November 28, 1995
DRAFT REPORT
STATISTICAL EVALUATION OF THE RELATIONSHIP
BETWEEN BLOOD-LEAD AND DUST-LEAD BASED ON
DATA FROM THE ROCHESTER LEAD-IN-DUST STUDY
for
Task 4-13
Battalia Task Leader
Warren Strauss
Battelle Task Team
Bruce Buxton, Steven Rust,
Halsey Boyd, and Claire Matthews
BATTELLE
505 King Avenue
Columbus, Ohio 43201
Contract No. 68-D2-0139
Janet Reamers, 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
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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.
ii
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TABLE OF CONTENTS
1.0 INTRODUCTION 1
2.0 DATA PREPARATION 1
3.0 THE STATISTICAL MODEL 3
4.0 STATISTICAL MODELING RESULTS 4
5.0 PROTECTIVE DUST LEAD LEVELS 6
6.0 EXCEEDANCE PROPORTIONS 6
7.0 PARTIAL SIGNIFICANCE OF WINDOW WELL PB MEASUREMENTS . . 20
APPENDICES
APPENDIX A. STATISTICAL MODELS A-l
APPENDIX B. ALTERNATIVE REGRESSION PARAMETER
ESTIMATION IN THE PRESENCE OF
MEASUREMENT ERROR B-l
APPENDIX C. TOLERANCE BOUNDS AND CONFIDENCE
INTERVALS FOR PERCENTILES AND
EXCEEDANCE PROBABILITIES IN A
REGRESSION SETTING C-l
APPENDIX D. ESTIMATION OF MEASUREMENT ERROR
VARIANCE COMPONENTS D-l
APPENDIX E. PARAMETER ESTIMATES FOR STATISTICAL
MODELS E-l
APPENDIX F. PROTECTIVE DUST LEAD LEVELS AND
EXCEEDANCE PROBABILITIES FOR ERRORS IN
VARIABLES SOLUTION F-l
APPENDIX G. PROTECTIVE DUST LEAD LEVELS AND
EXCEEDANCE PROBABILITIES FOR LEAST
SQUARES SOLUTION G-l
APPENDIX H.
PLOTS COMPARING THE ERRORS IN VARIABLES
MODEL RESULTS FOR BRM AND WIPE SAMPLING . . . . H-l
ill
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TABLE OF CONTENTS
(Continued)
LIST OF TABLES
Page
Table 1. Results of Fitting the Statistical Model to
the Rochester Lead-in-Dust Data Using the
Errors in Variables Approach 5
Table 2. Estimated Dust Lead Levels for Floors, Window
Sills, and Window Wells at Which the 85th,
90th, 95th, and 99th Percentiles of Childhood
Blood Lead Concentrations Reach 10, 15, and
20 /ig/dL (Based on the Errors in Variables
Approach) 16
Table 3. Estimated Proportion of Children with Blood-
Lead Concentrations Greater than 10, 15, and
20 /xg/dL as a Function of Floor, Window Sill,
or Window Well Lead Loadings (Based on the
Errors in Variables Approach) 18
Table 4. Results of Fitting Floor, window Sill, and
Window Well Lead Loadings or Concentrations
Simultaneously on Blood-Lead Concentrations
Based on the Least-Squares Approach 21
Table 5. Estimated Pearson Correlation Coefficients Between
Natural Log Transformed Lead Levels from Children's
Blood and Floor, Window Sill and Window Well Dust . 23
LIST OF FIGURES
Figure 1. Rochester Lead-in-Dust Study Floor-Lead
Loadings From BRM Sampling -- Estimated
Regression Curve and Tolerance Bounds 7
Figure 2. Rochester Lead-in-Dust Study Window Sill-Lead
Loadings From BRM Sampling -- Estimated
Regression Curve and Tolerance Bounds 8
Figure 3. Rochester Lead-in-Dust Study Window Well-Lead
Loadings From BRM Sampling -- Estimated
Regression Curve and Tolerance Bounds 9
Figure 4. Rochester Lead-in-Dust Study Floor-Lead
Loadings From Wipe Sampling -- Estimated
Regression Curve and Tolerance Bounds 10
Figure 5. Rochester Lead-in-Dust Study Window Sill-Lead
Loadings From Wipe Sampling -- Estimated
Regression Curve and Tolerance Bounds 11
Figure 6. Rochester Lead-in-Dust Study Window Well-Lead
Loadings From Wipe Sampling -- Estimated
Regression Curve and Tolerance Bounds 12
Figure 7. Rochester Lead-in-Dust Study Floor-Lead
Concentrations From BRM Sampling -- Estimated
Regression Curve and Tolerance Bounds 13
IV
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TABLE OF CONTENTS
(Continued) Page
Figure 8. Rochester Lead-in-Dust Study Window Sill-Lead
Concentrations From BRM Sampling -- Estimated
Regression Curve and Tolerance Bounds 14
Figure 9. Rochester Lead-in-Dust Study Window Well-Lead
Concentrations From BRM Sampling -- Estimated
Regression Curve and Tolerance Bounds 15
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STATISTICAL EVALUATION OF THE RELATIONSHIP BETWEEN
BLOOD-LEAD AND DUST-LEAD BASED ON DATA
FROM THE ROCHESTER LEAD-IN-DUST STUDY
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 data collected in
the Rochester Lead-in-Dust 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 fig/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.
This analysis follows a similar approach to that taken for
an analysis of data from the Repair and Maintenance (R&M) Study,
and the results are presented in the same format so that
comparisons between the two studies can be made.
2.0 DATA PREPARATION
The sample consisted of 205 homes with one child per home.
The response variable in the statistical analysis was the natural
logarithm of child 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 time trends in blood-lead concentrations. In 204
homes, blood samples and dust samples were all collected within a
three-week window of time. For one home the dust sampling date
was not available.
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Individual samples of dust lead were collected from multiple
locations of a given component type using both the Baltimore R&M
(BRM) vacuum sampling method and wipe sampling. The samples were
often collected from locations with different surface areas. For
example, homes with uncarpeted floors had between 1 and 5 floor
BRM dust samples with total area ranging from 1 to 5 ft2 sampled
per house. Each house also had 1 to 3 window sill BRM samples
with total area ranging from 0.06 to 1.7 ft2 sampled per house.
In addition, each house had between 1 and 3 window well BRM
samples with total area ranging from 0.05 to 1.2 ft2 sampled per
house. Since the area and mass of each individual sample varied
within a house, area weighted average lead loading and mass
weighted average lead concentration results were calculated for
floors, window sills and window wells. Thus, if two dust samples
were collected from floor locations within a house with sample
areas of 1 ft2 and 3 ft2, the lead loading results from the 3 ft2
sample were 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'.
Floor samples in the Rochester Lead-in-Dust Study were
collected from both carpeted and uncarpeted surfaces, while floor
samples in the R&M Study were collected from only uncarpeted
surfaces. Therefore, to maintain comparability analysis of the
Rochester data was restricted to the data for uncarpeted
surfaces. From the original sample of 205 Rochester homes, there
were a total of 193 homes with BRM floor-dust samples collected
from uncarpeted floor surfaces.
The median blood-lead level from all 205 homes was 6.1 /xg/dL
(range 1.4 to 31.7 pig/dL) . The median BRM floor dust-lead
loading from the 193 homes with uncarpeted floors was 13.2 jig/ft2
(range 0.1 to 74,100 jig/ft2) . The median window sill BRM dust-
lead loading from 197 homes was 265 jig/ft2 (range 0.7 to 118,000
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/xg/ft2) . The median window well BRM dust-lead loading from 189
homes was 48,000 /xg/ft2 (range 7 to 3,000,000 /xg/ft2) .
3.0 THE STATISTICAL MODEL
A 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 time
effect which adjusts for temporal trends in childhood blood-lead
concentrations. Since the dates of environmental sampling ranged
from August 31, 1993 to November 20, 1993 in the Rochester Lead-
in-Dust Study, there was not a large enough range of time points
to properly parameterize the sine-wave model for seasonal
variations in blood-lead that was used in the analysis of the
Repair and Maintenance Study data. Therefore, a simple linear
trend was fitted to capture the seasonal variations in the
Rochester data between August 31 and November 20, 1993. 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, both a simple least-squares approach (which
does not account for measurement error) and a statistical
approach that adjusts for measurement error in predictor
variables were 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 a simplifying assumption about the
Rochester Lead-in-Dust Study data. In particular, this analysis
does not attempt to account for the possible effect of
potentially important socioeconomic and behavioral factors.
Investigators in the Rochester Lead-in-Dust Study found that four
covariates were "significantly associated with higher blood lead
levels among children: Black race, parental reports that
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children put soil in their mouths, single parent household, and a
higher ferritin level".1
4.0 STATISTICAL MODELING RESULTS
The results of fitting the statistical model to the data
using an errors in variables approach are reported in Table 1.
