United States
Environmental Protection
Agency
Office of Pollution
Prevention and Toxics
7401
EPA 747-R-96-012
December 1997
&EPA CONVERSION EQUATIONS FOR
USE IN SECTION 403
RULEMAKING
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EPA747-R-96-012
December, 1997
CONVERSION EQUATIONS FOR USE IN
SECTION 403 RULEMAKING
Final Report
Technical Branch
National Program Chemicals Division
Office of Pollution Prevention and Toxics
Office of Prevention, Pesticides, and Toxic Substances
U.S. Environmental Protection Agency
Washington, D.C. 20460
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DISCLAIMER
The material in this document has been subject to Agency technical
and policy review, Mention of trade names, producti, or services doei not
convey, and should not be interpreted as conveying, official EPA approval,
endorsement, or recommendation.
This report is copied on recycled paper.
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CONTRIBUTING ORGANIZATIONS
This study was Rinded and managed by the U.S. Environmental Protection Agency. The
analysis was conducted by Battelle Memorial Institute under contract to the Environmental
Protection Agency. Each organization's responsibilities are listed below.
Battelle Memorial Inetltute (Battelle)
Battelle was responsible for identifying the relevant studies and obtaining the data, fitting
models to the data from the individual studies, developing an approach for combining data across
studies, and writing the report on the methodology and results.
U.S. Environmental Prottotlon Agency (EPA)
The Environmental Protection Agency was responsible for providing objectives for the
data analyses and the report, for contributing to the development of conclusions and
recommendations, for reviewing draft versions of the report, and for managing the peer review
and publication of the report. The EPA Work Assignment Managers were Janet Remmers and
Todd Holderman. The Deputy Work Assignment Managers were John Schwemberger and Brad
Sohultz. The Project Leader for this report was John Schwemberger. The EPA Project Officers
were Sineta Wooten and Karen Maher.
HI
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TABLE OF CONTENTS
EXECUTIVE SUMMARY vii
1. WHAT DOES THIS REPORT SAY? vii
2. WHY WERE THESE EQUATIONS DEVELOPED? ix
3. HOW LARGE IS THE UNCERTAINTY ASSOCIATED WITH THESE CONVERSION
EQUATIONS? ix
4. HOW WILL THESE CONVERSION EQUATIONS BE USED? x
1.0 INTRODUCTION 1
1.1 PEER REVIEW SUMMARY 2
1.2 DOCUMENT OVERVIEW 4
2.0 DATA 6
2.1 STUDIES INCLUDED 6
2.2 DESCRIPTIVE STATISTICS 10
2.3 RANGE ISSUES 10
2.4 OTHER ISSUES 13
3.0 STATISTICAL APPROACH 16
3.1 STATISTICAL METHODS USED IN DEVELOPMENT OF CONVERSION
EQUATIONS 20
3.1.1 Centering 20
3.1.2 Log Linear Regression 21
3.1.3 Measurement Error and Transportability Assessment 21
3.1.4 An Adjustment for a Lack of Transportability 27
3.1.5 Combining Parameters Across Data Sets 30
3.1.6 Uncentering 31
3.1.7 Accounting For Within-House Correlation 31
3.2 CONFIDENCE INTERVALS AND PREDICTION INTERVALS 33
4.0 RESULTS 38
4.1 PREDICTING WIPE LEAD LOADING FROM BLUE NOZZLE VACUUM LEAD
LOADING 38
4.2 PREDICTING BLUE NOZZLE VACUUM FROM WIPE LEAD LOADING 42
4.3 STATISTICAL ANALYSES FOR THE BRM VACUUM 45
5.0 DISCUSSION 50
5.1 ASSUMPTIONS COMMON IN PREVIOUS RESEARCH 50
5.2 IMPORTANT CHARACTERISTICS OF THE STATISTICAL DESIGN AND
ANALYSIS FROM THE INDIVIDUAL STUDIES 51
5.3 SUMMARY OF RESULTS 53
6.0 REFERENCES 55
iv
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TABLE OF CONTENTS
(Continued)
LIST OF APPENDICES
Page
APPENDIX A Correction Factor Development A-1
APPENDIX B Distribution of the Data used to Develop the Conversion Equations B-1
APPENDIX C Residual Analysis, Influential Observations, and Computation Details for
the BN Vacuum to Wipe Conversion Equations C-1
APPENDIX D Residual Analysis, Influential Observations and Computation Details
for the Wipe to BN Vacuum Conversion Equations D-1
APPENDIX E Residual Analysis, Influential Observations and Computation Details
for the BRM to Wipe Conversion Equations E-1
APPENDIX F Conversions from Wipe Lead Loading to BN Lead Concentration F-1
LIST OF TABLES
Table 1. Summary Table for the Studies from which Data were Used to Develop
Conversion Equations 7
Table 2. Descriptive Statistics for Vacuum Dust Lead Measures and Wipe Lead Loadings
by Study 11
Table 3. Observed Ranges, by Housing Component and Vacuum Type, for the Dust-Lead
Loading Data (//g/ft2) Used to Develop the Vacuum Loading to Wipe Loading
Conversion Equations and for the Dust-Lead Loading Data (//g/ft2) upon Which
the Conversion Equations Will Be Used 13
Table 4. Wipes Used in Various Studies 14
Table 5. Information Related to Non-detection for Lead Measures in Various Studies 15
Table 6. Distribution of Predictor Variable in Training and Application Data Sets for BN to
Wipe Conversions, For Application to HUD National Survey (log scale) 26
Table 7. Distribution of Predictor Variable in Training and Application Data Sets for BRM
to Wipe Conversions, For Application to Baltimore R&M Study (log scale) 27
Table 8. Statistical Significance of Within-House Correlation 32
Table 9. Estimates of Within-House Correlation 33
Table 10. Final Blue Nozzle to Wipe Conversion Equations 39
Table 11. Predicted Wipe Lead Loadings Based on Final Conversion Equations For Selected
Blue Nozzle Vacuum Lead Loadings 39
Table 12. Final Wipe to Blue Nozzle Conversion Equations 43
Table 13. Predicted Blue Nozzle Vacuum Lead Loadings Based on Final Conversion Equations
for Selected Wipe Lead Loadings 43
Table 14. Final BRM to Wipe Conversion Equations 45
Table 15. Predicted Wipe Lead Loadings Based on Final Conversion Equations For Selected
BRM Vacuum Lead Loadings 46
LIST OF FIGURES
Figure 1. Methods for Converting BN to Wipe Lead Loadings on Uncarpeted Floors and
Window Sills 17
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TABLE OF CONTENTS
(Continued)
Page
Figure 2. Methods for Converting Wipe to BN Lead Loadings on Uncarpeted Floors,
Window Sills, and Window Wells, and Methodology for Converting BN to
Wipe Lead Loadings on Window Wells 18
Figure 3. Methods for Converting BRM to Wipe Lead Loadings 19
Figure 4. Illustration of Transportability Adjustment and Its Necessity 23
Figure 5. BN to Wipe, Final Conversion Equations for Uncarpeted Floors. Predicted Values,
and 95% Confidence Bounds and Prediction Bounds; Houses Built Pre-1940,
1940-1959, and 1960-1979 41
Figure 6. BN to Wipe, Final Conversion Equations for Window Sills and Window Wells.
Predicted Values and 95% Confidence Intervals and Prediction Intervals 42
Figure 7. Wipe to BN. Final Conversion Equations for Uncarpeted Floors, Window Sills
and Window Wells. Predicted Values and 95% Confidence Bounds and Prediction
Bounds 44
Figure 8. BRM to Wipe, Final Conversion Equations for Carpeted Floors, Uncarpeted Floors,
Window Sills, Window Wells. Final Predicted Values and 95% Confidence Bounds
and Prediction Bounds 47
vi
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EXECUTIVE SUMMARY
1. WHAT DOES THIS REPORT SAY?
This report presents equations used to carry out various conversions between wipe lead
loading and vacuum lead loading, based on two different vacuum samplers, the Blue Nozzle
vacuum (BN) used in the HUD National Survey, and the modified HVS3 vacuum used in the
Baltimore Repair and Maintenance Study. The modified HVS3 vacuum will be referred to as the
BRM vacuum for the remainder of this report.
Two sets of equations are described using the BN vacuum sampler: 1) for converting a
BN lead loading to a wipe lead loading, 2) for converting a wipe lead loading to a BN lead
loading. Each set contains a separate equation for samples collected from uncarpeted floors,
window sills, and window wells. For the BN to wipe conversions on uncarpeted floors, a
separate equation is provided for each of three house age groups in the HUD National Survey
data.
The following equations were developed for converting a BN lead loading (ug/ft2) to a
wipe lead loading (ug/ft2):
Uncarpeted floors:
Homes Built Prior to 1940: Wipe = 5.66 BN°-809
Homes Built 1940-1959: Wipe = 4.78 BN0800
Homes Built 1960-1979: Wipe = 4.03 BN0707
Window sills: Wipe = 2.95 BNU8
Window wells: Wipe = 5.71 BN°864
Thus, a BN lead loading of 100 fig/ft2 on an uncarpeted floor, in homes built before 1940, would
be converted to a wipe lead loading of 235 ug/ft2, by applying the first of these equations. It has
an approximate 95% confidence interval of 160 to 344 ug/ft2. The 95% prediction interval is 31
to 1799 ug/ft2. The confidence interval contains, with 95% probability, the average wipe lead
loading associated with measured BN lead loadings of 100 ug/ft2. The prediction interval
VII
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contains, with 95% probability, 95 percent of individual future wipe measurements observed in
the immediate vicinity of a BN lead loading of 100 ug/ft2. Prediction intervals are wider because
they incorporate the inherent variability hi the dependent variable, whereas confidence intervals
do not.
The following equations were developed for converting a wipe lead loading (jug/ft2) to a
BN lead loading (ug/ft2):
Uncarpeted floors: BN = 0.185 Wipe0931
Window sills: BN = 0.955 Wipe0583
Window wells: BN = 4.91 Wipe0449
Applying the first of the above equations, for example, a wipe lead loading of 100 ug/ft2 on an
uncarpeted floor would be converted to a BN lead loading of 13.5 ug/ft2. It has an approximate
95% confidence interval of 9.47 to 19.0 ug/ft2. The 95% prediction interval is 1.912 to 94.3
ug/ft2.
For samples collected with the BRM vacuum sampler, from uncarpeted floors, carpeted
floors, window sills, and window wells, the following equations were developed for converting a
BRM lead loading (ug/ft2) to a wipe lead loading (ug/ft2):
Uncarpeted floors: Wipe = 8.34 BRM0371
Carpeted floors: Wipe = 3.01 BRM0227
Window sills: Wipe = 14.8 BRM0453
Window wells: Wipe = 13.9 BRM0630
For example, a BRM lead loading of 100 ug/ft2 on an uncarpeted floor would be converted to a
wipe lead loading of 46.0 fig/ft2 by applying the first equation. An approximate 95% confidence
interval for this prediction is 40.5 to 52.3 ug/ft2. The 95% prediction interval of the wipe
loadings associated with a BRM loading of 100 ug/ft2 is 5.9 to 262 fig/ft2.
viii
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2. WHY WERE THESE EQUATIONS DEVELOPED?
These conversion equations were developed for reasons related to the determination of
standards required by the Residential Lead-Based Paint Hazard Reduction Act of 1992 (Title X),
referred to as the Section 403 standards. It is likely that the Section 403 standards for dust lead
will be expressed as a measured lead loading collected by a dust wipe sample. In considering
different options for this standard, it is important to evaluate the number of homes that would be
affected by the different options. The HUD National Survey of pre-1980 housing (the only
national survey of dust lead levels) is the best source for making this assessment [1], [2], [3].
However, the BN vacuum was used in the National Survey to collect dust samples. Therefore, in
order to use this data appropriately, it was necessary to convert the raw BN lead loading data to
wipe lead loadings. Also, since the Baltimore Repair and Maintenance study dust samples were
collected using a BRM vacuum, a conversion to a wipe lead loading was necessary in order for
this data to be applicable to Section 403 analyses, such as sensitivity/specificity analyses and
prevalence statistics.
3. HOW LARGE IS THE UNCERTAINTY ASSOCIATED WITH THESE CONVERSION
EQUATIONS?
There is a considerable degree of uncertainty in the conversion equations based on BN
vacuum samples. For the BN vacuum to wipe conversion, there is relatively little data. For
example, on uncarpeted floors, one field study produced six pairs of side-by-side wipe and
vacuum measures, another produced seven pairs, and a third produced 24 pairs. A larger amount
of data was available to develop the conversion equations based on BRM vacuum samples. The
Rochester Lead-in-Dust study alone provided over 350 BRM and wipe pairs on each housing
component. Although this large amount of data allows fairly accurate characterization of the
relationship between the average wipe lead loading and an observed BRM lead loading, the
inherent variability in wipe measures makes it important to recognize the wide range of plausible
wipe lead loadings that could be associated with any observed BRM lead loading.
ix
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4. HOW WILL THESE CONVERSION EQUATIONS BE USED?
The BN to wipe conversion equations will be used to convert the BN dust-lead loadings
measured in the National Survey to equivalent lead loadings for wipe samples. The transformed
lead loadings will then be used to estimate the numbers and percentages of houses that would be
affected for various options for defining dust-lead standards.
Similarly, the BRM to wipe conversion equations will be used to transform the BRM
vacuum lead loadings in the Baltimore Repair and Maintenance study to equivalent wipe lead
loadings for use in estimating prevalence statistics and in completing a sensitivity/specificity
analysis which relates the incidence of elevated children's blood-lead levels to wipe lead
loadings.
The wipe to BN conversion equations will be used in two ways for the Section 403 risk
assessment. First, one window sill dust sample and one window well dust sample were collected
via the wipe method in the HUD National Survey. Because the vast majority of samples were
collected via the BN method, it was decided that these two samples should be converted to
appropriate BN loadings for consistency. Second, two models were used to predict blood-lead
levels: the IEUBK model and an empirical regression model. The empirical model uses as an
input dust-lead levels measured by the BN sampler. Therefore, no conversion of the HUD
National Survey data is necessary when using the empirical model to predict blood-lead levels
from pre-intervention environmental-lead levels, or from post-intervention environmental-lead
levels in homes where there is no expected intervention. However, in houses expected to
undergo an intervention because dust- or soil-lead levels exceed options for standards, the post-
intervention dust-lead loadings that are assigned in the analysis were estimated based on wipe
data. These post-intervention estimates will be converted to BN lead loadings to be used as input
to the empirical model.
The conversion equations presented in this report were developed for specific
applications. The conversion of Blue Nozzle vacuum lead loading to wipe lead loading was
developed for use with the HUD National Survey. The conversion of BRM vacuum lead loading
to wipe lead loading was developed for use with the Baltimore Repair and Maintenance Study.
The conversion of wipe lead loading to BN lead loading was developed primarily for converting
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estimated post-intervention wipe lead loadings to "equivalent" BN estimates. If the conversion
equations developed in this report are used for other applications, the underlying assumptions for
the statistical techniques used to derive the equations need to be confirmed for the new
application.
XI
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1.0 INTRODUCTION
The objective of this report is to present conversion equations for use in doing analyses
for the Section 403 Rule. Equations were developed for converting between wipe lead loadings
and vacuum lead loadings based on the Blue Nozzle (BN) vacuum sampler used in the HUD
National Survey [1], [2], [3], and the modified HVS3 (BRM) sampler used in the Baltimore
Repair and Maintenance study.
Specifically, three types of conversion equations were developed. The first type of
equation converts a dust-lead loading collected by the BN sampler to a dust-lead loading as
collected by a wipe. This type of equation was developed specifically for use with the HUD
National Survey. For uncarpeted floors, this type of equation was developed separately for
houses built before 1940, between 1940 and 1959, and between 1960 and 1979. A second type
of equation converts a dust-lead loading of a wipe sample to an equivalent dust-lead loading of a
vacuum sample collected via the BN sampler. These two types of conversion equations were
developed separately for samples collected from uncarpeted floors, window sills, and window
wells. A third type of equation was developed to convert from BRM vacuum lead loading to
wipe lead loading. Separate equations of this type were developed for samples collected on
uncarpeted floors, carpeted floors, window sills, and window wells. These were developed for
use with the Baltimore R&M study data.
The three sets of conversion equations were developed for three reasons. First, to
estimate the number of houses that would be affected by different options for standards requires
use of the HUD National Survey (the only national survey of dust lead levels). The HUD Survey
used the BN sampler, but the Section 403 standard for dust lead will likely be defined in terms of
a wipe lead loading. This will require converting lead loading measurements measured with the
BN sampler to an equivalent wipe lead loading for comparison with a standard. Second, two
models are used to predict blood-lead levels from environmental-lead levels in the risk analysis,
the IEUBK model and an empirical regression model. The empirical model uses lead loadings
measured with the BN samples as input because the HUD survey used the BN sampler.
However, estimating post-intervention blood-lead levels requires estimating post-intervention
environmental-lead levels. Most of the data available for estimating post-intervention dust-lead
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levels is measured with wipes, and therefore the average levels were estimated based on wipes.
For use in the empirical model, these wipe levels need to be converted to BN levels. This is the
primary reason for the second conversion.
Similarly, the Baltimore Repair and Maintenance data are used to perform a
sensitivity/specificity analysis and to calculate prevalence statistics. Since the BRM vacuum was
used to collect data in this study, a means of converting BRM lead loadings to wipe lead loadings
was required.
1.1 PEER REVIEW SUMMARY
This report was peer reviewed by three subject matter experts who were independent of
the project team that developed the report. The following is a summary of the peer review
comments that had an important impact on the report or are important for understanding major
issues.
A reviewer commented that the discussion of measurement error was insufficient. In
response, the measurement error issue was reexamined, and a type of measurement error
adjustment known in the statistical literature as a transportability adjustment was found to be
appropriate for some of the situations in the report. The report methodology was changed where
necessary and the discussion of measurement error was re-written in the text.
Another review comment indicated that there was insufficient reference to the work of
others in the area of conversion equations. In response, all the known references were examined
with respect to methodology and results. Two references included consideration of within-house
correlation. The issue of within-house correlation was examined, and for some of the situations
in the report, within-house correlation was found to be statistically significant. The methodology
in the report was modified to take within-house correlation into consideration in these cases. The
text dealing with the discussion of the work of other researchers was re-written.
Two reviewers commented on the lack of discussion of variability in one of the
adjustment factors introduced to make data from two studies comparable to data from other
studies. (The adjustment in question adjusts "bioavailable lead" measurements to "total lead"
measurements.) An examination of the appropriate data showed that there was a better way to
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make the adjustment which reduced the variability in the adjustment factor. There is still random
variability in the adjustment, and this is noted in the report.
A reviewer noted that the range of the data for the Blue Nozzle conversion equation did
not match the range of the data for the Blue Nozzle dust collection in the HUD National Survey.
hi general, the Blue Nozzle data collected in the HUD National Survey are lower than the Blue
Nozzle data from which the conversion equations were developed. This is a situation in which a
transportability adjustment may apply, and for the conversions from Blue Nozzle measurements
to wipe measurements for floors and window sills, a transportability adjustment was carried out.
Furthermore, it is worth noting that the values for options for dust standards under the EPA 403
rule will most likely be at the middle to high end of the data range. Hence low values from the
HUD National Survey will not be as applicable with respect to determining a dust standard.
A reviewer commented that the Blue Nozzle data in the report seemed to be inadequate to
serve as the basis for making national policy decisions. In response, a number of points should
be considered. This study utilized the only national survey of lead in residential housing, the
HUD National Survey, which used the Blue Nozzle vacuum to collect house dust. The wipe
method is the most commonly used method of dust collection, and is the method for which EPA
is likely to develop standards for the EPA 403 Rule. This report uses all available data to
develop a conversion from Blue Nozzle measurements to wipe measurements. Collection of new
data was not an option under the time constraints of the 403 analyses.
At the time of peer review, the report contained a conversion equation from a lead
loading as collected by a wipe sample to a lead concentration as collected by a Blue Nozzle
vacuum. After the peer review was completed, EPA decided to pursue alternative approaches in
the 403 analyses that have made use of the wipe loading to Blue Nozzle concentration conversion
equation unnecessary. All the material related to this conversion equation has been moved to an
appendix to document the developmental work that was done; however, it is unlikely the wipe
loading to Blue Nozzle concentration equation will be used in 403 analyses.
After completion of peer review, this report was substantially revised. The report was
included as an appendix to a report on the risk analysis for the 403 rule. This risk analysis was
peer reviewed by individuals different from those who peer reviewed this report initially. In this
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review, a reviewer commented on the lack of an adjustment for measurement error, and further
commented that the absence of an adjustment for measurement error limited the usefulness of the
conversion equations outside the context of the rulemaking process. An additional comment
was received recommending the collection of more data.
In response, the reviewer appears to be referring to an errors-in-variables adjustment. In
regression analysis, the independent variable is assumed to be known without error. An errors-
in-variables adjustment is generally done to adjust for the variability in the independent variable.
However, in this report, what is desired is a conversion from one observed value to another, so
that the independent variable is by definition known without error. Therefore, an errors-in-
variables approach, by itself, is not appropriate for this report. However, a type of measurement
error adjustment known as a transportability adjustment was appropriate for some cases in this
report and was carried out, as stated above. This adjustment involved an errors-in-variables
adjustment as an intermediate step. With respect to the collection of more data, this was not
possible under the time constraints of the 403 analyses.
EPA has established a public record for the peer review of this report under
Administrative Record 169. This Administrative Record is available in the TSCA Non-
Confidential Information Center, which is open from noon to 4 pm Monday through Friday,
except on legal holidays. The TSCA Non-Confidential Information Center is located in Room
NE-B607, Northeast Mall, 401 M Street SW, Washington, D.C.
1.2 DOCUMENT OVERVIEW
This chapter (Chapter 1) is the introduction to the report. It explains why the analyses in
the report were done. A summary of the peer review of the report and an overview of the layout
of the rest of the report are also included in Chapter 1. Chapter 2 discusses the data, which
studies were involved, descriptive statistics, range of the data and other technical issues.
Chapter 3 presents the statistical approach used hi developing the conversion equations. Detailed
explanations of measurement error, within house correlation, combining results across studies,
and confidence and prediction intervals are included. Chapter 4 presents the results (with figures
and tables) of the analyses for the Blue Nozzle Vacuum and for the BRM Vacuum. Chapter 5 is
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a discussion of the analyses and a summary of related efforts by other researchers. Chapter 6 is a
list of references. Appendix A explains the development of two correction factors employed in
the conversion equations analysis. Appendix B presents the distribution of the data used to
develop the BN and BRM vacuum conversion equations. Appendix C presents details of the
development of the BN to wipe conversion equations. This includes figures and tables which
justify the statistical analysis, and validation of the models used. Individual study regressions,
residual analyses, and influential observation analyses are provided. Appendices D and E present
details of developing the wipe to BN and BRM to wipe conversion equations, respectively,
including model building, residual analysis, and influential observations analysis. Appendix F
provides a wipe lead loading to BN lead concentration conversion based on the same approach
used for the loading to loading conversions discussed in the main body of the report.
