3456789 10
ln(Fkxx Duet-Pb Loading from Carpeted Surfaoaa (BRM))
11
Figure 011-11. Bivariate Relationship Between Blood-Lead Concentration and Floor Dust-
Lead Loading from Carpeted Surfaces (BRM Samples).
G-78
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and 1
Standard Errors
Po
s.e. (B0)
1.85
(0.0679)
6.32
(0.2836)
6.38
(0.4336)
15.43
(6.6736)
P,
s.a. (P,l
0.00
(0.0137)
0.00
(0.0001)
0.00
(0.0876)
0.02
(0.0398)
Associated
ew
s.e. (QHO-)
-
-
-
9.37
(2.5211)
o2
0.3804
0.3795
0.3804
0.3720
R*
0.0000
0.0025
0.0000
0.0317
Estimated
Log-
Llkellhood
-190.81
-190.56
-190.81
-187.52
Number of
Observations
205
205
205
205
50
40
30
20
10
VWuea
Predated (Alternate Log-AddHve)
Predjetad (Log-Additive)
Predicted (Log~LJneej)
Pradlctad (Active Uptake Modal)
-. • • •-:.:.' • •-. r,
-. . .•;..-~--,^—^.-r.r..-.
0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00
(Prop, of Carp. Fkxxs)*(Floor Dust-Pb Loading from Carp. Floors) (BRM) (
- -Obawvad VMua*
Pradtoted (Attemata Log-AddMve)
Prodtated (Log-AddMve)
---Pradtotad (Log-Unan)
Pradtoted (Active Uptake Modal)
V •
• • f
-3-2-10 1 2 3 4 5 6 7 8 9 10 11
ln((Prop. of Carp. Roors)*(Floor Dust—Pb Loading from Carp. ROOTS) (BRM))
Figure G11-12. Bivariate Relationship Between Blood-Lead Concentration and (Proportion
of Carpeted Floors Sampled)*(Floor Dust-Lead Loading from Carpeted
FloorsHBRM Samples).
G-79
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
s.e. (Po)
1.32
(0.1114)
5.84
(0.2692)
3.46
(0.6138)
10.15
(1.7822)
Pi
s.e. (p,)
0.09
(0.0177)
0.00
(0.0000)
0.51
(0.1123)
0.00
(0.0041)
ew
s.e. OHS,)
-
-
~
11.29
(2.0248)
a*
0.3382
0.3460
0.3428
0.3389
R1
0.1176
0.0974
0.1055
0.1249
Estimated
Log-
Likelihood
-171.75
-173.98
-173.09
-170.94
Number of
Observations
197
197
197
197
50
40
30
20
10
- -Obeerved Value*
Predated (Akemeta Log-AddMve)
Predated (Log-AddMva)
Predated (Log-Uneai)
Predated (Active Uptake Modal)
0.1 1.0 10.0 10O.O 1000.0 10000.0
Window sm Dust-Pb Loading (BRM) ( Mg/FL2 )
100000.0 1000000.0
• • Obeerved Vetuee
Predated (Alternate Log-Addttve)
Predated (Log-AddBve)
-—Predated (Laa-Uneer)
Predated (Active Uptake Model)
-101 2 3 4 5 6 7 8 9 10 11 12
ln(Wlndow SHI Dust-Pb Loading (BRM))
Rgure G11-13. Bivariate Relationship Between Blood-Lead Concentration and Window Sill
Dust-Lead Loading (BRM Samples).
