OCTOBER 3, 2007 

EPA 260-R-08-003 

FINAL REPORT FOR THE PILOT STUDY OF 

TARGETING ELEVATED BLOOD-LEAD LEVELS IN 

CHILDREN 

U.S. Environmental Protection Agency 

1200 Pennsylvania Avenue NW (7404T) 

Washington D.C. 20460 
Disclaimer 

The U.S. Environmental Protection Agency through its Office of Environmental 

Information funded and managed and collaborated with the Office of Pollution 

Prevention and Toxics in the research described herein under EPA Contract Number EPW-04-021 to Battelle. It has been subject to an administrative review but does not 

necessarily reflect the views of the Agency. No official endorsement should be inferred. 

EPA does not endorse the purchase or sale of any commercial products or services. 

Acknowledgements 

The EPA acknowledges the organizations whose contributions made this report possible 

including the Lead Poisoning Prevention Branch at the Centers for Disease Control and 

Prevention, the Childhood Lead Poisoning Prevention Program at the Massachusetts 

Department of Public Health, and the Office of Healthy Homes and Lead Hazard Control 

at the U. S. Department of Housing and Urban Development. 
 

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TABLE OF CONTENTS

Page

EXECUTIVE SUMMARY .............................................................................................................................. v 

1.0 INTRODUCTION.............................................................................................................................. 1 

1.1 Background and Purpose of Study ..................................................................................... 1 

1.2 Study Objectives ................................................................................................................. 2 

 1.2.1 Objective 1 – Combine and Manage Multiple Data Sources ................................. 2 

 1.2.2 Objective 2 – Conduct Analyses to Identify Predictive Variables and 

 Model Children’s Blood-Lead Levels ..................................................................... 2 

 1.2.3 Objective 3 – Develop Visualization Tool to Graphically Model Predicted 

 Blood-Lead Levels ................................................................................................. 2 

2.0 STUDY METHODOLOGY................................................................................................................ 3 

2.1 General Approach............................................................................................................... 3 

2.2 Data Management............................................................................................................... 3 

2.3 Descriptive Data Analyses .................................................................................................. 4 

2.4 Development of Multivariate Statistical Models ................................................................ 10 

 2.4.1 Statistical Models for the Broad Coverage – Low-Resolution Model................... 10 

 2.4.2 Statistical Models for the High-Resolution Model within Massachusetts............. 12 

3.0 DATA SOURCES AND DATABASE DEVELOPMENT ................................................................. 14 

3.1 Children’s Blood-Lead Measurements.............................................................................. 14 

3.2 Demographic Data ............................................................................................................ 16 

3.3 Environmental Data........................................................................................................... 21 

 3.3.1 Concentrations of Lead in Air............................................................................... 22 

 3.3.2 Toxics Release Inventory Data............................................................................ 23 

 3.3.3 Water Quality Data............................................................................................... 24 

3.4 Programmatic Data ........................................................................................................... 24 

 3.4.1 Programmatic Funding Variables......................................................................... 25 

 3.4.2 EPA Region.......................................................................................................... 25 

 3.4.3 Housing Inspection Data (Massachusetts) .......................................................... 25 

3.5 Data Linkages ................................................................................................................... 27 

4.0 EXPLORATORY DATA ANALYSES ............................................................................................. 29 

4.1 Relationship between National Blood-Lead Data and Explanatory Variables.................. 29 

4.2 Relationship between Local Blood-Lead Data and Explanatory Variables....................... 43 

5.0 STATISTICAL MODELING RESULTS .......................................................................................... 47 

5.1 Low-Resolution Modeling Results..................................................................................... 47 

5.2 High-Resolution Modeling Results.................................................................................... 59 

6.0 GRAPHICAL PRESENTATION OF MODELING RESULTS ......................................................... 70 

6.1 Maps of Observed and Predicted Blood-Lead Outcomes ................................................ 70 

6.2 Visualization Tool Development........................................................................................ 70 

7.0 DISCUSSION AND FUTURE WORK ............................................................................................ 77 

7.1 Major Findings................................................................................................................... 77 

7.2 Comparison of National Results and NHANES ................................................................ 78 

7.3 Data Issues ....................................................................................................................... 80 

 7.3.1 Biases from Geocoding........................................................................................ 80 

 7.3.2 Reporting Limits in Surveillance Data.................................................................. 80 

 7.3.3 Selection Bias in Surveillance Data ..................................................................... 81 

 7.3.4 Limitations of Ecological Models for Predicting Within-Area Relationships......... 81 
 

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Page

 7.3.5 Use of 2000 Census Data and Other Time Invariant Data as Predictors............ 82 

7.4 Model Validation Issues .................................................................................................... 82 