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2.0 DATA
A wide range of samplers and sampling protocols have been used in environmental-lead
studies for the collection of dust samples. This section describes the data used for detennining
relationships between lead loadings as measured by the wipe and BN methods. A description of
the data used to determine the relationship between wipe and BRM vacuum lead loadings is also
presented.
2.1 STUDIES INCLUDED
Table 1 provides information on the studies used to develop the conversion equations
discussed in this report. Details regarding the design of each study and the intervention history of
the houses included hi each study are presented. Comments are also provided to identify
limitations or special considerations, such as correction factors, associated with each study.
Three studies report side-by-side paired data on wipe lead loading and Blue Nozzle
vacuum lead loading and were used to develop the conversion equations for the BN vacuum:
1. CAP Pilot study [4]
2. National Center for Lead-Safe Housing (NCLSH)/Westat study [5]
3. Baltimore Repair and Maintenance (R&M) Pilot study [6, 7]
In the CAP Pilot and NCLSH/Westat studies, wipe samples were analyzed using the hot nitric
acid/peroxide digestion method typically used in HUD-related work, while the R&M Pilot study
employed the cold hydrochloric acid digestion procedure used hi the State of Maryland.
Therefore, it is necessary to use an additional correction factor to convert the wipe lead
measurements hi the R&M Pilot study to equivalent HUD wipe measurements. An estimate of
the correction factor was obtained from a log-linear regression analysis of total available lead
loading (hot nitric acid/peroxide) versus bioavailable lead loading (cold hydrochloric acid) using
data reported in the NCLSH 5-Method Comparison study [9]. This study reported wipe
measurements that were analyzed by both chemical extraction procedures. The regression results
indicate that the bioavailable lead loading, denoted by B, should be multiplied by B°1416 to
6
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Table 1. Summary Table for the Studies from which Data were Used to Develop Conversion Equations.
Vacuum
Type
Study
Surface Type
(N)
,(•1
Relevant Issues
of Study Design
Intervention History
Comments
CAP Pilot
Study [4]
Uncarpeted Floors (6)
Window Sills (6)
On floors, two side-by-side
vacuum samples, each
four square feet in area,
were taken near two side-
by-side wipe samples,
each one square foot in
area. Geometric average of
wipe pairs was related to
geometric average of BN
pairs.
On window sills, one wipe
half-window sill sample
was taken adjacent to one
BN half-window sill
sample.
2 methods of abatement: 2 homes were
abated primarily by encapsulation/enclosure
methods, and 2 homes were abated
primarily by removal methods approximately
1 year prior to sampling.
2 homes had relatively few lead-based paint
components, which were unabated.
Reduced variability resulting from
averaging side-by-side samples was
taken into account.
Blue
Nozzle
NCLSH/
Westat [5]
Uncarpeted Floors (7)
Window Sills (42)
Window Wells (6)
Side-by-side wipe and BN
vacuum samples were
collected from uncarpeted
floors, window sills, and
window wells.
Forty homes owned by the Baltimore
Housing Authority were included in this
study. Of these, 30 were rehabilitated and
10 were not. No description of the
rehabilitation of the homes was provided.
Additional samples were collected from 5
homes owned by City Homes after the
samples from the forty homes initially in the
study were analyzed. The intervention
status of those 6 homes was not available
from the reference. No interventions were
performed as a part of the NCLSH/Westat
Study.
BN concentrations were not available to
characterize the relation between wipe
and BN concentrations.
R&M Pilot
Study [6], (7]
Uncarpeted Floors (24)
Window Sills (23)
Window Wells (24)
Side-by-side wipe and BN
vacuum samples were
collected from uncarpeted
floors, window sills, and
window wells.
Of the 6 homes in the study, 2 homes were
occupied and had received comprehensive
abatement in 1986-87, 2 homes were
vacant, unabated, older urban homes, and 2
homes were vacant modern urban homes.
No interventions were performed as a part
of the R&M Pilot Study.
In the R&M Pilot study, the bioavailable
(cold HCI acid) digestion method was
used to determine the lead content in
wipe samples.
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Table 1. Summary Table for the Studies from which Data were Used to Develop Conversion Equations (Continued).
Vacuum
Type
BRM
Study
R&M Mini
Study [8]
NCLSH 5
Method
Comparison
Study [9]
Rochester
Lead-in-Dust
Study! 10]
Milwaukee
Low Cost
Interventions
Study (11]
Surface Type (N)M
Uncarpeted Floors (25)
Window Sills (27)
Window Wells (25)
Uncarpeted Floors (68)
Carpeted Floors (67)
Uncarpeted Floors(389)
Carpeted Floors (398)
Window Sills (362)
Window Wells (403)
Uncarpeted Floors(135)
Relevant Issues
of Study Design
Side-by-side wipe and BRM
vacuum samples were
collected from uncarpeted
floors, window sills, and
window wells.
Side-by-side wipe and BRM
vacuum samples were
collected from uncarpeted
and carpeted floors.
Side-by-side wipe and BRM
vacuum samples were
collected from uncarpeted
floors, carpeted floors,
window sills, and window
wells.
Side-by-side wipe and BRM
vacuum samples were
collected from uncarpeted
floors.
Intervention History
Seven pre-1940, vacant homes in Baltimore
City were included in this study. These
homes were not known to have undergone
any lead paint abatement. However, one
home was known to be free of LBP. No
interventions were carried out as a part of
the R&M Mini Study.
No interventions were carried out as a part
of the NCLSH 5-Method Comparison Study.
The 205 homes in this study were known to
have not undergone extensive renovation or
remodeling within the year prior to the
eligibility interview. No interventions were
performed as a part of the Rochester Study.
No interventions were received by residents
in the included homes, and no homes had
undergone abatement prior to the study.
Comments
The bioavailable (cold HCI acid)
digestion method was used to
determine the lead content in wipe
samples.
Wipe lead loadings were multiplied by
1 .25 to correct for only including 80%
of wipe samples in the chemical
analyses.
None
Duplicate vacuum samples were
excluded in determining the
relationships.
00
(a) Number of pairs.
-------
represent total lead loading. Using a correction factor that depends on the amount of lead
measured was found to significantly reduce the observed variability about the correction,
although variability still remains in the correction factor. Thus, wipe lead loadings in the R&M
Pilot study were adjusted to be more reflective of HUD wipe measurements. Appendix A
provides details on the development of this correction factor and addresses its applicability to the
studies involved in this analysis. Appendix B contains tables of the distribution of the Blue
Nozzle data. These tables present the number of pairs of side-by-side wipe and vacuum samples
within various ranges for each component in each of the three studies included.
The CAP Pilot study collected two side-by-side wipe and BN vacuum samples in each
house. The geometric average of these replicate samples was used in the development of the
conversion equations. The reduced variability associated with averaging side-by-side samples
was taken into account in developing the conversion equations.
Four studies report side-by-side paired data on wipe lead loading and BRM vacuum lead
loading and were used to develop the BRM loading to wipe loading conversion equations:
1. R&M Mini study [8]
4. NCLSH 5-Method Comparison study [9]
3. Rochester Lead-in-Dust study [10]
4. Milwaukee Low Cost Interventions study [11]
Notice from Table 1 that the housing components sampled varied by study. The Rochester Lead-
in-Dust study was the only study for which side-by-side wipe and BRM samples were collected
on all four components: uncarpeted floors, carpeted floors, window sills and window wells. In
the Rochester Lead-in-Dust, NCLSH 5-Method Comparison, and Milwaukee Low Cost
Interventions studies, wipe samples were analyzed using the hot nitric acid/peroxide digestion
method which yields total lead loading. The R&M Mini study, however, reported bioavailable
lead loadings using the cold hydrochloric acid digestion procedure mentioned above. The
correction factor discussed above for the R&M Pilot study was also used to adjust these loadings.
In the NCLSH 5-Method Comparison study, only 80 percent of each sample collected by
wipe was extracted using the hot nitric acid/peroxide digestion method (total lead digestion).
The lead loadings for total lead digestion reported in the NCLSH 5-Method Comparison study
-------
were therefore multiplied by 100/80 = 1.25 to adjust for the chemical analysis of a reduced
sample. Appendix A describes the derivation of the two correction factors used. The appendix
also motivates the use of these adjustments.
In the Milwaukee Low Cost Interventions study, there were duplicate BRM samples
collected from a location adjacent to the side-by-side samples provided for this analysis. These
duplicates were not included in the development of these conversion equations.
2.2 DESCRIPTIVE STATISTICS
Table 2 presents descriptive statistics for the variables used in developing the various
conversion equations in this report. Data were available for the relationship between wipe and
BN on uncarpeted floors, window sills, and window wells. No data regarding this relationship
on carpeted floors were found. For exploring the relationship between wipe loadings and BRM
loadings, data were available from uncarpeted floors, carpeted floors, window sills, and window
wells.
2.3 RANGE ISSUES
This section deals with issues involving the ranges of the data used to develop the
conversion equations and the impact of these ranges on the applicability of the equations. The
BN to wipe conversion equations will be used to convert the BN dust-lead loadings measured in
the National Survey to equivalent lead loadings for wipe samples. The transformed lead loadings
will then be used to determine the numbers and percentages of houses that would be affected for
various options for a lead dust standard.
The BN loadings used to develop the BN lead loading to wipe lead loading conversion
equation range from 1 to 2164 ug/ft2 for uncarpeted floors. The BN lead loadings for private
housing in the HUD National Survey range from 0.014 to 380 \ig/ft2 for uncarpeted floors. Of
the 364 non-missing BN vacuum lead loadings from uncarpeted floors for private housing in the
HUD National Survey, 190 (52%) fall below the minimum BN vacuum lead loading used to
develop the BN loading to wipe loading conversion equation. Of the 284 homes surveyed, 150
had at least one uncarpeted floor dust-lead loading falling below the range of the conversion data.
10
-------
Table 2. Descriptive Statistics for Vacuum Dust Lead Measures and Wipe Lead Loadings by Study.
Vacuum
Type
Blue Nozzle
BRM
Study
CAP Pilot Study [4]
NCLSW
Westat (5]
R&M Pilot Study*
16], 17]
R&M Mini Study" (8]
NCLSH 5 Method
Comparison Study**
[9]
Rochester
Lead-in-Dust Study
[10]
Milwaukee Low Cost
Interventions Study
(111
Surface Type
Uncarpeted Floors
Window Sills
Uncarpeted Floors
Window Sills
Window Wells
Uncarpeted Floors
Window Sills
Window Wells
Uncarpeted Floors
Window Sills
Window Wells
Uncarpeted Floors
Carpeted Floors
Uncarpeted Floors
Carpeted Floors
Window Sills
Window Wells
Uncarpeted Floors
No. of Pairs
6«
6"
7
42
6
24
23
24
25
27
25
68
67
389
398
362
403
135
Vacuum Loading (fig/ft1)
Geometric
Mean
10.7
36.0
11.2
14.7
171
16.6
48.1
6,030
320
4,400
262,000
26.6
413
12.8
180
227
11,400
37.1
Log
Std. Dev.
1.66
1.72
0.526
0.832
0.863
2.27
2.62
2.73
2.62
4.08
3.80
2.43
1.17
2.07
1.73
2.42
3.39
2.19
Wipe Loading (fig/ft1)
Geometric
Mean
51.0
164
50.6
133
13,400
128
582
4,800
288
5,260
108.000
25.8
4.97
16.6
11.3
163
2,590
38.4
Log
Std. Dev.
1.93
1.87
0.362
1.28
2.03
2.06
3.77
2.98
1.99
3.46
2.80
1.52
0.79
1.25
1.13
1.53
2.61
1.18
(a) On floors, two side-by-side vacuum samples, each four square feet in area, were taken next to two side-by-side wipe samples, each one square foot in area, from
each house in the CAP Pilot Study. Each member of each wipe-vacuum pair is an average of two side-by-side samples. Statistics were calculated from these
averages.
(b) On window sills, one wipe half-window sill sample was taken adjacent to one BN half-window sill sample.
(c) Wipe loading statistics were calculated using total wipe loadings adjusted from bioavailable wipe loadings.
(d) Wipe loading statistics were calculated using reported total wipe loadings multiplied by 1.25 to adjust for the analysis of a reduced sample.
-------
For window sills, the BN lead loadings from the HUD National Survey range from 0.004
to 11,899 ug/ft2 with 136 (35%) of the 392 non-missing observations falling outside the range of
the conversion data. One BN lead loading is above the maximum of the data used to develop the
window sill conversion equation (8964 |ig/ft2) and 135 BN loadings are below the minimum (1.4
Hg/ft2). Of the 284 homes surveyed, 107 have at least one window sill dust-lead loading falling
below the range of the conversion data.
The range of the BN lead loadings used to develop the BN loading to wipe loading
conversion equation for window wells is 35.5 to 761,842 ug/ft2. Forty-seven (30%) of the 158
non-missing BN vacuum lead loadings from window wells in the HUD National Survey fall
below the minimum of 35.5 |ig/ft2. Forty of the 284 homes included in the survey have at least
one window well dust-lead loading falling below this minimum. Table 3 lists the ranges of the
data used to develop the BN loading to wipe loading conversion equations for each housing
component. Also presented are the ranges of the HUD National Survey BN loadings that will be
converted using these equations. The distribution of the BN lead loadings used to develop the
conversion equations ("training data") is substantially different from the distribution of BN lead
loadings observed hi the HUD survey ("application data"). Because of this, a "transportability
adjustment" was applied, which is explained in Chapter 3.
Table 3 also includes the range of the data used hi developing the BRM loading to wipe
loading conversion equation for each housing component. These equations will be used to
transform the BRM vacuum lead loadings in the Baltimore Repair and Maintenance study to
equivalent wipe lead loadings for use in determining prevalence statistics and in completing a
sensitivity/specificity analysis which relates the incidence of elevated (^ 10 lig/dL) children's
blood-lead levels to wipe lead loadings. The ranges of the Baltimore Repair and Maintenance
BRM loadings are provided in Table 3 as well. With one exception for the minimum of carpeted
floors, these loadings fall within the range of the data used to develop the equations for each
component.
12
-------
Table 3. Observed Ranges, by Housing Component and Vacuum Type, for the Dust-Lead
Loading Data (//g/ft2) Used to Develop the Vacuum Loading to Wipe Loading
Conversion Equations and for the Dust-Lead Loading Data (A/g/ft2) upon Which
the Conversion Equations Will Be Used.
Data
Classification
Data Used to
Develop the
Conversion
Equations
Data Upon
Which the
Conversion
Equations
Will Be Used
Vacuum
Type
BN
BRM
BN
BRM
Data
CAP Pilot, R&M
Pilot, and
NCLSH/Westat
R&M Mini,
Rochester,
NCLSH 5-
Method,
Milwaukee
HUD National
Survey
Baltimore
R&M(W
Housing Component
Uncarpated
Floors
Mln.
1.00
0.080
0.014
0.525
Max.
2,164
74,100
380
59,074
Carpeted
Floors
Min.
NA
1.42
0.003'"
1.08
Max.
NA
141,000
272"'
26,417
Window
Sills
Min.
1.40
0.250
0.004
0.788
Max.
8,964
4,169,649
11,899
285,414
Window
Wells
Min.
35.5
1.88
0.042
26.6
Max.
761,842
6,610,797
40,457
3,360,469
(a) There were no data to develop a conversion equation from BN to wipe for carpeted floors.
(b) Floor dust samples in the Baltimore R&M study were composited. The statistics for uncarpeted floors reflect the
distribution of composite samples that included any subsamples from uncarpeted floors. Statistics for carpeted floors
reflect the distribution of samples that included any subsamples from carpeted floors. These two sets of samples
overlapped because some floor composite samples included both carpeted and uncarpeted subsamples. Of the 317
floor composite samples, 191 (60%) were exclusively from uncarpeted floors, 49 (16%) were exclusively from
carpeted floors, and 77 (24%) were from both carpeted and uncarpeted floors.
2.4 OTHER ISSUES
Seasonal rhythms in blood lead levels have been observed in several studies. For
example in the EPA report, Seasonal Trends in Blood Lead Levels in Milwaukee [12], found
that lead levels in blood were approximately 40% higher in the summer (August) than in winter
during 1990-1995. In addition, seasonal rhythms in environmental lead levels were observed in
Boston during 1979 to 1983 as reported in the EPA report Seasonal Rhythms of Blood-Lead
Levels: Boston, 1979-1983 [13]. In that study, floor dust-lead loadings were on average 50
percent higher in July compared to December. Environmental samples in the HUD National
Survey were collected during the whiter months and may have been higher if they were collected
during the summer. Because seasonal variations hi dust lead are most likely a function of
geographic location, the seasonal variations estimated hi Boston and Milwaukee may not be
13
-------
applicable to the HUD National Survey. Therefore, an adjustment to the floor dust-lead loadings
in the HUD National Survey to account for seasonal variations was not investigated.
The types of wipes used in the various studies are identified in Table 4, with an indication
of whether there is known to be background lead in these wipes. The wipes used in the CAP and
the Milwaukee studies had trace amounts of lead. These trace amounts would be expected to
only slightly increase the variability, and slightly bias the relationships.
Table 4. Wipes Used in Various Studies.
Vacuum
Type
Blue Nozzle
BRM
Study
CAP Pilot
NCLSH/Westat
R&M Pilot
R&M Mini
NCLSH 5-Method Comparison
Rochester Lead-in-Dust
Milwaukee Low Cost
Interventions
Wipes Used
Chubbs
Little Ones Baby
WetOnes
WetOnes
Little Ones Baby
Little Ones Baby
Wash-a-bye Baby
Background Lead
6-18 //g lead per wipe
None known
None known
None known
None known
None known
1 -2 fjg lead per wipe
In Table 5, information is presented related to the non-detection of lead loadings in the
sets of data used to develop the conversion equations. This includes the instrument detection
limit (IDL) in each study, the number of samples below the IDL, and a description of how these
samples were handled in the analysis. For the BRM conversion equations, a very small
percentage of the data was below the IDL, so their influence is likely to be small. For the BN
conversions, the vast majority of the samples collected in the NCLSH/Westat study were below
the IDL, and these were excluded. For the CAP and R&M Pilot studies, either IDL or
IDL/\/2 was used when non-detected results were the case. None of these points were found to
be influential observations. (Appendices C and D present analyses to identify influential data
points.)
14
-------
Table 5. Information Related to Non-detection for Lead Measures in Various Studies.
Vacuum
Type
Blue Nozzle
BRM
Study
CAP Pilot
NCLSH/
Westat
R&M Pilot
R&M Mini
NCLSH 5-
Method
Comparison
Rochester
Lead-in-Dust
Milwaukee
Low Cost
Interventions
Instrument Detection
Llmft (IDL)
1 3.77 //g/sample for wipe
5 fjg for blue nozzle
25 //g for wipe
An approximate value of 7 //g for
IDL of wipe samples was
determined from the data set
-
(b)
FAA: wipe < 1 0 //g/sample
BRM < 10 //g/sample
GFAA: wipe < 0.25 //g/sample
BRM <0.1 5 //g/sample
IDLs varied from 1 .69 to 1 .89
//g/ft* for wipe and from 1 .08 to
48.6 /ig/ft' for BRM.
Number of Samples
Below IDL
1"'
For 292 of the 351 side-
by-side pairs, one or both
measurements were
below IDL
3 wipe measurements (2
sills and 1 well)
None
(b)
wipe: 1 uncarpeted floor
1 window sill
BRM: 3 uncarpeted
floors
3 window sills
1 window well
These were below the
IDL for GFAA analysis.
1 wipe sample
9 BRM samples
How were Below IDL
samples handled in
this report
IDL was used to
compute wipe lead
loading
Only paired samples
with both members of
the pair above the IDL
were used in analysis
Measurements were
replaced by IDL//2
Samples below the
limit of detection for
flame AA were
reanalyzed by graphite
furnace AA, and for
these, the GFAA
response was used in
this report.
Samples below the
limit of detection for
flame AA were
reanalyzed by graphite
furnace AA, and for
these, the GFAA
response was used in
this report. The
reported values for the
9 samples below the
GFAA IDL were
included in the
analysis with no
changes.
Wipe and BRM
loadings below and
above the IDL were
handled the same
way. The detection
limit was ignored in
reporting of
instrument responses.
(a) Both wipe samples in a vacuum-wipe pairing were below the appropriate IDL for the analysis of the wipe samples. The
vacuum samples in the pairing were both above the appropriate IDL for the analysis of the vacuum samples. The wipe
sample IDL was used to compute the lead loading for the wipe samples in the pairing. The final calculated loading
depended on the sample dilution.
(b) Could not be determined from the report.
15
-------
3.0 STATISTICAL APPROACH
A log-linear model was used to characterize the relationship between lead loadings for
two different samplers on all housing components. For instance, the model relating wipe lead
loading to Blue Nozzle lead loading may be written as
log(BN) = log(90) +6, log(W) + log(E),
or equivalently as,
BN=eoWfl'E,
where BN=Blue Nozzle lead loading and W=wipe lead loading. E represents a random error
term.
A similar model is recommended for converting a lead loading from either vacuum
sampler to a wipe lead loading:
log(W) = log(90) + 9,log(V) + log(E),
or equivalently as,
w=e0ve'E,
where V=Blue Nozzle or BRM vacuum lead loading and W=wipe lead loading, with E
representing a random error term.
Depending on the conversion, different methods were used to obtain point estimators of
the model parameters, namely, 80 and 0,. Figures 1,2, and 3 illustrate the procedures used to
derive the three types of conversion equations. Figure 1 describes the procedure used to derive
the conversion from BN to wipe lead loading, with one exception. Figure 2 describes the
procedure used to estimate conversions from wipe to BN lead loading. Figure 3 describes the
procedure used to derive the conversion from BRM to wipe lead loading. The exception to
Figure 1 is the conversion for window wells from BN to wipe lead loading, which follows the
procedure hi Figure 2.
In these diagrams, the circles represent the data sets, the triangles represent the statistical
methods performed on the data set, the boxes represent the outcomes of the analytical step or
steps. The statistical methods named within each triangle are described in the subsections of 3.1.
The relevant section number is indicated within each triangle. In Figure 1, BN and the 6
parameters represent the observed values and the observed regression parameters, respectively.
16
-------
W =
W = Oltt BN*"
1
r
Elv Correction
Step 2
3.1.4
^Combining Parameters
^Across Data
3.1.5
Uncentering
3.1.6
c
R&M Pilot
T
Centering
3.1.1
Elv Correction
Step 2
3.1.4
W = Aj BN*J
-fc.^-
W = /?„ BNA-1
1
,^ —
W = /?0.3BN>-'
Transportability
Adj., Step 4
3.1.4
W = 0. BN*'
Figure 1. Methods for Converting BN to Wipe Lead Loadings on Uncarpeted
Floors and Window Sills.
17
-------
Linear Regression
3.1.2
Linear Regression
3.1.2
Combining Parameters
,Across Data Sets,
3.1.4
Uncentering
3.1.5
BN = 0Q W*'
Correction Factor
Apx A
Centering
3.1.1
og Linear Regressio
3.1.2
BN = 0Q , W*1-1
fe.
BN=00f2W*k
i
r
-^
BN=003W*k
Figure 2. Methods for Converting Wipe to BN Lead Loadings on Uncarpeted Floors,
Window Sills, and Window Wells, and Methodology for Converting BN to Wipe
Lead Loadings on Window Wells.