Separate models were fitted for the nine environmental-lead (PbE)
measurements -- lead loading by BRM and wipe sampling for
uncarpeted floors, window sills, and window wells, as well as
lead concentration by BRM sampling for uncarpeted floors, window
sills, and window wells. Slope (/i^) parameter estimates and
associated 95% confidence intervals are reported, as well as a
measure of the proportion of variability explained by the model
(R2) from a 'least squares' fit of the model.
The relationship between blood-lead concentrations and dust
lead loadings for floors, window sills, and window wells are
illustrated graphically in Figures 1 through 9. 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 to 9 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 median sampling date (October 13,
Department of Pediatrics, Biostatistics, and Environmental Medicine, The
University of Rochester School of Medicine, (June, 1995), "The Relation of
Lead-Contaminated House Dust and Blood Lead Levels Among Urban Children, Final
Report, Volume II, Results and Discussion", U.S. Department of Housing and
Urban Development Grant No. MLDP T0001-93.
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Table 1. Results of Fitting the Statistical Model to the Rochester Lead-in-Dust Data
Using the Errors in Variables Approach
Unit of Measure
Component
Tested
Slope Values
ft
Slope Estimate
95%
Confidence Interval
R2
(a)
Slope Values in Units of ln(0g Pb / dL Blood) / ln(//g Pb / ft2 Sampled) ( BRM Sampler)
Loading
(//g/ft2)
Floors
Window Sills
Window Wells
0.133
0.126
0.149
(0.089,0.177)
(0.087,0.165)
(0.115,0.183)
0.139
0.139
0.160
Slope Values in Units of ln(//g Pb / dL Blood) / ln(//g Pb / ft2 Sampled) (Wipe Samples)
Loading
(//g/ft2)
Floors
Window Sills
Window Wells
0.237
0.198
0.179
(0.155 ,0.319)
(0.133,0.264)
(0.130,0.229)
0.111
0.131
0.108
Slope Values in Units of ln(//g Pb / dL Blood) / ln(//g Pb / g Dust) (BRM Sampler)
Concentration
U/g/g)
Floors
Window Sills
Window Wells
0.104
0.126
0.111
(0.033 , 0.175)
(0.077 ,0.175)
(0.062 ,0.161)
0.033
0.083
0.066
(a) The reported R2 values are based on a least squares fit without adjusting for
the errors in predictor variables.
(b) Based on the results of this simple descriptive model, the predicted blood-lead
concentration for children living in houses with BRM floor lead loadings of 100 and
200 //g.ft2 would be 7.6 and 8.3 //g/dL respectively for a difference of 0.7 //g/dL.
1993). 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 BRM floor-lead loading.
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5.0 PROTECTIVE DUST LEAD LEVELS
The dashed curves in Figures 1 to 9 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 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 median sampling date (October 13, 1993).
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 1, the tolerance bound
for the 99th percentile of children's blood-lead concentrations
is always above a blood-lead concentration of 10 iig/dL. In Table
2 these cases have associated dust-lead values that are listed as
"Out of Range".
6.0 EXCEEDANCE PROPORTIONS
Table 3 provides estimates of the proportion of children
with blood-lead concentrations exceeding 10, 15, and 20 itg/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 median sampling date (October 13, 1993).
The results from this analysis suggest that for BRM dust-
lead loadings of 100 /zg/ft2 on floors, 500 iig/ft2 on window
sills, and 800 /ig/ft2 on window wells, approximately 31%, 19%,
and 2% of the children sampled in this study would be expected to
have blood-lead concentrations that exceed 10 itg/dL at the median
sampling date (October 13, 1993).
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50:
40-
73 30
U>
A 20-
O
_0
CD
#•*• •
* *
10
100 1000 10000 100000
Floor Pb Loading — BRM (yug/sq. ft)
* * * ObservaHons
Pr«dlct«d (EIV)
Pr»dlci«d (OLS)
85% Upper Bound (EIV)
90% Upper Bound (EIV)
95% Upper Bound (EIV)
99% Upper Bound (EIV)
1000000
Figure 1. Rochester Lead-in-Dust Study Floor-Lead Loadings From BRM Sampling -- Estimated Regression Curve
and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's Blood-Lead
Concentrations Based on Errors in Variables Fit.
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oo
50
40^
=U 30
D>
-Q 201
O
O
m 10
10 100 1000 10000 100000
Window Sill Pb Loading — BRM (M9/sq. ft)
* * * Observations
Pr»dlcf«d (EIV)
Predicted (OLS)
85% Upper Bound (EIV)
90% Upper Bound (EIV)
95* Upper Bound (EIV)
99% Upper Bound (EIV)
1000000
Figure 2. Rochester Lead-in-Dust Study Window Sill-Lead Loadings From BRM Sampling - Estimated Regression
Curve and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's Blood-Lead
Concentrations Based on Errors in Variables Fit
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50 -I
40
=0 30]
D>
-Q
Q_
20
O
O
m 10
10 100 1000 10000 100000
Window Well Pb Loading — BRM (/xg/sq. ft)
* * * Observations
Predicted (EIV)
Predicted (OLS)
85% Uppsr Bound (EIV)
1000000
90% Upper Bound (EIV)
95% Upper Bound (EIV)
99% Upper Bound (EIV)
Figure 3. Rochester Lead-in-Dust Study Window Well-Lead Loadings From BRM Sampling - Estimated
Regression Curve and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's
Blood-Lead Concentrations Based on Errors in Variables Fit.
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M
O
Q_
~O
O
£
DO
50 H
40-
30-
20-
10-
0-
10
100 1000 10000 100000
Floor Pb Loading — Wipe (^g/sq. ft)
* * * Observations
Predicted (EIV)
Predicted (OLS)
1000000
85% Upper Bound (EIV)
90% Upper Bound (EIV)
95% Upper Bound (EIV)
99% Upper Bound (EIV)
Figure 4. Rochester Lead-in-Dust Study Floor-Lead Loadings From Wipe Sampling - Estimated Regression Curve
and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's Blood-Lead
Concentrations Based on Errors in Variables Fit
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50 H
4CH
TJ 30-
-Q 20
Q_
TJ
O
O
m 10
10 100 1000 10000 100000
Window Sill Pb Loading — Wipe (//g/sq. ft)
* * * Observations
Predicted (EIV)
Pr»dlcUd (OLS)
85% Upper Bound (EIV)
1000000
90% Upper Bound (EIV)
95% Upper Bound (EIV)
99% Upper Bound (EIV)
Figure 5. Rochester Lead-in-Dust Study Window Sill-Lead Loadings From Wipe Sampling - Estimated Regression
Curve and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's Blood-Lead
Concentrations Based on Errors in Variables Fit
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50 -I
to
10 100 1000 10000 100000
Window Well Pb Loading — Wipe (/^g/sq. ft)
* * * Observations
Pradletcd (EIV)
Predicted (OLS)
85% Upper Bound (EIV)
1000000
90% Upper Bound (EIV)
95% Upper Bound (EIV)
99% Upper Bound (EIV)
Figure 6. Rochester Lead-in-Dust Study Window Well-Lead Loadings From Wipe Sampling — Estimated
Regression Curve and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's
Blood-Lead Concentrations Based on Errors in Variables Fit
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H
OJ
_Q
Q-
-o
O
£
CD
50 -I
40
30
20
10
*
~ * 3k~ ~* . . *
10
100 1000 10000
Floor Pb Concentration — BRM
100000 1000000
* *
Observations
Predicted (EIV)
Predicted (OLS)
85% Upper Bound (EIV)
90% Upper Bound (EIV)
95% Upper Bound (EIV)
99% Upper Bound (EIV)
Figure 7. Rochester Lead-in-Dust Study Floor-Lead Concentrations From BRM Sampling - Estimated Regression
Curve and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's Blood-Lead
Concentrations Based on Errors in Variables Fit
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50:
40
TJ 30
0)
-Q 20
o
o
m 10
0
*%* * *
10 100 1000 10000 100000
Window Sill Pb Concentration — BRM (y^g/g)
* * * Observations
Predicted (EIV)
Predicted (OLS)
85% Upper Bound (EIV)
90% Upper Bound (EIV)
95% Upper Bound (EIV)
99% Upper Bound (EIV)
1000000
Figure 8. Rochester Lead-in-Dust Study Window Sill-Lead Concentrations From BRM Sampling - Estimated
Regression Curve and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's
Blood-Lead Concentrations Based on Errors in Variables Fit
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50 4
40-
30-
20
O)
3
-Q
Q_
-o
O
O
m 10-
0-
10 100 1000 10000 100000
Window Well Pb Concentration — BRM (/xg/g)
* * * Observations
Predicted (EIV)
Predicted (OLS)
85% Upper Bound (EIV)
1000000
90% Upper Bound (EIV)
95% Upper Bound (EIV)
99% Upper Bound (EIV)
Figure 9. Rochester Lead-in-Dust Study Window Well-Lead Concentrations From BRM Sampling - Estimated
Regression Curve and Tolerance Bounds for the 85th, 90th, 95th, and 99th Percentiles of Children's
Blood-Lead Concentrations Based on Errors in Variables Fit
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Table 2. Estimated Dust Lead Levels for Floors. Window Sills, and Window Wells at
Which the 85th, 90th, 95th, and 99th Percentiles of Childhood Blood Lead
Concentrations Reach 10, 15, and 20/ig/dL (Based on the Errors in Variables
Approach)
BRM Sampler Lead Loading
Sample
Type
Floor
Pb Loading
(0g/ft2)
BRM Sampler
Window Sill
Pb Loading
Oag/ft2!
