REPORT
Final Report
Statistical Evaluation of the
Relationship Between
Blood-Lead and Dust-Lead on
Pre-Intervention Data from
the R&M Study
To
U.S. Environmental
Protection Agency
QBaltelie
. . . Putting Technology To Work
January 31, 1996
-------
February 1, 1996
NOTE TO: Cindy Stroup
Doreen Cantor
Jonathan Jacobson
Andrea Yang
Dave Topping
Barbara Leczynski
Ben Lim
John Schwemberger
Karen Hogan (7403)
Paul White (8603)
Larry Zaragoza (5204G)
Nishkam Agarwal (7406)
FROM: Janet Rename;
RE: Transmittal of report, "Sta'nstical Evaluation of the Relationship Between Blood-Lead
and Dust-Lead on Pre-Intervention Data from R&M Study", dated January 31, 1996
Attached is a copy of the subject report. This revision incorporates a change in the
estimation of the measurement error, which resulted in slight changes in the numbers in the
tables. This was the only change in the report from the previous version. If you have any
questions or comments please let me know by February 15, 1996.
A similarly-revised report on the analysis of the Rochester data will be forthcoming.
Thanks.
-------
January 31, 1996
FINAL REPORT
STATISTICAL EVALUATION OF THE RELATIONSHIP
BETWEEN BLOOD-LEAD AND DUST-LEAD BASED ON
PRE-INTERVENTION DATA FROM THE R&M STUDY
for
Task 4-13
Battelle Task Leader
Warren Strauss
Battelle Task Team
Steven Rust and Halsey Boyd
BATTELLE
505 King Avenue
Columbus. Ohio 43201
Contract No. 68-D2-0139
Janet Remmers, EPA Work Assignment Manager
Jill Hacker, EPA Project Officer
Technical Programs Branch
Chemical Management Division
Office of Pollution Prevention and Toxics
U.S. Environmental Protection Agency
Washington, DC 20460
-------
Battelle Disclaimer
This is a report of research performed by Battelle for the United States
Government. Because of the uncertainties inherent in experimental or
research work, the above parties assume no responsibility or liability for any
consequences of use, misuse, inability to use, or reliance upon the
information contained herein, beyond any express obligations embodied in
the governing written agreement between Battelle and the United States
Government.
-------
TABLE OF CONTENTS
1.0 INTRODUCTION 1
2.0 DATA PREPARATION 1
3.0 THE STATISTICAL MODEL 3
4.0 STATISTICAL MODELING RESULTS 3
5.0 PROTECTIVE DUST LEAD LEVELS 5
6.0 EXCEEDANCE PROPORTIONS 10
7.0 PARTIAL SIGNIFICANCE OF WINDOW WELL PB MEASUREMENTS 12
APPENDICES
APPENDIX A. ALTERNATIVE STATISTICAL MODELS A-1
APPENDIX B. ALTERNATIVE REGRESSION PARAMETER
ESTIMATION IN THE PRESENCE OF MEASUREMENT
ERROR B-1
APPENDIX C. TOLERANCE BOUNDS AND CONFIDENCE INTERVALS
FOR PERCENTILES AND EXCEEDANCE PROBABILITIES
IN A REGRESSION SETTING C-1
APPENDIX D. DETAILS ON MEASUREMENT ERROR D-1
APPENDIX E. PARAMETER ESTIMATES FOR STATISTICAL MODELS E-1
APPENDIX F. PROTECTIVE DUST LEAD LEVELS AND EXCEEDANCE
PROBABILITIES FOR ERRORS IN VARIABLES
SOLUTION F-1
APPENDIX G. PROTECTIVE DUST LEAD LEVELS AND EXCEEDANCE
PROBABILITIES FOR LEAST SQUARES SOLUTION G-1
APPENDIX H. SIDE-BY-SIDE PLOTS COMPARING THE RESULTS OF
THE DESCRIPTIVE MODEL TO THE SEPARATE
INTERCEPTS MODEL, AFTER ADJUSTING FOR
ERRORS IN PREDICTOR VARIABLES H-1
APPENDIX I. SIDE-BY-SIDE PLOTS COMPARING THE RESULTS OF
THE DESCRIPTIVE MODEL TO THE SEPARATE
INTERCEPTS MODEL, USING A LEAST SQUARES
SOLUTION 1-1
APPENDIX J. PLOTS COMPARING THE RESULTS OF THE
DESCRIPTIVE MODEL TO THE SEPARATE INTERCEPTS
MODEL, AFTER ADJUSTING FOR ERRORS IN
PREDICTOR VARIABLES J-1
in
-------
TABLE OF CONTENTS
(Continued)
Page
LIST OF TABLES
Table 1. Results of Fitting the Descriptive Model to the R&M Pre-
Intervention Lead Data Using the Errors in Variables Approach . . .
Table 2. Estimated Dust Pb Loadings for Floors, Window Sills, and Window
Wells at Which the 85th, 90th, 95th, and 99th Percentiles of
Childhood Blood Pb Concentrations Reach 10, 15, and 20/vg/dL
(Based on the Descriptive Model Using an Errors in Variables
Approach)
Table 3. Estimated Proportion of Children with Blood-Pb Concentrations
Greater than 10, 15, and 20//g/dL as Predicted by an Errors in
Variables Regression Model of Blood Pb versus Floor, Window Sill,
or Window Well Pb Loadings
Table 4. Results of Fitting Floor, Window Sill, and Window Well Lead
Loadings or Concentrations Simultaneously on Blood-Lead
Concentrations Based on the Descriptive Model Using a Least
Squares Approach
Table 5. Estimated Pearson Correlation Coefficients Between Natural Log
Transformed Lead Levels from Children's Blood and Floor, Window
Sill and Window Well Dust
11
13
15
LIST OF FIGURES
Figure 1. Estimated Regression Curve and Tolerance Bounds for the 85th,
90th, 95th and 99th Percentile of Children's Blood-Lead
Concentrations Based on the Estimated Relationship Between
Blood-Lead Concentrations and Floor-Lead Loadings from an Errors
in Variables Fit of the Descriptive Model
Figure 2. Estimated Regression Curve and Tolerance Bounds for the 85th,
90th, 95th and 99th Percentile of Children's Blood-Lead
Concentrations Based on the Estimated Relationship Between
Blood-Lead Concentrations and Window Sill-Lead Loadings from an
Errors in Variables Fit of the Descriptive Model
Figure 3. Estimated Regression Curve and Tolerance Bounds for the 85th,
90th, 95th and 99th Percentile of Children's Blood-Lead
Concentrations Based on the Estimated Relationship Between
Blood-Lead Concentrations and Window Well-Lead Loadings from
an Errors in Variables Fit of the Descriptive Model
6
8
IV
-------
STATISTICAL EVALUATION OF THE RELATIONSHIP BETWEEN BLOOD-LEAD
AND DUST-LEAD BASED ON PRE-INTERVENTION DATA FROM THE R&M STUDY
for
Task 4-13 Under Contract No. 68-D2-0139
by
Warren Strauss and Steven Rust
1.0 INTRODUCTION
The following statistical analysis investigated the
relationship between children's blood-lead concentrations and
levels of lead in interior household dust from pre-intervention
data collected in the Repair and Maintenance (R&M) Study. This
research was conducted to support regulatory decisions for
Section 403 of Title X being made by EPA's Office of Pollution
Prevention and Toxics. Specifically, this research was designed
to give information on the levels of interior dust lead found on
floors, window sills or window wells that would result in 85%,
90%, 95% and 99% of the distribution of childhood blood-lead
concentrations being below 10, 15, and 20 ng/dL. Additionally
this analysis investigated the importance of levels of lead in
window well dust as a predictor of blood-lead concentrations
after taking into account the levels of lead in floor and window
sill dust.
2.0 DATA PREPARATION
The sample consisted of 115 children in 87 homes that were
recruited during the pre-intervention phase of the R&M study.
Homes were categorized into three groups: the "Modern Urban" and
"Previously Abated" homes which served as two different control
groups, and the "R&M" group which consisted of occupied houses
for which R&M activities were performed. There were 19 children
living within 16 "Modern Urban" houses, 23 children living within
15 "Previously Abated" houses, and 73 children living within 56
"R&M" houses. There were several homes in the study which had
more than one child in residence, including 16 homes with two
children, 3 homes with three children, and two homes that
included four children.
-------
The response variable in the statistical analysis was the
natural logarithm of pre-intervention blood-lead concentration
measured in units of ln(/ig/dL) . Predictor variables included
lead loading and concentration results observed in dust from
floors, window sills and window wells, and the date of blood
sampling which was used to account for seasonal trends in blood-
lead concentrations. In roughly 75% of the data, blood samples
and dust samples were collected within a two-week window of time.
However, there were eight instances where there were more than 28
days in between blood sampling and dust sampling, ranging from 30
to 56 days.
To reduce analytical costs, samples of dust lead were
composited over multiple locations of a given component type.
The compositing acts as an averaging mechanism across the unit.
The composite samples were often collected from locations with
different surface areas. For example, each house had between 3
and 5 floor dust composite samples with total area ranging from 9
to 17 ft2 of floors sampled per house. Each house also had 1 or
2 window sill composite samples, and between 0 and 2 window well
samples. The majority of houses had 2 window sill and 2 window
well samples with total area ranging from 0.66 to 15.1 ft2 of
window sills sampled per house and total area ranging from 0.11
to 8.3 ft2 of window wells sampled per house. Since the area and
dust mass of each individual composite sample varies within a
house, area weighted average lead loading, and sample mass
weighted average lead concentration, results were calculated for
floors, window sills and window wells. Thus, if two dust
composite samples were collected from floor locations within a
house with sample areas of 1 ft2 and 3 ft2, the lead loading and
concentration results from the 3 ft2 composite sample would be
weighted by a factor of 3 when calculating the area weighted
averages. The natural log of these weighted average lead loading
and concentration results were used as predictor variables in the
statistical analyses, and therefore the estimated relationships
-------
between blood lead and dust lead correspond to dust lead averages
and not individual 'hot spots'.
3.0 THE STATISTICAL MODEL
A simple descriptive log-linear statistical model was used
which expresses blood lead concentrations as a function of
environmental lead levels. Specifically, the model contains a
single intercept, a single slope relating In(blood lead) to
In(dust lead) and a seasonal term which adjusts for seasonal
trends in childhood blood-lead concentrations. Details
concerning the mathematical form of the statistical model can be
found in Appendix A.
Due to the fact that environmental lead levels are usually
measured with error, a statistical approach that adjusts for
measurement error in predictor variables was used while fitting
the statistical model. Details concerning the statistical
adjustment for errors in predictor variables can be found in
Appendix B.
The model used makes two additional assumptions about the
pre-intervention data from the R&M study. The first assumption
is that blood-lead measurements from children in this study are
independently distributed. The second assumption-is that the
relationship found between blood-lead and dust-lead in each study
group is similar. There is statistical evidence provided in
Appendix A which demonstrates that these assumptions are probably
not satisfied. However, this model was chosen because of its
simplicity, and is recognized as being rather approximate.
Appendix A provides details of a somewhat more complicated model
which fits the data and the model assumptions better, and
therefore may be more appropriate for drawing statistical and
practical inferences about these data.
4.0 STATISTICAL MODELING RESULTS
The results of fitting the simple descriptive model to the
data using an errors in variables approach are reported in
-------
Table 1. Separate models were fitted for the six environmental-
lead (PbE) measurements. Slope ((3^) parameter estimates and
associated 95% confidence intervals are reported in units of
[ln(/ig Pb/dL Blood)/In (/ig Pb / g Dust)], as well as a measure of
the proportion of variability explained by the model (R2) from a
'least squares' fit of the model.
Table 1. Results of Fitting the Descriptive Model to the R&M Pre-lntervention Lead Data
Using the Errors in Variables Approach
Unit of Measure
Component
Tested
Slope Values
/?, lb)
Slope Estimate
95%
Confidence Interval
(C)
R2
Slope Values in Units of ln(//g Pb/dL Blood) / ln(/ig Pb/ft2 Sampled)
Loading
U/g/ft2)
Floors
Window Sills
Window Wells
0.310(al
0.115
0.078
(0.232 , 0.387)
(0.066, 0.164)
(0.032 , 0.124)
0.367
0.247
0.192
Slope Values in Units of ln(//g Pb/dL Blood) / ln(/ig Pb/g Dust)
Concentration
(pg/g)
Floors
Window Sills
Window Wells
0.347
0.167
0.128
(0.257 , 0.437)
(0.100, 0.233)
(0.054 , 0.202)
0.370
0.265
0.192
Based on the results of this simple descriptive model, the predicted blood-
lead concentration for children living in houses with floor lead loadings of
100 and 200//g/ft2 would be 5.6 and 7.0 fjg/dL respectively for a difference
of 1 .
b Results of a more complicated model which allows separate intercepts for
each study group suggest that the slopes relating blood-lead concentrations
to dust-lead levels are less than the values reported in this table.
c The reported R2 values are based on a least squares fit of the descriptive model
without adjusting for the errors in predictor variables.