18
-------
Log unear Regression
with correlation
3.1.7
W = 00, BRM*1'1
W = fl>0^BRM^2
J
r
W = 00^BRM*k
1
41
W = 004BRM^4
Figure 3. Methods for Converting BRM to Wipe Lead Loadings.
BN represents theoretically "true" BN values (without measurement error). The p parameters
are associated with the relationship without measurement error La the BN measurements. These
are discussed in more detail in Section 3.1.3.
The procedure illustrated in Figure 1 incorporates a "transportability" adjustment
documented below. This procedure was used for converting BN lead loadings to wipe lead
loadings on uncarpeted floors and window sills. Making the transportability adjustment in Step 4
required a measurement error adjustment hi Step 2. However, the conversion equation for
19
-------
window wells from BN to wipe lead loading was not done according to the Figure 1 approach
because there was only one data point available to estimate measurement error for window wells.
Hence a decision was made to use the methodology in Figure 2 for this type of conversion. The
Figure 2 approach does not include a transportability adjustment. It was felt that the use of the
Figure 2 methodology would be more reliable than the approach in Figure 1 for BN lead loadings
on window wells.
3.1 STATISTICAL METHODS USED IN DEVELOPMENT OF CONVERSION EQUATIONS
This section describes the several statistical methods used to develop the conversion
equations.
3.1.1 Centering
As the model is stated above, the intercept is the predicted log lead loading for an
associated sample with a lead loading of 1 [ig/ft2. A lead loading of 1 jig/ft2 (which has a
logarithm of 0) is near the lower bound of the range of lead loadings in each of the studies used
to develop these equations. Thus, an estimate of the intercept at a lead loading of 1 ug/ft2 would
have greater uncertainty than if the intercept was estimated near the "center" of the observed lead
loadings. In fact, the uncertainty of the intercept is minimized if it is estimated at the average, or
the "center," of the values taken on by the independent variable. Therefore, the log lead loading
of the independent variable in each study was centered by subtracting ^ the average log lead
loading obtained for the independent variable across the studies for which data was available for
that housing component and vacuum type. The model then becomes, for example,
log (W) = log (60) + 9, (log(BN) - uj + log (E).
This is done to make the estimates of slope and intercept (nearly) independent. For each study,
the regression model was then fitted to the centered data.
This approach was taken when developing conversion equations for both the BN and
BRM vacuum samplers for uncarpeted floors, carpeted floors (BRM only), window sills, and
window wells. Separate centering constants were determined for each sample type (i.e., carpeted
and uncarpeted floors, window sills or window wells), and predictor (i.e., BRM, BN, or wipe).
20
-------
3.1.2 Log Linear Regression
Simple log linear regression models were used to express the relationship between each
predictor variable and its converted value, e.g.,
log(BN) = log(90) +6, log(W) + log(E),
Exponentiating both sides of the model yields
BN = eX^E.
Within the log linear regression model, the parameters 90 and 6,, intercept and slope,
respectively, are the statistics of interest. This form of model has been used in many studies for
relating one lead measurement method to another (e.g., [4], [5], [9], [11]). Including a variable,
6j, to represent the exponent on the independent variable permits the ratio to depend on the level
of the predictor.
3.1.3 Measurement Error and Transportability Assessment
What is Measurement Error?
Measurement error is the difference between the observed value (the actual vacuum lead-
loading measurement) and the "true" lead loading at a location. "True" lead loading can only be
defined conceptually hi this application. It represents what would be the average of an infinite
number of replicated samples taken hi the immediate vicinity of the location sampled. True lead
loading in this context does not represent the actual amount of lead present at the location. It
represents the central tendency of the sampler under the present circumstances. Thus, true lead
loading for the BN sampling method may not be the same as the true lead loading for the wipe
sampling method.
This report uses the following notation to distinguish between observed and true values.
(Note that all values are log transformed, but notation indicating the log transformation is
omitted for ease of presentation.)
Xj 2 true value
Wj s observed value
Uj = Wj - Xj 3 measurement error.
21
-------
The relationship between X and Y is assumed linear and defined as:
Y, = PO + P.X. + E.
The E,'s represent the residuals from the true relationship and have variance
-------
10000.0
o> 1000.0
c
TJ
O
0
0
0
O
a
S
TJ
o
w
100.0
10.0
1.0
0.1
0.01
o Training
+ Application
o o
•H-
++
0.10 1.00 10.00 100.00
Observed Blue Nozzle Lead Loading
1000.00
True BN regression line
— Training regression line
Transportability-Adj. regression line
Rgure 4. Illustration of Transportability Adjustment and Its Necessity
23
-------
"Observed" wipe lead loading is plotted against "observed" BN vacuum lead loading1. Note that
when developing a conversion equation for a particular application data set, the pluses cannot be
plotted. Otherwise, there would be no reason to develop conversion equations. Thus, these are
hypothetical data.
On the plot, there are several lines. The long solid line represents the relationship
between "true" wipe and "true" BN lead loading (Yj = p0 + p,X; + Ej). The short dashed line in
the upper right represents the regression line based on observed wipe and BN measures in the
training data set (Yf = 00 + 6,Wj + T!J). If the distribution of BN vacuum lead loadings in the
application data set were the same as it was in the training data set, then the dashed line would be
used for prediction of wipe measures associated with BN lead loadings in the application data
set. The dashed line is better for prediction than the solid line representing the true relationship
because the dashed line implicitly takes into account the measurement error. Taking a careful
look at the circles, it can be seen that the dashed line passes through the center of the vertical
spread in the circles throughout the range of the BN measures, whereas the solid line passes
through the lower range of the circles on the left side and through the upper range of the circles
on the right side.
From the pluses and the circles, it is clear that the BN lead loadings in the application
data set are substantially lower than the BN lead loadings in the training data set. If the dashed
line developed from the training data set (which would have to be extended) were used to predict
wipe lead loadings in the application data set, the predictions would clearly be too high.
A compromise would be to adjust the regression line developed from the training data for
measurement error (a so-called "errors-in-variables" correction). This would result in a line close
to the long solid line representing the true relationship. This line would pass through the center
of the application data cloud. However, as in the training data set, this line would yield
predictions that are too low for BN loadings below the mean BN loading in the application data
set, and too high for BN loadings above the mean BN loading in the application data set.
'"Observed" is written in quotes to remind the reader that the values are not actually
observed, because these are only simulated data.
24
-------
The solution is to "put measurement error back into the prediction equation" for the
application data set. This is what is referred to as the transportability adjustment, and is
illustrated by the long-dash/short-dash line in the lower left portion of Figure 4. This line
represents the transportability-adjusted regression line, and reflects the best estimate of the
regression line that would be obtained by regressing the (unobserved) wipe measures on the BN
measures obtained hi the application data set. The adjustment recognizes the error known to be
present in the BN measures, and represents a substantial improvement over both the dashed line
and the solid line for predicting wipe lead loadings from BN lead loadings in the application data
set.
The remainder of this section discusses the differences between the training data and the
application data and assesses the need to adjust for transportability. The next section discusses
the calculations associated with the transportability adjustment.
Assessment of Transportability for Purposes of Section 403
An assessment of transportability is only possible for cases hi which the application data
set has been identified. Application data sets have been identified for only two of the these
conversion equations presented in this report. The HUD National Survey is the application data
set for the BN vacuum loading to wipe loading conversion equations, and the BRM vacuum
loading to wipe loading conversions will be applied to data from the Baltimore Repair and
Maintenance study. Because no application data set was identified for the wipe lead loading to
BN lead loading conversion, no transportability adjustment was considered for that conversion.
In the presence of an application data set, the first step is to determine if a transportability
adjustment is necessary. That means checking the assumption of equal means and variances
between the training data and the application data. In this case multiple training data sets were
used with different emphasis in the development of the conversion equations.
Table 6 presents the estimated means and variances of the training and application data
sets for the BN to wipe lead loading conversions. Results are presented separately by
component. Variability is expressed as the sum of within-house and between-house variance, so
it represents the variance of a measurement obtained from a randomly selected observation in a
25
-------
randomly selected house. Generally, there are multiple training data sets identified, and just one
application data set per component. However, there are three different age groups identified for
the application data for uncarpeted floors, because the distribution of dust-lead loadings on
uncarpeted floors was found to depend on house age. (Carpeted floor data were excluded from
the determination of the application data distribution.) There was no significant effect of house
age on window sills or wells.
Table 6. Distribution of Predictor Variable in Training and Application Data Sets for BN to
Wipe Conversions, For Application to HUD National Survey (log scale).
Component
Uncarpeted
Floors
Window
Sills
Window
Wells
Training Data (log scale)
Training Data
Set
CAP Pilot
NCLSH/Westat
R&M Pilot
CAP Pilot
NCLSH/Westat
R&M Pilot
NCLSH/Westat
R&M Pilot
Mean
//T
2.37
2.39
2.81
3.58
2.70
3.94
4.90
8.70
Variance of
Observed BN
c£ + al
2.85
0.482
5.83
3.07
0.791
6.55
1.01
7.28
Pre-1940
1940-1959
1960-1979
Application Data (log scale)
Mean
/*A
0.895
-0.019
-0.602
1.30
4.32
Variance of
Observed BN
°5 + °5
5.62
5.42
3.95
6.21
7.44
The means of the application data sets were all below the means of the associated training
data sets. There were also differences in variances between application and training data sets, but
not to the extent exhibited systematically for means. The fact that the distribution of BN dust-
lead loadings on uncarpeted floors was found to depend on house age indicates that there are
essentially three application data sets for uncarpeted floors: homes built before 1940, homes built
between 1940 and 1959, and homes built between 1960 and 1979. This would correspond, hi
Figure 4, to having three different sets of pluses - each representing a different house age. Each
age group requires its own transportability adjustment in the BN to wipe conversions. An
additional transportability adjustment was necessary for window sills. For window wells, there
were insufficient available data to assess measurement error, and therefore no transportability
adjustment was performed2.
2 Window wells were not used in the 403 risk analysis.
26
-------
Table 7 presents the estimated means and variances of the training and application data
sets for the BRM to wipe lead loading conversion equations in the same format. The means of
the application data sets fell within the range of the means of the training data sets, in all but one
case. In that case, the difference was slight. Variances in the application data sets were generally
similar to the variances in the associated training data sets. Therefore, no transportability
adjustment was used for the BRM to wipe conversions. However, there was much evidence of
positive within-house correlation, and an adjustment for within-house correlation was made and
is discussed in Section 3.1.7.
Table 7. Distribution of Predictor Variable in Training and Application Data Sets for BRM
to Wipe Conversions, For Application to Baltimore R&M Study (log scale).
Component
Uncarpeted
Floors
Carpeted
Floors
Window Sills
Window Wells
Training Data (log scale)
Data Set
Milwaukee
NCLSH
5-Method
R&M Mini
Rochester
NCLSH
5-Method
Rochester
R&M Mini
Rochester
R&M Mini
Rochester
Mean
//T
3.6
3.3
5.8
2.6
6.0
5.2
8.4
5.4
12.5
9.3
Variance of
Observed BRM
&T * Oj
5.92
7.03
7.99
5.40
1.36
3.00
16.6
5.85
14.5
11.5
Application Data (log scale)"'
Mean
PA
5.1
5.1
6.8
10.3
Variance of
Observed BRM
°4 + °W
4.91
4.99
8.54
10.2
(a) Dust samples in the Baltimore R&M study were composited. The statistics for uncarpeted floors reflect the distribution
of composite samples that included any subsamples from uncarpeted floors. Statistics for carpeted floors reflect the
distribution of samples that included any subsamples from carpeted floors. See Section 4.3 for a description of how the
conversion equations were applied to mixed composites.
3.1.4 An Adjustment for a Lack of Transportability
An adjustment to the estimated slope and intercept of the regression equation can be
made to correct for the lack of transportability (i.e., the difference in mean and variance of the
27
-------
lead loadings between the training data set and the application data set). This adjustment is
based upon the following theory (using terminology defined in Section 3.1.3) [16]:
If the Xj's are normally distributed, then the relationship for observed pairs of data (Wf,
Y,) is
Y; = 60 + 0, w, + ii, (1)
where
I); is normally distributed with mean 0 and variance oE2 +
and
°x
where o^2 represents the variance of the measurement error, Us.
Using this theory the transportability adjustment was accomplished by the following
series of steps involving a combination of statistical methods.
Step 1. The measurement error for the predictor method was estimated using data from
the CAP Pilot study and the Baltimore R&M study as described in Appendix C.
This provided an estimate of av. Due to the differences in sampling protocols,
measurement error is not the same for all studies. In particular in the CAP
study, BN samples each included dust from a four square foot area, and for
purposes of this analysis, a geometric average of two BN samples was paired
with a geometric average of two wipe samples. Therefore, each BN sample in
the CAP study represents an average lead loading over eight square feet. This is
compared with BN lead loadings averaged over one square foot for the other
two studies. Therefore, it is assumed that the measurement error variance for
the CAP BN lead loadings is one-eighth of that for the other two studies. That
28
-------
is, G^J /8 was used in place of cr^ to represent measurement error for the CAP
study.
Step 2. Using the estimate of measurement error obtained in Step 1 , the parameters of
the relationship between the response and the "true" predictor (i.e., P0 and P, as
defined in Section 3.1.3) were estimated using an errors-in- variables (EIV)
approach by the method of moments.
Step 3. The variability of the X's (i.e., the true lead loadings as defined in Section 3.1 .3)
in the application data set was estimated as
2 _ 2 2
°x^v ~ SXA " °u »
where s^2 is the estimated variance of the observed predictor in the application
data set, O02 is the estimated measurement error variance estimated in Step 1,
and Oj^2 is the estimated variance in true lead loadings in the application data
set.
Step 4. The transportability adjustment was made using the theory above, using the
mean, u^, variance, o^2, and A.A, calculated from the application data. That
is, given estimates of P0 and P,, the intercept and slope of the true regression
relationship, calculated in Step 2, the relevant theory yields:
where
the mean log lead loading in the application data set based on the
predictor method,
29
-------
y2 = the estimated measurement error associated with the observed
predictor, calculated in Step 1 , and
xA2 = me estimated variance of the true lead loadings in the application
data set calculated in Step 3.
The final conversion equation is then
Note that this methodology makes two key assumptions: 1) that the measurement error in
the predictor variable, oU} is the same in the training and application data sets; and 2) that the
relationship between true lead loadings for the predictor variable and the response, i.e.,
Y=P0 + P1X,
is the same in the training data set and the application data set.
3.1.5 Combining Parameters Across Data Sets
After fitting separate regression equations to data from the appropriate studies to predict a
lead loading obtained by one method from a lead loading obtained by another method (for a
given surface type), a weighted average was used to obtain a single conversion equation. As is
indicated in Figure 1, parameter estimates for the BN to wipe conversion equations are averaged
after the initial errors-in-variables adjustment for measurement error (Step 2 in Section 3.1.4) but
before the transportability adjustment (Step 4 in Section 3.1 .4). This is because, prior to
adjusting for measurement error, the observed relationship depends on the distribution of the
predictor variable, but the underlying relationship is assumed to be fixed. However, as Figures 2
and 3 indicate, a measurement error adjustment was not applied in developing the wipe to BN or
BRM to wipe conversion equations. For these, the parameter estimates were averaged without
adjustment.
In either case, a linear model on a log scale is assumed to describe the relationship
between wipe (W) and vacuum (V) measures within each study as well as across all studies. For
example,
log(W) = log(80 ) + 0, log(V) + log(E).
30
-------
Separate estimates of 00 and 0, (or PO and P, in the case of the BN to wipe conversions) were
obtained from each of the studies. A weighted average of the intercept estimates obtained from
each of the studies was used to determine a final estimate of the intercept. The weighting used
was the inverse of the variance of the intercept obtained in each study (that is, the squared inverse
of the standard error). An estimate of the slope was obtained similarly as the average of the slope
estimates obtained in the studies, each weighted by the inverse of its estimated variance.
It can be shown in general that if a single estimate is to be obtained based on two or more
independent, unbiased estimates of the same, fixed parameter using a weighted average of the
individual estimates, then weighting each individual estimate by the inverse of its variance
minimizes the variance of the final estimate.
3.1.6 Uncentering
Let 00* be the weighted average of the estimated intercept for the centered data, and 0,* be
the weighted average of the estimated slopes. The final uncentered intercept was computed as 00
= 00*- \IL 0,*, where \it represents the average of the lead loadings measured by the predictor
method across the studies included hi the analysis (this is the same |iL as described hi section
3.1.1). No uncentering is necessary for the slope, that is, 0, = 0,*.
3.1.7 Accounting For Within-House Correlation
One of the assumptions that is made when using linear regression is that all of the
observations are independent. If observations are correlated, then two main problems arise:
1) although parameter estimates may still be unbiased, standard regression techniques do not
generally yield the most efficient estimates, and 2) the estimated uncertainties (standard errors)
associated with parameter estimates are incorrect. Positive within-house correlation would lead
to underestimation of standard errors.
Some of the studies providing data for conversions developed in this report included
multiple observation pairs per house. A natural question arises regarding the potential
correlation between repeated observations at the same house. Generally, one would expect a lead
loading measured at a house to be more similar to another lead loading at the same house than to
a lead loading at another house in the same study.
31
-------
To investigate this, within-house correlations were estimated wherever possible for the
studies included in this analysis using a method called generalized estimating equations (GEE).
Tables 8 and 9 display the results of this within-house correlation analysis. Table 8 indicates the
degree to which data were available to estimate the correlation, and whether the correlation
estimate was statistically significant. Table 9 provides the correlation estimates that were
obtained from the data.
Notice that although there were numerous opportunities to estimate the correlation, it was
significant in only 5 cases. Also, whenever the correlation estimate was statistically significant,
it was positive. That is, there were no negative correlation estimates that were significant. This
supports the intuition described above regarding the correlation between lead loadings measured
at the same house.
Table 8. Statistical Significance of Within-House Correlation.
Conversion
BN Vacuum
Loading to Wipe
Loading
Wipe Loading to
BN Vacuum
Loading
BRM Vacuum
Loading to Wipe
Loading
Study
CAP Pilot
NCLSH/Westat
R&M Pilot
CAP Pilot
NCLSH/Westat
R&M Pilot
R&M Mini
NCLSH 5-
Method
Rochester
Milwaukee
Uncarpeted
Floors
Not
Estimable1
Insignificant
Insignificant
Not
Estimable
Insignificant
Insignificant
Insignificant
Insignificant
SIGNIFICANT
Not
Estimable
Carpeted
Floors
No Data
No Data
No Data
No Data
No Data
No Data
No Data
SIGNIFICANT
SIGNIFICANT
No Data
Window
Sills
Not
Estimable
SIGNIFICANT
Insignificant
Not
Estimable
Insignificant
Insignificant
Insignificant
No Data
SIGNIFICANT
No Data
Window Wells
Not
Estimable
(Minimal Data)
Insignificant
Not
Estimable
(Minimal Data)
Insignificant
Insignificant
No Data
Insignificant
No Data
1 Not Estimable - data collected in only one room per house,
correlation.
and therefore data did not permit estimation of within-house
32
-------
Table 9. Estimates of Within-House Correlation.
Conversion
BN Vacuum
Loading to Wipe
Loading
Wipe Loading to
BN Vacuum
Loading
BRM Vacuum
Loading to Wipe
Loading
Study
CAP Pilot
NCLSH/Westat
R&M Pilot
CAP Pilot
NCLSH/Westat
R&M Pilot
R&M Mini
NCLSH 5-
Method
Rochester
Milwaukee
Uncarpeted
Floors
Not
Estimable1
-0.22
-0.15
Not
Estimable
0.23
-0.15
-0.09
0.35
0.27
Not
Estimable
Carpeted
Floors
No Data
No Data
No Data
No Data
No Data
No Data
No Data
0.53
0.31
No Data
Window
Sills
Not
Estimable
0.49
-0.10
Not
Estimable
0.07
0.02
0.01
No Data
0.18
No Data
Window Wells
Not
Estimable
0.14
(Minimal Data)
0.32
Not
Estimable
0.16
(Minimal Data)
0.49
0.01
No Data
0.09
No Data
1 Not Estimable - data collected in only one room per house, and therefore data did not permit estimation of wrthin-house
correlation.
Also notice that four of nine studies study/sample type combinations used to develop the
BRM to wipe conversions reflected significant within-house correlation. Only one often
study/sample type combinations used to develop the wipe to BN or BN to wipe conversions had a
significant estimate of within-house correlation. Because of this, the linear models for the BRM
to wipe lead loading conversions were fitted using the GEE method to take into account
correlations within houses. This approach allows either negative or positive correlations.
3.2 CONFIDENCE INTERVALS AND PREDICTION INTERVALS
When one of the equations discussed in this report is used, the outcome is a prediction
(i.e., an estimate). A simple linear model was used to express each of the conversions in this
report, e.g., for converting a BN to a wipe lead loading,
log(W) = log(eo)+e,log(BN).
Confidence intervals and prediction intervals are used to assess how "precise" the estimate is.
33
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Confidence intervals are presented to indicate the probable range in which the mean of a
distribution lies with a specified confidence level. For example, a 95 percent confidence interval
is a range of values estimated by a method which will contain the mean 95 percent of the time
[19].
Prediction intervals indicate a range of values estimated to contain a pre-specified
proportion of the predicted population (e.g., 95%). Prediction intervals are necessarily wider
than confidence intervals (holding the confidence level fixed) because they incorporate
uncertainty in the estimated mean and random variability in the response. Throughout the
remainder of this report, the terms "mean" and "geometric mean" are used interchangeably
because the geometric mean is simply a mean associated with logarithmic values.
The following formulae were used to calculate an approximate 95% confidence interval
on the geometric mean of a predicted lead loading from one method based on the observed lead
loading, L, from another method:
Lower Confidence Bound = exp(log (00) + 6j(log(Z.) - L) -
Upper Confidence Bound = exp(log (60) + 6,(log(Z) - Z) +
where 60 represents the estimated intercept of the regression model, 6, represents the estimated
slope, L represents the mean log lead loading based on the predictor method, and s2 represents
the variance associated with the predicted mean value. This variance is dependent on the
observed lead loading, L, calculated as:
s2 = ^.(Oo)2 + (log(L) - L)2 * s.e.C
with s.e.(00) and s.e.(0,) being the standard errors of the parameter estimates from the combined
regression model.
The calculation of approximate 95% prediction intervals utilizes the same formula, with
one exception. Since the desired intervals are to encompass an estimate of a single future lead
loading, an extra component must be added to the variability associated with this prediction.
34
-------
Thus, for an approximate 95% prediction interval around a predicted lead loading from the above
model, the following equations are used:
Lower Prediction Bound = exp(log (60) + 0j(log(Z) - L) -
Upper Prediction Bound = exp(log (60) + 0,(log(Z,) - Z) +
In these equations, 00, 0i, and L are as before, and s.2 is the variance associated with the
prediction plus the total variance of an individual observation:
s.2 = s2 + a2,
with o2 being the best estimate of the variance associated with an individual observation.
hi this analysis, 60 and 0! were estimated using three different approaches (depending on
the conversion), and s2 was calculated by a different approach in each case. Different methods
were also used to estimate o. These methods are outlined separately, by type of conversion
below.