G-80
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
s.e. (p0)
1.08
(0.1444)
5.54
(0.2938)
2.41
(0.6968)
9.35
(1.6300)
Pi
s.e. (p,)
0.08
(0.0138)
0.00
(0.0000)
0.40
(0.0758)
0.00
(0.0001)
®tur
s.e. O^)
-
-
-
9.83
(1.4255)
o1
0.3366
0.3530
0.3414
0.3331
R2
0.1402
0.0983
0.1279
0.1581
Estimated
Log-
Ukenhood
-164.29
-168.78
-165.63
-162.30
Number of
Observations
189
189
189
189
50
40
30
20
10
Predteted (Alternate Log-Addttlva)
-••-Pradlctad (Log-AddMve)
~" PrBCfictod (LOQ~LJrMNf)
PrecScted (AcHva Uptato Model)
10 100 1000 10000 100000
Window Trough Dust-Pb Loading (BRM) ( ^g/IL2
1000OOO 10000000
•Obagnod VMuaa
— Predteted (Alternate Log-Additive)
•-- Pradteted (Log-AddHva)
--Pradoted (Log-Line^
--Pradtoted (Active Uptake ModaQ
2 3 4 5 6 7 8 9 10 11 12 13 14 15
(n(WbxJow Trough Dust-Pb Loading (BRM))
Figure G11-14. Bivariate Relationship Between Blood-Lead Concentration and Window
Well Dust-Lead Loading (BRM Samples).
G-81
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
s.e. (P0)
0.73
(0.2216)
5.31
(0.3700)
0.16
(1.0046)
6.53
(1.4373)
P,
s.e. (B,)
0.17
(0.0330)
0.00
(0.0003)
0.97
(0.1655)
0.01
(0.0092)
QH»
s.e. (6m,)
-
-
-
10.40
(2.1910)
0*
0.3410
0.3647
0.3414
0.3443
R1
0.1288
0.0683
0.1278
0.1299
Estimated
Log-
Ukelihood
-162.86
-169.11
-162.97
-162.75
Number of
Observations
186
186
186
186
50
£
40
30
20
10
•ObMfVKI VMUM
Log-Add**)
Praddad (Log-AddHve)
PraOcM (Log-Unw)
PradMKJ (AcDv* UpUke MocM)
10
100 1000
DripOne Soil-Pb Concentration (
10000
100000
4
• -ObMmd VMUM
PnddKl tf»*i*m Log-**•)«)
Pradfctad (Log-Addttw)
— PraddKl (Log-Un»)
Pmdctad (tadv* UpM
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
s.e.
-------
Statistical Modal
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
t.a. (BJ
3.15
(0.7032)
6.14
(0.2867)
1.31
(0.1269)
9.70
(2.1860)
Pi
«.a. (B,J
0.66
(0.1487)
0.00
(0.0002)
0.11
(0.0238)
0.06
(0.0491)
QBIP
s.a. (8H»)
-
-
-
9.29
(1.2981)
o1
0.3483
0.3752
0.3476
0.3488
R*
0.0903
0.0203
0.0922
0.0981
PcthrurfitH
Log-
Likelihood
-180.00
-187.53
-179.79
-179.14
Number of
Observations
205
205
205
205
£
50
40
30
20
10
- • ObMivKJ VWun
PradUed (Menu* Log-AddBvw)
—-Pmdctod (Loo-AddUw)
Pradtatod (Log-Una*)
PndkMd (Acft* Uptake Model)
10 100
Floor Dust—Pb Loading
1000 10000
Surfaces (BRM) (
100000
-PraddKi (ftltamati U3g-AdcHv*)
- PraddKi (Log-AdcWn)
-Pradrtad (Log-Urnv)
-Pradkttd (AoHm Updto Model)
23456789
ln(Roor Dust-Pb Loading from All Surfaces (BRM))
10 11
Figure G11-17. Bivariate Relationship Between Blood-Lead Concentration and the Total
Effect of Floor Dust-Lead Loading from All Surfaces (Carpeted or
Uncarpeted) (BRM Samples).
G-84
-------
Statistical Model
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
s.e. (BJ
3.57
(0.6925)
6.36
(0.2776)
1.45
(0.1109)
6.33
(1.6813)
P,
i.e. (B,)
1.01
(0.2547)
0.00
(0.0005)
0.14
(0.0358)
0.47
(0.2797)
8W
s.e. (OK,,)
-
-
-
11.44
(2.3671)
o2
0.3511
0.3800
0.3531
0.3438
R*
0.0771
0.0011
0.0717
0.1051
Estimated
Log-
Likelihood
-182.59
-190.70
-183.18
-179.44
Number of
Observations
203
203
203
203
50
40
30
20
10
• • Obearved VMUM
Pradded (Mamala Log-AddMve)
Predkaed (Ljog-AddUM)
~~~ PrauHtod (LoQ ~ LJn«Mf)
Pradtoted (Active Uptake Model)
10 100 1000
Floor Dust-Pb Loacfino from AH Surfaces (Wipe) (
10000
• Praddad (Log-AddHva)
-Pradcttd (Log-Llmar)
-Predteted (AeUva Uptake Model)
2345678
ln(Roor Dust-Pb Loading from All Surfaces (Wipe))
9
10
Figure G11-18. Bivariate Relationship Between Blood-Lead Concentration and the Total
Effect of Floor Dust-Lead Loading from All Surfaces (Carpeted or
Uncarpeted) (Wipe Samples).