The relationship between blood-lead concentrations and dust
lead loadings for floors, window sills, and window wells are
illustrated graphically in Figures 1, 2, and 3. In these plots
separate plotting symbols are used to represent each type of
study home (asterisks for "Modern Urban", stars for "Previously
-------
Abated", and circles for "R&M" homes). The fitted regression
curve from the least squares fit is plotted using a finely dashed
line, and the solution from the errors in variables model is
plotted using a solid line. The four upper dashed curves in
Figures 1, 2, and 3 represent upper 95% tolerance bounds for the
85th, 90th, 95th, and 99th percentiles of the distribution of
children's blood-lead concentration as a function of dust-lead
loadings. The line type employing the shortest dash corresponds
to the 85th percentile, the next shortest corresponds to the 90th
percentile, and so on. The estimated regression curves and
associated tolerance bounds were calculated for children's blood
lead levels measured near the seasonal median blood lead level
(November 1). Methods for calculating the tolerance bounds are
detailed in Appendix C. The tolerance bounds depicted in these
figures represent a 95% upper confidence bound for the 85th,
90th, 95th and 99th percentiles of the distribution of children's
blood-lead concentrations at each dust lead level, based on the
regression model results. Thus, the highest curve in Figure 1
corresponds to a 95% upper confidence bound on the 99th
percentile of children as a function of floor-lead loading, based
on the results of the descriptive model.
5.0 PROTECTIVE DUST LEAD LEVELS
The dashed curves in Figures 1, 2, and 3 can be used to
determine the levels of interior dust lead that would result in
85%, 90%, 95% and 99% of the distribution of childhood blood-lead
concentrations being below target values with 95% confidence.
This is accomplished by drawing a horizontal line at the blood-
lead level of interest, and then drawing a vertical line at the
point of intersection with the appropriate tolerance bound curve.
Table 2 reports such dust-lead loading (and concentration)
levels for floors, window sills and wells based on target blood-
lead levels of 10, 15, and 20 /zg/dL. The results in this table
are based on tolerance bounds calculated using the errors in
variables model at or near the seasonal median (November 1).
-------
TJ
o
£
m
50-
40
20-
10
10 100 1000
Floor Pb Loading (yug/sq. ft)
10000
* * * Modern Urban 855! Upper Bound (EIV)
ft ft * Previously Abated 90% Upper Bound (EIV)
O O O Repair and Maintenance 9555 Upper Bound (EIV)
Predicted (EIV) 9955 Upper Bound (EIV)
Predicted (Least Squares)
-r-n-rj
100000
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
Figure 1. Estimated Regression Curve and Tolerance Bounds for the 85th, 90th, 95th and 99th Percentile of Children's
Blood-Lead Concentrations Based on the Estimated Relationship Between Blood-Lead Concentrations and Floor-
Lead Loadings from an Errors in Variables Fit of the Descriptive Model.
-------
D)
=1
T3
O
J3
m
50-f
40:
30
20
10
10 100 1000 10000 100000
Window Sill Pb Loading (/ug/sq. ft)
1000000
* * * Modern Urban 85% Upper Bound (EIV)
fc A * Previously Abated 90% Upper Bound (EIV)
O O O Repair and Maintenance 95% Upper Bound (EIV)
Predicted (EIV) 99% Upper Bound (EIV)
Predicted (Least Squares)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
Figure 2. Estimated Regression Curve and Tolerance Bounds for the 85th, 90th, 95th and 99th Percentile of Children's
Blood-Lead Concentrations Based on the Estimated Relationship Between Blood-Lead Concentrations and
Window Sill-Lead Loadings from an Errors in Variables Fit of the Descriptive Model.
-------
01
0
0
m
50
40
30
°- 20
10
0
""I
10
100
1 III]
1000
n-TTTT
10000
100000
1000000 10000000
*
*
o
Window Well Pb Loading (/ug/sq. ft)
* * Modern Urban 8555 Upper Bound (EIV)
£ A Previously Abated 90% Upper Bound (EIV)
O O Repair and Maintenance 955! Upper Bound (EIV)
Predicted (EIV) 99% Upper Bound (EIV)
Predicted (Least Squares)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
Figure 3. Estimated Regression Curve and Tolerance Bounds for the 85th, 90th, 95th and 99th Percentile of Children's
Blood-Lead Concentrations Based on the Estimated Relationship Between Blood-Lead Concentrations and
Window Well-Lead Loadings from an Errors in Variables Fit of the Descriptive Model.
-------
In some cases, the tolerance bound is higher than the
blood-lead level of interest over the entire range of plausible
dust-lead levels. For example in Figure 2, where the tolerance
bound for the 99th percentile of children's blood-lead
concentrations is always above a blood-lead concentration of 10
/xg/dL. In Table 2 these cases have associated dust-lead values
that are listed as "Out of Range".
Table 2. Estimated Dust Pb Loadings for Floors, Window Sills, and Window Wells at
Which the 85th, 90th, 95th, and 99th Percentiles of Childhood Blood Pb
Concentrations Reach 10, 15, and 20 jig/dL (Based on the Descriptive Model
Using an Errors in Variables Approach)
Sample
Type
Floor
Lead
Loading
(//g/ft2)
Window
Sill
Lead
Loading
-------
Table 2. Estimated Dust Pb Concentrations for Floors, Window Sills, and Window Wells
at Which the 85th, 90th, 95th, and 99th Percentiles of Childhood Blood Pb
Concentrations Reach 10, 15, and 20//g/dL (Based on the Descriptive Model
Using an Errors in Variables Approach) (Continued)
Sample
Type
Floor
Lead
Concentration
0/g/ft2)
Wcndow
Sill
Lead
Concentration
U/g/ft2)
Window
Well
Lead
Concentration
to/ft2)
Tolerance Level
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
Target Blood-Lead Concentration "'
10//g/dL
141
86
40
9
13
3
Out of Range
Out of Range
Out of Range
Out of Range
Out of Range
Out of Range
1S//g/dL
529
328
159
38
341
95
13
Out of Range.
17
1
Out of Range
Out of Range
20 /yg/dL
1287
815
405
102
2733
840
130
3
519
70
2
Out of Range
(a)
A result of 'Out of Range' indicates that the tolerance bound for Blood-Pb is always above the target level.
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median
blood-lead concentrations.
6.0 EXCEEDANCE PROPORTIONS
Table 3 provides estimates of the proportion of children
with blood-lead concentrations exceeding 10, 15, and 20 /xg/dL at
various targeted dust lead loading values for floors, window
sills, and window wells. These exceedance proportions, and
associated 95% confidence intervals were calculated using methods
detailed in Appendix C. They are based on the errors in
variables model near the seasonal median (November 1).
The results from this descriptive model suggest that for
dust-lead loadings of 100 jig/ft2 on floors, 500 /ig/ft2 on window
sills, and 800 /xg/ft2 on window wells, approximately 16%, 32%,
and 28% of the children sampled in this study would be expected
to have blood-lead concentrations that exceed 10 /ig/dL at the
seasonal median.
10
-------
Table 3. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 10,
15, and 20//g/dL as Predicted by an Errors in Variables Regression Model of
Blood Pb versus Floor, Window Sill, or Window Well Pb Loadings
Surface
Tested
Floors
Window
Sills
Window
Wells
Pb
Loading
10)
0004
0012
0022
0031
0040
0050
0059
0068
0 159
0.265
0305
0 194
0229
0 267
0291
0308
0322
0333
0343
0231
0264
0 279
0 282
0306
0334
0356
0385
0415
95% Cl
(0 000. 0 047)
(0001. 0084)
(0002.0 114)
(0004, 0 139)
(0006, 0 162)
(0008, 0 182)
(0011. 0200)
(0014, 0217)
(0051,0357)
(0111, 0485)
(0 138, 0 528)
(0 059. 0 433)
(0 079, 0 469)
(0 104. 0 506)
(0 120. 0528)
(0 132. 0545)
(0 143, 0 557)
(0 151.0568)
(0 158.0576)
(0 069. 0 504)
(0090. 0531)
(0 101.0543)
(0 102. 0 545)
(0 120.0564)
(0 141, 0 586)
(0 158,0603)
(0 182, 0626)
10 208, 0 650)
Proportion Greater Than
15/jg/dL
Pr(PbB>15)
0000
0001
0003
0005
0007
0009
0011
0014
0044
0092
0 113
0070
0087
0 108
0 122
0 133
0 141
0 148
0 155
0093
0 112
0 121
0 122
0 137
0 155
0 169
0 190
0212
95% Cl
(0 000, 0 009)
(0 000. 0 020)
(0 000, 0 030)
(0 000, 0 040)
(0 000. 0 049)
(0 000. 0 057)
(0001, 0065)
(0001. 0073)
(0009, 0 149)
(0 026. 0 236)
(0 035, 0 270)
(0014, 0223)
(0 020. 0 250)
10 029, 0 280)
(0 035, 0 299)
(0041, 0313)
(0 045. 0 324)
(0 048, 0 334)
(0 052, 0 342)
10018. 0287)
(0026. 0310)
(0 030. 0 320)
(0031. 0322)
(0 038. 0 340)
(0 047. 0 360)
(0 055, 0 376)
(0 066, 0 399)
(0 079, 0 424)
Proportion Greater Than
20 ;ig/dL
Pr(PbB>20)
0000
0000
0000
0001
0001
0002
0002
0003
0014
0034
0044
0028
0036
0047
0055
0060
0065
0069
0073
0041
0051
0056
0057
0065
0076
0085
0098
0 112
95% Cl
(0 000. 0 002)
(0 000. 0 006)
(0 000, 0 009)
(0 000, 0 01 3)
(0000. 0016)
(0 000. 0 020)
(0 000. 0 023)
(0 000, 0.027)
(0.001, 0.065)
(0006. 0 116)
(0010, 0 138)
(0004, 0 119)
(0 006. 0 1 37)
(0 009. 0 1 58)
(0012, 0 172)
(0014, 0 182)
(0016. 0 191)
(0017. 0 198)
(0019, 0204)
(0006.0 168)
(0008,0 184)
(0010, 0 193)
(0010. 0 194)
(0013.0207)
(0017. 0 223)
(0021. 0.236)
(0 026. 0 255)
(0 033, 0 276)
Results are based on a seasonally adjusted analysis held fixed at November 1. and represent seasonal median blood-lead concentrations
11
-------
7.0 PARTIAL SIGNIFICANCE OF WINDOW WELL PB MEASUREMENTS
The final analysis performed was used to determine
whether the predictive ability of the model improves when adding
window well lead levels to a model which already accounts for
dust lead on floors and window sills. The analysis begins with a
base model which adjusts for seasonal variations in blood-lead
concentrations, and then sequentially adds variables representing
lead in floors, window sills, and window wells to the model. The
results of this analysis are reported in Table 4. The slope
parameters and associated 95% confidence intervals in each row
correspond to a statistical model which includes the variables in
the base model and the variable being added to the base model.
The coefficient of determination (R2) is provided for each model
fitted, where floors, sills and wells are added sequentially to
the base model. The difference in R2 values between the full
model and the base model is also presented. This value
corresponds to the extra amount of variability explained by the
variable being added to the model.
The estimated effect of well lead on blood lead was not
close to being statistically significant after adjusting for the
effects of floor lead, sill lead, and seasonal variation. Floor
lead appeared to explain most of the variability in blood lead in
both of the combined models. The model with only floor lead
loading and an adjustment for seasonal trends explained 36.5% of
the variability in blood-lead concentrations, adding window sill
lead loading to the model explained an additional 0.6% of the
variability, and adding window well lead loading with the other
two factors already in the model explained an additional 0.1% of
the variability. The amount of extra variability explained by
window sill-lead loading after already accounting for floor-dust
lead loading and seasonal variations is calculated by subtracting
the coefficient of determination from the base model (R2=0.365)
from the coefficient of determination from the full model
(R2=0.371). The model with only floor lead concentration and an
12
-------
Table 4. Results of Fitting Floor, Window Sill, and Window Well Lead Loadings or Concentrations Simultaneously
on Blood-Lead Concentrations Based on the Descriptive Model Using a Least Squares Approach
Unit of
Measure
Sample
Size
Variables
in the
Base Model
Variables
Added to the
Base Model
Slope Values
/M (Roors)
(95% CD
£1 (Sills)
(95% CD
01 (Wells)
(95% CD
R2
for the
Full Model
Additional
Variability
Explained
Slope Values in Units of ln(0g Pb / dL Blood) / ln(//g Pb / ft2 Sampled) (Oust Samples Collected with BRM Sampler)
Loading
(//g/ft2)
BRM Sampler
114
Season
Season. Floors
Season, Floors
Season. Floors,
Sills or Wells
Floors
Window Sills
Window Wells
Window Sills
Window Wells
0.239
(0.168,0.310)
0.211
(0.122.0.301)
0.231
(0.148.0.314)
0.212
(0.123.0.300)
0.027
(-0.026 , 0.080)
0.047
(-0.035,0.129)
0.008
(-0.037 , 0.053)
-0.022
(-0.091 , 0.047)
0.365
0.371
0.366
0.373
0.248
0.006
0.001
0.007 (s)
0.002 (w)
Slope Values in Units of ln(/sg Pb / dL Blood) / ln(//g Pb / g Dust) (Dust Samples Collected with BRM Sampler)
Concentration
0/9/9)
BRM Sampler
114
Season
Season, Floors
Season, Floors
Season, Floors,
Sills or Wells
Floors
Window Sills
Window Wells
Window Sills
Window Wells
0.287
(0.202 ,0.371)
0.250
(0.136,0.364)
0.289
(0.186.0.392)
0.253
(0.139.0.366)
0.039
(-0.025,0.117)
0.082
(-0.030,0.194)
-0.003
(-0.077,0.071)
-0.057
(-0.161 , 0.047)
0.369
0.374
0.369
0.381
0.252
0.005
0.000
0.01 2 (s)
0.007 (w)
M
10
* The reported values of the parameter estimates, standard errors, and coefficient of determination (R2) are based on a least squares fit of the descriptive
model without adjusting for the errors in predictor variables.