BN to Wipe Calculations
For the BN to wipe conversions for uncarpeted floors and window sills, simple linear
regression was used to estimate the slopes and intercepts from the individual studies, followed by
a transportability adjustment to "calibrate" the equations to be applicable to the HUD National
Survey data. Details of the matrix algebra leading to the final answers are laid out at the end of
Appendix C. (Equations for window wells were developed by the method described in the next
section, "Wipe to BN Calculations.")
The variability measure of interest, o, represents the standard deviation of errors OVs)
described in equation (1) of Section 3.1.3. These errors represent deviations in observed lead
loadings from the predicted lead loadings, incorporating measurement error. The formula for a2
is oE2 + P,2Aau2, where oE2 represents the variance associated with deviations from the model
without measurement error, P, represents the slope of the relationship without measurement
error, A represents the usual slope attenuation factor, and o^2 represents the variance of
measurement error.
35
-------
This is the general formula for residual variance in the presence of measurement error.
The o that we are interested in is the standard deviation of errors associated with the application
data set (HUD National Survey), but the relationships are observed on other (training) data sets.
Thus, just as for estimating the slopes and intercepts (explained in 3.1.3), parameters associated
with the true relationship (P0, P,, and OE) must be estimated, and then the parameters associated
with the application data set must be recalculated from the same equation, but at a different value
of A..
Since there were up to three studies available to estimate oE2, three estimates were
obtained, and a weighted average was taken, weighting by the degrees of freedom available to
estimate the error in each study. The final formula for o2 = oE2 + P,2A,Ou2 was then applied with
this estimate of oE2 to estimate o2.
Wipe to BN Calculations
For the wipe to BN conversions (and for the BN to wipe conversions for window wells),
simple linear regression was used to estimate the slopes and intercepts from the individual
studies. No transportability adjustment was applied. Standard error estimates for the slope and
intercept for each individual study follow from standard linear regression theory. As was
described above, the final conversion equation parameters were calculated as a weighted average
of the parameters from the individual studies. So the variances of the final coefficients were
calculated as the sum of squared standard errors scaled by their squared weights.
In these derivations, the mean squared error (MSE) from the individual regressions was
the only residual variance estimated. A weighted average of these MSE's was taken to estimate
o2, weighting each by the number of degrees of freedom available to estimate it
BRM to Wipe Calculations
For the BRM to wipe conversions, the GEE method was used to fit the simple linear
regression models, controlling for within-house correlation. No transportability adjustment was
applied. Standard error estimates for the slope and intercept for each individual study were
calculated, taking this correlation into account.
36
-------
Recall that with this method, correlation within houses was estimated. In particular, if
there was positive within-house correlation, this could be modeled as a within-house variance
(oE2), and a between-house variance (oH2). In this case, the sum of the estimates of these two
variance components was used to estimate o2 because this represents the variance of a randomly
selected data point at a randomly selected home. This is the measure of variability that should be
used to model the uncertainty hi a future predicted value. In cases of negative correlation, the
variance structure is more complicated than having two separate variance components, so the
total variance associated with an individual observation was used to estimate o2.
37
-------
4.0 RESULTS
This section presents conversion equations for determining lead loading based on one
method from a lead loading based on another method. The conversions include Blue Nozzle
(BN) to wipe lead loading, wipe to BN lead loading, and BRM to wipe lead loading. Separate
equations are presented for each component on which data were available for this analysis.
4.1 PREDICTING WIPE LEAD LOADING FROM BLUE NOZZLE VACUUM LEAD LOADING
As discussed earlier, the BN to wipe lead loading conversion equations were developed
based on data from the CAP Pilot, R&M Pilot, and NCLSH/Westat studies. Table 10 presents
the final BN to wipe conversion equations for uncarpeted floors, window sills and window wells.
Total sample sizes used to develop each conversion equation are also provided. Notice that, for
the BN to wipe conversions on uncarpeted floors, there are three different equations
corresponding to different house age groups for homes hi the HUD National Survey. The age
groups are: homes built before 1940, homes built between 1940 and 1959, and homes built
between 1960 and 1979. That is, the predicted wipe lead loading depends not only on the
observed BN lead loading, but also on the age of the home. Recall that a different methodology
was used to develop the conversion equations for BN lead loadings obtained from window wells
than was used to develop the equations for uncarpeted floors and window sills. (See Chapter 3.)
For nominal BN lead loading levels of 10,40,100,200,500, and 1000 ug/ft2, Table 11
presents the predicted wipe lead loadings, along with confidence intervals and prediction
intervals, for each housing component. Results for uncarpeted floors are also given separately
for the different age groups. For example, the BN loading of 200 jig/ft2 gets converted to a wipe
lead loading of 332 ng/ft2 for uncarpeted floors for houses built between 1940 and 1959.
The second line in each cell represents an approximate 95% confidence interval on the
conversion. These represent confidence bounds on the estimate of the geometric mean level,
associated with the nominal levels from which they are converted. For a house built between
1940 and 1959, with a BN vacuum lead loading of 10 ug/ft2 on uncarpeted floors, the geometric
mean wipe lead loading is 30.2 ^ig/ft2, and there is 95% confidence that the geometric mean wipe
lead loadings taken at the same location would be between 19.4 and 46.8 fig/ft2.
38
-------
Table 10. Final Blue Nozzle to Wipe Conversion Equations.
Component/House Age
Number of Observed Pairs
Conversion Equation
Uncarpeted Floors
Pre-1940
1940-1959
1960-1979
Window Sills
Window Wells
37""
37
37
71
30
Wipe = 5.66BN0809
Wipe = 4.78BN0800
Wipe = 4.03BN0707
Wipe = 2.95BN118
Wipe = 5.71 BN0884
(a) Units are tig/ft* for vacuum and wipe dust-lead loadings.
(b) The same data set was used to develop the conversion equation for all three age groups in the application data.
Table 11. Predicted Wipe Lead Loadings Based on Final Conversion Equations For
Selected Blue Nozzle Vacuum Lead Loadings.
Blue Nozzle
Vacuum Pb
Loading
(/ig/ff)
10
40
100
200
500
1000
Predicted Wipe Lead Loading (pg/ft*) by Dwelling Component
(95% Confidence Interval)
(95% Prediction Interval)
Uncarpeted Floors
Pre-1940
36.4
(24.0, 55.4)
(4.72, 281)
112
(78, 159)
(14.7, 853)
235
(160, 344)
(30.6, 1799)
411
(266, 635)
(53.0, 3185)
862
(505, 1472)
(109, 6840)
1510
(810, 2813)
(186, 12275)
1940-1959
30.2
(19.4,46.8)
(3.92, 232)
91.5
(64.1, 131)
(12.1,693)
190
(132,275)
(25.1, 1446)
332
(220, 501)
(43.3, 2540)
691
(418, 1142)
(88.4, 5397)
1203
(669, 2161)
(151,9606)
1960-1979
20.6
(12.6,33.5)
(2.81, 147)
54.7
(37.4, 80.2)
(7.81,384)
105
(73.5, 149)
(15.0,730)
171
(119,245)
(24.5, 1194)
327
(217,493)
(46.3, 2304)
533
(334, 852)
(74.6, 3810)
Window Sills
44.6
(32.7, 60.9)
(3.39, 589)
229
(180,292)
(17.5,3002)
676
(487, 938)
(51.2,8936)
1532
(1000, 2350)
(114,20500)
4520
(2580, 8060)
(327, 6240)
10200
(5100, 20600)
(721, 146000)
Window Wells
41.8
(5.18,338)
(0.358, 4890)
138
(25.6, 752)
(1.39, 13800)
306
(72.0, 1300)
(3.34, 28000)
556
(155, 2000)
(6.41,48500)
1230
(413, 3660)
(14.9, 102000)
2240
(834, 6010)
(27.7, 181000)
39
-------
The third line in each cell provides an approximate 95% prediction interval for the
conversions. These are bounds that are expected to contain 95% of the individual observations
associated with the specified nominal levels of the prediction variables. Thus, for a BN vacuum
lead loading of 10 |ig/ft2 on uncarpeted floors in a house built between 1940 and 1959, the
geometric mean point estimate of the wipe lead loading is 30.2 ng/ft2, and it is expected that 95%
of individual wipe lead loadings measured at the same location will be between 3.92 and 232 ng/ft2.
Appendix C provides the detailed analysis that led to these conversion equations.
Included in Appendix C are the results of individual regression analyses by study and component,
an assessment of influential data points, and a residual analysis. Because the BN to wipe
conversions included a transportability adjustment (for uncarpeted floors and window sills),
Appendix C also compares the observed relationship with the estimated true relationship,
adjusting for measurement error.
Figure 5 displays the predicted wipe loading from the final conversion equation,
associated with each BN vacuum lead loading observed in the HUD National Survey, for
uncarpeted floors, by age group. Also included on the plots are the approximate 95% confidence
and prediction intervals corresponding to each predicted wipe lead loading. The plot in the lower
right corner displays the prediction lines of the three age groups overlaid. (Refer to Section 3.1.3
for an explanation why the conversion equation for uncarpeted floors depends on house age.)
This plot illustrates the how differences in predicted values resulting from different age of home
depend on the lead loading measured in the HUD survey.
Figure 6 displays the predicted wipe loading from the final conversion equations, for
window sills and window wells, over the approximate range of BN vacuum lead loading
observed in the HUD National Survey. As above, the plots also include the approximate 95%
confidence and prediction intervals corresponding to each predicted wipe lead loading.
Note that there is greater uncertainty hi predicting wipe lead loadings from BN vacuum
lead loadings at the lower and upper ends of the data. The greatest precision (the narrowest
portion of the confidence bounds) for predicting a wipe lead loading from a BN lead loading
ranges from 20 to 100 ng/ft2 for uncarpeted floors and window sills, and ranges from 1000 to
10,000 ^g/ft2 for window wells.
40
-------
J.
Pre-1940
1940-1959
Predicted Wipe Loading
Lower Confidr "ice Bound
Upper Confidence Bound
— Lower Prediction Bound
~ Upper Prediction Bound
0.01 0.1 I 10 100 1,000 10.000 100.000
Floor BN Lead Loading (ng/ft3)
1960-1979
1 •
t
Predicted Wipe Loading
Lower Confidence Bound
Upper Confidence Bound
• — — Lower Prediction Bound
• — ~ Upper Prediction Bound
0.01 O.i
10O 1.000 10,000 IOO.OOO
Floor BN Lead Loading (jig/ft2)
o.oi o.i
1
O.OI 0.1
Predicted Wipe Loading
Lower Confidence Bound
Upper Confidence Bound
• - — Lower Prediction Bound
•— — Upper Prediction Bound
to too i.ooo 10,000 100.000
Floor BN Lead Loading (ng/ft1)
Combined
Pre-1940
1940-1959
1980-1979
100 i.ooo 10.000 100,000
Floor BN Lead Loading (fig/ft1)
Figure 5. BN to Wipe, Final Conversion Equations for Uncarpeted Floors. Predicted Values, and 95%
Confidence Bounds and Prediction Bounds; Houses Built Pre-1940, 1940-1959, and 1960-
1979.
-------
100.000
1O.OOO
I.OOO
too
• Predicted Wipe LaaCUnf
r Confidence P
__ Bound
Upper Confidence Bound
Lower Prediction Bound
Upper Prediction Bound
o.oi o.i t to too i.ooo 10.000 100.000
Sill BN Lead Loading Gig/ft*)
i
PredleUd Wipe Loading
Lower Confidence Bound
Upper Confidence Bound
Lower Prediction Bound
Upper Prediction Bound
0.01 0.1 t to too 1.000 10.000 100.000
Well BN Lead Loading Gig/ft?)
Figure 6. BN to Wipe, Final Conversion Equations for Window Sills and Window Wells.
Predicted Values and 95% Confidence Intervals and Prediction Intervals.
4.2 PREDICTING BLUE NOZZLE VACUUM FROM WIPE LEAD LOADING
Table 12 presents the corresponding results for predicting BN vacuum lead loading levels
associated with nominal wipe lead levels. Note that there is no distinction among house age
groups for the wipe to BN conversions. Table 13 presents predicted values along with
confidence intervals and prediction intervals by housing component for nominal wipe lead
loadings of 10,40,100,200,500, and 1000 ug/ft2.
42
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Table 12. Final Wipe to Blue Nozzle Conversion Equations.
Component
Uncarpeted Floors
Window Sills
Window Wells
Number of Observed Pairs
37
71
30
Conversion Equation
BN = 0.185 Wipe0931
BN = 0.955 Wipe0683
BN = 4.91 Wipe0449
Table 13. Predicted Blue Nozzle Vacuum Lead Loadings Based on Final Conversion
Equations For Selected Wipe Lead Loadings.
Wipe
Lead Loading
fc/g/ff)
10
40
100
200
500
1000
Predicted Blue Nozzle Lead Loading (pg/ft*) by Dwelling Component
(95% Confidence Interval)
(95% Prediction Interval)
Uncarpeted Floors
1.58
(0.916, 2.71)
(0.215, 11.5)
5.74
(3.90, 8.39)
(0.809, 40.4)
13.5
(9.47, 19.0)
(1.91,94.3)
25.7
(17.6,37.3)
3.62, 181)
60.3
(37.6, 96.0)
(8.34, 433)
115
(65.2, 201)
(15.5,845)
Window Sills
3.66
(2.60, 5.14)
(0.616, 21.7)
8.22
(6.47, 10.4)
(1.41,47.9)
14.0
(11.6, 16.9)
(2.42,81.2)
21.0
(17.6,25.0)
(3.63, 122)
35.9
(30.0, 43.3)
(6.18, 208)
53.8
(42,8, 67.3)
(9.22,313)
Window Wells
13.8
(4.75,40.1)
(0.250, 762)
25.7
(10.9, 60.9)
(0.489, 1350)
38.7
(18.6, 80.6)
(0.757, 1990)
52.9
(28.0, 100)
(1.05, 2670)
79.7
(47.3, 135)
(1.61, 3950)
109
(69.7, 170)
(2.22, 5340)
Figure 7 displays the predicted BN lead loadings, confidence intervals, and predicted intervals
over a range of wipe lead loadings — for uncarpeted floors, window sills, and window wells.
There was no application data set identified for this conversion, so the ranges over which the
predictions are plotted are the ranges of data used to develop the equations.
Appendix D provides the detailed analysis that led to the wipe to BN conversion
equations. Included in Appendix D are the results of individual regression analyses by study and
component, an assessment of influential data points, and a residual analysis.
43
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PndtaUd BN leadlni
bmrar Confldmo* Bound
Upptr Confldwoo Bound
lomr ProdloUon Bound
\lfptt ProdloUon Bound
• Predicted BN U.dlnj
— Lowor Confidence Bound
— Upper Coaftdanc* Bound
- Low.r PradlcUon Bound
' " Uppor ProaicUon Bound
id IN LOW lUoo iooj»o
Wipe Dun-Lewi Loading* GigrtP), Unettpeted Floor
10 100 1.000 10.000 100.000 I ml> 10 mil
Wipe Durt-Lead Loading* Gigffi"). Window SOI
I "
a
j' '•"
PndloUd BN Uxdlni
Low«r Conndonco Bound
Unpor Conndoneo Bound
Umr Pradlotlon Bound
UpptrProdloUoo Bound
10 100 1.000 10,000 100.000 1»U
W^pe Floor Dust-Lecd Lovlingi (ngW), Window WeU
Figure 7. Wipe to BN. Rnal Conversion Equations for Uncarpeted Floors, Window Sills and Window
Wells. Predicted Values and 95% Confidence Bounds and Prediction Bounds.
-------
4.3 STATISTICAL ANALYSES FOR THE BRM VACUUM
The estimated conversion equations for predicting a wipe lead loading from a BRM lead
loading were developed based on the R&M Mini, Rochester Lead-in-Dust, NCLSH 5-Method
Comparison, and Milwaukee Low Cost Interventions studies.
Table 14 summarizes, for each of the four housing components, the final conversion
equations and the total sample sizes used in developing these equations.
Table 14. Final BRM to Wipe Conversion Equations.
Dwelling
Uncarpeted Floors
Carpeted Floors
Window Sills
Window Wells
Number of
Observed Pairs
617
465
389
428
Conversion Equation1"
Wipe = 8.34 BRM0371
Wipe = 3.01 BRM0227
Wipe = 14.8 BRM0453
Wipe = 13.9 BRM0630
(a) Units are //g/ft* for vacuum and wipe dust-lead loadings.
Table 15 presents the predicted wipe lead loadings for nominal BRM lead loadings of 10,
40,100,200,500, and 1000 ug/ft2. For example, a BRM loading of 200 ug/ft2 on an uncarpeted
floor is converted to a wipe lead loading of 59.5 ng/ft2. Below the predicted values are
approximate 95% confidence and prediction intervals. The confidence bounds are expected to
contain the geometric mean wipe lead loading with 95 percent confidence; the prediction bounds
are expected to contain an individual wipe lead loading with 95 percent confidence. Thus, for a
BRM lead loading of 100 ug/ft2 from an uncarpeted floor, the estimated geometric average of
wipe lead loadings is 46.0 fig/ft2, and there is 95% confidence that the geometric average wipe
lead loadings taken at the same location would be between 40.5 and 52.3 ug/ft2.
45
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Table 15. Predicted Wipe Lead Loadings Based on Final Conversion Equations For
Selected BRM Vacuum Lead Loadings.
BRM Vacuum
Lead Loading
(//g/ft1)
10
40
100
200
500
1000
Predicted Wipe Lead Loading 0/g/ff) by Dwelling Component
(95% Confidence Interval)
(95% Prediction Interval)
Uncarpeted
Floors
19.6
(17.6,21.8)
(2.50, 1 54)
32.0
(29.4, 36.5)
(4.16,258)
46.0
(40.5, 52.3)
(5.84, 262)
59.5
(51.3, 69.0)
(7.54, 4.69)
83.6
(69.7, 100)
(10.6, 661)
108
(87.7, 133)
(13.6, 857)
Carpeted
Floors
5.07
(3.61, 7.13)
(0.674, 38.2)
6.95
(5.63, 8.57)
(0.939,51.4)
8.55
(7.41.9.86)
(1.16.62.9)
10.01
(8.86, 11.3)
(1.36,73.5)
12.32
(10.5, 14.4)
(1.67, 90.6)
14.4
(11.7, 17.8)
(1.95, 107)
Window
Sills
41.9
(33.7, 52.2)
(4.63, 379)
78.5
(66.3, 93.0)
(8.72, 708)
119
(103, 138)
(13.2, 1069)
162
(142, 187)
(18.1, 1460)
265
(214, 283)
(27.4, 2220)
337
(290, 392)
(37.5, 3040)
Window
Wells
59.2
(42.9,81.7)
(4.03, 869)
141.8
(108, 186)
(9.71,2070)
252
(198, 322)
(17.3, 3680)
391
(312,488)
(26.9, 5680)
695
(571,847)
(47.9, 10100)
1076
(899, 1289)
(74.3,15600)
Figure 8 displays the predicted wipe versus BRM lead loading, by housing component,
over the range of most BRM lead loadings observed in the Baltimore R&M study. Included on
the plots are the approximate 95% confidence and prediction intervals corresponding to each
predicted wipe lead loading. With the exception of the minimum dust-lead loading on carpeted
floors, the Baltimore R&M data fall within the range of the data used to develop the equations.
The BRM conversion equations are based on considerably more data than the BN to wipe
conversions, so the confidence interval widths are much narrower across the range of application
than are the widths of the analogous BN confidence intervals.
46
-------
• t*n»dicUd tto» Inciting
U»»or Prodlotten Bound
I 10 100 1.000 10.000 100.000 1 I
BRM Uncarpeted Floor Dust-Lead Loadings Gig/ft1)
Ln«r
Uppor
I 10 100 1.000 10.000 100.000
BRM Window Sill Dust-Lead Loadings (ug/tt*)
§.
* 1.000
I 10 100 1.000 10.000 100.000 I mil
BRM Carpeted Floor Dust-Lead Loadings (ug/fP)
r PndleUoa Bound
100 1.000 10,000 100.000 I mil 10 Ml
BRM Window Well Dust-Lead Loadings (ug/ft*)
Figure 8. BRM to Wipe, Final Conversion Equations for Carpeted Floors, Uncarpeted Floors, Window Sills,
Window Wells. Final Predicted Values and 95% Confidence Bounds and Prediction Bounds.
-------
It should be noted that some of the variability associated with the various equations is due
to the inherent variability hi wipe sampling. Estimates of the measurement error hi wipe samples
obtained from the Comprehensive Abatement Performance (CAP) pilot [4] and full studies [14,
15], and the Rochester Lead-in-Dust study [10] were used to characterize the uncertainty hi
individual wipe measures. Point estimates based on side-by-side variability predict that five
percent of the time a wipe measure will vary by a factor of at least 1.8 to 3.0 (depending on
which study is referenced) from the mean at that location (log standard deviation of estimates of
side-by-side wipe samples range form 0.30 to 0.55). Nonetheless, the range of prediction
intervals for BRM to wipe conversions are significantly larger than a factor of 9 (3 x 3)
suggesting that the wipe prediction intervals are due to more than just wipe measurement error
(e.g., BRM measurement error).
Compositing, In the sensitivity/specificity analysis each floor sample from the Baltimore
R&M study was converted using both the uncarpeted floor and carpeted floor conversion
equations, weighted by the proportion of the sample from the given substrate (carpeted or
uncarpeted). For example, a composite BRM vacuum lead loading of 100 ug/ft2 that consists of
8 subsamples (6 uncarpeted, 2 carpeted) would be converted hi the following manner:
1. Convert the composite BRM vacuum loading to a wipe loading using the uncarpeted
floor conversion equation:
Wipe = 8.34 * (100)0371 = 46.0 ug/ft2
2. Convert the composite BRM vacuum loading to a wipe loading using the carpeted
floor conversion equation:
Wipe = 3.01 * (100)0227 = 8.56 ug/ft2
3. Compute a weighted average of the uncarpeted floor prediction and the carpeted floor
prediction, with the weights corresponding to the proportion of total subsamples
represented by the given floor type:
Wipe . M46.0)*2»(8.56) _
O
48
-------
This approach was utilized because the conversion equations were not developed from composite
samples with varying proportions of carpeted and uncarpeted subsamples. This strategy attempts
to account for the differences in the carpeted and uncarpeted floor conversion equations. The
additional uncertainty associated with conversions of composite samples is not addressed in this
report.
49
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5.0 DISCUSSION
There have been several studies that included a characterization of the relationship
between wipe lead loading and vacuum lead loading. This section discusses 1) the assumptions
that were commonly made in those studies, and 2) important characteristics of the study design
and analysis relative to the wipe/vacuum relationship.
5.1 ASSUMPTIONS COMMON IN PREVIOUS RESEARCH
Certain assumptions have been made consistently by researchers when studying the
relationship between different lead sampling methods. (See [4], [5], [9], [11]). These include:
1. The wipe and vacuum data are each lognormally distributed and
2. The relationship between the log transformed measurements on the same surface type
is linear: log(Y) = A + B log(X) + error.