7.5 Other Recommendations for Immediate Future Work...................................................... 84 

8.0 REFERENCES ............................................................................................................................. 87 

Appendix A Exploratory Analysis Summary Pages.............................................................................A-1 

Appendix B Massachusetts Data: Exploratory Analysis Summary Pages.........................................B-1 

Appendix C Detailed Exploratory Analyses of 95th and 99th Percentile Variables 

 In National Models .......................................................................................................... C-1 

Appendix D Detailed Discussion of National Exploratory Analyses ................................................... D-1 

Appendix E Detailed Discussion of Massachusetts Exploratory Analyses .........................................E-1 

Appendix F U.S. Counties and Massachusetts Census Tracts with Highest Predicted BLLs ............F-1 

Appendix G Detailed Maps of National and State Model Outputs...................................................... G-1 

Appendix H Data Dictionaries for National and Massachusetts Databases....................................... H-1 

LIST OF TABLES 

Table 3-1 Initial Variables for Analysis Created From the 2000 Census .......................................... 17 

Table 4-1 Summary of Exploratory Analysis Fit as shown by -2 Log Likelihoods for Pr(PbB ≥ 5 

μg/dL) Models, National Data ........................................................................................... 31 

Table 4-2 Summary of Exploratory Analysis Fit as shown by -2 Log Likelihoods for Pr(PbB ≥ 10 

μg/dL) Models, National Data ........................................................................................... 34 

Table 4-3 Summary of Exploratory Analysis Fit as shown by -2 Log Likelihoods for Pr(PbB ≥ 15 

μg/dL) Models, National Data ........................................................................................... 37 

Table 4-4 Summary of Exploratory Analysis Fit as shown by -2 Log Likelihoods for Pr(PbB ≥ 25 

μg/dL) Models, National Data ........................................................................................... 40 

Table 4-5 Summary of Log-likelihood Ratios from each Model Fit to all Potential Explanatory 

Variables, Massachusetts Data ........................................................................................ 44 

Table 5-1 Summary of Variables Included in Final National Multivariate Model............................... 50 

Table 5-2 Model 1 (Proportion ≥5 μg/dL) Parameter Estimates for Multivariate National Model ..... 51 

Table 5-3 Model 2 (Proportion ≥10 μg/dL) Parameter Estimates for Multivariate National 

 Model ............................................................................................................................. 53 

Table 5-4 Model 3 (Proportion ≥15 μg/dL) Parameter Estimates for Multivariate 

 National Model .................................................................................................................. 55 

Table 5-5 Model 4 (Proportion ≥25 μg/dL) Parameter Estimates for Multivariate 

 National Model .................................................................................................................. 57 

Table 5-6 Summary of Variables Included in Final Massachusetts Multivariate Model.................... 61 

Table 5-7 Massachusetts Multivariate Model Estimates................................................................... 62 
 

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LIST OF FIGURES 

Figure 5-1 Histograms of Residuals from Fitted National Multivariate Model 1................................. 52 

Figure 5-2a Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with BLL ≥ 5 μg/dL. 52

Figure 5-2b Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 5 μg/dL (Logit Scale). ............................................................................................. 52 

Figure 5-3 Histograms of Residuals from Fitted National Multivariate Model 2................................. 53 

Figure 5-4a Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 10 μg/dL.................................................................................................................. 53 

Figure 5-4b Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 10 μg/dL (Logit Scale). ........................................................................................... 53 

Figure 5-5 Histograms of Residuals from Fitted National Multivariate Model 3................................. 56 

Figure 5-6a Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 15 μg/dL.................................................................................................................. 56 

Figure 5-6b Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 15 μg/dL (Logit Scale). ........................................................................................... 56 

Figure 5-7 Histograms of Residuals from Fitted National Multivariate Model 4................................. 58 

Figure 5-8a Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 25 μg/dL.................................................................................................................. 58 

Figure 5-8b Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 25 μg/dL (Logit Scale). ........................................................................................... 58 

Figure 5-9 Histograms of Residuals from Fitted Massachusetts Multivariate Model 1 ...................... 65 

Figure 5-10 Plots for Predicted versus Observed Values with 45° line from Fitted Massachusetts 

Multivariate Model 1.......................................................................................................... 65 

Figure 5-11 Histograms of Residuals from Fitted Massachusetts Multivariate Model 2 ...................... 66 

Figure 5-12 Plots for Predicted versus Observed Values with 45° line from Fitted Massachusetts 

Multivariate Model 2.......................................................................................................... 66 

Figure 5-13 Histograms of Residuals from Fitted Massachusetts Multivariate Model 3 ...................... 67 

Figure 5-14a Plot of Massachusetts Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 5 μg/dL.................................................................................................................... 67 