BRM Sampler
Window Well
Pb Loading
(/ug/ft2)
BRM Sampler
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
lOjig/dL
4
1
Out of Range
Out of Range
89
23
2
Out of Range
10,156
3,779
817
41
15/tg/dL
88
32
5
Out of Range
2,209
770
133
2
144,436
61.592
15,940
982
20/ig/dL
553
223
52
1
15,477
5,938
1,307
45
805,938
362,045
104,728
8,045
Wipe Sampling Lead Loading
Floor
Pb Loading
Gug/ft2>
Wipe Samples
Window Sill
Pb Loading
fog/ft2)
Wipe Samples
Window Well
Pb Loading
fog/ft2)
Wipe Samples
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
7
3
Out of Range
Out of Range
74
30
7
Out of Range
1,799
732
179
11
40
23
8
Out of Range
578
294
93
7
16,621
7,989
2,420
190
112
67
30
4
1.965
1,068
405
45
66,800
33,992
11,785
1208
16
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Table 2. Continued
BRM Sampler Lead Concentration
Sample
Type
Floor
Pb Concentration
(pg/g)
BRM Sampler
Window Sill
Pb Concentration
0/g/g)
BRM Sampler
Window Well
Pb Concentration
(pg/g)
BRM Sampler
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/ig/dL
14
Out of Range
Out of Range
Out of Range
593
125
11
Out of Range
1,104
162
8
Out of Range
15j*g/dL
2.450
685
23
Out of Range
16,270
5,586
830
10
49,044
14,463
1,488
6
20j/g/dL
16,581
6,088
1,106
1
104,638
40,827
8,974
228
378,000
131,306
23,482
280
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 time adjusted analysis held fixed at October 13, which was the median
sampling date.
17
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Table 3. Estimated Proportion of Children with Blood-Lead Concentrations Greater than
10, 15, and 20 fjg/dl as a Function of Floor, Window Sill, or Window Well Lead
Loadings (Based on the Errors in Variables Approach)
BRM Sampler Lead Loading
Surface
Tested
Floors
Window
Sills
Window
Wells
Pb
Loading
«J/*t2
5
10
15
20
25
30
35
40
100
200
250
50
100
200
300
400
500
600
700
200
500
750
800
1500
3000
5000
10000
20000
Proportion Greater Than
10/rg/dl
Pr(Pb>10)
0.11
0.15
0.17
0.19
0.20
0.21
0.22
0.23
0.31
0.37
0.39
0.08
0.11
0.14
0.16
0.18
0.19
0.20
0.21
0.00
001
0.02
0.02
0.03
0.05
0.07
0.10
0.15
95% Cl
(0.07,0.16)
(0.10,0.20)
(0.12 , 0.22)
(0.14,0.24)
(0.15,0.26)
(0.16 , 0.27)
(0.17 , 0.29)
(0.18,0.30)
(0.24 , 0.38)
(0.28 , 0.46)
(0.29 , 0.49)
(0.05,0.13)
(0.07,0.16)
(0.10,0.19)
(0.12,0.22)
(0.13,0.23)
(0.14,0.25)
(0.15,0.26)
(0.16,0.27)
(0.00 , 0.02)
(0.00 , 0.04)
(0.01 , 0.05)
(0.01 , 0.05)
(0.01 , 0.07)
(0.03 , 0.09)
(0.04,0.12)
(0.07,0.15)
(0.10,0.20)
IB
Pr(Pb>15)
0.02
0.04
0.04
0.05
0.06
0.06
0.07
0.07
0.11
0.14
0.16
0.01
0.02
0.03
0.04
0.05
0.05
0.06
0.06
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.02
0.03
Greater Than
pg/dl
95% Cl
(0.01 . 0.05)
(0.02 . 0.06)
(0.02 , 0.07)
(0.03 , 0.08)
(0.03 , 0.09)
(0.04.0.10)
(0.04,0.10)
(0.04,0.11)
(0.07,0.16)
(0.09,0.21)
(0.10,0.23)
(0.00 , 0.03)
(0.01 , 0.04)
(0.02 , 0.06)
(0.02 , 0.07)
(0.03 , 0.08)
(0.03 , 0.09)
(0.03 , 0.09)
(0.04,0.10)
(0.00 , 0.00)
(0.00 . 0.00)
(0.00 , 0.00)
(0.00,0.01)
(0.00, 0.01)
(0.00 , 0.02)
(0.00 , 0.02)
(0.01 , 0.04)
(0.02 , 0.06)
Proportion Greater Than
20//g/dt
Pr(Pb>20)
0.00
0.01
0.01
0.01
0.02
0.02
0.02
0.02
0.04
0.06
0.06
0.00
0.00
0.01
0.01
0.01
0.01
0.02
0.02
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
95% Cl
(0.00.0.01)
(0.00 , 0.02)
(0.00 , 0.02)
(0.00 . 0.03)
(0.01 . 0.03)
(0.01 . 0.04)
(0.01 , 0.04)
(0.01 , 0.04)
(0.02 . 0.07)
(0.03,0.10)
(0.03.0.11)
(0.00.0.01)
(0.00,0.01)
(0.00 . 0.02)
(0.00 , 0.02)
(0.00 , 0.03)
(0.00 . 0.03)
(0.01 , 0.03)
(0.01 , 0.04)
(0.00, 0.00)
(0.00 . 0.00)
(0.00 , 0.00)
(0.00 . 0.00)
(0.00 , 0.00)
(0.00 , 0.00)
(0.00 , 0.00)
(0.00,0.01)
(0.00 , 0.02)
18
-------
Table 3. Continued
Wipe Sampling Lead Loading
Surface
Tested
Floors
Window
Sills
Window
Wells
Pb
Loading
wjrtt2
5
10
15
20
25
30
35
40
100
200
250
50
100
200
300
400
500
600
700
200
500
750
800
1500
3000
5000
10000
20000
Proportion Greater Than
10/ig/dl
Pr(Pb>10)
0.08
0.13
0.17
0.20
0.23
0.25
0.27
0.29
0.44
0.55
0.59
0.08
0.12
0.18
0.22
0.25
0.28
0.30
0.32
0.02
0.05
0.06
0.06
009
0.14
018
0.25
0.32
95% Cl
(0.04.0.13)
(0.09,0.18)
(0.12.0.22)
(0.15,0.26)
(0.18,0.29)
(0.20 , 0.32)
(0.21 , 0.34)
(0.23 , 0.37)
(0.32 , 0.55)
(0.40 , 0.69)
(0.42 . 0.73)
(0.04,0.13)
(0.08,0.18)
(0.13, 0.24)
(0.17,0.28)
(0.19,0.32)
(0.21 , 0.35)
(0.23 , 0.38)
(0.24 , 0.40)
(0.00 , 0.05)
(0.02 , 0.09)
(0.03,0.10)
(0.03,0.11)
(0.06 ,0.14)
(0.10,0.19)
(0.13.0.24)
(0.19,0.31)
(0.25 . 0.41)
Proportion Greater Than
15/fg/dJ
Pr(Pb>15)
0.01
0.03
0.04
0.06
0.07
0.08
0.09
0.1
0.19
0.28
0.31
0.01
0.03
0.05
0.07
0.08
0.09
0.11
0.12
0.00
0.00
0.01
0.01
0.02
0.03
0.05
0.07
0.11
95% Cl
(0.00 . 0.03)
(0.01 , 0.06)
(0.02 , 0.07)
(0.03 , 0.09)
(0.04,0.11)
(0.05,0.12)
(0.06,0.14)
(0.06,0.15)
(0.12,0.28)
(0.16,0.42)
(0.18,0.47)
(0.00 , 0.03)
(0.01 , 0.05)
(0.03 , 0.08)
(0.04,0.10)
(0.05,0.12)
(0.06.0.14)
(0.07,0.16)
(0.07,0.17)
(0.00,0.01)
(0.00 . 0.02)
(0.00 , 0.02)
(0.00 , 0.02)
(0.01 , 0.04)
(0.02 , 0.06)
(0.03 , 0.08)
(0.05,0.12)
(0.07,0.17)
Proportion Greater Than
20/ig/dl
Pr(Pb>20)
0.00
0.01
0.01
0.02
0.02
0.03
0.03
0.04
0.08
0.14
0.16
0.00
0.00
0.01
0.02
0.03
0.03
0.04
0.04
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.02
0.04
95% Cl
(0.00.0.01)
(0.00 , 0.02)
(0.00 , 0.03)
(0.01 , 0.03)
(0.01 , 0.04)
(0.01 , 0.05)
(0.01 , 0.06)
(0.02 , 0.06)
(0.04,0.14)
(0.07 , 0.24)
(0.08 , 0.28)
(0.00,0.01)
(0.00 , 0.02)
(0.00 , 0.03)
(0.01 , 0.04)
(0.01 , 0.05)
(0.01 , 0.06)
(0.02 , 0.07)
(0.02 , 0.08)
(0.00 , 0.00)
(0.00 , 0.00)
(0.00 , 0.00)
(0.00 , 0.00)
(0.00,0.01)
(0.00 , 0.02)
(0.00 , 0.03)
(0.01 , 0.04)
(0.02 , 0.07)
Results are based on a time adjusted analysis held fixed at October 13, which was the median sampling date.