(s) .Indicates that window sills were added last to a model which includes seasonal variations, floors and window wells.
(w) Indicates that window wells were added last to a model which includes seasonal variations, floors and window sills.
-------
adjustment for seasonal trends explained 36.9% of the variability
in blood-lead concentrations, adding window sill lead
concentration to the model explained an additional 0.5% of the
variability, and adding window well lead concentration with the
other two factors already in the model explained an additional
0.7% of the variability.
The predictive ability of the model did not improve
significantly when measures of window well dust lead levels were
added to a model which already accounted for dust lead on floors
and window sills. One possible explanation is that dust lead
measurements from floors, window sills, and window wells within a
house are probably correlated. The predictive ability of a
regression model will not improve significantly when the variable
added to the model is highly correlated with another predictor
variable. Table 5 demonstrates estimated Pearson correlation
coefficients between natural log transformed lead levels from
children's blood and floor, window sill and window well dust.
This table demonstrates that for each measurement method
(Loadings and Concentrations) lead levels from window sills and
window wells are statistically significantly correlated with each
other, and with children's blood-lead concentrations.
14
-------
Table 5. Estimated Pearson Correlation Coefficients Between Natural Log Transformed
Lead Levels from Children's Blood and Floor, Window Sill and Window Well
Dust.
Blood
Floors
Window
Sills
P
p-value
n
P
p-value
n
P
p-value
n
Blood
Floors
Window
Sills
P
p-value
n
P
p-value
n
P
p-value
n
Blood
Floors
Window Sills
Window
Wells
Lead Loadings
1
0.495
< 0.001
115
1
0.416
<0.001
115
0.611
< 0.001
115
1
0.374
<0.001
114
0.490
<0.001
114
0.833
< 0.001
114
Lead Concentration
1
0.581
<0.001
115
1
0.468
<0.001
115
0.701
< 0.001
115
1
0.371
<0.001
114
0.608
<0.001
114
0.827
<0.001
114
15
-------
APPENDIX A.
ALTERNATIVE STATISTICAL MODELS
A-l
-------
Appendix A
Alternative Statistical Models
This statistical analysis investigated the relationship
between children's blood-lead concentrations and levels of lead
in interior household dust. The sample consisted of 115 children
in 87 homes that were recruited during the pre-intervention phase
of the R&M study. Homes were categorized into three groups: the
"Modern Urban" and "Previously Abated" homes which served as two
different control groups, and the "R&M" group which consisted of
occupied houses for which R&M activities were to be performed.
Following is a brief description of the variables that are
included in the statistical analysis. All of the variables can
be organized using identifiers for house (i), and child within a
house (ij) .
PbBi;) The blood-lead level in (/xg/dL) for the jth child in
the ith home.
tij The day of the year on which the PbBAj measurement was
taken.
PbFLt The area weighted arithmetic average floor, sill, and
well lead loading for house (i) based on pre-
intervention composite vacuum samples.
The area weighted arithmetic average floor, sill, and
well lead concentration for house (i) based on pre-
intervention composite vacuum samples.
The statistical model fitted to the data in the main report
was descriptive in nature and appears as follows:
log(PbB13) = p0 + MogtPbEi) + Cos(2it-i) + E1 (1)
A-2
-------
where PbB^ is the blood-lead level in ng/<&> for the jth child in
the ith home, PbEi is the environmental-lead level for the ith
home in /zg/ft2 for loadings and ^g/g for concentrations, t^ is
the day of the year on which the PbB^ measurement was taken, and
Eij is the random error term associated with PbB^. E± is assumed
to follow a normal distribution with mean zero and standard
deviation aError. PbE can represent either a lead loading or lead
concentration in floor, sill, or well dust.
j80, j8lf k, 6, <7Error are parameters that are estimated when
the model is fitted. j30 and ^ are the intercept and slope of
the assumed log-linear relationship between PbB and PbE; k is
ratio of the seasonal maximum PbB level to the seasonal minimum
PbB level; 6 is day of the year on which the seasonal maximum PbB
level is achieved; ffError characterizes the variability in blood-
lead left unexplained by the model.
There were three assumptions in the above descriptive model
that warranted investigation:
1) Due to the fact that environmental lead levels are
usually measured with error, a statistical approach
that adjusts for measurement error in predictor
variables was used while fitting the descriptive model.
2) The descriptive model assumes that the relationship
found between blood-lead and dust-lead in each study
group is similar. There may be some differences
between the three study groups which may influence the
relationship between blood-lead and environmental-lead.
3) The descriptive model also assumes that the blood-lead
concentration measurements used in the analysis are
statistically independent. Since the data represent
115 children living in 87 houses, it is reasonable to
assume that blood-lead levels of children living within
the same household may be positively correlated.
Errors in Variables Solution
Parameter estimates from a least squares regression model
for variables that are measured with error are usually biased
towards zero. Appendix B provides details on the statistical
A-3
-------
methodology used to correct the parameter estimates to reduce
this bias, and Appendix D details how measurement error in
composite dust lead measurements was estimated for use in these
adjusted models.
Tables El and E2 in Appendix E provide the parameter
estimates and associated standard errors for the intercept and
slope (j80 and j8x) from the descriptive model as estimated by both
ordinary least squares and the errors in variables statistical
approach. The models which account for errors in variables
assume that measurement error for predictor variables are equal
to the estimates provided in the alighted column of Table D2 in
Appendix D. The ordinary least squares solution assumes that
there is no measurement error in the dust lead variables (i.e.
loading = ^concentration = °) These least squares estimates are
provided as an example of the relationship between blood-lead and
environmental-lead in the absence of measurement error in
environmental lead.
A comparison of the slope parameter for dust lead ((3^)
between the least squares and errors in variables solution
demonstrates that for variables that have a strong relationship
with blood-lead (such as floor-lead loading), the bias in ft^
attributable to measurement error can be substantial. However,
when the relationship between the predictor variable and the
response variable is weak (such as window well loading) the bias
in J&! attributable to measurement error is not as large.
To facilitate a comparison between the assumed known
measurement error and zero measurement error., all statistical
results are presented in the Appendices for both the least
squares and the errors in variables solution.
Alternate Statistical Models
Although children were recruited into the R&M study from
three different groups of housing, the descriptive model which
A-4
-------
appears in the main report assumes a common slope and intercept
among all children for the relationship between blood-lead
concentration and the different measures of dust -lead. The
validity of this assumption was investigated by fitting a series
of statistical models which allowed for separate slopes and
intercepts for each study group (Modern Urban, Previously Abated,
and Repair and Maintenance) . While there was no statistical
evidence which supported the need for separate slopes relating
blood- lead to measures of lead in dust, these models demonstrated
statistically significant differences in the separate intercepts
fitted for each study group. The estimated intercept for the
Modern Urban group was consistently lowest in all models
considered.
The statistical model with separate intercepts for each
study group appears as follows:
= Po (Modern Urban) + ro (Previously Abated) + Po (Repair/Maintenance)
_Q (2)
This model is identical to the descriptive model found in the
main body of the report, except for the addition of separate
intercepts for each Study group (00 (Modern Urban) 00( Previously Abated)
and PO (Repair/Maintenance) '
Tables E3 and E4 in Appendix E provide the parameter
estimates and associated standard errors for the above "Separate
Intercepts" model as estimated by both ordinary least squares and
the errors in variables statistical approach. The Separate
Intercepts model also has an attractive biological
interpretation; the relationship between log blood-lead
concentrations of children and log lead in household dust is the
same for all houses considered in the study (due to a common
slope) , but there are differences between the geometric mean
baseline blood-lead concentration of each study group due to
A-5
-------
differences in lead exposures that are left unexplained by the
model.
When comparing the descriptive model found in the main body
of the report and the separate intercepts model, it was apparent
that the descriptive model over-estimates the slope relating
blood-lead to dust lead because it fits a common intercept to
three study groups which are significantly different. The degree
to which the descriptive model overestimates these slope
parameters are often statistically significant.
Within House Correlation
Both the descriptive model and the separate intercepts model
assume that each observation used in the statistical analysis are
independent. Since the data represent 115 children living in 87
houses, it is reasonable to assume that blood-lead levels of
children living within the same household may be positively
correlated. The assumption of independence was investigated
using the following two variance components models:
log(PbBi;)) = P0 ri--_ j. 0 365 .
log(PbBi;j) - p0 (Modern urban) + Po (Previously Abated) + Po (Repair/Maintenance)
These models are identical to the descriptive and separate
intercepts models already considered, with the addition of 1^.
Hx is assumed to follow a normal distribution with mean zero and
standard deviation <7Between, and E^ is assumed to follow a normal
distribution with mean zero and standard deviation aWlthin.
ffBetween characterizes the between-home variability and <7within
characterizes the within-home variability.
A-6
-------
The results of fitting the first variance components
(descriptive) model demonstrates that there is significant
correlation between blood-lead concentrations of children living
within the same household. This is shown with the statistically
significant estimates of aBetween in Tables El and E2 of Appendix
E. The results of the second variance components model show that
the correlation between blood-lead concentrations of children
living within the same household is not statistically significant
when considering separate intercepts for each study group, as
shown in Tables E3 and E4 of Appendix E.
Conclusions
Based on the statistical analyses pursued in this report,
Battelle recommends that any inferences drawn from the R&M pre-
intervention data on the relationship between blood-lead
concentrations and measures of lead in dust be made from the
results of the Separate Intercepts Model. There is ample
statistical evidence that the baseline geometric mean blood-lead
concentration among children is different between the three study
groups. The results also show that blood-lead concentrations of
children living within the same household are not as strongly
correlated when separate intercepts are fitted.
A-7
-------
APPENDIX B.
ALTERNATIVE REGRESSION PARAMETER ESTIMATION IN
THE PRESENCE OF MEASUREMENT ERROR
B-l
-------
Appendix B
Regression Parameter Estimation in the
Presence of Measurement Error
Let
Y = X0 + e (1)
where
Y = a nxl vector containing the n values of the
dependent variable;
X = a 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);
)8 = a pxl vector of regression coefficients; and
e = a nxl vector of random error terms.
In a standard regression model it is assumed that X is a matrix
of fixed and known constants, j8 is a vector of fixed and unknown
constants, and e is distributed as MVN(0,a2I) where MVN(/x,E)
represents a multivariate normal distribution with mean vector /i
and covariance matrix Z. Estimates of regression parameters for
this standard regression model are obtained as follows:
jB = (X'X)'1 X'Y
a2 = (Y'Y - j^'X'XJBj) / (n-p) (2)
^) = &2 (X'X)'1
In the presence of measurement error, it is assumed that
Y = UjS + e (3)
B-2
-------
where
U = a nxp matrix of fixed but unknown constants
representing the values of the independent variables
if measured without error;
X = U + A, and
A = a nxp matrix of the random measurement errors
associated with each of the observed values of the
independent variables.
Y and e are as defined above. It is assumed that A is
distributed as MVN(0,£A) where EA is known and A is
stochastically independent of e. Under this measurement error
model, estimates of regression parameters are obtained as
follows:
j§ = (X'X - nSj'1 X'Y
&2 = (Y'Y - jB' (X'X - (n-p)£A)j&) / (n-p) (4)
C8v(j8) = a2 (X'X - nEj'1
These estimators are equivalent to those recommended in Equations
(2.2.11) and (2.2.12) by Fuller (Measurement Error Models. 1987).
It can be shown that
(la) The difference between [(X'X - n£j / n] and [U'U /
n] converges in probability to zero as n-xx>;
(Ib) The difference between [(X'X - (n-p)E&) / (n-p)] and
[U'U / (n-p)] converges in probability to zero as
n-»oo; and
(2) The difference between [X'Y / n] and [U'Y / n]
converges in probability to zero as n-*».
Using these facts, it follows that the differences between the
regression parameter estimates of Equation (4) and
B-3
-------
j9 = (U'U)-1 U'Y
&2 = (Y'Y - jS'U'U/8) / (n-p) (5)
Cov(j&) = &2 (U'U)'1
converge in probability to zero as n-*».
Note that the estimators in Equation (5) are equivalent
to those of Equation (2) except that X has been replaced by U.
Thus, if U were known, the estimators of Equation (5) would be
used. However, since U is unknown, the asymptotically equivalent
estimators of Equation (4) are used. For the purpose of making
inferences involving the unknown parameters /8 and a2, it is
assumed that the estimators of Equation (4) have the same
distribution as those of Equation (5).
B-4
-------
APPENDIX C.