G-85
-------
oiausucai MOOM
Log-Linear
Log-Additive
Alternate
Log-Additive
Active Uptake
Parameter Estimates and (Associated
Standard Errors)
Po
a.e. (PJ
1.82
(0.0437)
6.15
(0.2696)
6.15
(0.2696)
6.15
(11.3986)
Pi
s.e. (p,)
0.33
(0.1058)
2.67
(1.0765)
2.67
(1.0765)
2.66
(13.2990)
...e(L.)
2.49E8
(1.8727E16)
0*
0.3628
0.3630
0.3630
0.3666
R*
0.0463
0.0457
0.0457
0.0457
Log-
Ukettwod
-185.95
-186.02
-186.02
-186.02
Number of
Observations
205
205
205
205
1
10
T 40
: 30
20
10
1
Paint/Pica Hazard Value
0 1 2
Paint/Pica Hazard Value
Figure 011-19. Bivariate Relationship Between Blood-Lead Concentration and Paint/Pica
Hazard Variable (Interior).
G-86
-------
G12: Appendix on Regression Diagnostics
G-87
-------
Regression Diagnostics
This section of the appendix describes the diagnostic analyses performed as part of
development of a multimedia exposure model using data from the Rochester Lead-in-Dust Study.
Through the use of regression diagnostics, the adequacy of fit of the various candidate models
developed (including the multi-media predictive model) to the data observed can be determined,
and model assumptions can be verified. Results are presented for the final chosen model in
particular, for which the following regression diagnostic "stages" were performed:
1. A normal quantile plot of the residuals was created. A normal quantile plot which can
best be described by a straight line indicates that residuals (errors) are approximately
normally distributed, as assumed. The quantile plot given in Figure G12-1 can best
be described by a straight line, and therefore the assumption of normal errors is
satisfied.
2. Residual values were plotted versus predicted values. This scatterplot could indicate
signs of nonconstant variance (if points spread out or tighten up as you move from left
to right) or nonlinearity (if points look quadratic or bow-shaped). A scatterplot
exhibiting no pattern indicates no such problems. Similarly, plots of residuals versus
predictors should indicate no discernible pattern. A plot of residuals versus predicted
values is given in Figure G12-2. A plot of residuals versus predictor variables are
given in Figure G12-3. Note that none of these plots indicate any relationship and
each resembles a somewhat random scattering of points.
3. A plot of Cook's distance and DFFITS (both measures of influence) versus
studentized residuals (a measure of how far an observation deviates from the modeled
relationship) can indicate potential outliers - points with undue influence and points
lying far outside the model's prediction. A plot of these two influence statistics are
given in Figure G12-4. Each of these plots point to two possible outliers:
observations with Child Identification Number (CID) 00166 and 04072. The
observation with CID 00166 is also the observation with the lowest PbB level, while
the observation with CID 04072 has the largest PbF level and the fifth smallest PbS
level, and thus may require further examination. Note that DFFITS and Cook's
distance are related to the studentized residuals and by definition are themselves
similar, so observable patterns in these plots indicate nothing. However, typically
those points with large studentized residuals (larger than 3 in absolute value) or
DFFITS (larger than 1 in absolute value), or Cook's distance (larger than 1) possibly
require further examination.
4. For a closer examination of how points influence model parameter estimates, the
models were fit while excluding a single point at a time. Analysis of the coefficients
adjusted for their standard error (intercept, and coefficients of PbS, PbF, PbW and
PbP), including plots, can provide information about the influence of specific
observations. Plots of the scaled measure of change in each parameter estimate are
provided in the scatterplot matrix of Figure G12-5. Typically, values exceeding 1 hi
G-88
-------
absolute value are suspect points. Note that none of the points in the multi-media
predictive model analysis is suspect by this criteria. Table G12-1 below provides the
parameter estimates while excluding the potential outliers flagged in stage (3).