19
-------
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 temporal 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 BRM well lead on blood lead was
only marginally statistically significant after adjusting for the
effects of floor lead, sill lead, and temporal variation. Floor
lead appeared to explain most of the variability in blood lead
for both BRM and wipe lead loading, but was less predictive for
BRM lead concentration. The model with only BRM floor lead
loading and an adjustment for temporal trends explained 16.2% of
the variability in blood-lead concentrations, adding window sill
lead loading to the model explained an additional 4.4% of the
variability, and adding window well lead loading with the other
two factors already in the model explained an additional 5.4% of
the variability. The amount of extra variability explained by
window sill-lead loading after already accounting for floor-dust
lead loading and temporal variations is calculated by subtracting
the coefficient of determination from the base model (R2=0.162)
20
-------
Table 4. Results of Fitting Floor, Window Sill, and Window Well Lead Loadings or Concentrations Simultaneously
on Blood-Lead Concentrations Based on the Least Squares Approach
Unit of Measure
Sample
Size
Variables
in the
Base Model
Variables
Added to the
Base Model
Slope Values
01 (floors)
(95% CD
01 (SUb)
(95% CI)
01 (Wells)
(95% CI)
R2
for the
Full Model
Additional
Variability
Explained
Slope Values in Units of ln(pg Pb / dL Blood) / ln(jig Pb / f? Sampled) (Dust Samples Collected with BRM Sampler)
Loading
fog/ft2)
BRM Sampler
177
Date
Date, Floors
Date, Floors
Date, Floors,
Window Sills
Floors
Window Sills
Window Wells
Window Wells
0 120
(0 077 . 0 162)
0090
(0.044 . 0 135)
0092
(O.OS1 . 0 134)
0.085
(0.041.0.129)
0.063
(0.023,0.103)
0023
(-0.022. 0 068)
0066
(0 039 , 0.094)
0.058
(0.026 . 0.090)
0.162
0.206
0.256
0.260
0.148
0044
0094
0.054 (W)
0.004 (S)
Slope Values in Units of ln(pg Pb / dL Blood) / ln(/tg Pb / ff Sampled) (Dust Samples Collected with Wipe Samples)
Loading
(Mg/ft2)
Wipe Samples
178
Date
Date, Floors
Date, Floors
Date, Floors,
Window Sills
Floors
Window Sills
Window Wells
Window Wells
0.190
(0.112.0.267)
0138
(O.OS4 . 0 222)
0.140
(O.OS7 , 0.223)
0.125
(0.040 , 0.210)
Slope Values in Units of ln(/tg Pb / dL Blood) / ln(/ig Pb / g Dust)
Concentration
(W5/B)
BRM Sampler
175
Date
Date, Floors
Date, Floors
Date, Floors,
Window Sills
Floors
Window Sills
Window Wells
Window Wells
0.070
(0.013 , 0.127)
0.043
(-0.014, 0 100)
0.054
(-0.003.0.111)
0.041
(-0 017, 0.098)
0.105
(0.038,0.172)
0.067
(-0.013,0.147)
0062
(0023.0.101)
0.040
(-0.007 . 0.087)
(Dust Samples Collected with BRM Sampler)
0076
(0.030.0.122)
0.060
(0.006, 0.114)
0.052
(0.013 . 0.091)
0.026
(-0.019.0071)
0.123
0168
0.168
0.181
0.112
0.045
0.045
0.013 (W)
0 013 (S)
0.047
0.102
0.083
0.108
0.032
0.055
0.036
0006 (W)
0.025 (S)
10
The reported values of the coefficient of determination (R2) are based on a least squares fit of the descriptive model without adjusting for the errors in predictor variables.
(w) Represents the addition variability explained by window wells when it is the last variable added to the model.
(s) Represents the additional variability explained by window sills when it is the last variable added to the model.
-------
from the coefficient of determination from the full model
(R2=0.206) and then multiplying by 100. The model with only
BRM floor lead concentration and an adjustment for seasonal
trends explained 4.7% of the variability in blood-lead
concentrations, adding window sill lead concentration to the
model explained an additional 5.5% of the variability, and
adding window well lead concentration with the other two
factors already in the model explained an additional 0.6% 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. 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. Therefore, one possible
explanation for the results seen in Table 4 is that dust
lead measurements from floors, window sills, and window
wells within a house are correlated. Table 5 demonstrates
estimated Pearson correlation coefficients among natural log
transformed lead levels from children's blood and floor,
window sill and window well dust. These tables demonstrate
that for each measurement method (BRM Loading, Wipe Loading,
BRM Concentration), lead levels from window sills and window
wells are statistically significantly correlated with each
other, and with children's blood-lead concentrations. In
addition, the correlations between window sills and wells
are consistently the highest concentrations shown in
Table 5.
22
-------
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
P
p-value
n
P
p-value
n
P
p-value
n
Floors
Window Sills
Window
Wells
Lead Loadings (BRM Sampler)
0.344
0.001
193
1
0.343
< 0.001
197
0.411
< 0.001
189
1
0.374
<0.001
189
0.271
0.001
179
0.558
<0.001
184
Lead Loadings (Wipe Samples)
0.310
<0.001
197
1
0.338
< 0.001
196
0.395
< 0.001
189
1
0.305
< 0.001
189
0.365
<0.001
182
0.627
<0.001
184
Lead Concentration (BRM Sampler)
0.125
0.084
192
1
0.236
< 0.001
199
0.325
0.047
189
1
0.211
0.004
188
0.225
0.003
177
0.552
<0.001
183
23
-------
APPENDIX A
STATISTICAL MODELS
-------
The Statistical Model
The statistical model fitted to the data in the main
report was descriptive in nature and appears as follows:
logiPbB,) = 4, + ^logfPbE,) «• i2(t,-0) + E, (1)
where PbBj is the blood-lead level in iig/dL for the ith
child, PbEi is the environmental-lead level for the ith home
in /xg/ft2 for loadings and itg/g for concentrations, t± is
the day of the year on which the PbBi measurement was taken,
and E± is the random error term associated with PbBi. Ei 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.
00' 0i» 02 and ffError are parameters that are estimated
when the model is fitted. /30 and /^ are the intercept and
slope of the assumed log-linear relationship between PbB and
PbE. Since the dates of environmental sampling range from
August 31, 1993 through November 20, 1993 there was not
enough of a range of sample dates to properly parameterize a
sine wave model for seasonal variations in blood-lead.
Therefore, a simple linear trend was fitted between August
31 and November 20, where j32 is the slope and 9 is the mean
date of sampling (October 13, 1993). ffError characterizes
the variability in blood-lead left unexplained by the model.
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 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.
A-l
-------
Tables El and E2 in Appendix E provide the parameter
estimates and associated standard errors for the intercept
and slope (j30 and j^) from the descriptive model as
estimated by both ordinary least squares and the errors in
variables statistical approach. The errors in variables
solution assumes that the measurement error in dust samples
is known, and fixed at the values presented in Appendix D.