TOLERANCE BOUNDS AND CONFIDENCE
INTERVALS FOR PERCENTILES AND EXCEEDANCE
PROBABILITIES IN A REGRESSION SETTING
C-l
-------
Appendix C
Tolerance Bounds and Confidence Intervals for Percentiles
and Exceedance Probabilities in a Regression Setting
Assume the standard regression model of Equation (1) of
Appendix B. Estimates of regression parameters are obtained as
follows:
]8 = (X'X)'1 X'Y (1)
a2 = (Y'Y - )8'X'Xj8) / (n-p)
An 95% upper tolerance bound on (l-q)% of the distribution pf Y
for values of the independent variables given by x0 is
T0 = x0'£ + ka (2)
where
k = L1/2 t0.95
-------
TL = x0'j8 + kLS
TU = X0'j8 + ]<& (5)
= L1/2 t0.oa5iB.p[«-l(l-q) /
t0.97Sy) is
where qL is the value of q for which TL=y and qw is the value of
q for which To=y.
Under the measurement error model of Equation (3) of
Appendix B, Equations (2) through (6) above still apply.
However, under this measurement error model, values of j8A, <7A,
and L should be calculated as follows :
jS = (X'X - nZ^)-1 X'Y
&2 = (Y'Y - jBMX'X - (n-p)EA)j5) / (n-p)
L = x0' (X'X - nZj^x,,
C-3
-------
APPENDIX D.
DETAILS ON MEASUREMENT ERROR
D-l
-------
APPENDIX D
Details on Measurement Error
The statistical models which adjust for measurement error
require estimates of the variability associated with the
predictor variables. The predictor variables which are measured
with error in these models represent area-weighted arithmetic
average composite dust-lead loadings and mass-weighted arithmetic
average composite dust-lead concentrations from floors, window
sills and window wells. The following equation represents the
three sources of variability that must be accounted for in an
estimate of measurement error for composite samples:
2 222
a Measurement Error = a Spatial + ° Sampling + ° Laboratory
where CT2Spatiai represents the variability in dust-lead levels from
all locations considered as possible subsamples within a
composite sample, Campling represents variability in the
collection of dust from each subsampling location, and ^Laboratory
represents variability in the chemical analysis of the composite
sample.
Several sources of data were considered for providing
information about the variability in composite dust sample
results due to measurement error, including field duplicate data
and data which included multiple composite dust samples (of a
given component type) collected from within the same house.
The field duplicate data represented lead-loading and lead-
concentration results from side-by-side composite vacuum dust
samples from the R&M Pilot Study, the R&M pre-intervention study
data, data from all campaigns of the R&M study (to date) and data
from the Lead Abatement Effectiveness Study in Milwaukee. These
field duplicate samples were all collected from uncarpeted floor
surfaces, and can be evaluated using the following variance
components model:
D-2
-------
ln(Dusti;j)
where Dust^ is the jth (first or second) lead- loading or lead-
concentration result from the ith side-by-side paired sample, n
is the geometric mean of Dust^ among all side-by-side pairs, Pi
is the random effect associated with the ith side-by-side pair,
and Eij is the random within-pair error term associated with
Dustij . Px is assumed to follow a normal distribution with mean
zero and variance ff2Between Pairs anc* Eij ^s assumed to follow a
normal distribution with mean zero and variance o2within Pairs-
^Between Pairs characterizes the variability between pairs,
and a2within Pairs characterizes the variability within pairs. The
withUn-pair variability can be interpreted as error due to
sampling and laboratory analysis, and is a candidate estimate of
measurment error associated with a single composite sample
result. However, since the field duplicates were collected as
side-by-side paired samples, spatial variability may be under-
estimated in this estimate of measurement error. Table Dl
provides estimates of a2Between Pairs and j2within pairs as calculated
from each source of field duplicate data.
Table D1. Estimates of Between Pairs and Within Pairs Variability Among Side-by-Side
Field Duplicate Composite Samples
Data Source
R&M Pilot Study
R&M Pre-lntervention
R&M All Campaigns
Lead Abatement
Effectiveness Study
(Milwaukee)
Number of
Pairs
6
9
42
39
Sample Type
Loading
Concentration
Loading
Concentration
Loading
Concentration
Loading
Concentration
''Between Pairs
2.350
1.095
4.663
4.119
4.298
3.285
4.530
1.884
» Within Pairs
0.116
0.078
0.448
0.528
2.145
1.684
0.844
1.006
D-3
-------
Since the predictor variables included in the statistical
models represented area or mass weighted averages of multiple
composite dust sample results collected within a house, the
individual composite sample lead loading or concentration results
from the R&M pre- intervention data can also be used to assess the
measurement error. Specifically, let
represent the dust-lead loading (or concentration)
from the kth component type (floor, window sill or well)
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
Massiik represent the dust loading in the sample from the
kth component type from the jth location within the ith
residential unit.
The following model was then fitted separately for floors,
window sills and wells to estimate the within house variability
in dust -lead loadings and concentrations for composite dust
samples from the Baltimore Repair and Maintenance Study:
ln(Dustijk) = ln(Mk) + Hik + Eijk
where /ik is the geometric mean of Dust^ among all samples of
component k, Hik is the random effect associated with the ith
House, and Eijk is the random within-house error term associated
with Dusti;jk. Hik is assumed to follow a normal distribution with
mean zero and variance ff2Between Houses' and Eijk is assumed to
follow a normal distribution with mean zero and variance a2within
Houses
ff2Between Houses characterizes the variability between houses,
and ff2Wlthin Houses characterizes the variability within a house,
attributed to a combination of room-to-room, sampling and
laboratory variability.
D-4
-------
Since area and mass weighted (arithmetic) means were used to
characterize the lead levels in each house for use in the
statistical models, the above model was also fitted using weights
corresponding to the percent of total area (or mass) that was
associated with each sample:
Weightijk =
Area
ilk
Maasljt
"Ik
E
Nik
£
Mass
ijk
where Nik is the number of samples collected from component k
within the ith house.
The estimate of ff2within Houses in the weighted analysis
(which we will denote as ff2Weighted) corresponds to the area (or
mass) weighted geometric mean dust-lead loading (or
concentration) within each house. The calculated tf2Weighted are
candidate estimates of measurement error in the predictor
variables, however these estimates correspond to weighted
geometric means rather than weighted arithmetic means, and they
may also overestimate the spatial variability since the composite
samples were collected from different rooms within each house.
Table D2. Estimated Within House Variability in Dust-Lead Loadings and
Concentrations for Composite Samples.
Measure
Loading
Concentration
Surface
Type
Floors
Sills
Wells
Floors
Sills
Wells
"Within House
2.595
1.715
1.506
1.362
0.981
1.054
_2
" Weighted
0.565
0.789
0.693
0.302
0.318
0.351
D-5
-------
The estimates of a2Weighted as calculated from the R&M pre-
intervention data were selected for use in the statistical models
which adjust for measurement error in predictor variables. This
decision was based on the following three reasons:
1. The estimates of ff2weighted are calculated from the same
lead loading and lead concentration results as were
used to calculate the predictor variables, using a
similar weighting scheme. The estimates of 02within Pairs
based on field duplicate pairs represented only small
subsets of the data from several different sources.
2. Use of ff2Weighted allows for separate estimates of
measurement error with respect to composite samples
collected from floors, window sills and window wells.
Since the field duplicate data were all collected from
floor dust composite samples, use of o2wittiin Pairs would
require assumptions that the measurement error for
window sills and window wells is equal to that for
floors.
3. The estimates of ff2Weighted may overestimate the
variability due to measurement error, and may therefore
result in more conservative inferences with respect to
the statistical models which account for errors in
predictor variables.
D-6
-------
APPENDIX E.
PARAMETER ESTIMATES FOR STATISTICAL MODELS
E-l
-------
Table E1. Results of Fitting Descriptive Model to the R&M Pre-lntervention Lead Loading Data
Component
Tested
Floors
Window
Sills
Window
Wells
Statistical
Approach
Least
Squares
Variance
Components
Errors in
Variables
Least
Squares
Variance
Components
Errors in
Variables
Least
Squares
Variance
Components
Errors in
Variables
Parameter Estimates
for Dust
V
se(00»
0.791
(0.230)
0.707
(0.249)
0.711
(0.236)
1.424
(0.2O2)
1.374
(0.217)
1.398
(0.206)
1.417
(0.263)
1.269
(0.294)
1.393
(0.269)
*,«
set/9,)
0.239
(0.036)
0.249
(0.039)
0.252
(0.037)
0.102
(0.024)
0.106
(0.025)
0.106
(0.024)
0.072
(0.022)
0.083
(0.025)
0.074
(0.023)
Parameter Estimates
for Seasonal Variation
Magnitude of
Peak (K)
2.16
2.26
2.19
1.84
1.86
1.82
1.68
1.67
1.66
Peak PbB Time
(0)
07/28/93
07/25/93
07/27/93
07/27/93
07/26/93
07/26/93
08/10/93
08/04/93
08/09/93
Estimates of
Variance Components
^Between
se<°Between>
0.152
(0.058)
0.205
(0.073)
0.241
(0.077)
°~Whhln
S8w Within^
0.375
0.219
(0.050)
0.374
0.446
0.238
(0.058)
0.445
0.480
0.236
(0.057)
0.479
M
to
|a) Intercept values reported in units of ln(pg Pb/dL Blood).
lb> Slope values reported in units of ln(//g Pb/dL Blood) / Infoig Pb/ft2 sampled).
-------
Table E2. Results of Fitting Descriptive Model to the R&M Pre-lntervention Lead Concentration Data
Component
Tested
Floors
Window
Sills
Window
Wells
Statistical
Approach
Least
Squares
Variance
Components
Errors in
Variables
Least
Squares
Variance
Components
Errors in
Variables
Least
Squares
Variance
Components
Errors in
Variables
Parameter Estimates
for Dust
Po
se(/?0)
0.090
(0.329)
0.017
(0.357)
-0.119
(0.341)
0.830
(0.307)
0.775
(0.324)
0.719
(0.319)
1.140
(0.345)
1.004
(0.373)
1.039
(0.362)
e,
sel/7,)
0.287
(0.043)
0.294
(0.047)
0.315
(0.045)
0.152
(0.032)
0.157
(0.034)
0.164
(0.034)
0.114
(0.036)
0.126
(0.038)
0.125
(0.037)
Parameter Estimates
for Seasonal Variation
Magnitude of
Peak (K)
1.51
1.61
1.49
1.64
1.69
1.64
1.69
1.69
1.66
Peak PbB Time
(0)
07/29/93
07/20/93
07/24/93
07/23/93
07/22/93
07/20/93
08/11/93
08/07/93
08/09/93
Estimates of
Variance Components
"Between
sel^B^J
0.143
(0.061)
0.199
(0.069)
0.241
(0.077)
" Within
Se^Whhln>
0.373
0.230
(0.054)
0.366
0.435
0.232
(0.056)
0.433
0.480
0.236
(0.057)
0.475
M
to
|a) Intercept values reported in units of ln(//g Pb/dL Blood).
lb> Slope values reported in units of ln(//g Pb/dL Blood) / Infyig Pb/g Dust sampled).
-------
Table E3. Results of Fitting Separate Intercept Model to the R&M Pre-lntervention Lead Loading Data
Component
Tested
Floors
Window
Sills
Window
Wells
Statistical
Approach
Least
Squares
Variance
Components
Errors in
Variables
Least
Squares
Variance
Components
Errors in
Variables
Least
Squares
Variance
Components
Errors in
Variables
Parameter Estimates for Dust
Separate Intercepts1'1
Modern
Urban
*01
se(/?01)
0.792
(0.210)
0.757
(0.224)
0.751
(0.215)
1.103
(0.187)
1.113
(0.197)
1.090
(0.192)
0.982
(0.311)
0.982
(0.331)
0.939
(0.336)
Previously
Abated
4»
sedu)
1.840
(0.299)
1.757
(0.324)
1.765
(0.310)
2.378
(0.269)
2.363
(0.291)
2.347
(0.285)
2.308
(0.376)
2.285
(0.408)
2.251
(0.410)
Repair and
Maintenance 003
seu?03)
1.526
(0.287)
1.434
(0.312)
1.448
(0.300)
1.968
(0.385)
1.943
(0.412)
1.918
(0.413)
1.845
(0.593)
1.818
(0.627)
1.750
(0.655)
Overall11"
Slope
/»,
sell,)
0.120
(0.044)
0.134
(0.047)
0.132
(0.046)
0.035
(0.042)
0.038
(0.045)
0.040
(0.045)
0.034
(0.047)
0.036
(0.049)
0.041
(0.052)
Parameter Estimates
for Seasonal Variation
Magnitude of
Peak (K)
1.85
1.86
1.88
1.69
1.66
1.69
1.62
1.58
1.61
Peak PbB
Time (0)
07/27/93
07/27/93
07/27/93
07/30/93
07/31/93
07/30/93
07/31/93
07/31/93
07/31/93
Estimates of
Variance Components
" Between
S««^B«we.n)
0.087
(0.054)
0.089
(0.062)
0.089
(0.062)
** Wlihm
SeJtTwuhin)
0.312
0.227
(0.053)
0.309
0.331
0.245
(0.060)
0.331
0.333
0.247
(0.061)
0.333
n
I
la> Intercept values reported in units of ln(//g Pb/dL Blood).
lb> Slope values reported in units of Infoig Pb/dL Blood) / Infysg Pb/ft2 sampled).