In some studies it has been further assumed that loadings measured by different methods on the
same surface will be proportional to each other. This assumption is driven by the intuitive
assumption that measured loadings are proportional to the amount of dust present. This
corresponds to assuming that the slope, B, equals 1 in the equation above in item (2). In the
development of the conversion equations in this report, there was no assumption made that the
slope would be equal to one. The slope parameter, B, was treated as random and allowed to take
on whatever value was necessary to fit the regression.
Some researchers have taken into account estimates of within-house correlation when
estimating the relationship between wipe and vacuum sampling methods. For each of the three
conversions developed for this report, within-house correlation was investigated. Only the data
for the BRM to wipe conversions exhibited significant within-house correlation. This correlation
was incorporated into the analysis for developing the BRM to wipe conversion equations.
50
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5.2 IMPORTANT CHARACTERISTICS OF THE STATISTICAL DESIGN AND ANALYSIS
FROM THE INDIVIDUAL STUDIES
Despite similar basic assumptions, different statistical design and analysis approaches
were described in the reports for the seven studies included in this analysis. Following is a
summary of the distinctions relevant to this report. First, the BN studies are discussed, then the
BRM studies are discussed.
BN/Wipe Conversion
The CAP Pilot study included one BN vacuum-wipe grouping from each house [4].
Thus, within-house correlation was not an issue. However, two issues should be pointed out
regarding the CAP data. First, by design, each BN vacuum sample in the CAP Pilot study
covered four square feet and was normalized to units of ng/ft2. Second, one of the objectives of
the CAP study was to estimate the true relationship between wipe loading and BN vacuum
loading. Therefore, replicate side-by-side samples were taken with each method (wipe and
vacuum). These replicates permitted estimation of replicate sampling error for both methods and
therefore permitted an errors-in-variables correction of the observed relationship between wipe
and vacuum lead loading. Both in that analysis, and hi this one, instead of discarding the
replicate samples of the same type, they were averaged (geometric means) before estimating their
relationship. Thus, for the CAP data, two wipes covering one square foot each were averaged
(on a log scale) and two vacuum samples covering four square feet each were averaged (on a log
scale) and used for the regressions in this report. Because of this up-front "averaging", and the
fact that the BN samples were collected over a larger area, the error variability of the (geometric
mean) wipe and vacuum loading measures can be expected to be smaller from the CAP study
than from the other studies. In Section 3.1.4, step 1, it is explained how the differences in the
CAP sampling protocol were taken into account in this analysis to ensure a "level playing field"
across studies.
The goal of the NCLSH/Westat Blue Nozzle Study [5] was to "describe the observed
statistical relationship between the two sampling methods and to predict, from the HUD National
Survey, the measurements which would have been obtained if the wipe sampling method had
51
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been used." In the original analysis (reported in [5]), the same variability was assumed for the
log transformed BN and log transformed wipe measures. Within-house correlation was
considered, but was eventually disregarded because there was insufficient data on floors and
window wells to estimate it. In addition, regression results based on house-aggregated data were
similar to results based on individual observations. Finally, because most of the observation
pairs from floors and wells had at least one measurement below the detection limit, and what was
available was not sufficient to reject the hypothesis that the slope was different from 1.0, the final
relationship was reported as a ratio. There was significant evidence that the log-linear
relationship on window sills had a slope greater than 1.0, and therefore the two-parameter log-
linear model was used in the report [5] to characterize the relationship on window sills.
Based on the R&M Pilot study data, Farfel, et. al., [6], [7], found no significant
interaction between the slope associated with BN (on a log scale) and surface type for predicting
BN loadings from wipe lead loadings. (Results were not published in the opposite direction.)
Therefore, in their analysis, a common slope term was assumed across floors, window sills, and
window wells. In fitting the model, a term was included in the model for within-house
correlation.
BRM/Wipe Conversions
In the R&M Mini study, Farfel, et. al., [8] again found no significant interaction between
the log(BRM) and surface type (floor, window sill, window well), and therefore estimated the
slope (B, in the above model) using data from all three surfaces. Separate intercepts were
estimated for each of the three surface types. A term was also included in the model for possible
correlation between repeated measures within houses.
A simple linear regression was performed to estimate the relationship between the wipe
and BRM lead loadings using data collected from the NCLSH 5-Method study [9]. An analysis
of variance showed that lead dust loadings were significantly different according to sampling
method, locations within houses, and locations within rooms.
A primary goal of the Rochester study [10,20] was to determine which method of lead
dust collection was most correlated with blood-lead concentrations. Therefore, although the
52
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Rochester study contributed the most data to this analysis, little has been documented regarding
the relationships between different dust lead collection methods. Emond et al. [21] characterized
the error in dust lead measurements made by five different measurement methods and described
the impact of measurement error when estimating the relationship between lead in dust and
children's blood lead levels.
The Milwaukee study included only one pair of wipe and BRM samples (from uncarpeted
kitchen floors) to characterize the log linear relationship between the two methods [12]. Thus,
no within-house correlation needed to be accounted for in the analysis. An errors-in-variables
approach was used to estimate the parameters in the model, using the estimate of the
measurement error associated with the BRM sampling method (obtained by side-by-side BRM
samples). Although side-by-side wipe samples were not collected in Milwaukee, wipe
measurement error was estimated from the Milwaukee data under the constraint that models
estimated in both directions would be "commutative." In this context, commutative refers to the
property that if a wipe value of x is converted to a vacuum value of y, then a vacuum value of y
would be converted to a wipe value of x. The Milwaukee study also examined this relationship
using simple log-linear OLS regression models, which did not take measurement error into
account.
5.3 SUMMARY OF RESULTS
The data included in this analysis indicate that, in general, the BN vacuum method yields
lower lead loadings than the wipe method which, in turn, yields lower lead loadings than the
BRM vacuum method. With some exceptions, this was supported by the data sets examined. An
additional study, published in the EPA report "Laboratory Evaluation of Dust and Dust Lead
Recoveries for Samplers and Vacuum Cleaners, Volume I: Objectives, Methods and Results"
[22], which was not part of this analysis (because it was a laboratory analysis which did not
include results for side-by-side wipe and vacuum samples) exhibited similar relationships
between these three sampling methods.
In addition, ratios of wipe to BN, and wipe to BRM depend on the magnitude of the lead
loading and component being sampled. That is, over the full range of loadings observed, the
53
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relationships cannot be described simply by a scale factor, which has been done in some cases in
the past. The only possible exception is the conversion of wipe to BN on uncarpeted floors,
where BN lead loadings are estimated at about one fifth of wipe lead loadings.
The results here represent an aggregation of data from several studies, and therefore are a
compromise in the relationships observed in each of the studies included. In general, the
aggregated relationships reflect trends from all data sets represented.
54
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6.0 REFERENCES
[1] U.S. Environmental Protection Agency (April, 1995) "Report on the National Survey of
Lead-Based Paint in Housing: Base Report." Office of Pollution Prevention and Toxics,
U.S. Environmental Protection Agency, EPA Report No. 747-R95-003.
[2] U.S. Environmental Protection Agency (April, 1995) "Report on the National Survey of
Lead-Based Paint in Housing: Appendix I: Design and Methodology." Office of
Pollution Prevention and Toxics, U.S. Environmental Protection Agency, EPA Report
No. 747-R95-004.
[3] U.S. Environmental Protection Agency (April, 1995) "Report on the National Survey of
Lead-Based Paint in Housing: Appendix II: Analysis." Office of Pollution Prevention
and Toxics, U.S. Environmental Protection Agency, EPA Report No. 747-R95-005.
[4] U.S. Environmental Protection Agency (February, 1995) "Comprehensive Abatement
Performance Pilot Study, Volume I: Results of Lead Data Analyses," EPA Report No.
747-R-93-007.
[5] NCLSH Westat Blue Nozzle Study. Prepared by Westat Inc. Revised January, 1995.
[6] U.S. Environmental Protection Agency (August, 1996) "Lead-Based Paint Abatement
and Repair and Maintenance Study in Baltimore: Pre-Intervention Findings." EPA
Report No. 747-R-95-012.
[7] Farfel, M.R., Las, P.S.J., Rhode, C.A., Lim, B.S., Bannon, D. and Chisolm J.J., Jr.,
"Comparison of a Wipe and a Vacuum Collection Method for the Determination of Lead
in Residential Dusts," Environmental Research, 65,290-301 (1994).
[8] Farfel, M.R., Las, P.S. J., Rhode, C. A., Lim, B.S., and Bannon, D., "Comparison of Wipe
and Cyclone Methods for the Determination of Lead in Residential Dusts," Applied
Occupational and Environmental Hygiene, 9:1006-1012 (1994).
[9] "Comparison of Five Sampling Methods for Settled Lead Dust: A Pilot Study." (June,
1993). Preliminary Draft Report prepared by The National Center for Lead-Safe
Housing, Columbia, Maryland.
[10] "The Relation of Lead-Contaminated House Dust and Blood Lead Levels Among Urban
Children." Volumes I and D (June, 1995). Final Report to the U.S. Department of
Housing and Urban Development, The University of Rochester School of Medicine,
Rochester, New York, and The National Center for Lead-Safe Housing, Columbia,
Maryland.
55
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[11] Schultz, B., Strauss, W., Murphy, A., Kanarek, M. (1997) "Comparison of Wipe and
Vacuum Sampling Methods for Assessing Dust Lead Levels in Homes: Data from the
Milwaukee Lead Intervention Study," draft journal article.
[12] U.S. Environmental Protection Agency (August, 1996) "Seasonal Trends in Blood Lead
Levels in Milwaukee," EPA Report No. 747-R-95-010.
[13] U.S. Environmental Protection Agency (September, 1995) "Seasonal Rhythms of Blood-
Lead Levels: Boston, 1979-1983," EPA Report No. 747-R-94-003.
[14] U.S. Environmental Protection Agency (April, 1996) "Comprehensive Abatement
Performance Study, Volume 1: Summary Report," EPA Report No. 230-R-94-013a.
[15] U.S. Environmental Protection Agency (April, 1996) "Comprehensive Abatement
Performance Study, Volume 2: Detailed Statistical Results," EPA Report No. 230-R-94-
013b.
[16] Carroll, R. J., Measurement Error in Nonlinear Models. (1995), Chapman & Hall.
[17] Draper, N.R., and Smith, H., Applied Regression Analysis, (1981), John Wiley & Sons.
[18] Fuller, W.A., Measurement Error Models. (1989), John Wiley & Sons.
[19] Neter, J., Wasserman, W., Kutner, M.H., Applied Linear Statistical Models. (1990),
Richard D. Irwin, Inc.
[20] Lanphear, B.P., Emond, M. Jacobs, D.E., Weitzman, M., Tanner, M., Winter, N.L.,
Yakir, B., and Eberly, S., "A Side-by-Side Comparison of Dust Collection Methods for
Sampling Lead-Contaminated Dust," Environmental Research, 68,114-123 (1995).
[21] Emond, M.J., Lanphear, B.P., Watts, A., Eberly, S., and Members of the Rochester Lead-
in-Dust Study Group, "Measurement Error and Its Impact on the Estimated Relationship
Between Dust Lead and Children's Blood Lead," Environmental Research, 72,82-92
(1997).
[22] U.S. Environmental Protection Agency (March, 1995) "Laboratory Evaluation of Dust
and Dust Lead Recoveries for Samplers and Vacuum Cleaners, Volume I: Objectives,
Methods, and Results," EPA Report No. 747-R-94-004A.
56
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APPENDIX A
Correction Factor Development
A-1
-------
APPENDIX A
Correction Factor Development
As described in Section 2.1, two separate correction factors were employed in the
conversion equations analysis. An adjustment was made to the wipe samples from the NCLSH
5-Method Comparison study to compensate for the chemical analysis of reduced samples, and a
separate correction factor was used to convert the bioavailable wipe lead loadings reported in the
R&M Pilot and R&M Mini studies to total available wipe lead loadings. The latter correction
was necessary for the wipe loadings to be consistent with those in the other studies which
reported total available lead loadings.
Adjustment for the Analysis of a Reduced Sample
Each wipe sample in the NCLSH 5-Method Comparison study was split and analyzed
using both the cold hydrochloric acid digestion procedure, which yields "bioavailable" lead
loadings, and the hot nitric acid/peroxide digestion method, which yields total lead loadings.
Only 80% of each sample was analyzed using the hot nitric acid/peroxide digestion procedure.
As a result, the reported total lead loadings are based on a reduced sample. Assuming the lead is
uniformly distributed throughout the wipe, multiplying the total loading by 1.25 will estimate the
total available lead loading based on 100% of the sample (100/80 = 1.25). Thus, the total wipe
lead loadings from the NCLSH 5-Method Comparison Study were multiplied by 1.25 for use in
the development of the BRM loading to wipe loading conversion equations.
Adjustment for Bioavailable to Total Available Lead Loadings
The NCLSH 5-Method Comparison study collected wipe samples from floors of varying
substrates, such as vinyl, wood, concrete, low-pile carpet, high-pile carpet, and "other." Using
the data from this study, a correction factor was developed to translate bioavailable lead loadings
to equivalent total available lead loadings in the R&M Pilot and R&M Mini studies. Since these
studies do not contain data from carpeted floor samples, the correction factor is calculated using
data from only the uncarpeted substrates (vinyl, wood, concrete, and "other"). Before the
A-2
-------
correction factor can be calculated, the total available loadings must be multiplied by the 1.25
adjustment described above to compensate for the analysis of a reduced sample.
Figure A-l displays the ratio of total lead to bioavailable lead versus bioavailable lead for
each of the uncarpeted substrates sampled. Included on the graphs are a fitted regression line and
a reference line at 1.58. This reference line represents the geometric mean of the ratio of total
lead to bioavailable lead. Originally, this geometric mean was used as a constant correction
factor for translating bioavailable loadings to total available loadings. The plots hi Figure A-l
illustrate that utilizing this constant correction factor overestimates the relationship between
bioavailable lead and total available lead at lower levels of bioavailable lead, and underestimates
the relationship at higher levels of bioavailable lead.
This underrepresentation of the relationship between bioavailable and total available lead
highlights the need for a more efficient correction factor. Thus, a regression analysis was
performed on the natural log-transformed total lead loadings (based on a full sample) versus the
natural log-transformed bioavailable lead loadings. The following model was fit:
log(T) = p,*log(B) + error
where T represents the total available lead and B represents the bioavailable lead determined
using wipes. It was found that the ratio of total available to bioavailable lead is significantly
dependent on the amount of lead hi the sample (p=0.0001), but not on the substrate from which
the sample was collected (p = 0.6996). The plots in Figure A-l illustrate that the fit of the
regression tine to the data is much better than that of the reference line, and is consistent across
the substrates. From the regression analysis, the correction factor is as follows:
•p _ gl.1416 _ g*g0.1416
The variability hi the ratio about the regression-based correction is approximately 13% smaller
than the variability about the constant 1.58 correction factor.
A-3
-------
The bioavailable lead to total available lead correction factor was developed from
uncarpeted floor samples, but was also applied to samples from window sills and window wells.
No data were available to derive separate correction factors for these housing components.
However, because the relationship was not found to depend on substrate, it was assumed that the
correction factor would not significantly depend on the housing component sampled. Thus, the
bioavailable lead loadings from the R&M Pilot and R&M Mini studies, denoted by B, were
multiplied by B°1416 for use in the development of the various BN and BRM conversion
equations.
A-4
-------
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Wood
+
*>*" '*'
I 10 100 1000 1 10 100 1000
Bioavailable Lead Loading (/ig/oq.ft) Bioavailable Lead Loading (pg/sq.ft)
12
JJ I0
ja
JS
1 *
1
•o
J
3 4
o
E=
^
r
0
Concrete
*
* jJf -h.
j^_ j. «^-**—"
T T + *
ve
i,.
JS
A
J5
1 8
^ 8
3 *
J^
o
&
0
Other
^.—
10 100
Bioavailable Lead Loading (/ug/sq.ft)
1000
10 100
Bioavailable Lead Loading 0*g/*q.ft)
1000
Figure A-1. Ratio of Total Lead to Bioavailable Lead versus Bioavailable Lead Loading (/tig/ft2)
from Uncarpeted Substrates in the NCLSH 5-Method Comparison Study
-------
APPENDIX B
Distribution of the Data used to Develop
the Conversion Equations
B-1
-------
APPENDIX B
Distribution of the Data used to Develop
the Conversion Equations
Blue Nozzle/Wipe Data
Table B-l presents the number of uncarpeted floor samples by groupings of wipe lead
loading and vacuum lead loading for the CAP Pilot study. Similarly, Table B-2 provides
combined information for uncarpeted floors and window sills. In Tables B-3 through B-6,
results are presented in a similar manner for the R&M Pilot and NCLSH/ Westat studies. As
seen in the tables, the bulk of the data for uncarpeted floors are available for vacuum lead
loadings less than 50 ug/ft2 and wipe lead loadings less than 200 fig/ft2. Data are present at the
higher ends of the ranges for window sills and window wells.
Table B-1. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading, CAP
Pilot Study — Uncarpeted Floors.
Wipe Lead Loading
(//g/ft»)
0-50
1 50-200
200 +
Total
Blue Nozzle Vacuum Lead Loading (/ig/ft1)
0-50
5
0
0
5
50-100
0
0
0
0
100-150
0
0
1
1
200 +
0
0
0
0
Total
5
0
1
6
Table B-2. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading, CAP
Pilot Study — Uncarpeted Floors and Window Sills.
Wipe Lead Loading
U/g/ft1)
0-50
1 50-200
200 +
Total
Blue Nozzle Vacuum Lead Loading (//g/ft1)
0-50
7
1
1
9
50-100
0
1
0
1
100-150
0
0
1
1
200 +
0
0
1
1
Total
7
2
3
12
B-2
-------
Table B-3. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading, R&M
Pilot Study — Uncarpeted Floors.
Wipe Lead
Loading
fo/g/ft*)
0-25
25-50
50-75
75-100
100-150
1 50-200
200 - 400
400 +
Total
Blue Nozzle Vacuum Lead Loading (/ig/ft2)
0-25
9
0
4
0
2
1
0
0
16
25-50
0
0
0
0
0
0
1
0
1
50-75
0
0
0
0
0
0
1
0
1
75-100
0
0
0
0
0
0
0
1
1
100-150
0
0
0
0
0
1
0
0
1
150-200
0
0
0
0
0
0
0
0
0
200-400
0
0
0
0
0
0
0
0
0
400 +
0
0
0
0
0
1
0
3
4
Total
9
0
4
0
2
3
2
4
24
Table B-4. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading, R&M
Pilot Study - Uncarpeted Floors, Window Sills, and Window Wells.
Wipe Lead
Loading
U/g/ft*)
0-25
25-50
50-75
75-100
100-150
150-200
200 - 400
400 +
Total
Blue Nozzle Vacuum Lead Loading (pg/ft*)
0-25
17
0
5
0
2
2
1
0
27
25-50
0
0
0
0
0
0
1
1
2
50-75
0
0
0
0
0
0
1
0
1
75-100
0
0
1
0
0
0
0
2
3
100-150
0
0
0
0
0
1
1
0
2
150-200
0
0
0
0
0
0
2
0
2
200-400
0
0
0
0
0
0
0
2
2
400 +
1
0
0
0
1
2
2
26
32
Total
18
0
6
0
3
5
8
31
71
B-3
-------
Table B-5. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading,
NCLSH/Westat Study — Uncarpeted Floors.
Wipe Lead
Loading
(A/g/ff)
25-50
50-75
75-100
100-150
1 50-200
200 - 400
400 +
Total
Blue Nozzle Vacuum Lead Loading U/g/ft1)
0-25
3
3
1
0
0
0
0
7
25-50
0
0
0
0
0
0
0
0
100-150
0
0
0
0
0
0
0
0
150-200
0
0
0
0
0
0
0
0
200-400
0
0
0
0
0
0
0
0
400 +
0
0
0
0
0
0
0
0
Total
3
3
1
0
0
0
0
7
Table B-6. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading,
NCLSH/Westat Study - Uncarpeted Floors, Window Sills, and Window Wells.
Wipe Lead
Loading
(/ig/ft1)
25-50
50-75
75-100
100-150
1 50-200
200 - 400
400 +
Total
Blue Nozzle Vacuum Lead Loading (//g/ft2)
0-25
10
13
6
4
3
3
1
40
25-50
0
1
0
1
0
2
3
7
100-150
0
0
0
0
0
0
3
3
150-200
0
0
0
0
0
0
2
2
200-400
0
0
0
0
0
0
2
2
400 +
0
0
0
0
0
0
1
1
Total
10
14
6
5
3
5
12
55
B-4
-------
BRM/Wipe Data
Table B-7 presents the distribution of uncarpeted floor samples by interval of wipe lead
loading and vacuum lead loading for the R&M Mini study. Similarly, Table B-8 provides
combined information for uncarpeted floors, window sills, and window wells. Table B-9
presents the distribution of uncarpeted floor samples by interval for the NCLSH 5-Method study,
and Table B-10 presents the analogous results for uncarpeted and carpeted floors, combined.
Table B-l 1 presents the distribution of uncarpeted floor sample results by interval for uncarpeted
floors sampled in the Rochester study; Table B-12 presents the corresponding results pooled
across all sample types represented in the Rochester study (uncarpeted floors, carpeted floors,
window sills, and window wells). Table B-l 3 shows the distribution of uncarpeted floor sample
results obtained in the Milwaukee Low Cost Intervention study. As seen in the tables, the range
of the data from uncarpeted floors varies significantly from study to study.
Table B-7. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading, R&M
Mini Study — Uncarpeted Floors.
Wipe Lead
Loading
U/g/ft»)
0-25
25-50
100-150
200-400
400 +
Total
BRM Vacuum Lead Loading (pg/ft*)
0-25
2
4
0
0
0
6
150-200
0
0
0
1
0
1
200-400
0
1
0
0
1
2
400+
0
0
2
6
8
16
Total
2
5
2
7
9
25
B-5
-------
Table B-8. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading, R&M
Mini Study — Uncarpeted Floors, Window Sills, Window Wells.
Wipe Lead
Loading
(//g/fta)
0-25
25-50
100-150
1 50-200
200-400
400 +
Total
BRM Vacuum Lead Loading (//g/ft2)
0-25
5
4
0
2
0
0
11
25-50
1
0
0
0
0
0
1
100-150
0
1
0
0
0
0
1
150-200
0
0
0
0
1
0
1
200-400
0
1
0
0
1
2
4
400 +
0
0
2
0
6
51
59
Total
6
6
2
2
8
53
77
Table B-9. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading, NCLSH
5 Method Comparison Study — Uncarpeted Floors.
Wipe Lead
Loading
(//g/ft2)
0-25
25-50
50-75
75-100
100-150
150-200
200-400
400 +
Total
BRM Vacuum Lead Loading (fig/ft1)
0-25
32
4
2
1
0
0
0
0
39
25-50
2
1
0
0
0
0
0
0
3
75-100
0
0
0
1
0
0
0
0
1
100-150
1
0
0
0
1
0
0
1
3
150-200
0
0
1
1
0
0
0
0
2
200-400
4
2
1
0
1
0
1
0
9
400 +
1
1
0
0
0
1
6
2
11
Total
40
8
4
3
2
1
7
3
68
B-6
-------
Table B-10. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading,
NCLSH 5 Method Comparison Study — Uncarpeted Floors, Carpeted Floors.