The ordinary least squares solution assumes that there is no
measurement error in the dust lead variables (i.e.
ff Concentration = ' •
A comparison of the slope parameter for dust lead (/Sj)
between the least squares and errors in variables solution
demonstrates that for variables that have a strong
relationship with blood- lead (such as floor wipe lead
loading) , the bias in j8x attributable to measurement error
can be substantial. However, when the relationship between
the predictor variable and the response variable is weak
(such as floor- lead concentration) the bias in /3X
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
The descriptive model presented in the main body of the
report makes a simplifying assumption about the data from
the Rochester Lead in Dust Study. The model, as fitted,
does not account for the effects of potentially important
socioeconomic and behavioral factors. Investigators in the
Rochester Lead-in-Dust Study found that four covariates in
particular were "significantly associated with higher blood
lead levels in children: Black Race, parental reports that
A-2
-------
children put soil in their mouths, single parent household,
and higher ferritin level".2
No attempts have been made at this time to investigate
changes in the relationship between blood-lead concentration
and measures of lead in dust that would be caused by the
presence of these important covariates in the log-linear
regression models.
Department of Pediatrics, Biostatistics, and Environmental Medicine. The University of Rochester School of Medicine, (June,
1995), "The Relation of Lead Contaminated House Dust and Blood Lead Leveies Among Urban Children. Final Report, Volume II,
Results and Discussion", U.S. Department of Housing and Urban Development Grant No. MLDP T0001-93
A-3
-------
APPENDIX B
ALTERNATIVE REGRESSION PARAMETER ESTIMATION IN
THE PRESENCE OF MEASUREMENT ERROR
-------
Appendix B
Regression Parameter Estimation in the
Presence of Measurement Error
Let
Y = Xj8 + 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);
jS = a pxl vector of regression coefficients; and
c = 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, 0 is a vector of fixed
and unknown constants, and e is distributed as MVN(0,a2I)
where MVN(fi,E) represents a multivariate normal distribution
with mean vector \L and covariance matrix Z. Estimates of
regression parameters for this standard regression model are
obtained as follows:
ft = (X'X)'1 X'Y
o2 = (Y'Y - p i'X'X p ^ / (n-p) (2)
C a v( p ^ = a2 (X'X)'1
B-l
-------
In the presence of measurement error, it is assumed
that
Y = U0 + e (3)
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,EA) where EA is known and A is
stochastically independent of e. Under this measurement
error model, estimates of regression parameters are obtained
as follows:
p = (X'X - nZ^r1 X'Y
o2 = (Y'Y - 0 '(X'X - (n-p)EA) p ) / (n-p) (4)
C( » ) = 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£&) / n] and [U'U
/ n] converges in probability to zero as n-»co;
B-2
-------
(Ib) The difference between [(X'X - (n-p)E4) / (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-»co.
Using these facts, it follows that the differences between
the regression parameter estimates of Equation (4) and
(Y'Y -
C a ( 0
P
)
(U'U)'1
'U'U
= o2
U'Y
j ) /
(U'U)'1
(n-p)
(5)
converge in probability to zero as n-*x>.
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 j8 and a2, it is assumed that the
estimators of Equation (4) have the same distribution as
those of Equation (5).
In this application of obtaining regression parameter
estimates in the presence of measurement error, the
covariate represents a weighted average of several observed
dust-lead levels that are measured with error. Therefore,
the estimate of measurement error in an individual sample
obtained from Appendix D must be divided by the number of
individual samples that were used to construct the dust-lead
variable being used in the regression model. Thus each
diagonal entry of EA (^(ii>) becomes the estimate of
B-3
-------
measurement error from Appendix D divided by the number of
individual dust samples (of a given component type) that
were collected from the ith house.
B-4
-------
APPENDIX C
TOLERANCE BOUNDS AND CONFIDENCE
INTERVALS FOR PERCENTILES AND EXCEEDANCE
PROBABILITIES IN A REGRESSION SETTING
-------
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:
j? = (X'X)-1 X'Y (1)
o2 = (Y'Y - 0 'X'X i ) / (n-p)
A 95% upper tolerance bound on (l-q)% of the distribution of
Y for values of the independent variables given by x0 is
TO = x0' p + k a (2)
where
k - L1/2 to.ss.n.pEft'Ml-q) / L1/2], (3)
L = x0' (X'X)'1^,, is the leverage of the vector x0/ and tUiV[5]
is the orth percentile of the noncentral t distribution with
v degrees of freedom and noncentrality parameter 6.
Similarly, a 95% confidence interval for the (l-q)th
percentile of the distribution of Y for values of the
independent variables given by x0 is given by
(TL, T0) (4)
where
C-l
-------
TL = X0' J9 + kL a
TU = X0' ft + kw a (5)
A 95% confidence interval for qy = Prob(Y>y) is
where qL is the value of q for which TL=y and q0 is the
value of q for which T0=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 /?*,
crA, and L should be calculated as follows:
"ft = (X'X - nEJ'1 X'Y
o2 = (Y'Y - ft '(X'X - (n-p)EA) ft ) / (n-p)
L = XQ' (X'X - nEJ^Xn
C-2
-------
APPENDIX D
ESTIMATION OF MEASUREMENT ERROR
VARIANCE COMPONENTS
-------
APPENDIX D
Details on Measurement Error Estimation
The statistical models which adjust for measurement error
in predictor variables assume that the variability due to
sampling and chemical analysis of dust samples is fixed and
known. Several sources of data were considered for
providing information about the variability in dust sample
results due to measurement error including information from
the Rochester Lead-in-Dust Study, the R&M study, data from
the Lead Abatement Effectiveness Study in Milwaukee, and
data from the Comprehensive Abatement Performance Study
(CAPS). These data represent side-by-side field duplicate
vacuum dust samples from floors, and can be evaluated using
the following variance components model:
In(Dust^) = ln(fi) + Pi + E^
where Dust^ is the jth (first or second) lead-loading or
lead-concentration result from the ith side-by-side sample,
H is the geometric mean of Dustij among all side-by-side
pairs, P± is the random effect associated with the ith side-
by-side pair, and Eij is the random within-pair error term
associated with Dustij • pi ^s assumed to follow a normal
distribution with mean zero and variance ff2Between' an<* Eij is
assumed to follow a normal distribution with mean zero and
variance a2Error.
^Between characterizes the variability between pairs, and
cr2Error characterizes the variability attributed to
measurement error in each source of data. Table Dl provides
estimates of <72Error found from each source of data.
D-l
-------
Estimates of variability in Side-by-Side dust sample
results from the Rochester Lead-in-Dust Study were used in
the statistical models which account for measurement error
in predictor variables. These values were chosen to promote
internal consistency within the data being analyzed.
Table 01. Estimates of Variability In Side-by-Side Dust Sample Results
Attributable to Measurement Error.
Data Source
Rochester
Lead-in-Dust
Study
Milwaukee
Repair and
Maintenance
CAPS
Sampling
Method
BRM
Wipe
BRM
BRM
Wipe
Component
•type
Floors
Window
Sills
Window
Wells
Floors
Window Sills
Window Wells
Kitchen
Floor
Interior
Entryways
Floors
Measure
Loading
Concentration
Loading
Concentration
Loading
Concentration
Loading
Loading
Loading
Loading
Concentration
Loading
Concentration
Loading
"Error
(In Std Dev)
1.107
1.382
1.494
1.745
2.872
2.201
0.764
0.801
2.383
1.022
1.151
1.279
0.624
0.56
Number of
Fairs
22
22
15
14
14
14
22
16
15
42
12
35
D-2
-------
APPENDIX E
PARAMETER ESTIMATES FOR STATISTICAL MODELS
-------
Table E1. Results off Fitting Statistical Models to BRM Lead-Loading Data from the
Rochester Lead-in-Dust Study
Statistical
Approach
Least
Squares
Errors in
Variables
Component
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Parameter Estimates
for Dust
/»o(a)
setfo)
1.540
(0.072)
1.290
(0.111)
1.064
(0.143)
1.471
(0.076)
1.108
(0.123)
0.345
(0.179)
*,*
seOS,)
0.109
(0.020)
0.09S
(0.018)
0.077
(0.014)
0.133
(0.022)
0.126
(0.020)
0.149
(0.017)
Parameter
Estimate for
Time Effect
ti*
setf^
-0.004
(0.002) •
•0.004
(0.002)
-0.004
(0.002)
-0.004
(0.002)
-0.005
(0.002)
-0.005
(0.002)
Estimate of
Error
Variance
Dmjig/dL)]2
0.332
0.332
0.330
0.322
0.316
0.279
(a) Intercept values reported in units of ln(pg Pb/dL Blood).
w Slope values reported in units of ln(/ig Pb/dL Blood) / ln(pg Pb/fi? sampled).