Table G12-1. Influence of Possible Outlying Observations
Pantm.
Po
Pi
p,
Pa
P«
RJ
a
j f
f
• . DfttClfplMil
Intercept
log (PbS): Drip-line Soil-Lead
Concentration (fine soil fraction)
PbP: Indicator of Interior Paint/Pica
Hazard
log (PbF): Area-Weighted Arithmetic
Mean (Wipe) Dust-Lead Loading from
Any Floor (Carpeted or Uncarpeted)
log (PbW): Area-weighted Arithmetic
Mean (Wipe) Dust-Lead Loading from
Window Sills
Coefficient of Determination
Root Mean-Square Error (Residual Error)
£ 04O72J
0.427484
(0.234447)
0.101146
(0.035592)
0.229457
(0.097897)
0.119694
(0.044423)
0.075433
(0.035178)
23.98%
0.54670
£*tfcnatft
(tototinpCID
OOTC66}
0.403628
(0.234713)
0.115042
(0.034462)
0.236655
(0.098118)
0.090483
(0.039976)
0.077318
(0.035277)
23.23%
0.54861
Crfiwrt*
{Mod»fwfth
tio dttttfen*}
0.41 7648
(0.240347)
0.114038
(0.035294)
0.248043
(0.100421)
0.066338
(0.040151)
0.087010
(0.035987)
21.67%
0.56188
This table indicates that excluding these points changes the parameter estimates only
slightly.
5. Partial regression leverage plots were created for the environmental measures of lead
exposure: dripline soil, floor dust from carpeted and uncarpeted floors, paint/pica
hazard, and window sill dust. A partial regression leverage plot that exhibits a linear
relationship between blood-lead and the variable under consideration is indicative of
a linear relationship between blood lead and the environmental measure of lead
exposure while controlling for all the other variables in the model. The partial
regression leverage plots given hi Figure G12-6 indicate adjusted linear relationships
for the lead-exposure variables included hi the log-linear multimedia exposure model
fitted to the data from the Rochester Lead-in-Dust Study. Note that a partial
regression leverage plot is produced by plotting the residuals from a regression of the
response variable (LPbBiJk) on all predictor variables excluding the lead exposure
variable under consideration, versus the residuals from a regression of the lead
exposure variable under consideration on the remaining predictor variables.
6. Partial R2 comparisons can be made between predictor variables included hi the
model. A high partial R2 indicates greater importance in predicting blood-lead
concentration. Table G12-2 below provides the coefficient of determination (R2) for a
series of models in which one of the four predictor variables is excluded from the log-
linear model. The additional amount of variability in blood-lead concentrations
explained by the excluded predictor variable once added to the model is also
provided.
G-89
-------
Table G12-2. Partial R-squared Comparisons.
Variable Excluded
from the Model
Paint/Pica Hazard
Floor Dust-Lead
Dripline Soil-Lead
Window Sill Dust-Lead
Coefficient of
DeterminationtR2}
18.93%
20.44%
16.97%
19.04%
Partial Coefficient of
Determination (Partial
R*r
3.38%
1.54%
5.67%
3.25%
Additional
Variability Explained
m <21iKrtK3JW
2.74%
1.23%
2.63%
4.70%
• Partial R2 gives the contribution to the percent variation explained by adding in the variable of
interest. It is calculated as: *' '*"> - «'
I - H1 (REDUCED)
b 21.67% denotes the coefficient of determination (R2) for the full multi-media predictive model.
The multi-media predictive model explains 21.67% of the variability in childhood
blood-lead concentrations. Exposure from soil is the best predictor of blood-lead
concentration, with the highest partial R2 of around five percent.
7. An analysis into the effects of collinearity using several methods was conducted
during the development of the multi-media predictive model. Issues pertaining to
collinearity and strong correlation among potential lead-exposure predictor variables
had a prominent role in the variable selection for the multi-media predictive model.