Wipe Lead
Loading
-------
Table B-12. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading,
Rochester Lead-in-Dust Study — Uncarpeted Floors, Carpeted Floors, Window
Sills and Window Wells.
Wipe Lead
1 ««M«JiMM
Loading
(//g/ft1)
0-25
25-50
50-75
75-100
100-150
1 50-200
200-400
400 +
Total
BRM Vacuum Lead Loading (//g/ft1)
0-25
278
62
17
9
8
4
3
6
387
25-50
72
15
12
11
13
3
5
2
133
50-75
48
12
10
7
10
3
3
3
96
75-100
27
10
2
9
9
4
1
4
66
100-150
28
11
7
3
8
9
7
3
76
150-200
24
6
2
3
7
5
5
7
59
200-400
60
17
6
7
9
8
15
27
149
400 +
103
34
11
11
20
16
58
333
586
Total
640
167
67
60
84
52
97
385
1552
Table B-13. Number of Samples by Wipe Lead Loading and Vacuum Lead Loading,
Milwaukee Low Cost Intervention Study — Uncarpeted Floors.
Wipe Lead
Loading
(//g/fta)
0-25
25-50
50-75
75-100
100-150
1 50-200
200-400
400 +
Total
BRM Vacuum Lead Loading (//g/fta)
0-25
36
15
4
4
4
1
2
0
66
25-50
5
6
5
0
1
0
0
0
17
50-75
4
1
2
0
2
0
1
0
10
75-100
1
0
2
0
0
1
0
0
4
100-150
1
3
0
0
1
1
0
1
7
150-200
1
1
0
0
1
1
0
0
4
200-400
1
3
3
0
0
1
1
1
10
400 +
1
2
4
2
0
2
4
2
17
Total
50
31
20
6
9
7
8
4
135
B-8
-------
APPENDIX C
Residual Analysis, Influential Observations and Computation Details
for the BN Vacuum to Wipe Conversion Equations
C-1
-------
APPENDIX C
Residual Analysis, Influential Observations and Computation Details
for the BN Vacuum to Wipe Conversion Equations
Model Development
The individual regression equations for predicting a wipe lead loading from a Blue
Nozzle vacuum lead loading based on the CAP Pilot, NCLSH/Westat, and R&M Pilot studies are
displayed in Table C-l. Results for uncarpeted floors, window sills, and window wells are
presented separately in each table. As described in the main body of the report, the regression
models were fitted as log(W) = log(cc) + p*log(BN), with log referring to natural logarithm. The
results in Table C-l are presented using the actual scale of the data as W = a*BNp.
Table C-1. Regression Equations for Predicting Wipe Lead Loading from Blue Nozzle
Vacuum Lead Loading.
Surface
Floors
(Uncarpeted)
Window Sills
Window Wells
Estimated Regression Model for
Blue Nozzle Vacuum Pb Loading to Wipe Pb Loading1"
CAP Pilot
W = S.ie'BN04*8
n = 6 R2=0.683W
Range W: 13.8-2498.5
Range BN: 1.9-149.1
W = 3.90"BN104
n = 6 R2 =0.927
Range W: 24.4-4217
Range BN: 6.3 - 600
(0
NCLSH/Westat
W = 48.9"BN°-oie
n = 7 Ra=0.001
Range W: 33.5-81.4
Range BN: 5.4 - 20.9
W = 7.61 'BN1-07
n=42 R2'0.476
Range W: 26.7-6197
Range BN: 4.2-149
W = 0.262'BN211
n = 6 R2= 0.806
Range W: 229.3-47616
Range BN: 35.5 - 479
R&M Pilot
W = 12.9'BN0-8111
n = 24 R2-0.810
Range W: 6.3-13969
Range BN: 1-2164
W = 4.26'BN1-27
n = 23 R2 -0.777
Range W: 2.2-1578000
Range BN: 1.4-8964
W = 8.94'BN0-72*
n = 24 R2 =0.438
Range W: 5.5-1206000
Range BN: 78 - 762000
(a) Units are //g/ft1 for vacuum and wipe dust-lead loadings.
(b) R2 represents the amount of variation explained by the log-linear regression model.
(c) Equation was not fitted because data were insufficient.
C-2
-------
Figures C-l, C-2, and C-3 display the modeled relationships for BN vacuum to wipe lead
loadings for the CAP Pilot, NCLSH/Westat, and R&M Pilot studies, respectively. In each of
these figures, the relationships for floors, sills, and wells are plotted individually. In addition,
the plots for uncarpeted floors and window sills also display the estimated "true regression
relationship" as a dashed line, after making the errors-in-variables correction described in
Chapter 3 of the report. All relationships are plotted on axes with the same scales for ease of
comparison and interpretation.
In the figures, notice how similar the estimated true relationship is to the observed
relationship, but in each case the slope is slightly steeper after an errors-in-variables correction
was made. The estimated true relationship based on different studies should be more similar to
each other than to the observed relationships. This was more evident for window sills than for
floors. Differences are due in part to the scarcity of the BN data and are minimized by the errors-
in-variables correction.
Figures C-4, C-5 and C-6 present graphs for the wipe lead loading versus BN lead loading
for uncarpeted floors, window sills and window wells, respectively. The data from each of the
three studies are plotted with different symbols. Included in these graphs are the estimated true
regression lines from the individual studies, with the combined true regression line overlaid.
Using these plots, a comparison can be made of the estimated relationships across the three
studies.
Figure C-4 for uncarpeted floors and Figure C-5 for window sills illustrate that, for the
most part, the combined true regressions appear to fit the data. Figure C-6 for window wells
exhibits considerable discordance between the individual regression relationships. However, the
R&M Pilot study has by far the greater amount of data and is given more weight than the
NCLSH/Westat equation.
Influential Observations
When conducting a regression analysis, it is important to note any points that are
influential. There are several approaches to determining influential data points. One measure of
C-3
-------
influence is known as the DFBETA statistic, which is a scaled measure of the influence of any
one data value upon the separate parameter estimates. For a simple linear regression, DFBETA
is calculated for the intercept (a) and for the slope (P), respectively. The statistic is a measure of
the difference between the parameter estimate (a or P) as calculated by including all data values
and as calculated by excluding the i* data value. The threshold value for determining which
points are most influential is recommended by Belsley, Kuh, and Welsch to be 21. Thus, for each
regression performed in this analysis, DFBETA was calculated for a and p, and compared to the
threshold value of 2. In figures C-l, C-2, C-3, the data for the individual regression is plotted
with triangles indicating the observations with significant influence on the intercept, squares
indicating the observations with significant influence on the slope, and circles indicating the
observations with significant influence on both the intercept and the slope.
Figures C-l, C-2, C-3 display the data, with indicated influential observations, for
predicting a wipe lead loading from a BN lead loading from uncarpeted floors, window sills and
window wells, for CAP Pilot, NCLSH/Westat, and R&M Pilot, respectively.
It should be noted that only 2 observations are influential in the BN to wipe regressions
(see figures C-l and C-2). In both cases, the data point is influential to the estimate of both the
intercept and the slope. One influential observation is in the CAP Pilot study regression for
uncarpeted floors. One influential observation is in the NCLSH/Westat study regression for
window wells. Each of the influential observations had predicted value significantly distant from
the other observations in the data set. This is not surprising given the limited amount of data
available in these two studies. Note that if an influential observation is removed, and the
regression repeated, the parameter estimates from that study may change substantially. However,
the methodology employed in this analysis to combine the parameter estimates from the
individual studies weights each estimate according to the inverse of the uncertainty associated
with it. Therefore, if a study has little data or much variability in its parameter estimates,
removing an influential point from that study will not significantly affect the combined parameter
estimates.
1 SAS/STAT User's Guide. Version 6, Fourth Edition, Volume 2,1990, SAS Institute Inc., pg 1419.
C-4
-------
For instance, consider the regression of wipe lead loading on BN vacuum lead loading for
uncarpeted floors shown in Figure C-l. When the influential point in the CAP Pilot Study is
removed, the estimates of a and P change for this study. The estimate of a including the point is
4.22 with a standard error of 0.51. By excluding the observation, the estimate of a becomes 3.28
with a standard error of 0.19. Likewise, the estimate of p is 0.97 with a standard error of 0.33
with the influential observation and 0.17 with a standard error of 0.15 without the influential
observation. In addition, the estimates of a in the other two studies change minimally due to the
centering of the data by the overall mean log BN vacuum lead loading which was altered slightly
by the removal of the data value. However, the combined conversion equation is not
significantly affected by this deletion.
The equations developed for uncarpeted floors based on all data points are compared with
the equations developed for uncarpeted floors after removing the most influential observations in
Table C-2. Three different equations are presented to reflect the transportability adjustment that
was necessary. Details of this adjustment are discussed in Sections 3.1.3 and 3.1.4 of this report.
Table C-2. A Comparison of Final Conversion Equations With and Without Influential
Observation, Uncarpeted Floors
Uncarpeted Floor Samples for
Houses Built
Pre-1940
1940-1959
1960-1979
Equations Based on Data with
Influential Data Points Removed
Wipe = 6.12BN0fl'7
Wipe = 5.38BN0810
Wipe = 4.73BN0639
Equations Based on
All Data Points
Wipe - 5.66BN0809
Wipe = 4.79BN0800
Wipe = 4.03BN0707
The final conversion equations are similar because the uncertainty associated with the slope in
the CAP Pilot Study (using all observations) is high, thereby lessening its contribution to the
combined slope estimate. However, there is no basis for eliminating any of the influential
observations from this analysis. The design of the analysis minimizes the effect of such
observations.
C-5
-------
Residual Analysis
There are also underlying assumptions that are made when conducting a regression
analysis that must be validated. One such assumption is that the variability in the data remains
constant across the range of the data. Residual plots (i.e., residual values (log scale) versus
predicted values) have been provided for all BN regressions performed. A random scatter of the
points on the graph around the reference line at zero with similar range across predicted values is
an indication that the assumption of the homogeneity of variance is satisfied. However, if there
are more data points at one predicted value than at another, the range should be commensurately
wider because there is greater likelihood of observing more extreme values with more
observations.
Figure C-7 presents the residuals versus the predicted wipe loadings from the regression
of wipe loading on BN loading for uncarpeted floor samples from CAP Pilot, NCLSH/Westat
and R&M Pilot studies. Figures C-8 and C-9 present analogous information for window sills and
window wells. Regarding the residual plots, no patterns or. trends can be seen, and variability
appears constant across predicted values for each of the regressions performed.
Calculation of Measurement Error Estimates Used in the BN to Wipe Conversions
Although there were three types of conversions developed in this report, only the BN to
wipe conversion included a measurement error adjustment. A justification for this is provided
elsewhere in this report. To apply the adjustment, it is necessary to have an estimate of Oy2 — the
variance associated with the errors (Uj). Side-by-side data from floors and window sills sampled
in the CAP Pilot study were used to derive these estimates.
Because of differences in the sampling protocols on uncarpeted floors between the CAP
pilot study and the other studies, BN measurement error estimated from the CAP data was
adjusted appropriately to reflect measurement error in the other two BN studies (i.e.,
measurement error associated with side-by-side, 1 ft2 samples).
The point estimate of measurement error (obtained in the CAP study) was larger than the
total variability in the measured BN values observed in the NCLSH/Westat study. This would
prevent a measurement error adjustment for this study. Therefore, the lower 95 percent
C-6
-------
confidence bound on the estimate of measurement error was used for adjusting the regression
relationships observed for the NCLSH/Westat data. Regardless of the measurement error
assumed, the parameter estimates obtained from the NCLSH/Westat study had the greatest
uncertainty (by up to a factor of 400 to 1), and therefore are given the least weight in deriving the
final estimates. Thus, the point estimate from the CAP Pilot study was used to adjust the CAP
pilot regression parameter estimates and the R&M pilot regression parameter estimates and the
lower 95 percent confidence bound on the measurement error estimate was used to adjust the
NCLSH/Westat estimates. (The actual choice of a measurement error estimate for the latter
study had little impact on the final estimates because of the relatively low weight the
NCLSH/Westat estimates are given.)
Data from the R&M pilot study were also used to obtain separate estimates of the
spatial, side-by-side, and laboratory analysis variability. This analysis resulted hi a comparable
estimate of side-by-side variance on uncarpeted floors as was estimated from the CAP pilot
study.
Matrix Algebra for Computing BN to Wipe Confidence Intervals and Prediction
Intervals.
This section describes the approach used to estimate confidence and prediction intervals
for the BN to wipe conversion.
Beginning with the parameters for the centered regressions
efl
6
U
i = 1,2,3 for the three training data sets.
Estimates of the parameters of the regression relationship, after correcting for measurement error,
are
P
U
where
C-7
-------
0
and P,=A,6.
But then, the variance of ft is Aj $]}e A, . The variance of the combined vector of parameter
estimates, (p,, p2, p3), is
0
o o
. Note that, because the individual Pi's are
actually bivariate vectors, this covariance matrix has 6 rows and 6 columns.
A weighted average of the p,'s (from the individual studies) was then taken; the weights
used were the inverses of the squared standard errors of the individual parameter estimates. This
can be written out as a linear combination of the Pi's. Let
B =
W0,i 0 W0>2 0
0 WM 0 Wlr
0
o
, where
W0(j - normalized weights associated with the centered intercept estimates, and
W, j = normalized weights associated with the centered slope estimates.
Then Pcentered = B Pnew and
Foruncentering, Puncentered =
represents the overall mean of natural log-transformed lead loadings across studies.
Po
K.
=C Pcentered' where C =
i -ML'
01
c-8
-------
To represent the transportability adjustment, let D =
HA(1-AA)
0
, where UA
represents the mean of natural log-transformed lead loadings in the application data set,
_2
and
with the numerator representing variability in true log lead loadings in the
U
application data set, and the denominator representing the same plus measurement error. Then
the adjusted parameter estimates of the prediction equation for the application data set are given
by
er
uncentertd'
Its covariance matrix is given by = D
^"^
interest and can be derived using the above steps as follows:
D'. This is the covariance matrix of
= DC
ct>'
= DCB B'Ct)
where
0
o
o
A,Ee, A,' 0
0
0
0
C-9
-------
9
o
I mil
100.000
10.000
1.000
* + + CAPS Pilot. Data
ooo Influential ouUIn-
Tru* relationship
ilodoi relationship
10 100 1.000 10.000 100.000 ImU 10 mil 100 Ml
Floor BN Lead Loading Gig/fP)
+ * * CAPS Pilot. Dala
ooo Influential outlier
Trw relationship
Uod«lr«UUonmhlp
10 too IJDOO 10.000 100.000 imn io ma 100 •
SfflBN Lead Loading (jig/ft^
Figure C-1. Modeled Relationship Between Wipe and BN lead loadings. Before and After Correcting for Measurement Error
(Errors in Variable Correction); Uncarpeted Floors and Window Sills, CAP Pilot Study.
-------
10 mil
Imll
^P* 100.000
•g 10.000
8 1.000
jj 100
* ..
I ..
01
O.OI
**
* * * NCLSH/Westat. Data
000 Influential outlier
— - — • True relationship
Model relationship
10 mil
ImB
g- 100400
"5 "OJOOO'
8 1.000
>-J 100
f -
0.1-
OX)I-
4
**ss
«r
* * * NCLSH/Weatat. Data
000 Influential outlier
True relationship
10 too 1.000 toon looxno n
Floor BN Lead Lowlingi Oig/ft*)
10 nil 100 mil
100 1.000 IO.OOO lOOcOOO I mU 10 mU 1OO r
Sill BN Lead Loading Oig/ft1)
3
t
i
100.000
10.000
I.OOO
IOO
+ + + NCLSH/WnUt. Data
ooo Influential outlier
Model reletlenehlp
1.000 IO.OOO 1OO.OOO I mil 10 mil lOOmll
Well BN Lewi Loading (jig/ft1)
Figure C-2. Modeled Relationship Between Wipe and BN lead loadings. Before and After Correcting for Measurement Error
(Errors-in-Variables Correction), Uncarpeted Floors, Window Sills, and (No Correction for Measurement Error)
Window Wells, NCLSH/Westat.
-------
(J^ 1OO.O001
•S 10.000
3 1.000
1 .0.
•*•••••*• RAM PUot. Data
000 Influential ouUi.r
Tru* r«laUon«hlp
Mod«l r»l«Uon.hTp
» » + R*M Pilot, D.U
000 Influential ouUlar
Tru« r«lAUonahlp
— Modal r«l«Uon»hlp
10 100 1.000 10.OOO 100.000
Floor BN Lead Loadings Gig/ft1)
10 mU IOO mU
10 100 1.OOO lOjOOO 1OO.OOO 1
Sill BN Lead Loading (ps/tl1)
10 nil 100 mil
o
•Jt
K)
IOO.OOO
10.000
1.000
100
1
+ * * R*M PUot. D«U
000 Influential oullter
Model reUtloMhlp
> too 1.000 toaoo lOOjooo imu lOmll lOOnUl
Well BN Lead Loading Gig/ft1)
Figure C-3. Modeled Relationship Between Wipe and BN lead loadings. Before and After Correcting for Measurement Error
(Errors-in-Variables Correction), Uncarpeted Floors, Window Sills, and (No Correction for Measurement Error)
Window Wells, R&M Pilot.
-------
10
9
«•*
to
>
»
H3
«J
cfl
JS
o
I
1 mll-
10O.OOO -
10.000-
1 .000 -
1OO-
10-
i -
O.I -
O.O1 -I,
0.01
CAPS Pilot. Data
CAPS Pilot, True relationship
A A A NCLSH/Westat. Data
NCLSH/Westat. True relationship
ana R&M Pilot. Data
R&M Pilot, True relationship
Combined True relationship
O.I
i 10 100 i.ooo
Floor BN Lead Loading (ug/sq.ft)
1O>OOO
100.000
Figure C-4. Errors-in-Variables Corrected BN to Wipe Relationship Based on Individual Studies and Averaged Across
Studies; Uncarpeted Floors.
-------
o
cr
00
QB
C
*•••*
"O
(O
03
.3
OJ
a.
1O mil -i
I mil-
100,GOO r
IQ.QOQ-
1,000-
100-
1O-
1 -
0.1 -
O.O1 A
O.Ol
O.I
a
a
a
a
a
o
-4-4-4-4- CAPS Pilot, Data
CAPS Pilot, True relationship
A A A NCLSH/Westat. Data
NCLSH/Westat, True relationship
ana R&M Pilot, Data
R&M Pilot. True relationship
Combined True relationship
i 10 100 i.ooo
Sill BN Lead Loading (ug/sq.ft)
10.000
100,000
Figure C-5. Errors-in-Variables Corrected BN to Wipe Relationship Based on Individual Studies and Averaged Across
Studies; Window Sills
-------
O
01
O*
tn
T3
a.
1O mi! i
1 mil -
i OO.OOO -
10.OOO i
l.OOO-
100 •.
1 i
0.1 :
O.O1 H
O.O1
0.1
NCLSH/Westat, Data
NCLSH/Westat, True relationship
A A A RScU PILOT, Data
R&M PILOT, True relationship
Combined True relationship
1 1O 1OO l.OOO 1O.OOO 1OO.OOO 1 mil
Well BN Lead Loading (ug/sq.ft)
Figure C-6. Estimated BN to Wipe Relationship, Without Adjusting for Measurement Error, Based on Individual Studies and
Averaged Across Studies; Window Wells
-------
0.1 I 10 100 1.000 10.000 100.000 I mil 10 mil 100 mil
CAPS Uncaipeted Floors Predicted Wqw Lead Loading Qigtt*)
O.I I 10 100 1.000 10.000 100400 I mil 10 nil 100 mil
NCLSH Uncaipeted Floors Predicted Wipe Lead Loading Gig/fl*)
9
CD
10 100 IJDOO 10.000 100.000 I mil 10 mil 100 mil
KM Mot Uncaipeted Floors Predicted Wipe Lead Loading Gig/ft?)
Figure C-7. Residual (Log Scale) versus Predicted Wipe Lead Loading from the Regression of Wipe Lead Loading on Blue
Nozzle Lead Loading for Uncarpeted Floors from the CAP Pilot, NCLSH/Westat, and R&M Pilot Studies.
-------
I.1
i
CO
1 °
1-1.
*; +
01 I 10 100 1.000 10.000 100.000 I mil lOrnU 100mil
CAPS Window Sills Predicted Wipe Lead Loading (jig/ft1)
0.1 I 10 100 1.000 10.000 100.000 IBU IOOU1 100 mil
NCLSH Window Sills Predicted Wipe Lead Loading (jig/ft1)
i •
1 °
I -
0.1 I 10 100 1.000 10.000 100.000 I mil 10 mil 100 mil
RAM Pilot Window Sills Predicted Wipe Lead Loading (fig/ft*)
Figure C-8. Residual (Log-Scale) and Predicted Wipe Lead Loading from the Regression of Wipe Lead Loading on Blue
Nozzle Vacuum Lead Loading for Window Sills from the CAP Pilot, NCLSH/Westat, and R&M Pilot Studies.
-------
1 to too 1,000 10.000 100.000 i mil itmU loo mil
NCLSH Window Well* Predicted Wipe Lead Loading dig/tff)
9
oo
01 i 10 ion IMC lOvQoa 100.000 \m» ttwa
RM Pilot Window WMb Predicted Wipe Lead LowfingGigftP)
Figure C-9. Residual (Log Scale) and Predicted Wipe Lead Loading from the Regression of Wipe
Lead Loading on Blue Nozzle Vacuum Lead Loading for Window Wells from the
NCLSH/Westat and R&M Pilot Studies.
-------
APPENDIX D
Residual Analysis, Influential Observations and Computation
Details for the Wipe to BN Vacuum Conversion Equations
D-1
-------
APPENDIX D
Residual Analysis, Influential Observations and Computation
Details for the Wipe to BN Vacuum Conversion Equations
Model Development
The individual regression equations for predicting a BN vacuum lead loading from a wipe
lead loading for the CAP Pilot, NCLSH/Westat, and R&M Pilot studies are displayed in Table
D-l. Results for uncarpeted floors, window sills, and window wells are presented separately in
each table. As described in the main body of the report, the regression models were fit as log(W)
= log(a) + P*log(BN), with log referring to natural logarithm. The results in Table D-l are
presented using the actual scale of the data as W = a*BNp.
Table D-1. Regression Equations for Predicting Blue Nozzle Vacuum Lead Loading
from Wipe Lead Loading.
Surface
Floors
(Uncarpeted)
Window Sills
Window Wells
Estimated Regression Model for
Wipe Pb Loading to Blue Nozzle Vacuum Pb Loading"'
CAP Pilot
BN = 0.662»W070e
n = 6 R2=0.683W
Range W: 13.8-2498.5
Range BN: 1.9-149.1
BN = O.SgO'W0887
n = 6 R2 =0.927
Range W: 24.4-4217
Range BN: 6.3 - 600
(c)
NCLSH/Westat
BN = 9.87»Waw»
n = 7 R2=0.001
Range W: 33.5-81.4
Range BN: 5.4 - 20.9
BN = 1.66'W0-447
n=42 R2'0.476
Range W: 26.7-6197
Range BN: 4.2-140
BN - 4.53»W°3M
n = 6 R2=0.806
Range W: 229.3-47616
Range BN: 35.5 - 479
R&M Pilot
BN = 0.134 •WMM
n = 24 R2=0.810
Range W: 6.3-13969
Range BN: 1-2164
BN = 0.977 »W°«t2
n = 23 R2 =0.777
Range W: 2.2-1578000
Range BN: 1.4-8964
BN - 35.2'W0907
n = 24 R2 =0.438
Range W: 5.5-1206000
Range BN: 78 - 762000
(a) Units are //g/ft1 for vacuum and wipe dust-lead loadings.