-------
Table E4. Results of Fitting Separate Intercept Model to the R&M Pre-lntervention Lead Concentration Data
Component
Tested
Floors
Window
Sills
Window
Wells
Statistical
Approach
Least
Squares
Variance
Components
Errors in
Variables
Least
Squares
Variance
Components
Errors in
Variables
Least
Squares
Variance
Components
Errors in
Variables
Parameter Estimates for Dust
Separate Intercepts1''
Modern
Urban
/»oi
se(0oi>
0.462
(0.318)
0.400
(0.344)
0.310
(0.340)
0.919
(0.325)
0.858
(0.342)
0.817
(0.369)
1.476
(0.399)
1.492
(0.420)
1.671
(0.495)
Previously
Abated
002
se(/J02)
1.500
(0.432)
1.404
(0.467)
1.275
(0.468)
2.171
(0.443)
2.060
(0.468)
2.021
(0.513)
2.951
(0.497)
2.960
(0.535)
3.205
(0.626)
Repair and
Maintenance /?03
se(/?03)
1.169
(0.434)
1.052
(0.474)
0.935
(0.473)
1.771
(0.544)
1.623
(0.576)
1.580
(0.636)
2.798
(0.6501
2.802
(0.690)
3.140
(0.829)
Overall11"
Slope
/»,
sel/?,)
0.144
(0.055)
0.158
(0.060)
0.174
(0.060)
0.051
(0.054)
0.067
(0.057)
0.070
(0.063)
-0.052
(0.063)
-0.052
(0.067)
-0.085
(0.081)
Parameter Estimates
for Seasonal Variation
Magnitude
of Peak (K)
1.55
1.56
1.54
1.63
1.60
1.64
1.66
1.61
1.66
Peak PbB
Time (0}
07/29/93
07/27/93
07/28/93
07/29/93
07/29/93
07/28/93
07/27/93
07/28/93
07/26/93
Estimates of
Variance Components
""Between
se(
-------
Table E5. Results of Fitting Floor. Window Sill, and Window Well Lead Loadings Simultaneously on Blood-Lead
Concentrations in the Descriptive Model.
Statistical
Approach
Least Squares
Variance
Components
Errors in Variables
Component
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Parameter Estimates
for Dust
V
se(£0)
0.825
(0.275)
0.722
(0.300)
0.787
(0.281)
/?,""
set/?,)
0.212
(0.045)
0.047
(0.042)
-0.022
(0.035)
0.223
(0.050)
0.039
(0.044)
-0.016
(0.039)
0.228
(0.048)
0.049
(0.046)
-0.029
(0.039)
Parameter Estimates
for Seasonal Variation
Magnitude
of Peak (K)
1.49
1.51
1.54
Peak PbB
Time (0)
07/22/93
07/20/93
07/21/93
Estimates of
Variance Components
0.156
(0.060)
"Within
0.380
0.223
(0.051)
0.373
w
CTl
la) Intercept values reported in units of ln(//g Pb/dL Blood).
-------
Table E6. Results of Fitting Floor, Window Sill, and Window Well Lead Concentrations Simultaneously on Blood-
Lead Concentrations in the Descriptive Model.
Statistical
Approach
Least Squares
Variance
Components
Errors in
Variables
Component
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Parameter Estimates
for Dust
00 '"
se(yS0»
O.113
(O.359)
0.049
(0.384)
0.035
(0.367)
V0
seOS,)
0.253
(0.058)
0.082
(0.057)
-0.057
(0.053)
0.259
(0.065)
0.085
(0.061)
-0.060
(0.058)
0.287
(0.064)
0.112
(0.074)
-0.105
(0.068)
Parameter Estimates
for Seasonal Variation
Magnitude
of Peak (K)
1.25
1.30
1.21
Peak PbB
Time (0)
07/14/93
07/08/93
07/10/93
Estimates of
Variance Components
** Between
O.146
(0.062)
°Whhln
0.375
0.230
(0.054)
0.360
M
i
lal Intercept values reported in units of InU/g Pb/dL Blood).
n» Slope values reported in units of Info/g Pb/dL Blood) / ln(pg Pb/g Dust sampled).
-------
Table E7. Results of Fitting Floor, Window Sill, and Window Well Lead Loadings Simultaneously on Blood-Lead
Concentrations in the Separate Intercepts Model.
Statistical
Approach
Least Squares
Variance
Components
Errors in Variables
Parameter Estimates for Dust Lead Loading
Intercept
Study
Group
Modern
Urban
Previously
Abated
Repair and
Maintenance
Modern
Urban
Previously
Abated
Repair and
Maintenance
Modern
Urban
Previously
Abated
Repair and
Maintenance
BO""
se(R0)
0.731
(0.321)
1.764
[0 435)
1.390
(0.640)
0.676
(0.345)
1.647
(0.479)
1.244
(0.690)
0.697
(0.340)
1.704
(0.459)
1.339
(0.686)
Slope
Surface
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
B,n>»
se(B,)
0.116
(0.047)
0.004
(0.042)
0.009
(0.048)
0.130
(0.050)
0.007
(0.046)
(0.012
(0.050)
0.129
(0.050)
0.001
(0.048)
0.009
(0.053)
Parameter Estimates
for
Seasonal Variation
Magnitude of
Peak (K)
1.36
1.37
1.40
Peak PbB
Time
(0)
07/25/93
07/24/93
07/24/93
Estimates of
Variance Components
0.094
(0.0561
0.320
0.228
(0.053)
0.318
M
i
00
(a)
(b)
Intercept values reported in units of InUig Pb/dL Blood).
Slope values reported in units of ln(//g Pb/dL Blood) / ln(pg Pb/ft2 sampled).
-------
Table E8. Results of Fitting Floor, Window Sill, and Window Well Lead Concentrations Simultaneously on Blood-
Lead Concentrations in the Separate Intercepts.
Statistical
Approach
Least Squares
Variance
Components
Errors in
Variables
Parameter Estimates for Dust Lead Concentration
Intercept
Study
Group
Modern
Urban
Previously
Abated
Repair and
Maintenance
Modern
Urban
Previously
Abated
Repair and
Maintenance
Modern
Urban
Previously
Abated
Repair and
Maintenance
/»o<"
se«?0)
0.742
(0.479)
1.843
(0.645)
1.647
(0.792)
0.637
(0.513)
1.694
(0.695)
1.443
(0.849)
0.867
(0.543)
1.963
(0.726)
1.889
(0.907)
Slope
Surface
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
/*,""
se(/?,)
0.140
(0.058)
0.033
(0.058)
-0.078
(0.064)
0.151
(0.064)
0.049
(0.061)
-0.082
(0.067)
0.169
(0.066)
0.053
(0.073)
-0.143
(0.084)
Parameter Estimates
for
Seasonal Variation
Magnitude of
Peak (K)
1.27
1.27
1.30
Peak PbB
Time (0)
07/19/93
07/1 5/93
06/01/93
Estimates of
Variance Components
"^Between
0.091
(0.055)
^Within
0.317
0.229
(0.053)
0310
n
vo
lal Intercept values reported in units of ln(/ig Pb/dL Blood).
lbl Slope values reported in units of ln(//g Pb/dL Blood) / ln(//g Pb/g Dust sampled).
-------
APPENDIX F.
PROTECTIVE DUST LEAD LEVELS AND EXCEEDANCE
PROBABILITIES FOR ERRORS IN VARIABLES SOLUTION
F-l
-------
Table F1. Estimated Dust Pb Loadings for Floors, Window Sills, and Window Wells at Which the 85th, 90th, 95th, and
99th Percentiles of Childhood Blood Pb Concentrations Reach 10, 15, and 20/ig/dL (Based on the Errors in
Variables Regression Model)
Sample
Type
Floor
Lead
Loading
fog/ft2)
Window
Sill
Lead
Loading
fog/ft2)
Window
Well
Lead Loading
-------
Table F2. Estimated Dust Pb Concentrations for Floors, Window Sills, and Window Wells at Which the 85th, 90th,
95th, and 99th Percentiles of Childhood Blood Pb Concentrations Reach 10, 15, and 20//g/dL (Based on the
Errors in Variables Regression Model)
Sample
Type
Floor Lead
Cone.
U/g/g)
Window
Sill Lead
Cone.
ufl/g)
Window
Well Lead
Cone.
U/g/g)
Tolerance
Level
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
All
Houses
10//g/dL
141
86
40
9
13
3
15//g/dL
529
328
159
38
341
95
13
17
1
20 //g/dL
1287
815
405
102
2733
840
130
3
519
70
2
Modern Urban
Houses
10//g/dL
343
186
66
5
899
169
> 1M
287282
15 //g/dL
1633
978
433
70
16613
6467
1307
> 1M
> 1M
>1 M
20 //g/dL
4457
2757
1312
276
95776
40288
10431
403
> 1M
> 1M
> 1M
>1 M
Previously Abated Houses
10 //g/dL
15 //g/dL
11
3
20 //g/dL
104
36
7
-
Repair & Maintenance Houses
10 //g/dL
7
2
15 //g/dL
203
69
12
20 //g/dL
1263
555
129
5
U)
A result of'.' indicates that the tolerance bound for Blood-Pb is always above the target level.
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F3. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 10 //g/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Floor Pb Loadings.
Hoar Pb
Loading
10)
0.004
0.012
0.022
0.031
0.04
0.05
0.059
0068
0.159
0.265
0305
95% Cl
(0.000. 0.047)
(0.001,0.084)
(0.002, 0.114)
(0.004,0.139)
(0.006,0.162)
(0.008,0.182)
(0.011,0.200)
(0.014,0.217)
(0.051. 0.357)
(0.111. 0.485)
(0.138,0.528)
Modern Urban Houses
Pr(PbB>10)
0.003
0.006
0.009
0.013
0.016
0.018
0.021
0.024
0.050
0.083
0096
95% Cl
(0.000. 0.037)
(0.000, 0.056)
(0.000,0.071)
(0.001, 0.084)
(0.001,0.096)
(0.001,0.107)
(0.002.0.117)
(0.002.0.126)
(0.006.0.213)
(0.011, 0.306)
(0.013.0.341)
Previously Abated Houses
Pr(PbB>10)
0.111
0.166
0.205
0.236
0.262
0.284
0.304
0.321
0.448
0548
0.580
95% Cl
(0.007, 0.489)
(0.020, 0.546)
(0.032, 0.580)
(0.044, 0.605)
(0.056, 0.624)
(0.067. 0.640)
(0.077, 0.654)
(0.087. 0.665)
(0.177,0.747)
(0.266, 0.807)
(0.297. 0.826)
Repair & Maintenance Houses
Pr(PbB>10)
0.034
0.058
0.077
0.093
0.108
0.120
0.132
0.143
0.232
0.315
0.345
95% Cl
(0.001,0.251)
(0.004. 0.295)
(0.008. 0.322)
(0012.0.343)
(0.017.0.360)
(0.021,0.374)
(0.026, 0.387)
(0.030, 0.398)
(0.078. 0.481)
(0.137. 0.553)
(0.159.0.578)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F4. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 15 //g/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Floor Pb Loadings.
Roor Pb
Loading
fe/g/ft2)
5
10
15
20
25
30
35
40
100
200
250
All Houses Combined
Pr(PbB>15)
0.000
0.001
0.003
0.005
0.007
0.009
0.011
0.014
0044
0.092
0.113
95% Cl
(0.000. 0.009)
(0.000. 0.020)
(0.000. 0.030)
(0.000. 0.040)
(0.000, 0.049)
(0.000. 0.057)
(0.001.0.065)
(0.001, 0.073)
(0.009. 0.149)
(0.026, 0.236)
(0.035, 0.270)
Modern Urban Houses
Pr(PbB>15)
0.000
0.000
0.001
0.001
0.001
0.002
0.002
0.003
0.008
0.016
0.020
95% Cl
(0.000, 0.006)
(0.000,0.011)
(0.000, 0.01 5)
(0.000, 0.01 8)
(0.000, 0.022)
(0.000, 0.025)
(0.000. 0.029)
(0.000, 0.032)
(0.000, 0.066)
(0.001,0.111)
(0.001,0.130)
Previously Abated Houses
Pr(PbB>15)
0.024
0.043
0.059
0.072
0.084
0.095
0.105
0.114
0.192
0.268
0.295
95% Cl
(0.000, 0.226)
(0.002,0.271)
(0.004, 0.300)
(0.007, 0.323)
(0.009,0.341)
(0.012.0.356)
(0.014,0.370)
(0.017,0.382)
(0.047, 0.473)
(0.085, 0.553)
(0.101, 0.580)
Repair & Maintenance Houses
Pr(PbB>15)
0.005
0.010
0.015
0.019
0.024
0.028
0.031
0.035
0.070
0.111
0.127
95% Cl
(0.000. 0.083)
(0.000, 0.104)
(0.000, 0.119)
(0.001. 0.131)
(0.001.0.141)
(0.002, 0.150)
(0.003,0.157)
10.004,0.164)
(0.014.0.221)
(0.032, 0.278)
(0.039, 0.299)
I
l/l
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F5. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 20 //g/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Floor Pb Loadings.