(c) Time effect reported in units of -——^L,..-,-, •
* date -10/13/93
E-l
-------
Table E2. Results of Fitting Statistical Models to Wipe Lead-Loading Data from the
Rochester Lead-in-Dust Study
Statistical
Approach
Least
Squares
Errors in
Variables
Component
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Parameter Estimates
for Dust
V«
seOV
1.367
(0.113)
1.014
(0.165)
1.162
(0.159)
1.179
(0.127)
0.797
(0.181)
0.328
(0.218)
*,*
setf,)
0.172
(0.036)
0.157
(0.030)
0.080
(0.018)
0.237
(0.042)
0.198
(0.033)
0.179
(0.025)
Parameter
Estimate for
Time Effect
&
se(ft)
-0.004
(0.002)
-0.004
(0.002)
-0.004
(0.002)
-0.004
(0.002)
-0.004
(0.002)
-0.004
(0.002)
Estimate of
Error
Variance
Dnfog/dL)]2
0.339
0.336
0.349
0.325
0.324
0.306
W Intercept values reported in units of ln(pg Pb/dL Blood).
w Slope values reported in units of ln(/tg Pb/dL Blood) / ln(pg Pb/ft2 sampled).
(c) Time effect reported in units of
Intug/dL)
date -10/13/93
E-2
-------
Table E3. Results of Fitting Statistical Models to BRM Lead-Concentration Data
from the Rochester Lead-in-Dust Study
Statistical
Approach
Least
Squares
Errors in
Variables
Component
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
FlEtrsunctcr Estinmtcs
for Dust
jS8W
seOV
1.493
(0.178)
1.215
(0.167)
1.301
(0.177)
1.201
(0.233)
0.8S4
(0.202)
0.832
(0.232)
*»
setf,)
0.058
(0.027)
0.080
(0.020)
0.060
(0.019)
0.104
(0.036)
0.126
(0.025)
0.111
(0.025)
Parameter
Estimate for
Time Effect
#
setfj)
-0.004
(0.002)
-0.005
(0.002)
-0.004
(0.002)
-0.005
(0.002)
-0.006
(0.002)
-0.005
(0.002)
Estimate of
Error
Variance
WfffOLSf
0.376
0.352
0.370
0.369
0.337
0.353
(a) Intercept values reported in units of ln(pg Pb/dL Blood).
w Slope values reported in units of ln(pg Pb/dL Blood) / ln(/ig Pb/g Dust).
(c) Time effect reported in units of . . „. ..„ .
^ date - 10/13/93
E-3
-------
Table E4. Results of Fitting Floor, Window Sill, and Window Well Lead Loadings
(BRM Sampler) Simultaneously on Blood-Lead Concentrations for the
Rochester Lead-in-Dust Study.
Statistical
Approach
Least
Squares
Errors in
Variables
Component
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Parameter Estimates
for Dust
fc{"
sefcV
0.876
(0.148)
-0.226
(0.197)
*«
seOS,)
0.08S
(0.022)
0.023
(0.023)
0.058
(0.016)
0.125
(0.024)
-0.219
(0.043)
0.297
(0.037)
Parameter
Estimate for
Time Effect
*"
seQSj)
-0.005
(0.002)
-0.004
(0.002)
Estimate of
Error
Variance
pnfeg/dL)]2
0.300
0.233
(a) Intercept values reported in units of ln(/tg Pb/dL Blood).
w Slope values reported in units of ln(/ig Pb/dL Blood) / ln(^g Pb/ft2 sampled).
(c) Time effect reported in units of — .
date -10/13/93
E-4
-------
Table E5. Results of Fitting Floor, Window Sill, and Window Well Lead Loadings
(Wipe Samples) Simultaneously on Blood-Lead Concentrations for the
Rochester Lead-in-Dust Study.
Statistical
Approach
Least
Squares
Errors in
Variables
Component
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Parameter Estimates
for Dust
V
setfg)
0.790
(0.188)
(d)
*i«
setf,)
0.125
(0.043)
0.067
(0.041)
0.040
(0.024)
Parameter
Estimate for
lime Effect
&*>
se<&)
-0.004
(0.002)
Estimate of
Error
Variance
Onfcg/dL)]2
0.330
(a) Intercept values reported in units of ln(/xg Pb/dL Blood).
w Slope values reported in units of ln(/ig Pb/dL Blood) / ln(pg Pb/fi2 sampled).
(c) Time effect reported in units of «„,„»«.» •
date - 10/13/93
(d) The simultaneous fitting of dust-lead from floors, window sills and window wells was
conducted on a subset of the data which had non-missing values for all three variables.
The variability of the observed dust-lead loadings from window sills and window wells in
this restricted subset of the data was less than the estimate of variability attributed to
measurement error that was being used as input to the errors in variables regression
models. Attempts to compute the errors in variables solution under these circumstances
resulted in nonsensical parameter estimates with associated negative variances. Therefore,
it was inappropriate to provide these parameter estimates for the errors in variables
solution to the simultaneous fitting of wipe dust-lead loadings from floors, window sills
and window wells.
E-5
-------
Table E6 Results of Fitting Floor, Window Sill, and Window Well Lead
Concentrations (BRM Sampler) Simultaneously on Blood-Lead
Concentrations for the Rochester Lead-in-Dust Study.
Statistical
Approach
Least
Squares
Errors in
Variables
Component
Tested
Floors
Window
Sills
Window
Wells
Floors
Window
Sills
Window
Wells
Parameter Estimates
for Dust
ft*
setf,,)
0.870
(0.244)
0.617
(0.289)
V*
seQy
0.041
(0.030)
0.060
(0.028)
0.026
(0.023)
0.048
(0.043)
0.1S2
(0.080)
-0.032
(0.070)
Parameter
Estimate for
Time Effect
**
setfj)
-0.006
(0.002)
-0.008
(0.002)
Estimate of
Error
Variance
Dmjtg/dL)]2
0.36S
0.352
(a) Intercept values reported in units of ln(/ig Pb/dL Blood).
w Slope values reported in units of ln(pg Pb/dL Blood) / ln(/tg Pb/g Dust).
(c) Time effect reported in units of . . ^L^,.,. .
^ date -10/13/93
E-6
-------
APPENDIX F
PROTECTIVE DUST LEAD LEVELS AND EXCEEDANCE
PROBABILITIES FOR ERRORS IN VARIABLES SOLUTION
-------
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 A/g/dL (Based on the Errors in
Variables Regression Models of the Rochester Lead-in-Dust Study Data)
Sample
-type
Floor
Pb Loading
(Mg/ft2)
BRM Sampler
Window Sill
Pb Loading
Gig/ft2)
BRM Sampler
Window Well
Pb Loading
(/*g/ft2)
BRM Sampler
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 jtg/dL
4
1
Out of Range
Out of Range
89
23
2
Out of Range
10,156
3,779
817
41
15/tg/dL
88
32
5
Out of Range
2,209
770
133
2
144,436
61,592
15,940
982
20/tg/dL
553
223
52
1
15,477
5,938
1,307
45
805,938
362,045
104,728
8,045
Floor
Pb Loading
Gtg/ft2)
Wipe Samples
Window Sill
Pb Loading
0*g/ft2)
Wipe Samples
Window Well
Pb Loading
(/tg/ft2)
Wipe Samples
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