(b) R2 represents the amount of variation explained by the log-linear regression model.
(c) Equation was not fined because data were not available or insufficient.
Figures D-l, D-2, and D-3 display the modeled relationships for wipe to BN vacuum lead
loadings for the CAP Pilot, NCLSH/Westat, and R&M Pilot studies, respectively. In each of
D-2
-------
these figures, the relationships for floors, sills, and wells are displayed simultaneously. All
relationships are plotted on axes with the same scales for ease of comparison and interpretation.
The reader is reminded that since there is no application data set for the conversion of
wipe lead loading to BN vacuum lead loading, so no errors-in-variables conversion or
transportability adjustment was made for this set of conversion equations.
Figures D-l, D-2, and D-3 reveal differences in the relationships between wipe lead
loading and BN loading among the three studies. This is due in part to the scarcity of the BN
data. For example, consider the uncarpeted floor lead loading plot. The estimated slope is much
lower for the NCLSH/Westat study.
Figure D-4 displays the BN lead loading versus wipe lead loading results observed for
uncarpeted floors with the data from each of the three studies plotted with different symbols.
Included in this graph are the regression lines from the individual studies and a solid line
representing the estimated average relationship across studies. Using this plot, a comparison can
be made of the relationships across the three studies with the combined estimate.
Figures D-5 and D-6 present similar information on window sills and window wells.
Figures D-4 for uncarpeted floors and D-5 for window sills, illustrate that for the most part the
combined regression equations appear to fit the data. In particular, although the estimated
relationship from the NCLSH/Westat study does not agree with the other two studies, it can be
observed that the range of the relationship estimated from this study is very narrow compared
with the other two studies. When all the data are combined and overlaid with the (combined)
estimated average relationship, the fit is reasonable across the range.
However, Figure D-6 for window wells exhibits considerable discordance between the
individual regression relationships. Consider Figure D-6. Note the number of data points
contained in each study. The R&M Pilot study has by far the greater amount of data. However,
when the regression equations are combined, more weight is given to the NCLSH/Westat
equation. This is because the uncertainty in the parameter estimates from the NCLSH/Westat
study is estimated to be smaller than the uncertainty in the parameter estimates from the R&M
Pilot study.
D-3
-------
Influential Observations
When conducting a regression analysis, it is important to note any points that are
influential. There are several approaches to determining influential data points. One measure of
influence is known as the DFBETA statistic, which is a scaled measure of the influence of any
one data value upon the separate parameter estimates. For a simple linear regression, DFBETA
is calculated for the intercept (a) and for the slope (p), respectively. The statistic is a measure of
the difference between the parameter estimate (a or p) as calculated by including all data values
and as calculated by excluding the i* data value. The threshold value for determining which
points are most influential is recommended by Belsley, Kuh, and Welsch to be 21. Thus, for each
regression performed in this analysis, DFBETA was calculated for a and p, and compared to the
threshold value of 2. In figures D-l, D-2, D-3, the data for the individual regression is plotted
with triangles indicating the observations with significant influence on the intercept, squares
indicating the observations with significant influence on the slope, and circles indicating the
observations with significant influence on both the intercept and the slope.
Figures D-l, D-2, D-3 display the data, with indicated influential observations, for
predicting a wipe lead loading from a BN lead loading from uncarpeted floors, window sills and
window wells, for CAP Pilot, NCLSH/Westat, and R&M Pilot study data, respectively.
It should be noted that only 1 observation is influential in the wipe to BN regressions (see
Figure D-l). This data point is influential to the estimate of both the intercept and the slope.
This influential observation is in the CAP Pilot regression for uncarpeted floors. This influential
observation had a predicted value significantly distant from the other observations in the data set
This is not surprising given the limited amount of data available in this study. Note that if an
influential observation is removed, and the regression repeated, the parameter estimates from that
study may change substantially. However, the methodology employed in this analysis to
combine the parameter estimates from the individual studies weights each estimate according to
the inverse of the uncertainty associated with it. Therefore, if a study has little data or much
variability hi its parameter estimates, removing an influential point from that study will not
significantly affect the combined parameter estimates.
1 SAS/STAT User's Guide. Version 6, Fourth Edition, Volume 2,1990, SAS Institute Inc., pg 1419.
D-4
-------
The effects removing an influential observation are illustrated in Appendix C for the
conversion of BN vacuum samples to wipe lead loading values. The basic result is that the final
conversion equations are similar because the uncertainly associated with the slope in the CAP
Pilot Study (using all observations) is high, thereby lessening its contribution to the combined
slope estimate. However, that there is no basis for eliminating this point (or any of the other
influential observations) from this analysis. The design of the analysis minimizes the effect of
such observations.
Residual Analysis
There are also underlying assumptions that are made when conducting a regression
analysis that must be validated. One such assumption is that the variability in the data remains
constant across the range of the data. Residual plots (i.e., residual values (log scale) versus
predicted values) have been provided for all BN regressions performed. A random scatter of the
points on the graph around the reference line at zero with similar range across predicted values is
an indication mat the assumption of the homogeneity of variance is satisfied. However, if there
are more data points at one predicted value than at another, the range should be commensurately
wider because there is greater likelihood of observing more extreme values with more
observations.
Figure D-7 presents the residuals versus the predicted wipe loadings from the regression
of wipe loading on BN loading for uncarpeted floor samples form CAP Pilot, NCLSH/Westat
and R&M Pilot studies. Figures D-8 and D-9 present analogous information for window sills
and window wells. Regarding the residual plots, no patterns or trends can be seen, and
variability appears constant across predicted values for each of the regressions performed.
D-5
-------
D
6>
§
0.1 I 10 100 1.000 10.000 100.000 1 mil 10 mil tOO mil
Uncarpeted Floor Lead Loading fag/ft3), Wipe Samples
I
I 10 too 1.000 10.000 100.000 I mil 10 mil 100 mil
Window Sill Lead Loading (ug/fP), Wipe Samples
Figure D-1. Blue Nozzle Vacuum Lead Loading versus Wipe Lead Loading for Uncarpeted Floors and Window Sills from
the CAP Pilot Study.
-------
0.1 1 10 100 1,000 10.000 100.000 Imil 10 mil 100 mil
Uncarpeted Floor Lead Loading (ng/ft1), Wipe Samples
I 10 100 1.000 10.000 10D.OOO 1 mil 10 mil 100 mil
Window Sill Lead Loading (ng/ft3), Wipe Samples
(B 10.000
3 i.ooo
1
0.1 I 10 100 1.000 10.000 100.000 1 mil 10 mil 100 mil
Window Well Lead Loading Gig/ft1), Wipe Samples
Figure D-2. Blue Nozzle Vacuum Lead Loading versus Wipe Lead Loading for Uncarpeted Floors, Window Sills, and
Window Wells from the NCLSH/Westat Study.
-------
01 I 10 IN 1.000 10.000 lOOjMO iBll 10 041 100 mU
UiKaipeted HOOT Lead Loading ((ig/fi1), Wipe Samples
01 I 10 100 IJMO lOMO lOOjON I nil IOMI 100 n
Window Sill Lead Loading (ug/ft3). Wipe SunpVa
D
00
j
j
i
0.1 I 10 100 MOO IOMO 100.010 I m* IOMI lOOmU
Window Wdl LMd LM^nt (MWX Wipe Snides
Figure D-3. Blue Nozzle Vacuum Lead Loading versus Wipe Lead Loading for Uncarpeted Floors, Window Sills, and
Window Wells from the R&M Pilot Study.
-------
9
(O
•o
.2
0)
a,
g
10 mil -
1 mil
100,000
J 10,000 i
"5.
s
CO
co 1,000
o
cr
CO
tao
(O
5
1OO-
1O-
1 -
O.I -
0.01 -\
oo
+ CAPS Pilot, Data
* RScM Pilot, Data
o NCLSH/Westat, Data
Combined Prediction Line
— CAPS Pilot, Predicted
— R&M Pilot, Predicted
- NCLSH/Westat, Predicted
o.oi
0.1 1 10 10O 1,000 1O.OOO 10O.OOO 1 mil 10 mil 100 mil
Lead Loading (ug/sq. ft), Wipe Samples, Uncarpeted Floor
Figure D-4. Estimated Wipe to BN Relationship; Without Adjusting for Measurement Error, Based on Individual
Studies and Averaged Across Studies; Uncarpeted Floors.
-------
10 mil -i
to 1 mil -
I
13
;S 100,000 -
ja>
"H.
S
CO
CO
|
O
or
I
Qfl
C
1
eo
3
10,000 -.
l.OOO-
100-
10-
1 -
0.1 -
0.01
O.O1
+ + + + CAPS Pilot. Data
* * 4 K&M Pilot. Data
ooo NCLSH/Weatat. Data
Combined Regression Line
CAPS Pilot. Predicted
R&M Pilot. Predicted
- — NCLSH/Westat. Predicted
0.1 1 10 100 1,000 10,000 100.00O 1 mil 10 mil 100 mil
Lead Loading (ug/sq. ft), Wipe Samples, Window Sill
Figure D-5. Estimated Wipe to BN Relationship; Without Adjusting for Measurement Error, Based on Individual
Studies and Averaged Across Studies; Window Sills.
-------
10 mil -i
1 mil-
O
.S 100.000 -
6
-------
9
ro
0.1 I 10 100 1.000 UlMO 100MO 1MB 10 M 1001>1
CAPS Uncttpetod Floon Predicted BN Vacuum Lead Lowiiog (ngW)
0.1 i 10 io> i.ooo 10.000 icojon i_u io«u IOIBII
NCLSH Uncnpeted Floon Predicted BN Vacuum Lewi Loading (jig/ft1)
It 100 IMO
I Ml UMI 100•«
RAMPOotUmqidedFloanFlmfietod
Figure D-7. Residual (Log Scale) versus Predicted Blue Nozzle Vacuum Lead Loading from the Regression of Blue Nozzle
Lead Loading on Wipe Lead Loading for Uncarpeted Floors from the CAP Pilot, NCLSH/Westat, and R&M
Pilot Studies.
-------
0.1 I 10 100 IjOOO 10.000 100.000 Inn 10 DU lOOmO
CAPS Window SDb Predicted BN Vacuum Lead Loading Gig/ft")
0.1 I 10 IN 1400 IOMO 100.000 I Ml Wall 100.
NCLSH Window Sffli Predicted BN Vacuum Lead Lending ftig/ft*)
9
CJ
01 I 10 100 1.000 10.000 100.000 I mil lOnll 100 mil
RAM Pilot Window Silli Predicted BN Vacuum Lead Loading (jig/ft1)
Figure D-8. Residual (Log Scale) and Predicted Blue Nozzle Vacuum Lead Loading from the Regression of Blue Nozzle
Lead Loading on Wipe Lead Loading for Window Sills from the CAP Pilot, NCLSH/Westat, and R&M Pilot
Studies.
-------
f •
01 I 10 100 1.000 10.000 100.000 1 nil 10 Wl 100 nil
NCLSH Window Wells Predicted BN Vacuum Lewi Loading (jig/ff)
f •
01 I 10 100 UWO 10.000 100.000 I ma Um» 100mil
RAM Pilot Window Welb Predicted BN Vacuum Lead Looting GigffP)
Hgure D-9. Residual (Log Scale) and Predicted Blue Nozzle Lead Loading from the Regression of
Blue Nozzle Vacuum Lead Loading on Wipe Lead Loading for Window Wells from
the NCLSH/Westat and R&M Pilot Studies.
-------
APPENDIX E
Residual Analysis, Influential Observations and Computation
Details for the BRM to Wipe Conversion Equations
E-1
-------
APPENDIX E
Residual Analysis, Influential Observations and Computation
Details for the BRM to Wipe Conversion Equations
Model Development
The individual regression equations for predicting a wipe lead loading (W) from a BRM
lead loading for the R&M Mini, Rochester Lead-in-Dust, NCLSH 5-Method Comparison, and
Milwaukee Low Cost Interventions studies are displayed in Table E-l. The regression models
were fit as log(W) = log(cc) + P*log(BRM), with log referring to natural logarithm. However, the
results in Table E-l are listed using the actual scale of the data as W = a*BRMp. As explained in
Section 3.1.7, within-house correlation was taken into account in the estimation process.
As described in Section 2, the results presented for the R&M Mini study in Table E-l
include an adjustment for the chemical extraction procedure employed for the HUD wipe
samples. The correction factor is based on uncarpeted floor samples but was applied to all
samples.
Figures E-l to E-4 display the modeled relationships for wipe to BRM lead loadings for
the R&M Mini, NCLSH 5-Method Comparison, Rochester Lead-in-Dust, and Milwaukee Low
Cost Interventions studies, respectively. In each of these figures, the relationships for all housing
components sampled are displayed individually. All plots use axes with identical scales for ease
of interpretation and comparison.
Figure E-5 presents the data from each of the four studies plotted with different symbols,
for wipe lead loading versus BRM lead loading results observed for uncarpeted floors. Included
in this graph are the regression lines from the individual studies and the combined regression
line. Using this plot a comparison can be made of the BRM loading to wipe loading relationship
across the four studies. Figures E-6, E-l, and E-8 display the same type of information for
carpeted floors, window sills, and window wells, respectively; information was available from
fewer than four studies for these three housing components. It can be seen hi these figures that
the combined regression equation averaged across studies appears to fit the data hi each case.
E-2
-------
Consider Figure E-7 for window sills. The slope of the R&M Mini regression line is steeper than
that for Rochester. However, the combined regression equation is more reflective of the
Rochester regression. This is because the Rochester study has 362 observations compared to 27
for the R&M Mini study. The method of combining the regression equations across studies
ensures more weight is given to the study with more precise parameter estimates.
Influential Observations
When conducting a regression analysis, it is important to note any points that are
influential. There are several approaches to determining influential data points. One measure of
influence is known as the DFBETA statistic, which is a scaled measure of the influence of any
one data value upon the separate parameter estimates. Although the individual regression
displayed in Table E-l were estimated using GEE (generalized estimating equations), values for
the statistic DFBETA were calculated based on simple linear regression to identify influential
data points. For a simple linear regression, DFBETA is calculated for the intercept (a) and for
the slope (p), respectively. The statistic is a measure of the difference between the parameter
estimate (a or P) as calculated by including all data values and as calculated by excluding the Ith
data value. The threshold value for determining which points are most influential is
recommended by Belsley, Kuh, and Welsch to be 21. Thus, for each regression performed in this
analysis, DFBETA was calculated for a and p, and compared to the threshold value of 2. No
individual data points were identified as being significantly influential according to this method.
Residual Analysis
There are also underlying assumptions that are made when conducting a regression
analysis that must be validated. One such assumption is that the variability in the data remains
constant across the range of the data. Residual plots (i.e., residual values on a log scale versus
predicted values) have been provided for all BRM regressions performed. A random scatter of
1 SAS/STAT User's Guide. Version 6, Fourth Edition, Volume 2,1990, SAS Institute Inc., pg 1419.
E-3
-------
the points on the graph around the reference line at zero with similar range across predicted
values supports the homogeneity of variance assumption of the log linear regression model.
Figure E-9 presents the corresponding residuals versus the predicted wipe loadings from
the regression of wipe loading on BRM loading for uncarpeted floor samples from the four
studies included in the analysis. Figure E-10 presents similar information for carpeted floors.
Analogous information is displayed in Figure E-l 1 for window sills and E-12 for window wells.
No patterns or trends can be seen hi the residual plots from the BRM regressions. The analysis
did not reveal any deviations from underlying assumption for the model used to develop the
BRM conversion equations.
E-4
-------
Table E-1. Regression Equations for Predicting Wipe Lead Loading From BRM Vacuum Lead Loading.
Surface
Floors
(Uncarpeted)
Floors
(Carpeted)
Window Sills
Window Wells
Estimated Regression Model for
BRM Vacuum Pb Loading to Wipe Pb Loading"
R&MMmr"
W - 3.965 •BRMas17
n = 26
Range W: 11.1 - 18960
Range BRM: 1.1-8337
(e)
W = 6.524"BRM0798
n = 27
Range W : 6.0 - 261400
Range BRM : 0.8 - 4170000
W = 9.551 •BRM0*"
n=25
Range W : 1 74 - 2220000
Range BRM : 2.4 - 4540000
NCLSH 5-Method(d
W = 3.151"BRMa4al
n= 68
Range W: 1.0-918
Range BRM : 0.5 - 7770
W « 1.453"BRMOJ13
n= 67
Range W : 0.8 - 60
Range BRM : 47.0 - 5640
(e)
(e)
Rochester Lead-in-Dust
W = 2.898"BRMaM'
n = 389
Range W: 0.1 -18130
Range BRM : 0.1 - 74100
W = 2.432-BRM™3*
n = 398
Range W : 0.5 - 34600
Range BRM: 1.4- 141000
W = 5.174"BRMMM
n = 362
Range W: 0.4 -420100
Range BRM : 0.3 - 231000
W - 7.967" BRMaMO
n=403
Range W: 2.7 -1362000
Range BRM: 1.9-6611000
Milwaukee Low Cost
lnterventionsw
W = 3.47«BRMaM3
n = 135
Range W : 0.4 - 636
Range BRM : 0.2 - 22600
(e)
(e)
(e)
•71
01
(a) Units are pg/ft* for vacuum and wipe dust-lead loadings.
(b) Bioavailable wipe lead loadings in the R&M Mini study were adjusted to represent total available lead loadings.
(c) Wipe lead loadings In the NCLSH 5-Method study were multiplied by 1.25 to correct for only including 80% of wipe samples in chemical analyses.
(d) Duplicate vacuum samples were excluded in determining the relationship.
(e) Equation was not fitted because data were not available or insufficient.
-------
o>
t
~J too
0-1 1 10 10O 1^00 IO.OOO 100.000 lodl 10 mU 100 mil
Uncarpeted Floor Lead 1 ***!*,% (Mg/fP). BRM Vacuum Samples
-g 100
3
1 10
•^J
I
O.I I 10 100 1.000 1OMO 100.000 1 mil 10 nil 100 >
Window Sill Lead Loading dig/ft1), BRM Vacuum Samples
0.1 I 10 IOO I.OOO 10,000 100.000 I mil 10 mil 10O nil
Window Well Lead Loading* (ugW), BRM Vacuum Samples
Figure E-1. Modeled Relationship Between Wipe and BRM Lead Loadings, Controlling for Wfthin-House Correlation;
R&M Mini Study.
-------
sj
I
0.1 I 10 100 1*00 10.000 101X000
Uncatpeted Floor Lead Losing* Gig/ft*), BUM Vi
10 mil 10
Sampta
-J
i'
]
«*>*
0.1 1 10 100 1.000 10,000 100.000 I mil 10 nil 100 o
Cwpetad Floor Lead Undiogi Gigtt*X BRM V«cmim Sample*
Figure E-2. Modeled Relationship Between Wipe and BRM Lead Loadings, Controlling for Within-House Correlation;
NCLSH 5-Method Comparison Study.
-------
f
\
I ..
0.1 1 10 100 IjOOD MMO IOHOOO I _• 10•• WtmH
Uncarpeted Floor Lead Loading Cig/fi*), BRM Vacuum Samples
f-
1
0.1 I 10 100 1.000 lOuMO UOJMO I •• 10 Ml IOOM
Cupeled Floor Lead Loading (ug/ft>), BUM Vacuum Sample*
00
v*
t
0.1 I 10 100 1X00 10409 IOOOOO I mm lOmt 100•
Window SU1 Lead Loading (jig/fP). BRM Vmconrn Sample*
O.I I 10 100 1.000 IOOOO 1OMOO 1-H 10M1 100 =•
Window WeU Lead Loading Gig/ft"). BRM Vacuum Samples
Figure E-3. Modeled Relationship Between Wipe and BRM Lead Loadings. Controlling for Within-House Correlation;
Rochester Lead-in-Dust Study.
-------
to
0.
s
10 mil 1
I mil-.
:«* 100.000 -.
I
60
C
• «M«
•o
CO
-------
m
O
10 mil -
1 mil-
a> 10O.OOO -
r*~t
CX
6
a
°£ 10.0001
a.
~j 1.000-
6*
^ 100-y
em
^ 10^
•o
-------
10 mil
1 mil
100.000
03
GO
O>
0,
QO
I
CO
10.000
"2" 1.000-
6*
•S
100,
10-
1 -
0.1 -
0.01 -I
n
a
Combined Reg Line
ODD Rochester, Data
Rochester, Predicted
A A A NCLSH 5-M, Data
- - — NCLSH 5-M. Predicted
0.01 0.1 1 10 100 1.000 10,000 100.000 1 mil 10 mil 100 mil
Lead Loading (ug/sq. ft), Vacuum Samples
Figure E-6. Estimated BRM to Wipe Relationship, Controlling for W'rthin-House Correlation, Based on Individual
Studies and Averaged Across Studies; Carpeted Floors.
-------
10 mil
1 mil-;
ju 100,000
"B.
6
CO
* 10.000
*> 1,0001
CO
3
CO
3
1OO-
10-=
0.1 -.
0.01-1
00
Combined Reg Lane
++++ Rochester, Data
Rochester, Predicted
O O O R&M Mini, Data
R&M Mini. Predicted
O.O1 0.1 1 10 10O 1,000 10.000 100.000 1 mil
Lead Loading (ug/sq. ft), Vacuum Samples
10 mil 100 mil
Figure E-7. Estimated BRM to Wipe Relationship, Controlling for Wrthin-House Correlation, Based on Individual
Studies and Averaged Across Studies; Window Sills.
-------
Ill
u
-------
"1
I 10 100 1.000 10.000 100.000 I mil 10 nil 100 mil
RAM Mini Uncaipeted Floats Predicted Wipe Lead Loading Gig/ft")
O.I 1 10 100 1.000 10.000 100.000 I mil Wnll 100 mil
hJLSCH Uncaipeted Floor* Predicted Wipe Lead Loafing Oig/ff)
0.1 1 10 100 1.000 10.OOO 100.000 I nil 10 mil IOO mil
Rochester Uncaipeted Floon Predicted Wipe Lead Loading Oig/ft*)
01 I 10 100 I.OOO 10.000 • IOO.OOO 1 mil IO mil 100 a
Milwaukee Uocnpeted Ploon Predicted Wipe Lead Loading Gig/ft")
Figure E-9. Model Residuals (Log Scale) versus Predicted Wipe Lead Loading from the Regression of Wipe Lead
Loading on BRM Vacuum Lead Loading for Uncaipeted Floors.