Floor Pb
Loading
20)
0.000
0.000
0.000
0.001
0.001
0.002
0.002
0.003
0.014
0.034
0.044
95% Cl
(0.000, 0.002)
(0.000. 0.006)
(0.000, 0.009)
(0.000,0.013)
(0.000,0.016)
(0.000, 0.020)
(0.000, 0.023)
(0.000. 0.027)
(0.001. 0.065)
(0.006. 0.116)
(0.010,0.138)
Modern Urban Houses
Pr(PbB>20)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.004
0.005
95% Cl
(0.000,0.001)
(0.000. 0.002)
(0.000, 0.003)
(0.000, 0.005)
(0.000, 0.006)
(0.000. 0.007)
(0.000. 0.008)
(0.000. 0.009)
(0.000. 0.022)
(0.000. 0.042)
(0.000,0.051)
Previously Abated Houses
Pr(PbB>20)
0.006
0.012
0.018
0.023
0.028
0.033
0.037
0.041
0.081
0.126
0.144
95% Cl
(0.000, 0.104)
(0.000,0.131)
(0.000, 0.151)
(0.001,0.166)
(0.001.0.179)
(0.002. 0.190)
(0.003. 0.200)
(0.004, 0.209)
(0.013,0.281)
(0.028,0.351)
(0.035, 0.377)
Repair & Maintenance Houses
Pr(PbB>20)
0.001
0.002
0.003
0.004
0.006
0.007
0.008
0.009
0.022
0.040
0.048
95% Cl
(0.000, 0.029)
(0.000, 0.039)
(0.000, 0.046)
(0.000, 0.052)
(0.000, 0.057)
(0.000. 0.062)
(0.000. 0.066)
(0.000, 0 069)
(0.003,0.102)
(0.008, 0.137)
(0.010,0.151)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F6. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 10 //g/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Window Sill Pb Loadings.
Window
Sill Pb Loading
0/g/ftz)
50
100
200
300
400
500
600
700
All Houses Combined
Pr(PbB>10)
0.194
0.229
0.267
0.291
0.308
0.322
0.333
0.343
95% Cl
(0.059, 0.433)
(0.079, 0.469)
(0.104, 0.506)
(0.120,0.528)
(0.132.0.545)
(0.143, 0.557)
(0.151, 0.568)
(0.158,0.576)
Modern Urban Houses
Pr(PbB>10)
0.036
0.043
0.050
0.056
0.059
0.063
0.065
0.068
95% Cl
(0.004,0.171)
(0.004, 0.204)
(0.004, 0.246)
(0.004, 0.275)
(0.004, 0.298)
(0.004, 0.316)
(0.004, 0.332)
(0.004, 0.346)
Previously Abated Houses
Pr(PbB>10)
0.597
0.628
0.658
0.675
0.687
0.696
0.703
0.710
95% Cl
(0.283, 0.856)
(0.331, 0.862)
(0.374, 0.872)
(0.395, 0.880)
(0.408, 0.886)
(0.417,0.892)
(0 424, 0.896)
(0.429, 0.900)
Repair & Maintenance Houses
Pr(PbB>10)
0.255
0.281
0.309
0.326
0.338
0.348
0.355
0.362
95% Cl
(0.030.0.711)
(0.047, 0.698)
(0.069, 0.685)
(0.086. 0.679)
(0.099. 0.675)
(0.109,0.672)
(0.119.0.670)
(0.127,0.669)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F7. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 15 //g/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Window Sill Pb Loadings.
Window
Sill Pb Loading
fog/ft2)
50
100
200
300
400
500
600
700
All Houses Combined
Pr(PbB>15)
0.070
0.087
0.108
0.122
0.133
0.141
0.148
0.155
95% Cl
(0.014. 0.223)
(0.020. 0.250)
(0.029. 0.280)
(0.035. 0.299)
(0.041. 0.313)
(0.045. 0.324)
(0.048, 0.334)
(0.052. 0 342)
Modern Urban Houses
Pr(PbB>15)
0.006
0.007
0.009
0.010
0.011
0.012
0.013
0.014
95% Cl
(0.000, 0.052)
(0.000, 0.066)
(0.000, 0.086)
(0.000.0.100)
(0.000.0.112)
(0.000.0.123)
(0.000.0.132)
(0.000. 0.140)
Previously Abated Houses
Pr(PbB>1S)
0.323
0.353
0.383
0.401
0.414
0.424
0.432
0.439
95% Cl
(0.100, 0.641)
(0.127.0.650)
(0.152,0.666)
(0.166.0.680)
(0.175,0.692)
(0.181,0.701)
(0.185,0.710)
(0.189,0.718)
Repair & Maintenance Houses
Pr(PbB>15)
0.086
0.099
0.114
0.124
0.131
0.136
0.141
0.145
95% Cl
(0.004, 0.446)
(0.008, 0.430)
(0.014,0.416)
(0.018, 0.409)
(0.022, 0.405)
(0.025. 0.402)
(0.028, 0.400)
(0.031.0.398)
CO
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F8. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 20 //g/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Window Sill Pb Loadings.
Window
Sill Pb
Loading
(pg/ft2)
50
100
200
300
400
500
600
700
All Houses Combined
Pr(PbB>20)
0.028
0.036
0.047
0.055
0.060
0.065
0.069
0.073
95% Cl
(0.004,0.119)
(0.006, 0.137)
(0.009,0.158)
(0.012, 0.172)
(0.014,0.182)
(0.016.0.191)
(0.017,0.198)
(0.019,0.204)
Modern Urban Houses
Pr(PbB>20)
0.001
0.001
0.002
0.002
0.002
0.003
0.003
0.003
95% Cl
(0.000,0.018)
(0.000, 0.023)
(0.000, 0.032)
(0.000, 0.039)
(0.000, 0.045)
(0.000. 0.050)
(0.000, 0.055)
(0.000, 0.059)
Previously Abated Houses
Pr(PbB>20)
0.169
0.190
0.212
0.226
0.236
0.244
0.251
0.257
95% Cl
(0.037, 0.448)
(0.049, 0.457)
(0.062. 0.475)
(0.070, 0.490)
(0.074, 0.502)
(0.078,0.514)
(0.080, 0.523)
(0.082, 0.532)
Repair & Maintenance Houses
Pr(PbB>20)
0.031
0.037
0.044
0.049
0.052
0.055
0.057
0.059
95% Cl
(0.000, 0.266)
(0.001,0.253)
(0.003, 0.242)
(0.004, 0.237)
(0.005, 0.233)
(0.006,0.231)
(0.007, 0.230)
(0.008, 0.228)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F9. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 10 //g/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Window Well Pb Loadings.
Window
Well Pb
Loading
(fig/ft2)
200
500
750
1,500
3,000
5,000
10,000
20.000
All Houses Combined
Pr|PbB>10)
0.231
0.264
0.279
0.282
0.306
0.334
0.356
0.385
95% Cl
(0.069, 0.504)
(0.090,0.531)
(0.101,0.543)
(0.102.0.545)
(0.120, 0.564)
(0.141,0.586)
(0.158,0.603)
(0.182,0.626)
Modem Urban Houses
Pr(PbB>10)
0.022
0.029
0.033
0.033
0.039
0.047
0.054
0.064
95% Cl
(0.002,0.125)
(0.003, 0.151)
(0.003,0.168)
(0.003,0.171)
(0.003, 0.205)
(0.003, 0.255)
(0.003, 0.298)
(0.003, 0.367)
Previously Abated Houses
Pr(PbB>10)
0.575
0.618
0.636
0.639
0.667
0.697
0.719
0.746
95% Cl
(0.251,0.853)
(0.318,0.858)
(0.344, 0.864)
(0.348, 0.865)
(0.381,0.878)
(0.405, 0.898)
(0.416,0.915)
(0.420, 0.936)
Repair & Maintenance Houses
Pr(PbB>10)
0.175
0.205
0.220
0.222
0.245
0.273
0.294
0.323
95% Cl
(0.004, 0.784)
(0.009, 0.758)
(0.013,0.747)
(0.014, 0.745)
(0.023, 0.727)
(0.039, 0.708)
(0.055, 0.695)
(0.083, 0.679)
H
O
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F10. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 15 //g/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Window Well Pb Loadings.
Window
Well Pb
Loading
(pg/ft2)
200
500
750
1.500
3.000
5,000
10.000
20,000
All Houses Combined
Pr(PbB>15)
0.093
0.112
0.121
0.122
0.137
0.155
0.169
0.190
95% Cl
(0.018,0.287)
(0.026,0310)
(0 030, 0.320)
(0.031,0.322)
(0.038, 0.340)
(0.047, 0.360)
(0.055, 0.376)
(0.066, 0.399)
Modem Urban Houses
Pr(PbB>15)
0.003
0.004
0.005
0.005
0.007
0.008
0.010
0.013
95% Cl
(0.000, 0.034)
(0.000, 0.044)
(0.000,0.051)
(0.000, 0.052)
(0.000, 0.067)
(0.000, 0.090)
(0.000. 0.113)
(0.000,0.153)
Previously Abated Houses
Pr(PbB>15)
0.304
0.344
0.362
0.365
0.394
0.427
0.451
0.484
95% Cl
(0.084, 0.636)
(0.120,0.644)
(0.135,0.654)
(0.137,0.656)
(0.158,0.679)
(0.174,0.715)
(0.181,0.747)
(0.184, 0.794)
Repair & Maintenance Houses
Pr(PbB>15)
0.051
0.063
0.070
0.071
0.082
0.095
0.106
0.123
95% Cl
(0.000, 0.537)
(0.001,0.503)
(0.001, 0.489)
(0.001, 0.486)
(0.003, 0.465)
(0.006, 0.443)
(0.010, 0.428)
(0.018, 0.411)
"3
i
H
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table F11. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 20 /ig/dL as Predicted by a
Errors in Variables Model of Blood Pb versus Window Well Pb Loadings.
Window
Well Pb
Loading
(pg/ft2)
200
500
750
1.500
3.000
5,000
10,000
20,000
All Houses Combined
Pr(PbB>20)
0.041
0.051
0.056
0.057
0.065
0076
0.085
0.098
95% Cl
(0.006,0.168)
(0.008,0.184)
(0.010,0.193)
10.010,0.194)
(0.013,0.207)
(0.017,0.223)
(0.021,0.236)
(0.026, 0.255)
Modern Urban Houses
Pr(PbB>20)
0.000
0.001
0.001
0.001
0.001
0.002
0.002
0.003
95% Cl
(0.000,0.011)
(0.000, 0.014)
(0.000,0.017)
(0.000.0.018)
(0.000, 0.024)
(0.000, 0.034)
(0.000, 0.045)
(0.000, 0.066)
Previously Abated Houses
Pr(PbB>20)
0.156
0.184
0.197
0.199
0.221
0.247
0.267
0.295
95% Cl
(0.029, 0.443)
(0.046, 0.452)
(0.054, 0.462)
(0.055. 0.464)
(0.065, 0.489)
(0.074, 0.530)
(0.078, 0.568)
(0.080, 0.627)
Repair & Maintenance Houses
Pr(PbB>20|
0.016
0.021
0.024
0.024
0.029
0.035
0.040
0.048
95% Cl
(0.000, 0.346)
(0.000,0.316)
(0.000, 0.303)
(0.000.0.301)
(0.000. 0.283)
(0.001,0.264)
(0.002, 0.252)
(0.004, 0.239)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
APPENDIX G.
PROTECTIVE DUST LEAD LEVELS AND EXCEEDANCE
PROBABILITIES FOR LEAST SQUARES SOLUTION
G-l
-------
Table G1. Estimated Dust Pb Loadings for Floors, Window Sills, and Window Wells at Which the 85th, 90th, 95th, and
99th Percentiles of Childhood Blood Pb Concentrations Reach 10. 15, and 20 //g/dL (Based on the Least
Squares Regression Model)
Sample
Type
Floor
Lead
Loading
U/g/ft2)
Window
Sill
Lead
Loading
0/g/ft2)
Window
Well
Lead
Loading
0/g/ft2)
Tolerance
Level
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
All
Houses
10
//g/dL
7
3
1
15
//g/dL
55
25
8
-
4
20
//g/dL
207
101
33
3
174
21
173
3
Modern Urban
Houses
10
//g/dL
106
35
4
170
4
3155
150
15
//g/dL
1588
653
156
5
29261
5580
330
356596
76363
5654
20
//g/dL
8797
3847
1066
67
634961
138183
12856
35
> 1 mil
> 1 mil
164372
758
Previously Abated Houses
10
//g/dL
15
//g/dL
20
//g/dL
1
.
Repair & Maintenance
Houses
10
//g/dL
.
.
.
.
15
//g/dL
3
.
.
.
.
.
20
//g/dL
166
29
1
.
.
.
.
.
a
to
A result of '.' indicates that the tolerance bound for Blood-Pb is always above the target level.
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G2. Estimated Dust Pb Concentrations for Floors, Window Sills, and Window Wells at Which the 85th, 90th,
95th, and 99th Percentiles of Childhood Blood Pb Concentrations Reach 10, 15, and 20 /ig/dL (Based on the
Least Squares Regression Model)
Sample
Type
Floor
Lead
Cone.
u/g/g)
Window
Sill
Lead
Cone.
0/g/g)
Window
Well
Lead
Cone.
0>g/g)
Tolerance
Level
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
All
Houses
10 j/g/dL
59
31
11
1
5
1
15//g/dL
312
167
64
10
191
44
4
4
20 /ig/dL
943
522
210
34
1982
521
62
278
25
Modern Urban
Houses
10/ig/dL
433
171
31
1403
124
> Imil
27862
15//g/dL
3974
1915
590
33
63443
18555
2287
> 1 mil
> 1 mil
> 1 mil
20 /ig/dL
16102
8176
2855
293
621789
200836
34506
460
> 1 mil
> 1 mil
> 1 mil
225772
Previously Abated Houses
10/yg/dL
15//g/dL
20 pg/dL
8
1
Repair & Maintenance Houses
10//g/dL
15/tg/dL
22
2
20//g/dL
749
164
8
Q
i
LJ
A result of'.' indicates that the tolerance bound for Blood-Pb is always above the target level.