Estimates of the tolerance statistic and variance inflation factor associated with each
predictor variable in the model are provided hi Table G12-3, together with a single
value decomposition for the design matrix of observed predictor variables hi the
Rochester Study.
To aid in the interpretation of these collinearity diagnostics, note that a large
condition index indicates the data are ill-conditioned, or when extremely large, that
parameter estimates are subject to substantial numerical error. A collinearity problem
occurs whenever a variable with a high condition index is also a chief contributor to
the variability between two or more variables.
Variance inflation factors measure how much the variability associated with a
particular parameter estimate is inflated due to collinearity between the predictors hi a
regression model. Although no formal criteria exists for establishing a critical
variance inflation factor, it is common practice to associate a condition index of 10
with the notion that weak dependencies may be starting to affect the regression
estimates. Condition indices of 30 to 100 indicate moderate to strong dependencies,
and indices of greater than 100 indicate serious collinearity problems. The number of
condition indices in the critical range indicates the number of near dependencies
contributing to the collinearity problem.
G-90
-------
Finally, another collinearity diagnostic is the condition number K, defined by K =
(largest eigenvalue / smallest eigenvalue)'7', where large values suggest collinearity.
Tabled 2-3. Collinearity Diagnostics
*****
1
2
3
4
eigenvalue ,
1 .70803
0.95248
0.81482
0.52466
Condition
Index
1.00000
1.33912
1 .44783
1 .80430
w
PDW | Pbs | PbP
Proportion o* Variability fxplainad
0.1395
0.0264
0.4116
0.4225
0.820436
0.1659
0.0360
0.0009
0.7972
0.1295
0.0013
0.6107
0.2585
0.0380
0.9450
0.0105
0.0065
Tolerance
0.736608
0.855715
Variance Inflation
1.218864
1 .357574
1.168613
0.976984
1 .0235585
Note that the largest condition index in Table G12-3 is 1.8, and the largest inflation
factor is 1.36 (PbW). Therefore, the multi-media predictive model (in its current
form) does not appear to suffer from a severe collinearity problem, nor does it appear
to be ill-conditioned (numerically unstable or fragile). The following matrix contains
the correlation coefficients among the four predictor variables used in the multi-media
predictive model. The coefficients are based on a sample size of 179 children/
households included in the current model.
PbF
PbW
PbS
PbP
PbF
1.000
0.417
0.186
0.110
PbW
0.417
1.000
0.370
0.101
PbS
0.186
0.370
1.000
0.119
PbP
0.110
0.101
0.119
1.000
Plots are provided hi Figure G12-7 of each continuous predictor variable versus
another continuous predictor variable, where each observation is coded for values of
the paint/pica hazard variable (0,1 or 2). These plots provide insight into the range of
possible values over which the multi-media predictive model was constructed, and
over which inferences can be drawn.
Based on the regression diagnostics on the multi-media predictive model it was
concluded that:
G-91
-------
• no influential or outlying points should be deleted from the analysis,
• the model developed fits the data observed,
• model assumptions are verified, and
• the model does not appear to suffer from a severe problem with collinearity.
Table G12-4. Formulae of Regression Diagnostic Statistics
Vafabte and Description
Foitntita
Predicted
Residual
«• =
Leverage (or hat matrix
diagonals)
h, = x, ( X'X )-' X,'
Quantity x calculated
without/th observation
Externally Studentized
Residual
r, =
0(1)
Cook's Distance
DFFITS
DFF/TS,
0())VTB,
COVRATIO
(e1(X'X)-1)
DFBETA
G-92
-------
I
-1
-2
Straight line indicates normality
-3 -2-10 1
Normal Quantile
Figure G12-1. Quantile Plot of Residuals.
~ 3
I
; %v;.. ;• ,*
p5*
»• »•
**
%* ^
•* •
-2
1 0
Residual PbB (
Figure G12-2. Plot of Residuals versus Predicted Values.
G-93
-------
I
-1
-2
10
. . .»;..-
•" -••-", '.
%•
100
I
-1
-2
0----;
1000 10000 100000
10
K»
1000 10000
2
1
f
ffl Q
1
2
£
-1
-2
4
1
1
!