Figure 5-14b Plot of Massachusetts Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 5 μg/dL (Logit Scale) .............................................................................................. 67 

Figure 5-15 Histograms of Residuals from Fitted Massachusetts Multivariate Model 4 ...................... 68 

Figure 5-16a Plot of Massachusetts Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 10 μg/dL.................................................................................................................. 68 

Figure 5-16b Plot of Massachusetts Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 10 μg/dL (Logit Scale) ............................................................................................ 68 

Figure 5-17 Histograms of Residuals from Fitted Massachusetts Multivariate Model 5 ...................... 69 

Figure 5-18a Plot of Massachusetts Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 15 μg/dL.................................................................................................................. 69 
 

iv

Figure 5-18b Plot of Massachusetts Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children with 

 BLL ≥ 15 μg/dL (Logit Scale) ............................................................................................ 69 

Figure 6-1 Observed and Predicted Proportion of Children with Blood-Lead Levels ≥ 10 μg/dL in the 

U.S. by County, 2000 and 2005........................................................................................ 71 

Figure 6-2 Observed and Predicted Proportion of Children with Blood-Lead Levels ≥ 10 μg/dL 

 in Region V by County, 2000 and 2005 ............................................................................ 72 

Figure 6-3 Observed and Predicted Proportion of Children with Blood-Lead Levels ≥ 10 μg/dL 

 in Massachusetts by Census Tract, 2000 and 2005......................................................... 73 

Figure 6-4 Response Surface of Predicted Geometric Mean Blood-Lead Concentration Across 

 the State of Illinois from the Visualization Tool ................................................................. 75 

Figure 6-5 Time Series Plot of Observed and Predicted Geometric Mean Blood-Lead 

 Concentration in Cook County Illinois from the Visualization Tool ................................... 76 

Figure 7-1 Comparison of National Surveillance Data to NHANES Data .......................................... 79 
 

v

EXECUTIVE SUMMARY 

This pilot study seeks to develop statistical models to predict risk of childhood lead poisoning 

within specified geographic areas based on a combination of demographic, environmental, and 

programmatic information sources. Exposure factors associated with childhood lead poisoning 

were investigated within census tracts for a community-focused set of models in Massachusetts, 

as well as within counties across the United States in a series of national models. Aggregated 

summary measures of the proportion of children screened at or above 5, 10, 15 and 25 μg/dL 

within defined geographic areas (census tracts and counties) were used as the response variable 

in the statistical models. These summary measures were constructed at 3-month (quarterly) 

intervals from 1995 through 2005, in counties across the nation using data from CDC’s National 

Surveillance Database, and from 2000-2006 in census tracts within the Commonwealth of 

Massachusetts based on data provided by the Massachusetts Department of Public Health. 

The results of this study suggest that longitudinal predictive models can be developed at the 

county level across the nation, based on the use of quarterly summary information from CDC’s 

National Surveillance Database, and at the census-tract level within states that have a long 

history of universal screening and reporting, such as Massachusetts. These models can be used 

to describe how risk of childhood lead poisoning changes over time within different regions of 

the country, as well as within small geographic areas within states (e.g., counties) and even 

smaller geographic areas within counties (e.g., census tracts). They can be used to predict the 

risk of childhood lead poisoning in counties (or census tracts) with little or no surveillance data, 

and also can be used to identify those counties (or census tracts) that are at highest risk at the end 

of the period of observation. 

The statistical model chosen (a random effects model with separate intercepts and slopes 

estimated within each county or census tract) also allows ranking of geographic areas based on 

the rate of decline over time after accounting for the fixed-effects variables of the model 

(although only among those areas that provided adequate surveillance data). These randomeffects models were fit to the exceedance proportions within the context of a logistic regression 

model. Within the context of the Broad-Based National Model, these random effects allow EPA 

to identify those counties that are experiencing a more rapid reduction in risk of childhood lead 

poisoning over time (to identify best practices) and those counties that are experiencing a 

significantly less rapid decline over time (to identify areas in need of additional attention and 

resources for combating lead poisoning), after already accounting for the demographic, 

programmatic, and environmental factors included in the multivariate model. 

Within the series of national models at the county level of geographic specificity, the data 

suggest that there are significant differences in the distribution of childhood blood-lead 

concentrations among the different regions of the country, and that the manner in which these 

distributions change over time and are impacted by seasonality also is regionally specific. The 

risk of childhood lead poisoning had a statistically significant downward trend over time in all 

areas of the country. 