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G3 . Estimated Proportion of Children with Blood-Pb Concentrations Greater than 10 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Floor Pb Loadings.
Floor Pb
Loading
0/g/ft2)
5
10
15
20
25
30
35
40
100
200
250
All Houses Combined
Pr(PbB>10]
0.030
0.054
0.074
0.091
0.106
0.120
0.132
0.144
0.240
0.331
0.363
95% Cl
(0.003,0.152)
(0.008. 0.205)
(0.014. 0.242)
(0.019,0.270)
(0.025. 0.294)
(0.031, 0.314)
(0.036, 0.331)
(0.041,0.347)
(0.093, 0.463)
(0.154,0.558)
(0.178,0.589)
Modern Urban Houses
Pr(PbB>10)
0.008
0.012
0.015
0.018
0.020
0.022
0.024
0.025
0.039
0054
0.059
95% Cl
(0.000, 0.067)
(0.000, 0.083)
(0.001, 0.094)
(0.001,0.104)
(0.001. 0.112)
(0.002, 0.119)
(0.002,0.125)
(0.002,0.131)
(0.004,0.179)
(0.006, 0.227)
(0.007, 0.245)
Previously Abated Houses
Pr(PbB>10)
0.301
0.355
0.387
0.411
0.430
0.445
0.458
0.470
0.548
0.605
0.624
95% Cl
(0.061,0.693)
(0.093,0.718)
(0.116,0.734)
(0.134,0.745)
(0.149,0.754)
(0.162,0.761)
(0.173.0.767)
(0.183. 0.773)
(0.259,0.812)
(0.320, 0.842)
(0.339, 0.852)
Repair & Maintenance Houses
Pr(PbB>10)
0.140
0.175
0.198
0.216
0.230
0.242
0.253
0.262
0.329
0.385
0.403
95% Cl
(0.021.0.449)
(0.035, 0.474)
(0.047, 0.489)
(0.058,0.501)
(0.066, 0.510)
(0.074, 0.518)
10.081,0.525)
(0.088, 0.531)
10.141,0.577)
(0.188,0.617)
(0.204.0.631)
o
I
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G4. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 15 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Floor Pb Loadings.
Floor Pb
Loading
fog/ft2)
5
10
15
20
25
30
35
40
100
200
250
All Houses Combined
Pr(PbB>15)
0.005
0.011
0.017
0.023
0.028
0.033
0.037
0.042
0.085
0.136
0.156
95% Cl
(0.000. 0.048)
(0.001,0.072)
(0.001.0.091)
(0.003,0.106)
(0.004,0.119)
(0.005.0.131)
(0.006,0.141)
(0.007.0.151)
(0.022.0.231)
(0.045, 0.308)
(0.055. 0.336)
Modern Urban Houses
Pr(PbB>15)
0.000
0.001
0.001
0.002
0.002
0.003
0.003
0.003
0.006
0.009
0.011
95% Cl
(0.000, 0.014)
(0.000, 0.019)
(0.000, 0.022)
(0.000, 0.025)
(0.000, 0.028)
(0.000, 0.030)
(0.000, 0.033)
(0.000, 0.035)
(0.000, 0.053)
(0.000, 0.074)
(0.000, 0.082)
Previously Abated Houses
Pr(PbB>15)
0.106
0.136
0.156
0.171
0.184
0.194
0.203
0.212
0.273
0.324
0.341
95% Cl
(0.011,0.417)
(0.019,0.4461
(0.026, 0.464)
(0.032, 0.477)
(0.038, 0.488)
(0.043, 0.497)
(0.047, 0.505)
(0.051. 0.513)
(0.084, 0.565)
(0.116,0.610)
(0.127, 0.626)
Repair & Maintenance Houses
Pr(PbB>15)
0.035
0.048
0.058
0.065
0.072
0.077
0.082
0.086
0.122
0.154
0.166
95% Cl
(0.002, 0.202)
(0.005, 0.220)
(0.008, 0.232)
(0.010,0.241)
(0.012,0.248)
(0.014, 0.254)
(0.016,0.260)
(0.018,0.265)
(0.034, 0.303)
(0.052, 0.340)
(0.059, 0.353)
I
ui
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G5. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 20 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Floor Pb Loadings.
Floor Pb
Loading
20)
0.001
0.003
0.005
0.006
0.008
0.010
0.012
0.014
0033
0.058
0.069
95% Cl
(0.000.0.017)
(0.000. 0.028)
(0.000, 0.037)
(0.000, 0.045)
(0 000, 0.052)
(0.001,0.058)
(0.001,0.064)
(0.001, 0.069)
(0.006,0.118)
(0.014,0.170)
(0.018,0.190)
Modern Urban Houses
Pr(PbB>20)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.002
0.002
95% Cl
(0.000, 0.003)
(0.000, 0.005)
(0.000, 0.006)
(0.000, 0.007)
(0.000. 0.008)
(0.000, 0.009)
(0.000,0.010)
(0.000,0.010)
(0.000,0.018)
(0.000, 0.026)
(0.000, 0.030)
Previously Abated Houses
Pr(PbB>20)
0.039
0.053
0.063
0.071
0.078
0.084
0.089
0.094
0.131
0.166
0.178
95% Cl
(0.002, 0.239)
(0.004, 0.262)
(0.007, 0.277)
(0.008. 0.288)
(0.010. 0.297)
(0.012, 0.305)
(0.014, 0.312)
(0.015. 0.319)
(0.028, 0.367)
(0.043.0.411)
(0.048, 0.427)
Repair & Maintenance Houses
Pr(PbB>20)
0.010
0.014
0.018
0.021
0024
0.026
0.028
0.030
0.046
0.062
0.069
95% Cl
(0.000. 0.092)
(0.001,0.102)
(0.001, 0.110)
(0.002,0.115)
(0.002. 0.120)
(0.003, 0.124)
(0.003,0.127)
(0.004,0.130)
(0.009.0.156)
(0.015,0.182)
(0.018.0.192)
o
I
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G6. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 10 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Window Sill Pb Loadings.
Window
Sill Pb
Loading
(pg/ft2)
50
100
200
300
400
500
600
700
All Houses Combined
Pr(PbB>10)
0.227
0.260
0.296
0.318
0.333
0.346
0.356
0.365
95% Cl
(0.076. 0.473)
(0.098. 0.504)
(0.122,0.536)
(0.138.0.556)
(0.150,0.570)
(0.159.0581)
(0.167,0.590)
(0.174,0.597)
Modern Urban Houses
Pr(PbB>10)
0.031
0.035
0.038
0.040
0.042
0.043
0.044
0.045
95% Cl
(0.003,0.155)
(0.003,0.170)
(0.003.0.190)
(0.003. 0.203)
(0.003.0.213)
(0.003. 0.222)
(0.003, 0.229)
(0.003, 0.236)
Previously Abated Houses
Pr(PbB>10)
0.639
0.655
0.670
0.679
0.685
0.689
0.693
0.697
95% Cl
(0.338, 0.870)
(0.365, 0.873)
(0.388. 0.878)
(0.399, 0.882)
(0.406, 0.885)
(0.410,0.888)
(0.414, 0.890)
(0.416. 0.892)
Repair & Maintenance Houses
Pr(PbB>10)
0.362
0.377
0.393
0.403
0.409
0.415
0.419
0.422
95% Cl
(0.094, 0.727)
(0.116, 0.714)
(0.141.0.703)
(0.156,0.698)
(0.167.0.694)
(0.175,0.692)
(0.182,0.690)
(0.188.0.689)
o
I
>o
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G7. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 15 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Window Sill Pb Loadings.
Window
Sill Pb Loading
15)
0.088
0.106
0.126
0.140
0.150
0.158
0.165
0.171
95% Cl
(0.020, 0.255)
(0.027. 0.281)
(0.037, 0.308)
(0.043, 0.325)
(0.049, 0.338)
(0.053. 0.348)
(0 057, 0.357)
(0.060, 0.364)
Modern Urban Houses
Pi(PbB>15)
0.005
0.005
0.006
0.007
0.007
0007
0.008
0.008
95% Cl
(0.000, 0.045)
(0.000, 0.052)
(0.000, 0.060)
(0.000, 0.066)
(0.000, 0.070)
(0.000, 0.074)
(0.000, 0.078)
10.000,0.081)
Previously Abated Houses
Pr(PbB>15)
0.364
0.380
0.396
0.405
0.412
0.417
0.422
0.425
95% Cl
(0.131,0.665)
(0.147.0.669)
(0.162,0.677)
(0.169,0.684)
(0.173,0.690)
(0.177,0.695)
(0.179, 0.700)
(0.181, 0.704)
Repair & Maintenance Houses
Pr(PbB>15)
0.145
0.155
0.165
0.171
0.175
0.179
0.182
0.184
95% Cl
(0.021, 0.464)
(0.028, 0.449)
(0.036, 0.437)
(0.042, 0.430)
(0.046, 0.426)
(0.050, 0.424)
(0.052, 0.422)
(0.055, 0.420)
o
03
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G8. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 20 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Window Sill Pb Loadings.
Window
Sill Pb Loading
(//g/ft2)
50
100
200
300
400
500
600
700
All Houses Combined
Pr(PbB>20)
0.037
0.046
0.058
0.065
0.071
0.076
0.080
0.083
95% Cl
(0.006. 0.142)
(0.009.0.160)
(0.012, 0.180)
(0.015.0.193)
(0.017,0.202)
(0.019. 0.210)
(0.021,0.217)
(0.022. 0.222)
Modern Urban Houses
Pr(PbB>20)
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
95% Cl
(0.000,0.015)
(0.000.0.018)
(0.000,0.021)
(0.000, 0.023)
(0.000, 0.025)
(0.000, 0.027)
(0.000. 0.029)
(0.000, 0.030)
Previously Abated Houses
Pr(PbB>20)
0.199
0.211
0.223
0.230
0.235
0.240
0.243
0.246
95% Cl
(0.052, 0.474)
(0.060, 0.478)
(0.068, 0.487)
(0.071.0.495)
(0.074,0.501)
(0.076. 0.507)
(0.077,0.512)
(0.078.0.517)
Repair & Maintenance Houses
Pr(PbB>20)
0.059
0.065
0.070
0.073
0.076
0.078
0.079
0.081
95% Cl
(0.005. 0.282)
(0.007, 0.270)
(0.010, 0.259)
(0.012,0.254)
(0.014,0.251)
(0.015, 0.249)
(0.016,0.247)
(0.01 7, 0.246)
o
vo
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G9. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 10 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Window Well Pb Loadings.
Window
Well
Pb Loading
«//B/ft2)
200
500
750
1,500
3,000
5,000
10.000
20,000
All Houses Combined
Pr(PbB>10)
0.252
0.283
0.298
0.323
0.349
0.369
0.396
0.424
95% Cl
(0.081,0.526)
(0.102, 0.550)
(0.112,0.561)
(0 131,0.580)
(0.152,0.600)
(0.168, 0.615)
(0.191.0.636)
(0.215,0.658)
Modern Urban Houses
Pr(PbB>10)
0.023
0.027
0.028
0.031
0.034
0.036
0.040
0.043
95% Cl
(0.002,0.128)
(0.002, 0.141)
(0.002,0.148)
(0.002,0.165)
(0.002,0.185)
(0.002, 0.204)
(0.002. 0.233)
(0.002. 0.266)
Previously Abated Houses
Pr(PbB>10)
0.622
0.642
0.651
0.666
0.680
0.691
0.705
0.719
95% Cl
(0.313,0.866)
(0.348, 0.868)
(0.361,0.871)
(0.379, 0.878)
(0.391,0.887)
(0.395, 0.896)
(0.397, 0.909)
(0.394, 0.923)
Repair & Maintenance Houses
Pr(PbB>10)
0.313
0.332
0.340
0.355
0.370
0.382
0.397
0.413
95% Cl
(0.040. 0.780)
(0.058, 0.758)
(0.068, 0.748)
(0.087, 0.732)
(0.109, 0.716)
(0.126,0.705)
(0.152,0.693)
(0.179,0.684)
Q
H
O
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G10. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 15 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Window Well Pb Loadings.