7
3
Out of Range
Out of Range
74
30
7
Out of Range
1,799
732
179
11
40
23
8
Out of Range
578
294
93
7
16,621
7,989
2,420
190
112
67
30
4
1,965
1.068
405
45
66,800
33,992
11,785
1,208
F-l
-------
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 Models of the Rochester Lead-in-Dust
Study Data)
Sample
Type
Floor
Pb Concentration
G
-------
Table F3. Estimated Proportion of Children with Blood Pb Concentrations Greater
than 10, 15, and 20^g/dL as Predicted by Errors in Variables Regression
Models of Blood Pb versus BRM Lead Loadings from Floors. Window Sills
and Wells
Surface
Tested
Floors
Window
Sills
Window
Wells
Pb
Loading
Mg/ft*
5
10
IS
20
25
30
35
40
100
200
250
50
100
200
300
400
500
600
700
200
500
750
800
1500
3000
5000
10000
20000
Proportion Greater Than
lOfig/di
Pr(Pb>10)
0.11
0.15
0.17
0.19
0.20
0.21
0.22
0.23
0.31
0.37
0.39
008
Oil
0.14
0.16
0.18
0.19
0.20
021
0.00
0.01
0.02
0.02
003
005
0.07
010
015
95% CI
(0.07,0.16)
(0 10 . 0.20)
(0.12,0.22)
(0.14,0.24)
(0.15 , 0.26)
(0.16,0.27)
(0.17,0.29)
(0.18,0.30)
(0.24 . 0.38)
(0.28 , 0.46)
(0.29 , 0 49)
(0.05 , 0 13)
(007.0.16)
(0.10.0.19)
(0.12,0.22)
(0.13 . 0.23)
(0.14,0.25)
(0 15 , 0.26)
(0.16,0.27)
(0 00 , 0.02)
(0 00 . 0 04)
(0.01 , 0.05)
(0.01 , 0.05)
(0.01 , 0 07)
(0.03 , 0.09)
(0.04.0.12)
(0.07,0.15)
(0.10,0.20)
Proportion Grcnter Th&n
15pg/dl
Pr(Pb>15)
0.02
0.04
0.04
0.05
0.06
006
0.07
0.07
0.11
0.14
016
0.01
002
0.03
0.04
0.05
005
006
0.06
0.00
0.00
000
000
000
0.00
0.01
0.02
0.03
95% CI
(0.01 , 0.05)
(0.02 . 0.06)
(0.02 . 0.07)
(0 03 , 0.08)
(0.03 , 0.09)
(0.04 , 0.10)
(004,0.10)
(0.04,0.11)
(007,0.16)
(0 09 , 0.21)
(0.10 , 0.23)
(0.00 , 0.03)
(0.01 , 0.04)
(0.02 , 0.06)
(0 02 , 0.07)
(0.03 , 0.08)
(0.03 , 0.09)
(0.03 , 0.09)
(0.04 , 0.10)
(0.00 , 0.00)
(0 00 , 0 00)
(0 00 , 0.00)
(0.00 , 0.01)
(0.00 , 0.01)
(0.00 , 0.02)
(0.00 , 0.02)
(0.01 , 0.04)
(0.02 . 0.06)
Proportion Greater Than
20pg/dl
Pr(Pb>20)
0.00
0.01
0.01
0.01
0.02
0.02
0.02
0.02
0.04
0.06
006
0.00
0.00
0.01
0.01
0.01
001
0.02
002
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
95% CI
(0.00 , 0.01)
(0.00 , 0.02)
(0.00 , 0.02)
(0.00 . 0 03)
(0.01 , 0.03)
(0.01 . 0.04)
(0.01 . 0.04)
(0.01 , 0.04)
(0.02 , 0.07)
(0.03 , 0.10)
(0.03,0.11)
(0.00.001)
(0.00 , 0.01)
(0 00 , 0.02)
(0.00 , 0.02)
(0.00 , 0.03)
(0.00 , 0.03)
(0.01 , 0.03)
(0.01 , 0.04)
(0.00, 0.00)
(0.00 , 0.00)
(0.00 , 0.00)
(0.00 . 0.00)
(0.00 . 0.00)
(0.00 , 0.00)
(0 00 , 0.00)
(0.00 , 0 01)
(0.00 . 0.02)
F-3
-------
Table F4. Estimated Proportion of Children with Blood Pb Concentrations Greater
than 10, 15, and 20 //g/dL as Predicted by Errors in Variables Regression
Models of Blood Pb versus Wipe Lead Loadings from Floors, Window Sills
and Wells
Surface
Tested
Floors
Window
Sills
Window
Ufollc
Pb
Loading
Mgffl2
5
10
IS
20
25
30
35
40
100
200
250
50
100
200
300
400
500
600
700
200
500
750
800
1500
3000
5000
10000
20000
10
Pr(Pb>10)
0.08
0.13
0.17
0.20
0.23
0.25
0.27
0.29
0.44
0.55
0.59
0.08
0.12
018
0.22
0.25
0.28
0.30
032
0.02
0.05
006
0.06
0.09
0.14
018
0.25
032
Greater Than
Kg/dl
959, Cl
(0.04,0.13)
(0.09 , 0.18)
(0.12.0.22)
(0.15 , 0.26)
(0.18 , 0.29)
(0.20 , 0.32)
(0.21 , 0.34)
(0.23 , 0.37)
(0.32 , 0.55)
(0.40 , 0.69)
(0.42 , 0.73)
(0.04,0.13)
(0.08,0.18)
(0.13 , 0.24)
(0.17.0.28)
(0.19 , 0.32)
(0.21 , 0.35)
(0.23 , 0.38)
(0.24 , 0.40)
(0 00 , 0.05)
(0.02 . 0.09)
(0.03 , 0.10)
(003 ,0 11)
(0.06.0.14)
(0.10.0.19)
(0.13,024)
(0.19,031)
(0.25 . 0 41)
Proportion Greater Than
15pg/dl
Pr(Pb>15)
0.01
0.03
0.04
0.06
0.07
0.08
0.09
0.1
0.19
0.28
0.31
0.01
0.03
0.05
0.07
0.08
0.09
0.11
0.12
0.00
0.00
0.01
001
0.02
0.03
0.05
007
Oil
95* CI
(0.00 . 0.03)
(0.01 . 0.06)
(0.02 , 0.07)
(0.03 , 0.09)
(0.04,0.11)
(0.05 , 0.12)
(0.06,0.14)
(0.06 , 0.15)
(0.12 , 0.28)
(0.16,0.42)
(0.18 . 0.47)
(0.00 . 0.03)
(0.01 , 0.05)
(0.03 . 0.08)
(0.04,0.10)
(0.05.0.12)
(0.06.0.14)
(0.07.0.16)
(0.07 , 0.17)
(0.00 , 0.01)
(0 00 . 0.02)
(0.00 , 0.02)
(0.00 , 0.02)
(0.01 , 0.04)
(0.02 . 0 06)
(0.03 . 0.08)
(0.05 . 0.12)
(0.07 , 0.17)
Proportion Greater Than
2008/41
Pr(Pb>20)
0.00
0.01
0.01
0.02
0.02
0.03
0.03
0.04
0.08
0.14
0.16
0.00
0.00
0.01
0.02
0.03
0.03
0.04
0.04
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.02
0.04
95% CI
(0.00 , 0.01)
(0.00 , 0.02)
(0.00 , 0.03)
(0.01 , 0.03)
(0.01 ,004)
(0.01 , 0.05)
(0.01 , 0.06)
(0.02 , 0.06)
(0.04.0.14)
(0.07 , 0.24)
(0.08 . 0 28)
(0.00 . 0.01)
(0.00 , 0.02)
(0.00 , 0.03)
(0.01 , 0.04)
(0.01 , 0.05)
(0.01 . 0.06)
(0.02 , 0.07)
(0 02 , 0.08)
(0.00 , 0.00)
(0.00 , 0.00)
(0.00 , 0.00)
(0.00 . 0 00)
(0 00 , 0.01)
(0.00 , 0.02)
(0.00 . 0.03)
(0.01 . 0 04)
(0.02 . 0.07)
F-4
-------
APPENDIX G
PROTECTIVE DUST LEAD LEVELS AND EXCEEDANCE
PROBABILITIES FOR LEAST SQUARES SOLUTION
-------
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 /ig/dL (Based on the Least
Squares Regression Models of the Rochester Lead-in-Dust Study Data)
Sample
Type
Floor
Pb Loading
(pg/ft2)
BRM Sampler
Window Sill
Pb Loading
dig/ft2)
BRM Sampler
Window Well
Pb Loading
(^g/ft2)
BRM Sampler
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/tg/dL
2
Out of Range
Out of Range
Out of Range
41
5
Out of Range
Out of Range
1,797
173
4
Out of Range
15 pg/dL
108
31
3
Out of Range
3.138
764
65
Out of Range
339,046
59,738
3,079
4
20 /ig/dL
956
319
54
2
38,277
10,884
1,456
12
> 1 Million
> 1 Million
131,989
442
Floor
Pb Loading
(/ig/ft2)
Wipe Samples
Window Sill
Pb Loading
(/tg/ft2)
Wipe Samples
Window Well
Pb Loading
(/tg/ft2)
Wipe Samples
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
0.85
0.90
0.95
0.99
4
1
Out of Range
Out of Range
49
14
2
Out of Range
230
16
Out of Range
Out of Range
41
22
5
Out of Range
687
291
64
2
42,597
8,025
359
Out of Range
189
95
31
1
3,079
1,441
426
23
714,210
167,331
15,874
37
G-l
-------
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//g/dL (Based on the