<
4
(
'
•
.
*
•
*
| '
1
1
) 1 2
PbP
2
1
1
*./
03
3
^
I
-1
-2
*
•
*• •"•" *"! • •
* * • *
• <•* v • •
'•• ••-••r • .•
•.*./•*. *
•*•**« . •" *
« * a a
. * %«
*
1 10 100 1000 10000 mow
RttHuoiM
Figure G12-3. Plots of Residuals versus Predictors.
G-94
-------
0.10
0.08
0.06
0.04
0.02
0.00
Child ID: 00168
Minimum PbB
ID:
Maximum PbF/Low PbS
-4-3-2-10 1 2
Externally Studentized Residual PbB (
0.8
0.4
0.0
-0.4
-0.8
- :«£ .** «..
-rJTs-*
*"*•• -~
O> Child ID: 04072
ChlkJ ID: 00166 W Maximum PbF/Low PbS
Minimum PbB
-4-3-2-10 1 2
Externally Studentized Residual PbB (
Figure G12-4. Plots of Influence Statistics (Cook's Distance (D,) and DFFITS,) versus
Externally Studentized Residuals.
G-95
-------
05T
01
*
-05
-075 000 075
PbP
04
00
-04
-(
04
00
-04
-
07!
00!
-075
X
' •' f :' •
04
I M
-04
*5 "•
X75 000 075 -05 00 05
Ftp m
•• I.' .-
• '
X75 000 07
FtP
t
-i-'-
04
-04
5
07!
-07!
• ''fc.
• ' :
05 00 0!
FW
_ 1
• t
04
2 «
-04
)
075
| 000
-075
• ir-
f i
14 00 04
Ftf
, 1
** *^flb^ * *
075
\
' ' • ' •*
-075
075 000 075 -05 00 05 -04 00 04 -04 00 04
Ftp van w Fts
Figure G12-5. Plot of Changes in Parameter Estimates Relative to Standard Error for
Intercept and Coefficients of PbS, PbW, PbF and PbP.
G-96
-------
-5-4-3-2-10 1 2 3 4 5
Residual PbS(^)
2
-1
-2
-1
0 1 2
Residual PbP
|
p
IT
-1
-2
• : r
-6-5-4-3-2-10 1 2 3 4 5 6
Residual PbF(Mg/IL2)
i
5
-1
-2
-4-3-2-10 1
Residual PW (
Figure G12-6. Partial Leverage Regression Plots.
G-97
-------
1OOOOO
10000
1000
£ 100
88
10
10
10000
1000
-
10
3
1 1
10
~ 10000
1000
e 10
I 1
0 0
10O 1000 1OOOO
Dripllne Soll-Pb Concentration ( Mg/g )
100 1000 10OOO
Dripllne Soll-Pb Concentration (
10 100 1OOO
Window Sill Dust-Pb Loading (Wipe) (
1OOOOO
100000
10000 10OOOO
Rgure G12-7. Plots of One Predictor Variable versus Another Predictor Variable Coded for
Values of Paint/Pica Hazard Variable.
G-98
-------
G13: Appendix on Parameter Estimates for Candidate
Multimedia Exposure Models
G-99
-------
Parameter Estimates for Candidate Multimedia Exposure Models
Table G13-1. Comparison of Parameter Estimates (Standard Errors) Obtained from Five
Competing Statistical Models Which Regress Blood-Lead Concentration on
Measures of Drip-Line Soil-Lead Concentration, Floor Dust-Lead Loading,
Paint/Pica Hazard and Race.
Parameter
Po
Intercept
Pi
Floor
P2
Soil
33
Paint/Pica
P*
Black
eb
Fp«i»lv»C
o2
R2
ln(A)d
,; Parameter EstimatesfStafidard Errors) lor the Five Statistical Models
Ltig4Jrtaa**
0.533
(0.200)
0.070
(0.032)
0.134
(0.029)
0.219
(0.090)
0.524
(0.076)
•. •" A
f -,
0.256
0.357
-134.595
Log-Additive
4.279
(0.312)
0.0002
(0.0003)
0.0006
(0.0002)
1.798
(0.897)
3.642
(0.605)
% f
0.286
0.280
-145.104
Alternative*
Log-Additive
-0.593
(0.924)
0.249
(0.186)
0.772
(0.148)
1.667
(0.819)
3.422
(0.569)
f f .