Window
Well Pb
Loading
(pg/ft2)
200
500
750
1.500
3.000
5.000
10.000
20,000
All Houses Combined
Pr(PbB>15)
0.105
0.124
0.132
0.148
0.166
0.179
0.199
0.219
95% Cl
(0.023, 0.307)
(0.031,0.328)
(0.035. 0.338)
(0.043, 0.355)
(0.052, 0.374)
(0.060, 0.389)
(0.071,0.410)
(0.083, 0.433)
Modern Urban Houses
Pr(PbB>15)
0.003
0.004
0.004
0.005
0.005
0.006
0.007
0.007
95% Cl
(0.000. 0.035)
(0.000, 0.040)
(0.000. 0.043)
(0.000, 0.050)
(0.000. 0.058)
(0.000. 0.066)
(0.000. 0.080)
(0.000, 0.096)
Previously Abated Houses
Pr(PbB>15)
0.348
0.368
0.377
0.393
0.408
0.420
0.436
0.452
95% Cl
(0.117.0.659)
(0.138,0.662)
(0.146. 0.666)
(0.157,0.678)
(0.164, 0.696)
(0.168,0.712)
(0.169, 0.737)
(0.167, 0.765)
Repair & Maintenance Houses
PrlPbB>15)
0.117
0.128
0.133
0.142
0.151
0.158
0.168
0.178
95% Cl
(0.006. 0.532)
(0.011,0.503)
(0.013,0.491)
(0.019,0.471)
(0.026, 0.452)
(0.032, 0.440)
(0.041, 0.426)
(0.051,0.416)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
Table G11. Estimated Proportion of Children with Blood-Pb Concentrations Greater than 20 //g/dL as Predicted by a
Least Squares Regression Model of Blood Pb versus Window Well Pb Loadings.
Window
Well Pb
Loading
(pg/ft2)
200
500
750
1.500
3.000
5,000
10,000
20,000
All Houses Combined
Pr(PbB>20)
0.048
0.058
0.063
0.072
0.083
0.091
0.103
0.117
95% Cl
(0.007,0.182)
(0.010, 0.198)
(0.012,0.206)
(0.016.0.220)
(0.020. 0.235)
(0.023, 0.247)
(0.029, 0.265)
(0.035, 0.284)
Modern Urban Houses
Pr(PbB>20)
0.000
0.000
0.000
0.001
0.001
0.001
0.001
0.001
95% Cl
(0.000, 0.011)
(0.000,0.013)
(0.000, 0.014)
(0.000,0.017)
(0.000, 0.020)
(0.000, 0.024)
(0.000, 0.030)
(0.000, 0.037)
Previously Abated Houses
Pr(PbB>20)
0.187
0.202
0.209
0.221
0.233
0.242
0.255
0.268
95% Cl
(0.045, 0.468)
(0.055, 0.471)
(0.059, 0.475)
(0.065, 0.488)
(0.069, 0.508)
(0.071,0.527)
(0.072, 0.557)
(0.071,0.591)
Repair & Maintenance Houses
Pr(PbB>20)
0.046
0.051
O.053
O.058
0.063
0.067
0.072
0.078
95% Cl
(0.001, 0.342)
(0.002,0.316)
(0.003, 0.305)
(0.004, 0.288)
(0.007, 0.273)
(0.009. 0.263)
(0.012,0.252)
(0.016, 0.243)
o
I
H
to
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent seasonal median blood-lead concentrations.
-------
APPENDIX H.
SIDE-BY-SIDE PLOTS COMPARING THE RESULTS OF
THE DESCRIPTIVE MODEL TO THE SEPARATE INTERCEPTS MODEL,
AFTER ADJUSTING FOR ERRORS IN PREDICTOR VARIABLES
H-l
-------
All Houses
Modern Urban
I 100 1000 10000
Floor Pb Loading C^g/jq. ft.)
Previously Abated
so so
4O 40
10 100 1000 10000
Floor Pb Loading (/ug/«q. ft.)
Repair and Maintenance
80 90
SO J SO
I 100 1000 10000 100000
Floor Pb Loading (>jg/aq. ft.)
D IOO IOOO tOt
Floor Pb Loading (^g/sq. ft.)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure H1. Blood Pb Concentration versus Floor Pb Loading (Errors in Variables Solution)
H-2
-------
All Houses
Modern Urban
50 90-1
40 4O
30 SO
10 1O
IO 100 IOOO IOOOO 10OOOO 1
Window Sill Pb Loading p> i- Bound
O 71 LJ p» p> r- B o LJ r-l d
>»>- Bout-id
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure H2. Blood Pb Concentration versus Window Sill Pb Loading (Errors in Variables
Solution)
H-3
-------
All Houses
Modern Urban
too 1000 «
window Well Pb Leadin
.ft.)
Previously Abated
50 50
4O 40
£
to 1OO tOOO tOOOO 1*0000
Window W.ll Pb Loading G"0/»q- «.)
Repair and Maintenance
so so
*O 40
M ^ 30
£
20 .2 20
10 100 1000 10000 1
Window w.il Pb Loading (/xg/iq. ft.)
10 100 1000 10000 100000
Window Well Pb Loading (ug/iq. It.)
and Mdlntvrtano*
rn urban
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure H3. Blood Pb Concentration versus Window Well Pb Loading (Errors in Variables
Solution)
H-4
-------
All Houses
Modern Urban
0 1OO 1000
Door Pb Concentration
Previously Abated
so so
30 T^ 30
i
20 J 20
10 100 1000
Floor Pb Concentration
Repair and Maintenance
so so
30 SO
J
£
*
20 2 20
1O 1O
9 100 1000
Floor Pb Concentration
10000 100000
10O 1000
or Pb Concentration
10000 1OOOOO
CD
-£*
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure H4. Blood Pb Concentration versus Floor Pb Concentration (Errors in Variables
Solution)
H-5
-------
All Houses
Modern Urban
10 10
O 0
10 100 1000 10000 100000 1000000
window SHI Pb Concentration (MB/O)
BO SO
JO 30
i
10 100 1000 10000 I
Window Sill Pb Concentration
Previously Abated
Repair and Maintenance
£
20 J 20
1O 10
10 too 1000 10000 100000 1000000
Window Sill Pb Concentration (
o / /
10 1OO 1000 1OOOO 1
Window SIM Pb Concentration (MO/g)
>de»r-ri UfbC
*»dle + *»*al
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure H5. Blood Pb Concentration versus Window Sill Pb Concentration (Errors in
Variables Solution)
H-6
-------
All Houses
Modern Urban
/ /
60 »0
30 ^ 30
J!
£
20 J 20
10 1OO 10OO 10OOO 10OOOO 10OOOOO
Window W.ll Pb Concentration C"g/g)
10 100 1000 10000 100000 1
Window Well Pb Concentration Os/fl)
Previously Abated
Repair and Maintenance
50 SO
O 4O
3O ^ 3O
J
fi"
20 J 20
1O 1O
10 100 1000 10000 i
Window Well Pb Concentration
1O 1OO 1000 10000
Window Well Pb Concentration C"g/9)
4oed«r*ri Ur-toar-i
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure H6. Blood Pb Concentration versus Window Well Pb Concentration (Errors in
Variables Solution)
H-7
-------
APPENDIX I.
SIDE-BY-SIDE PLOTS COMPARING THE RESULTS OF THE
DESCRIPTIVE MODEL TO THE SEPARATE INTERCEPTS MODEL,
USING A LEAST SQUARES SOLUTION
1-1
-------
All Houses
Modem Urban
Floor Pb \jotttng (^o/*q. ft.)
Previously Abated
X
X
X
1 n 100 1000 i
Floor Pb Loading (^g/feq. ft)
00 60
40 40
ao ^ 30
1
e
20 2 20
10 10
X
X
1O 100 1000
Floor Pb Loadng O4)feq. ft.)
Repair and Maintenance
60
30 B 30
1
e
30 S 00
O
10 10
1O 100 1OOO
Boor Pb Loading («g/«q. It)
Bound
Bound
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure 11. Blood Pb Concentration versus Floor Pb Loading (Least Squares Solution)
1-2
-------
All Houses
Modem Urban
Window em Pb LoaoVig (Mo*q. t)
Previously Abated
00 eo
40 40
30 30
e
20 20
10 10
0 0
00 60
40 40
30 Jj SO
1
£
20 8 20
10 10
0 O
Window SB Pb UMdklg (;.»*q. ft.)
Repair and Maintenance
Window S» Pb LcMdkig
t>
Window SM Pb LcMdng
ft)
«-l
Bound
Bound
Bound
Bound
F»rwvlou»ly Aborted
tv1ocJ»m LJrt>«rn
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure 12. Blood Pb Concentration versus Window Sill Pb Loading (Least Squares
Solution)
1-3
-------
All Houses
Modem Urban
Window Wai Pb LcMdng
-------
All Houses
Modem Urban
so so
40 40
30 * 30
1
£
20 5 20
K> 10
« «X> ttOO
Boor Pb Concentrator)
Floor Pb ConotrtnOan
Previously Abated
Repair and Maintenance
BO
o 9 ao
1
e
g
30 S 20
Boor Pb OonoMiMtan
1O 100 1000 10000
Floor Pb ConomMlon
l_Jp>p>«r Bound
i_ip>p>«r Bound
l_lp|3«r Bound
Bound
F=
-------
All Houses
Modern Urban
Tt so so
/'/
//;
I 10 100 1000 10000 100000 1
Window SHI Pb Concentration (Mg/g)
Previously Abated
10 100 1000 toooo 100000 i
Window SMI Pb Concentration
Repair and Maintenance
30 SO
30^ 30
£
1
/
10 100 1000 10000 100000 1000000
Window SIM Pb Concentration I
10 100 1000 10OOO 100000 1000000
Window Sill Pb Concentration (MO/fl)
997* <-lf>fsm
9SVS l_lp>F=«
»OfS. l_lpp.»
CISTS LJF>P«.
I- B CD i_j n d
Reipcalr- caned K4a1rit*f
F* r-wl ocj ei I V >^fc=»c3 + »cJ
Ivl ^cJ «> r-l-i UJfbart
PreKdloteicI
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure 15. Blood Pb Concentration versus Window Sill Pb Concentration (Least Squares
Solution)
1-6
-------
All Houses
Modern Urban
40 40
SO ^ 30
£
1
\
s
10 100 1000 10000 100000 1000000
Window w.ll Pb Concentration {
Previously Abated
SO SO
*0 40
30 .J 30
&
1
10 100 1000 10000 100000 1000000
Window Well Pb Concentration (Aig/g)
1 10 100 1000 10000 100000 1
Window Well Pb Concentration
Repair and Maintenance
10 100 1000 10000 100000 1000000
Window Well Pb Concentration (
9975 LJ|Z>p>e>r-
9S7E Up>F3e»r-
905=5 Up>p>»r
aS?Z LJ|=>p>e>i-
B o v-i n cd
3 o UJ r~) d
S o LJ r~t ca I r- a n cd rv4 r-n LJr"bdm
Rr-e>dlot«>cl
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure 16. Blood Pb Concentration versus Window Well Pb Concentration (Least Squares
Solution)
1-7
-------
APPENDIX J.
PLOTS COMPARING THE RESULTS OF THE DESCRIPTIVE
MODEL TO THE SEPARATE INTERCEPTS MODEL, AFTER
ADJUSTING FOR ERRORS IN PREDICTOR VARIABLES
J-l
-------
-Q
Q-
CD
10
100 1000
Floor Pb Loading (/xg/sq. ft.)
10000
100000
Predicted (All Houses)
Predicted MU
Predicted PA
Predicted RM
* * * Modern Urban (MU)
-------
T3
\
D)
_Q
CL
-o
O
_0
m
50
40
30
20-
10
o9 CP p
7, b ' o
^
10
100
1000
10000
-n-rr|
100000
1 ' '"I
1000000
Window Sill Pb Loading (/xg/sq. ft.)
Predicted (All Houses)
Predicted MU
Predicted PA
Predicted RM
* * Modern Urban (MU)
* * Previously Abated (PA)
O O Repair and Maintenance (RM)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure J2. Blood Pb Concentration versus Window Sill Pb Loading (Errors in Variables
Solution)
J-3
-------
_Q
CL
-o
O
_O
m
50
40
30
20
10
10
100
1000
10000
100000
1000000
10000000
Window Well Pb Loading (/ag/sq. ft.)
Predicted (All Houses)
Predicted MU
Predicted PA
Predicted RM
* * * Modern Urban (MU)
A * * Previously Abated (PA)
O o o Repair and Maintenance (RM)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure J3. Blood Pb Concentration versus Window Sill Pb Loading (Errors in Variables
Solution)
J-4
-------
T>
0)
.Q
0.
-D
O
(3
CD
50
40
30
20-
10
"1
10
100
1000
10000
1 "I
100000
Floor Pb Concentration (yug/g)
Predicted (All Houses)
Predicted MU
Predicted PA
Predicted RM
* * * Modern Urban (MU)
A
-------
-o
\
a>
T3
O
0
50
40
30-
20-
10-
o
10 100 1000 10000
Window Sill Pb Concentration
Predicted (All Houses)
Predicted MU
Predicted PA
Predicted RM
100000
* * * Modern Urban (MU)
it £ ir Previously Abated (PA)
O O o Repair and Maintenance (RM)
1000000
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure J5. Blood Pb Concentration versus Window Sill Pb Concentration (Errors in
Variables Solution)
J-6
-------
c
\
Q)
XI
Q-
T3
O
_0
DQ
40
30
20
10
TTi
10
100
1000
10000
100000
n-rrrf
1000000
Window Well Pb Concentration (/ig/g)
Predicted (All Houses)
Predicted MU
Predicted PA
Predicted RM
* * * Modern Urban (MU)
it ft * Previously Abated (PA)
O O O Repair and Maintenance (RM)
Results are based on a seasonally adjusted analysis held fixed at November 1, and represent
seasonal median blood-lead concentrations.
Figure J6. Blood Pb Concentration versus Window Well Pb Concentration (Errors in
Variables Solution)
J-7
------- |