Least Squares Regression Models of the Rochester Lead-in-Dust Study
Data)
Sample
Type
Floor
Pb Concentration
(Mg/g)
BRM Sampler
Window Sill
Pb Concentration
0*g/g)
BRM Sampler
Window Well
Pb Concentration
(Mg/g)
BRM Sampler
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/ig/dL
Out of Range
Out of Range
Out of Range
Out of Range
118
6
Out of Range
Out of Range
45
Out of Range
Out of Range
Out of Range
15/tg/dL
5,33
584 '
Out of Range
Out of Range
28,655
5,438
196
Out of Range
127,010
13,934
83
Out of Range
20pg/dL
107,321
21,623
1,333
Out of Range
442,459
108,134
10,705
16
> 1 Million
647,078
31,183
1
G-2
-------
Table G3. Estimated Proportion of Children with Blood Pb Concentrations Greater
than 10. 15. and 20 /ig/dL as Predicted by Least Squares Regression
Models of Blood Pb versus BRM Lead Loadings from Floors, Window Sills
and Wells
Surface
Tested
Floors
Window
Sills
Window
Pb
Loading
pgltf
5
10
15
20
25
30
35
40
100
200
250
50
100
200
300
400
500
600
700
200
500
750
800
1500
3000
5000
10000
20000
Proportion Greater Than
lOpg/dl
Pr(Pb>10)
0.13
0.16
0.18
0.19
0.20
0.21
0.22
0.23
0.29
0.33
0.35
0.11
0.13
0.16
0.17
0.19
0.20
0.20
0.21
0.06
0.07
0.08
0.08
010
Oil
0.13
0.15
0.17
95% CI
(0.08 , 0.18)
(0.11 ,0.21)
(0.13 . 0.23)
(0.14 . 0.25)
(0.15,0.26)
(0.16 . 0.27)
(0.17 , 0.28)
(0.18,029)
(0.22 . 0.36)
(0.25 . 0.42)
(0.26 , 0.44)
(007,0.16)
(0.09 ,0.18)
(0.11 ,0.21)
(0.13.0.23)
(0 14 , 0.24)
(0 15 , 0.25)
(0.15 , 0.26)
(0.16 , 0.27)
(0.03.0.11)
(004.0.13)
(0.05 , 0 13)
(0.05,0.14)
(0.06 . 0 15)
(0.07 , 0.17)
(0.09 . 0.18)
(011.020)
(0.13 . 0.23)
Proportion Greater Than
Upg/dl
Pr(Pb>15)
0.03
0.04
0.05
0.05
0.06
0.06
0.07
007
0.1
0.13
0.14
0.02
0.03
0.04
0.05
0.05
0.06
006
006
0.01
0.01
0.01
0.01
0.02
0.03
0.03
004
0.05
95% CI
(0.01 , 0.06)
(0.02 , 0.07)
(0.03 . 0.08)
(0.03 . 0.09)
(0 04 . 0.09)
(0.04 , 0.10)
(0.04,0.11)
(0.04,011)
(0.06 , 0.15)
(0.08 , 0.19)
(0.08 , 0.20)
(0.01 . 0.05)
(0.01 , 0.06)
(0.02 , 0.07)
(0.03 , 0.08)
(0.03 . 0 08)
(0.03 , 0.09)
(0 04 , 0.09)
(0.04 , 0.10)
(0 00 , 0.03)
(0 00 , 0.03)
(0.00 . 0.04)
(0.00 , 0.04)
(0.01 , 0.04)
(0 01 , 0.05)
(0.01 . 0.06)
(0.02 , 0.07)
(0.03 , 0.08)
Proportion Greater Than
20fig/dl
Pr(Pb>20)
001
0.01
0.01
0.01
0.02
0.02
0.02
0.02
0.04
0.05
0.05
0.00
0.01
0.01
0.01
0.01
0.02
002
0.02
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.01
95% CI
(0.00 . 0 02)
(0.00 . 0.02)
(0.00 , 0.03)
(0 01 , 0.03)
(0.01 . 0.04)
(0.01 , 0.04)
(0.01 . 0.04)
(0.01 . 0.04)
(0.02 , 0.06)
(0.02 , 0.09)
(0.03 , 0.09)
(0.00 , 0.01)
(0.00 . 0 02)
(0.00 , 0.02)
(0.00 . 0.03)
(0.00 , 0.03)
(0.01 , 0.03)
(0.01 . 0.04)
(0.01 , 0.04)
(0.00 . 0.01)
(0 00 , 0.01)
(0.00 . 0 01)
(0.00 . 0.01)
(0.00 . 0.01)
(0.00 , 0.01)
(0 00 . 0 02)
(0.00 . 0.02)
(0.00 , 0.03)
G-3
-------
Table G4. Estimated Proportion of Children with Blood Pb Concentrations Greater
than 10, 15, and 20//g/dL as Predicted by Least Squares Regression
Models of Blood Pb versus Wipe Lead Loadings from Floors, Window Sills
and Wells
Surface
Tested
Floors
Window
Sills
Window
Wells
Pb
Loading
Jig/ft2
5
10
IS
20
25
30
35
40
100
200
250
50
100
200
300
400
500
600
700
200
500
750
800
1500
3000
5000
10000
20000
Proportion Greater Than
lOjig/d!
Pr(Pb>10)
0.11
0.15
0.18
0.20
0.22
0.24
0.26
0.27
0.36
044
0.47
0.10
0.14
0.19
0.22
024
026
0.28
0.29
0.09
0 12
0.13
0.13
015
017
0.19
0.22
0.25
95% CI
(0.06,0.17)
(0.11,0.21)
(0.13 , 0.24)
(0.16.0.26)
(0.17 , 0.28)
(0.19.030)
(0.20 , 0.32)
(0.21 . 0.34)
(0.27 , 0.47)
(0.32 , 0.58)
(0.33 , 0.61)
(0.06 , 0.16)
(0 10 , 0 19)
(0.14 , 0.24)
(0.17 , 0.28)
(0.18,031)
(0.20 . 0.33)
(0.21 . 0.35)
(0.22 . 0.37)
(005.0.15)
(0.07 , 0 17)
(0.08 . 0.18)
(0.09 ,0.19)
(0.10 , 0.21)
(0.13,023)
(0 14 , 0 25)
(0.16.0.28)
(0.19.0.32)
Proportion Greater Than
ISpg/dl
Pr(Pb>15)
0.02
0.04
0.05
0.06
0.07
0.08
0.09
0.09
0.15
0.20
0.22
0.02
0.03
0.05
007
0.08
0.09
0.10
0.10
002
0.03
0.03
0.03
0.04
005
0.06
007
008
95% CI
(0.01 , 0.05)
(0.02 , 0.07)
(0.03 , 0.08)
(0.04 . 0.10)
(0.04.0.11)
(0.05.0.12)
(0.05 , 0.13)
(0.06 , 0.14)
(0.09 , 0.22)
(0.12 , 0.31)
(0.13 , 0.34)
(0.01 , 0.04)
(0.02 , 0.06)
(0.03 , 0.08)
(0.04 . 0.10)
(0.05 , 0.12)
(0.05,0.13)
(0.06 , 0 14)
(0.06 , 0.16)
(0.01 . 0.04)
(0.01 . 0.05)
(0.01 , 0.06)
(0.01 , 0.06)
(0.02 . 0.07)
(0.03 , 0 08)
(0.03 . 0.09)
(0.04.0.11)
(0.05.0.13)
Proportion Greater Than
20/ig/dl
Pr(Pb>20)
0.00
0.01
0.01
0.02
0.02
0.03
0.03
0.03
0.06
0.09
0.10
0.00
0.01
0.01
0.02
0.03
0.03
0.03
0.04
0.00
0.00
0.01
0.01
0.01
0.01
0.02
0.02
0.03
95% CI
(0.00,001)
(0 00 , 0.02)
(0.00 . 0.03)
(0.01 . 0.04)
(0.01 . 0.04)
(0.01 , 0.05)
(0.01 , 0.05)
(0.01 . 0.06)
(003,0.11)
(0.04 , 0 16)
(0.05,0.19)
(0.00 , 0.01)
(0.00 , 0.02)
(0.00 . 0.03)
(0.01 , 0.04)
(0.01 , 0.05)
(0.01 , 0.05)
(0.02 . 0 06)
(0.02 . 0.07)
(0 00 , 0.01)
(0.00 . 0.02)
(0.00 , 0.02)
(0.00 . 0.02)
(0 00 . 0.02)
(0.00 , 0.03)
(0.01 . 0.03)
(0.01 , 0.04)
(0.01 , 0.05)
G-4
-------
APPENDIX H
PLOTS COMPARING THE ERRORS IN VARIABLES
MODEL RESULTS FOR BRM AND WIPE SAMPLING
-------
50 ^
40
30
TJ
§ 20
CD
10
10
100
1000
10000
Floor Lead Loading (yug/sq. ft.)
Predicted EIV — BRM Predicted EIV — Wipe
100000
1000000
Figure H1. Rochester Lead-in-Dust Study Floor Lead Loadings - Estimated Regression Curve for Errors in
Variables Model From BRM and Wipe Sampling
-------
to
50 •{
40
30
-Q
Q_
8 20
m
10-
10 100 1000 10000 100000
Window Sill Lead Loading (/zg/sq. ft.)
1oooooo
Predicted EIV — BRM Predicted EIV — Wtp«
Figure H2. Rochester Lead-in-Dust Study Window Sill-Lead Loadings - Estimated Regression Curve for Errors
in Variables Model From BRM and Wipe Sampling
-------
50 H
40
30
-O
EL
TJ
| 20
DO
10
10
100 1000 10000 100000
Window Well Lead Loading (yug/sq. ft.)
1000000
Predicted EIV — BRM Predicted EIV — WIp.
Figure H3. Rochester Lead-in-Dust Study Window Well-Lead Loadings - Estimated Regression Curve for Errors
in Variables Model From BRM and Wipe Sampling.
------- |