«
f /
0.262
0.341
-136.920
Active
uptake
4.610
(0.768)
0.0002
(0.0005)
0.001 1
(0.0008)
2.570
(2.491)
5.409
(3.832)
36.086
(52.295)
"
0.289
0.281
-145.011
Active/
Passive
Uptake
4.610
(2.940)
0.0002
(0.0006)
0.0011
(0.0019)
2.571
(5.329)
5.410
(10.451)
36.075
(415.797)
0.000
(5.550)
0.289
0.281
-145.029
a In the implementation of the log-linear and alternate log-additive models, the categorical
variables Paint/Pica and Black were not log-transformed.
b The parameter 9 appears in the Active Uptake and Active/Passive Uptake Models described in
Section G3.0.
6 The parameter fniavu appears in the Active/Passive Uptake Model described in Section G3.0.
d Ln(A) represents the log-likelihood of the observed Rochester data given each model, and can
be used to assess the plausibility of one model in comparison to another, as described in
Section G4.3.
G-100
-------
Table G13-2. Comparison of Parameter Estimates (Standard Errors) Obtained from Five
Competing Statistical Models Which Regress Blood-Lead Concentration on
Measures of Drip-Line Soil-Lead Concentration, Floor Dust-Lead Loading, and
Paint/Pica Hazard.
;
Parameter
Po
Intercept
3,
Floor
02
Soil
33
Paint/Pica
6"
Fc
Paulva
O2
R2
ln(A)d
Parameter E*timates(StarKJard ErroreJ fw the Five Statistical Model*
Log-Linear*
0.608
(0.224)
0.089
(0.036)
0.146
(0.033)
0.252
(0.101)
>
a.•^<^.•J
0.321
0.189
-156.216
Log-Additive
5.221
(0.361)
0.00001
(0.0004)
0.0008
(0.0002)
2.434
(1.075)
> s
0.354
0.105
-165.340
Alternative'
Log-Additive
-0.494
(1.079)
0.474
(0.242)
0.834
(0.177)
2.131
(0.985)
_.
••
0.324
0.182
-156.979
Active
Uptake
6.424
(1.323)
0.00006
(0.0008)
0.009
(0.006)
21.857
(34.860)
11.315
(2.760)
0.340
0.149
-160.687
Active/
Passive
Uptake
6.424
(1.763)
0.00006
(0.0008)
0.009
(0.010)
21.857
(43.079)
11.315
(6.623)
0.000
(0.054)
0.340
0.149
-160.702
' In the implementation of the log-linear and alternate log-additive models, the categorical
variable Paint/Pica was not log-transformed.
b The parameter 8 appears in the Active Uptake and Active/Passive Uptake Models described in
Section G3.0.
0 The parameter Fp,,,^ appears in the Active/Passive Uptake Model described in Section G3.0.
d Ln(A) represents the log-likelihood of the observed Rochester data given each model, and can
be used to assess the plausibility of one model in comparison to another, as described in
Section G4.3.
G-101
-------
Table G13-3. Comparison of Parameter Estimates (Standard Errors) Obtained from Five
Competing Statistical Models Which Regress Blood-Lead Concentration on
Measures of Drip-Line Soil-Lead Concentration, Floor Dust-Lead Loading,
Window Sill Dust-Lead Loading, Paint/Pica Hazard and Race.
V -. f
Parameter
Po
Intercept
Pi
Floor
P2
W. Sill
3a
Soil
04
Paint/Pica
05
Black
&>
Fpunbn"
O2
R2
ln(A)d
; ^ Pmime^nr £stira^^(St«ttda*d £rr or«^*0r ihe Five Stai$ttic*l Models
'-.-. •.
Log^nesr*
0.399
(0.216)
0.058
(0.036)
0.065
(0.033)
0.109
(0.032)
0.209
(0.090)
0.514
(0.079)
•'-.•tip •• '<<.