-------
I
IM IJW IMN
•71
•«
cn
Roan todielBd W|pt UM! LiMdhf OifW)
Figure E-10. Model Residual (Log Scale) and Predicted Wipe Lead Loading from the Regression of Wipe
Loading on BRM Vacuum Lead Loading for Carpeted Floors.
-------
1 to 100 1.000 10.000 100.000 1 mil 10 mil 100 •
RAM Mini Window Sills Predicted Wipe Lead Loading (jigW)
0.1 i 10 IOD 1.000 10.000 IOOJMO i«u a ma ion ma
Rochester Window Sflb Predicted Wipe Lead Looting On/ft")
Figure E-11. Model Residual (Log Scale) and Predicted Wipe Lead Loading from the Regression of Wipe Lead Loading
on BRM Vacuum Lead Loading for Window Sills.
-------
i;]
0
-I
-I
01 I 10 100 1.000 10.000 100400 I mil 10 «U 100 mil
RAM Mini Window WeDs Predicted Wq>e Lead Loafing (ng/ff)
•1
0.1 I 10 100 1.000 10.000 100.000 I nil lOnll lOOmll
Rocfaefter Window Wdb Predicted Wipe Lead Loading (ngffi")
Rgure E-12. Model Residual (Log Scale) and Predicted Wipe Lead Loading from the Regression of Wipe Lead Loading
on BRM Vacuum Lead Loading for Window Wells.
-------
APPENDIX F
Conversions from Wipe Lead Loading
to BN Lead Concentration
F-1
-------
APPENDIX F
Conversions from Wipe Lead Loading
to BN Lead Concentration
This appendix presents the development of a set of equations for converting a wipe lead
loading to a BN vacuum lead concentration using data from the CAP Pilot and R&M Pilot
studies. The development of these equations was motivated by the use of the IEUBK model to
predict post-intervention blood-lead levels from an assumed post-intervention dust-lead level that
will be stated as a wipe lead loading. Because lead concentrations are used as inputs to the
IEUBK model, an intermediate step is required to bridge the gap between a wipe lead loading
and a vacuum lead concentration. The conversion equations presented in this appendix were
previously used to convert the post-intervention dust-lead loading based on a wipe sample to a
comparable BN dust-lead concentration. This dust-lead concentration was then to be used as
input to the IEUBK model to predict a childhood blood-lead concentration. This approach was
initially used in the Section 403 risk analysis. It was later dropped in favor of a more direct
approach. It is included here to document all major work done on the Section 403 risk analysis.
Distribution of Data
Tables F-l through F-4 display the distribution of data by groupings of wipe lead loading
and BN vacuum lead concentration for the CAP Pilot and R&M Pilot studies. Tables F-l and
F-2 show that about half of the data from the CAP Pilot study have wipe lead loadings less than
50 ug/ft2. Tables F-3 and F-4 indicate that a large portion of the R&M Pilot study has vacuum
lead concentrations greater than 400 ug/g.
Abated versus Unabated
It is reasonable to suggest that children's blood-lead concentrations will differ depending
on whether or not they reside in a dwelling that has undergone some sort of lead intervention.
Therefore, it may be important to account for this in the wipe loading to BN concentration
F-2
-------
conversion equation, since the converted concentration could be used to predict post-intervention
blood-lead levels. Figure F-l displays all of the data used to develop the wipe loading to BN
concentration conversion equation (i.e., CAP Pilot and R&M Pilot) for each housing component.
Abated and unabated homes are plotted with different symbols. It can be seen that for each
housing component, both types of homes span the range of the data. This suggests that there is
no reason to separate abated homes from unabated homes to develop the wipe loading to BN
concentration conversion equation.
Statistical Approach and Results
A model analogous to that described in the report for converting a wipe lead loading to a
BN lead loading is useful for characterizing the relationship between wipe lead loading and BN
lead concentration. The model can be written as follows:
log(BN) = log(a)+P log(W)+log(E)
or equivalently as,
= aWpE,
where BN represents Blue Nozzle vacuum lead concentration, W represents wipe lead loading,
and E represents a random error term. Similar models were fit separately for each study and
housing component The parameter estimates were then combined across studies as described in
Section 3.1.5 of the report
Table F-5 presents the equations for predicting a Blue Nozzle lead concentration from a
wipe lead loading for the CAP Pilot and R&M Pilot studies. Equations are presented separately
for uncarpeted floors, window sills, and window wells. The results presented for the R&M Pilot
study in Table F-S include an adjustment for the chemical extraction procedure employed for the
HUD wipe samples. Figures F-2 and F-3 illustrate the modeled relationships between wipe lead
loading and Blue Nozzle vacuum lead concentration for each housing component in the studies
involved. Table F-6 presents the final conversion equations for uncarpeted floors, window sills
and window wells, as well as the number of samples included in the analysis. Table F-7 displays
F-3
-------
the predicted levels associated with nominal wipe lead loadings of 10,40,100,200,500, and
1000 ng/ft2 for uncarpeted floors, window sills, and window wells. For example, an uncarpeted
floor wipe loading of 200 ug/ft2 would be converted to a BN lead concentration of 799 ug/g.
The second line in each cell of Table F-7 represents an approximate 95% confidence
interval on the conversion. These represent confidence bounds on the estimate of the geometric
mean level, associated with the nominal levels from which they are converted. Thus, for an
uncarpeted floor wipe lead loading of 100 ug/ft2, the geometric mean BN lead concentration is
545 ug/g, and there is 95% confidence that the geometric mean of the BN lead concentrations
taken at the same location would be between 433 and 684 ug/g.
The third line in each cell provides an approximate 95% prediction interval for the
conversions. These are bounds that are expected to contain 95% of the individual observations
associated with the specified nominal levels of the prediction variables. Thus, for an uncarpeted
floor wipe lead loading of 100 fig/ft2, the geometric mean point estimate of the BN lead
concentration is 545 ug/g, and it is expected that 95% of BN concentration loadings measured at
the same location will be between 157 and 1,890 ug/g.
Figure F-4 displays the BN lead concentration versus wipe lead loading relationship for
uncarpeted floors. The first plot in the figure presents the data from the CAPS Pilot and R&M
Pilot studies plotted with different symbols. Included hi this graph are the regression lines from
the individual studies. Using this plot, a comparison can be made of the wipe loading to BN
concentration relationships across the two studies. The second graph in the figure displays the
data for each study, and the combined regression line and its approximate 95% confidence
bounds. Figures F-5 and F-6 display analogous information for window sills and window wells,
respectively.
Influential Observations and Residual Analysis
Figures F-7, F-8, and F-9 display the data for predicting a BN lead concentration from a
wipe loading from uncarpeted floors, window sills and window wells, respectively, indicating
those data values which were significantly influential in estimating the relationship between BN
lead concentration and wipe lead loading. (See Appendices C and D for a description of the
F-4
-------
statistical analysis used to identify influential data values.) The figures for uncarpeted floors and
window sills each indicate one observation as significantly influential, for both alpha and beta.
The influential observations have predicted values significantly distant from the other
observations in each data set Both of these influential points are from the CAP Pilot study.
Figures F-10, F-l 1, and F-12 present the corresponding residuals versus the predicted
BN lead concentrations obtained from the respective regression analyses, for uncarpeted floors,
window sills and window wells. No notable departures from the model assumptions were
demonstrated by the residual analysis.
An important assumption in the development of these conversion equations is that dust
levels in the houses used to develop the equations are similar to dust levels in the houses on
which the equations will be applied. The relationship between dust-lead loading and dust-lead
concentration is dictated by the amount of dust present. Before using the conversion equations
provided in this section, it would be necessary to check this assumption.
F-5
-------
Table F-1. Number of Samples by Wipe Lead Loading and Vacuum Lead Concentration,
CAP Pilot Study - Uncarpeted Floors.
Wipe Lead
Loading
(//g/ft»)
0-50
50-200
200 +
Total
Blue Nozzle Vacuum Lead Concentration (//g/g)
50-100
2
0
0
2
100-200
1
0
0
1
200-300
1
0
0
1
300-400
1
0
0
1
400 +
0
0
1
1
Total
5
0
1
6
Table F-2. Number of Samples by Wipe Lead Loading and Vacuum Lead Concentration,
CAP Pilot Study — Uncarpeted Floors and Window Sills.
Wipe Lead
Loading
Uig/ft»)
0-50
50-200
200 +
Total
Blue Nozzle Vacuum Lead Concentration (//g/g)
50-100
2
0
0
2
100-200
1
1
0
2
200-300
1
0
0
1
300-400
2
0
0
2
400 +
1
1
3
5
Total
7
2
3
12
Table F-3. Number of Samples by Wipe Lead Loading and Vacuum Lead Concentration,
R&M Pilot Study — Uncarpeted Floors.
Wipe Lead
Loading
(//g/ft1)
0-25
25-50
50-75
100-150
1 50-200
200-400
400 +
Total
Blue Nozzle Vacuum Lead Concentration (//g/g)
75-100
1
0
0
0
0
0
0
1
100-150
1
0
0
0
0
0
0
1
150-200
3
0
0
0
0
0
0
3
200-400
3
0
2
0
0
0
0
5
400 +
1
0
2
2
3
2
4
14
Total
9
0
4
2
3
2
4
24
F-6
-------
Table F-4. Number of Samples by Wipe Lead Loading and Vacuum Lead Concentration,
R&M Pilot Study — Uncarpeted Floors, Window Sills, and Window Wells.
Wipe Lead
Loading
fc/g/ft»)
0-25
25-50
50-75
100-150
150-200
200-400
400 +
Total
Blue Nozzle Vacuum Lead Concentration 0/g/g)
75-100
1
0
0
0
0
0
0
1
100-150
2
0
0
0
0
0
0
2
150-200
4
0
0
0
0
0
0
4
200-400
6
0
2
0
0
2
1
11
400 +
5
0
4
3
5
6
30
53
Total
18
0
6
3
5
8
31
71
Table F-5. Regression Equations for Predicting Blue Nozzle Vacuum Lead Concentration
From Wipe Lead Loading.
Surface
Floors
(Uncarpeted)
Window Sills
Window Wells
frttmated Regression Model for
Wipe Pb Loading1" to Blue Nozzle Vacuum Pb Concentration1 '
CAP Pilot
BN = 26.6
n = 6
Range W:
Range BN:
BN = 83.1
n = 6
Range W:
Range BN:
• yyO.U8
R2=0.781W
13.8-2498.5
82.2-1772.3
"W""2
R* =0.520
24.4-4216.9
176.8-3580.9
(d)
R&M Pilot
BN = 47.9"W055a
n = 24
Range W: 6.3-13969
Range BN: 91 - 9052
BN = ISS'W0-404
n = 23
Range W: 2.2-1578393
Range BN: 1 50 - 52547
BN = 32. l-W*590
n = 24
Range W: 5.5-1205554
Range BN: 235-366121
R2 =0.785
R2 =0.687
R2 =0.534
(a) Units are ig/ftx for wipe dust-lead loadings.
(b) Units are j/g/g for vacuum dust-lead concentrations.
(c) R2 represents the amount of variation explained by the log-linear regression model.
(d) Equation was not fined because data were not available or insufficient.
F-7
-------
Table F-6. Final Conversion Equations for Uncarpeted Floors, Window Sills and Window
Wells Based on Combined Data.
Wipe Loading to
BN Concentration Conversion
Uncarpeted Floors
Window Sills
Window Wells
Number of
Observed Pairs
30
29
24
Conversion Equation
BN = 43.0»W°W1
BN - 144.0'W0402
BN - 32.1»W°"°
Table F-7. Predicted Vacuum Lead Concentrations For Selected Wipe Lead Loadings
Based on Weighted Average of Regression Coefficients on Uncarpeted Floors,
Window Snis and Window Wells.
wipe n>
Loading
U*wft*i
10
40
100
200
500
1000
Uncarpeted Floors
Hue Nozzle Vacuum
Concentration (fig/g)
(95% Confidence Interval)
(95% Prediction Interval)
153
(108,218)
(42.8, 546)
329
(255, 423)
(94.2, 1150)
545
(433, 684)
(157, 1890)
799
(628, 1010)
(229, 2770)
1320
(992, 1760)
(376, 4650)
1940
(1380, 2730)
(544, 6900)
Window Safe
BfcM Nozzle Vacuum
Concentration v/o/g)
(95% Confidence Interval)
I9D7D PrwBCtfon inwffV4Vi
364
(207, 645)
(44.5, 3000)
636
(401, 1010)
(79.8 , 5090)
919
(610, 1390)
(117,7270)
1210
(826, 1790)
(155, 9560)
1760
(1200,2560)
(224, 13800)
2320
(1580, 3420)
(296. 18300)
Window Weto
Blue Nozzle Vacuum
Concentration v*g/g)
(95% Confidence Interval)
fABOC ItiMillntlnn kiftttMBMll
IVOTD piouMiuon ntervaii
125
(25.2, 618)
(3.03, 5140)
283
(75.9, 1050)
(7.68, 10400)
486
(156, 1510)
(14.0. 16800)
731
(265, 2010)
(21.9,24400)
1260
(527, 2990)
(39.1, 40200)
1890
(867.4110)
(60.2, 59300)
F-8
-------
WMI
9
Vacaum Lad Cone. (jif
! ! { i
£ _
1 .
1 •
n
i
0 °
M-
1* * * *b«Ud Homn o o o UiwtaUd Homo*
WMI
jj IMM*
3
!-
f-
?
§ -
§ „
1
. 00
o
O J. * +
rf* o
I * * + AbtUd HMD** o o o UutxUd Horn**
LI 1 II IM IJM ICLM* IMjM» IMI WMI M*MI O.I 1 W IM MM IMM IMlOM 1 Ml WMI IMl
UbMqMtd Floor Wtw Lad Lotdtaf On/ft") Window Sffl W|pe Lad LowHaf (ptfP)
jg MMM
•a
2 IM*°
{i I*M
*
S -
)
i
* .: .*
o
o o
* 0 +
*o
+ + + AbaUd Homm o O o Uiubattd Hamn
.1 1 10 IM 1.000 10.000 100,000 IMl 10 Ml IM
Window WeU Wine Lad iMdhu (utftf)
ad
Figure F-1. Blue Nozzle Vacuum Concentration versus Wipe Lead Loading Displaying the Distribution of Abated and
Unabated Homes Across the CAP Pilot and R&M Pilot Data Used to Develop the Conversion Equations for
Uncarpeted Floors, Window Sills, and Window Wells.
-------
100.000
I
3
0.1 I 10 IM 1.000 10,000 INMO I nil 10 mil 100 Ml
Uocupeted Floor Lead taading Gig/ft1), Wipe Samples
i
0.1 I 10 100 IjOOD 10*00 IWJOOO twM 10 Ml
Window Sffl Lead Loading (jjg/ft1), Wipe Stmplei
Figure F-2. Blue Nozzle Vacuum Lead Concentration versus Wipe Lead Loading for Uncarpeted
Floors and Window Sills from the CAP Pilot Study.
-------
a
CO
I M UD MO MM* MMO !•• 10 •• Wtmt
Uncaipeted Floor Lead Loading OuWX Wipe Sample*
I 10 MO UBO MM
Window Sill Lead Loading (jtgflP), Wipe Samples
I
0.1 I W MO IJOH
Window WeO Lead Loading &igWX Wipe Samples
Figure F-3. Blue Nozzle Lead Concentration versus Wipe Lead Loading for Uncarpeted Floors, Window Sills, and Window
Wells from the R&M Pilot Study.
-------
10 mil
I 100400
Oi
§ 10400
"3 1400
e too
..
0.1
001
+ + + CAPS Pilot Data
A A A Ridf pilot. Data
CAPS Pilot. Predicted
Rftlf Pilot. Predicted
041 0.1 1 10 100 1400 10400 100400 Indl Iflmfl 100 mil
Lead Loading (ug/«q. ft). Wipe Samples
eo
10 mil
I mil
100400
10400
I
"3 1400
e too
10
0.1
041
Combined Regression Line Lower Confidence Bound
- - Upper Confidence Bound + + + CAPS Pilot. Data
R»M Pilot
A A A
[Pilot. Data
041 0.1 1 10 100 1400 10400 100400 1 nO 10 mil 100 mil
Lead loading (ug/aq. ft). Wipe Sample*
Figure F-4. Predicted BN Lead Concentration Versus Wipe Lead Loading on Uncarpeted
Floors, Individual and Combined Regressions. Confidence Bands for
Combined Regressions and Data Overlaid.
M2
-------
1
10 mil
Imll
100400
10*00
•j ifloo
i
too
»
0.1
0*1
10 mO
ImU
100*00
10*00
•3 1*00
100
10
0.1
0.01
+ + + CAPS Pilot. Data
A A A RUI Pilot, Data
CAPS Pilot. Predicted
RftM Pilot, Predicted
0.1 1 10 100 1*00 10*00 100*00 ImB 10 mil 100 ml]
Lead Loading (ug/*q. R). Wipe Sample*
t^
- Cembinad Rayeuloo line
--- Upper Confidence Bound
A A A RUt Pilot. Data
Lover Confidence Bound
CAPS Pilot. Data
0*1 0.1 1 10 100 1*00 10*00 100*00 InU 10 mil 100 mil
, Laad Loadlaf (ug/aq. ft). Wipe Sample*
Figure F-5. Predicted BN Lead Concentration Versus Wipe Lead Loading on Window Sills,
Individual and Combined Regressions. Confidence Bands for Combined
• Regressions and Data Overlaid.
M3
-------
101
IOOOO
-j IjOOO
too
.
0.1
OOI
aoi ai i to too 1*00 touoao loojooo i
LMd Loadlnf (uf/*q. ft). Wipe Sample*
nn ioaui
g IOOUOOO
o!
10400
•5 1.000
too
to
I
0.1
OAI
041 ai I 10 100 1.000 10400 lOOyOOO I
Lnd Loedinc (u«/«q. ft). W|p« Skmpto
ma 10 BU 100 mffl
Figure F-6. Predicted BN Lead Concentration Versus Wipe Lead Loading on Window
Wells, Individual and Combined Regressions. Confidence Bands for Combined
Regressions and Data Overlaid.
M4
-------
T
en
1.000
• • • CAPS. D«U
• • • InfliunlUl OuUtor
10 100 1.000 10.000
CAPS Uflcupeted Floor Wipe Lett Loading (pgfff)
>^
I
• • • KM Pilot. 0*U
• • • Influential Outllar
10 100 1.000 10.000
RAM PUol Uncaipeled Floor Wipe Lead Loading (us/ft*)
Figure F-7. Influential Observations In the Regression of Blue Nozzle Lead Concentration on
Wipe Lead Loading for Uncarpeted Floors from the CAP Pilot and R&M Pilot Studies.
-------
^^
I
100
• • • CAM.IM*
• • • MltMBttal OuUltr
CAPS Window Sfflt Wipe Lead Loading (w/fP)
•*^
I
i .
' » InOmntial OiiUltr
RAM Wot Window Sflb W^e Lad Load* Oi|W)
F-8. Influential Observations in the Regression of Bhis Nozzle Vacuum Laad Concentration
on Wipe Laad Loading for Window SIHs from the CAP Pilot and R&M PHot Studies.
-------
1.000.000
e 100,000
m
i
*
I
10.000
1.000
100
* * * RM Pilot. Data
000 Influential Outlier
10 100 1.000 10.000 100.000
RM Pilot Window Wells Wipe Lead Loading (ug/ft2)
1.000,000
Figure F-9. Individual Observations in the Regression 1
Window Weds from the R&M Pilot Study.
Vacuum
Lead Loading for
-------
T
oo
01 I 10 100 1.000 IOMO IOOMO I mi 10 Ml 100 mil
CAPS UDCttpcted Floon Predicted BN Vacuum LMd Cone. (utf)
0.1 I 10 100 IjOOO lOlMO IOOMO I mil 10 mil 109 •
RAM PUot Uncapetod Moon Predicted BN Vacuum Lad Cone, (ng/g)
Figure MO. Residual (Log Scale) and Predicted Blue Nozzle Lead Concentration from the
Regression of Blue Nozzle Vacuum Lead Concentration on Wipe Lead Loading for
Uncarpeted Floors from the CAP Pilot and R&M Pilot Studies.
-------
0.1 I IB ICO 1.000 10.000 100.000 I Ml 10 loll 100 mil
CAPS Wta&w SOU Predicted BN Vacuum Lead Cone, (jitfg)
T
-------
«J
w
0)
PS
&
£
.1-1
o,
5-
4-
3-
-i
-8
-3
-4
-5
+ +
0.1
1 10 100 1,000 10,000 100,000 Imil 10 mil 100 mil
RM Pilot Window Wells Predicted BN Vacuum Lead Cone (ug/g)
Figure F-12. Residual (Log Scale) and Predicted Blue Nozzle Vacuum Lead Concentration from the Regression of Blue
Nozzle Vacuum Lead Concentration on Wipe Lead Loading for Window Wells from the R&M Pilot Study.
-------
50272-101
REPORT DOCUMENTATION
PAGE
1. REPORT NO.
EPA 747-R-96-012
3. Recipient's Accession No.
4. Title and Subtitle
Conversion Equations for Use in Section 403 Rulemaking
5. Report Date
December, 1997
6.
7. Author(s)
John Kinateder, Abi Katz-Stein, Shawna Collins
8. Performing Organization Rept. No.
9. Performing Organization Name and Address
Battelle Memorial Institute
505 King Avenue
Columbus, Ohio 43201-2693
10. Project/Task/Work Unit No.
G 003243-28
11. Contract(C) or Grant(G) No.
(C) 68-D5-0008
(G)
12. Sponsoring Organization Name and Address
U.S. Environmental Protection Agency
Office of Pollution Prevention and Toxics (7401)
401 M Street, S.W.
Washington. D.C. 20460
13. Type of Report & Period Covered
Final Report
14.
15. Supplementary Notes
Other Battelle staff involved in the production of this report included Ron Menton, Priti Kumar, Ying-Liang Chou, Jyothi
Nagaraja, and Melissa Smith. Dr. Ray Carroll of Texas A&M University was a consultant to Battelle.
16. Abstract (Limit 200 words)
This report presents equations used to carry out various conversions between wipe lead loadings and vacuum lead
loadings and vacuum concentrations, based on two different vacuum samplers, the Blue Nozzle (used in the HUD National
Survey) and the BRM (used in the Baltimore Repair and Maintenance study). These equations were developed for use in
the determination of health-based standards of environmental lead in residential settings as required by Section 403 of
Title IV TSCA. Various equations were derived to facilitate the development of a proposed set of options for the Section
403 standards, to enable a risk analysis of these options to be conducted, and to provide a means of predicting the post-
Section 403 blood-lead levels nationally.
17. Document Analysis
a. Descriptors
Lead, Lead in Dust, Vacuum Collection of Dust, Wipe Collection of Dust, Conversion Equations
b. Identifiers/Open-Ended Terms
Blue Nozzle (BN) Vacuum, BRM Vacuum, Measurement Error, Transportability Adjustment, Conversion
Equations, Regression
c. COSATI Field/Group
18. Availability Statement
Release Unlimited
1 9. Security Class (This Report)
Unclassified
20. Security Class (This Page)
Unclassified
21. No. of Pages
149
22. Price
(SeeANSI-239.18)
OPTIONAL FORM 272 (4-77)
(Formerly NTIS-35)
Department of Commerce
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