' Xv
-<$( f
f
0.255
0.371
-128.623
•.
log-Addttive
4.083
(0.308)
0.00008
(0.00031)
0.00097
(0.00037)
0.00042
(0.0001 8)
1.688
(0.870)
3.567
(0.622)
/f
-•-,
,;
0.277
0.316
-136.253
Alternative*
Log-Additive
-0.658
(0.952)
0.131
(0.213)
0.280
(0.191)
0.609
(0.169)
1.604
(0.835)
3.483
(0.604)
,•<
,*' f
0.265
0.346
-132.190
••>•, s ••••
Active
Uptake
4.409
(0.559)
0.00002
(0.00047)
0.003
(0.002)
0.00090
(0.00056)
2.741
(2.387)
6.413
(3.516)
25.174
(17.194)
-
0.278
0.323
-135.353
Active/
Pasiiv* -
Uptake
4.409
(1.262)
0.00002
(0.00048)
0.003
(0.004)
0.00090
(0.00100)
2.741
(3.719)
6.412
(7.491)
25.175
(76.900)
0.000
(0.994)
0.278
0.323
-135.375
' In the implementation of the log-linear and alternate log-additive models, the categorical
variables Paint/Pica and Black were not log-transformed.
b The parameter 6 appears in the Active Uptake and Active/Passive Uptake Models described in
Section G3.0.
c The parameter Fp,^. appears in the Active/Passive Uptake Model described in Section G3.0.
d Ln(A) represents the log-likelihood of the observed Rochester data given each model, and can
be used to assess the plausibility of one model in comparison to another, as described in
Section G4.3.
G-102
-------
Table G13-4. Comparison of Parameter Estimates (Standard Errors) Obtained from Five
Competing Statistical Models Which Regress Blood-Lead Concentration on
Measures of Drip-Line Soil-Lead Concentration, Floor Dust-Lead Loading,
Window Sill Dust-Lead Loading and Paint/Pica Hazard.
Parameter
3o
Intercept
3i
Floor
02
W. Sill
Pa
Soil
P4
Paint/Pica
eb
rpaulva0
o2
R2
ln(A)d
Parameter EstimatesOtandard Errors} tot the Five Statistical Models
Log-Uneai**
0.418
(0.240)
0.066
(0.040)
0.087
(0.036)
0.114
(0.035)
0.248
(0.100)
X "•': ' ''??•-"• ' : -:'
:;:::|;?l;i||lli:;:^;; >:;>::,
0.316
0.217
-148.303
Log-Additive
4.932
(0.355)
0.00000
(0.00037)
0.00126
(0.00046)
0.00050
(0.00022)
2.304
(1.035)
i^^^^SjisSw^^^
>>S: '*'''.-:. ...:.?&... "H2
0.342
0.153
-155.331
Alternative*
Log-Additive
-0.528
(1.124)
0.371
(0.276)
0.276
(0.213)
0.651
(0.206)
2.139
(0.996)
0.323
0.190
-151.361
Active
Uptake
5.229
(1.034)
0.00000
(0.00172)
0.012
(0.009)
0.003
(0.002)
10.823
(11.740)
13.365
(3.317)
^M^W:WSXmm'.ii;A
Wmmf:y^Mm-&s^fM
0.327
0.198
-150.393
Active/
Passive
Uptake
5.229
(1.134)
0.00000
(0.00173)
0.012
(0.012)
0.003
(0.002)
10.824
(14.748)
13.365
(7.597)
0.000
(0.063)
0.327
0.198
-150.412
8 In the implementation of the log-linear and alternate log-additive models, the categorical
variable Paint/Pica was not log-transformed.
b The parameter 6 appears in the Active Uptake and Active/Passive Uptake Models described in
Section G3.0.
c The parameter FPaMlve appears in the Active/Passive Uptake Model described in Section G3.0.
d Ln(A) represents the log-likelihood of the observed Rochester data given each model, and can
be used to assess the plausibility of one model in comparison to another, as described in
Section G4.3.
8 Note that the log-linear model which regresses blood-lead on floor dust-.lead loading, window
sill dust-lead loading, dripline soil-lead concentration and paint/pica hazard is the unadjusted
Multi-media predictive model described in Section 5 of this document.
G-103
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