After accounting for these regional differences, a number of demographic, environmental, and 

programmatic variables were found to be highly predictive of childhood blood-lead 
 

vi

concentrations among the different response variables modeled within this project. The specific 

variables that were found to be predictive within the multivariate models varied based on the 

response variable; however, there were certainly some variables that were found to be predictive 

in multiple models. In addition to various census demographic variables that were identified in 

previous risk modeling efforts (e.g., age of housing, percent single parent families, 

race/ethnicity), air modeling data, variables constructed from EPA’s Safe Drinking Water 

Information System, and programmatic funding information from HUD and CDC were found to 

be highly predictive in the multivariate models. 

Within the context of the high-resolution model developed using data from the Commonwealth 

of Massachusetts, a highly significant downward trend in the risk of childhood lead poisoning 

also was identified among the five models developed. Due to a very small number of children 

observed at or above 25 μg/dL within Massachusetts over the 2000-2006 period of observation, 

we were unable to fit this sixth model. After accounting for the long-term reduction over time 

and seasonality using similar methods that were employed in the Broad-Based National Model, 

only the demographic and programmatic variables were included in the multivariate models for 

risk of childhood lead poisoning at the census-tract level. Of particular interest were the 

variables that described the proportion of housing units within each census tract that were found 

to be in compliance and out of compliance with the Massachusetts Standard of Care. In all five 

of the multivariate models, the risk of childhood lead poisoning was significantly reduced as the 

proportion of housing units in compliance increased within a census tract. In addition, for the 

last two models (which predicted proportion of children at or above 10 and 15 μg/dL), the risk of 

childhood lead poisoning increased significantly as the proportion of housing units out of 

compliance increased within a census tract. 

The observed and predicted values from the multivariate models (including predicted values 

where there were no observed surveillance data) were used to generate static maps using ArcView software, and were loaded into a customized dynamic visualization tool that allows users 

to interact with the modeling results to assess how risk of childhood lead poisoning changes over 

time within specific regions of the country. This tool will help EPA and others identify areas 

that remain at risk for childhood lead poisoning as we approach the 2010 goal of elimination of 

this preventable adverse health outcome. 
 

1 

1.0 INTRODUCTION 

1.1 Background and Purpose of Study

Over the past 15 years, various childhood lead poisoning prevention programs (CLPPPs) 

throughout the United States have conducted analyses of their screening data to develop “risk 

indices,” or mathematical models for predicting the prevalence of childhood lead poisoning in 

different geographic areas within their regions of concern. These modeling efforts generally are 

intended to characterize the extent of the prevalence of childhood lead poisoning within their 

geographic areas and to support the development of targeted screening and outreach plans in 

order to reach the 2010 goal of eliminating childhood lead poisoning throughout the United 

States. 

To date, the majority of modeling efforts have focused on combining blood-lead testing 

information and demographic data available from the U.S. Census. Previous studies have 

combined childhood surveillance data (aggregated at the zip-code or census-tract level) with 

demographic predictor variables from the Census Bureau for the purposes of targeting 

geographic areas at higher risk of childhood lead poisoning (Miranda, Dolinoy, and Overstreet 

2002; Miranda et al. 2005; Strauss et al. 2001a). These studies have led to recommendations for 

using age of housing and percent of population below the poverty line for targeting 

neighborhoods that may be of increased risk for childhood lead poisoning (CDC 1997). 

Numerous studies also have been used to document the relationship between children’s bloodlead concentrations and measures of lead in residential environmental media (dust, soil, air, 

water, and food) (HUD 1995; Lanphear et al. 1998; Strauss et al. 2001b). These studies have 

contributed to EPA and HUD regulations and policies for identifying and reducing residential 

childhood lead exposures (24 CFR Part 35; 40 CFR Part 745; 40 CFR Part 745; U.S. Department 

of Housing and Urban Development September 15, 1999). Other studies have combined bloodlead surveillance data with programmatic information on housing units treated to determine the 

positive impact of housing-based intervention programs (Strauss et al. 2006). 

The goal of this study is to explore models based on a hierarchical combination of demographic, 

environmental, and programmatic information sources in order to predict the number of children 

at risk of elevated blood-lead levels for a given geographic area. While the models are highly 

dependent on available data, this study provides a statistical methodology that combines each 

data source in an appropriate manner, adjusting for global and local trends over time. In doing 

so, the models build upon concepts of hierarchical modeling and longitudinal data analysis. 

As EPA, CDC, and other federal and state agencies prepare to meet the 2010 goal of eliminating 

childhood lead poisoning, this pilot study of integrating several different types of data sources 

hopefully improves the predictive power of models that rely on a single information source. This 

allows for more efficient targeting of those geographic areas that need the most help in 

eliminating childhood lead poisoning. 
 

2 

1.2 Study Objectives

1.2.1 Objective 1 – Combine and Manage Multiple Data Sources 

The first objective of the study was to combine multiple sources of information in order to assess 

the impacts of various factors on children’s blood-lead levels. The study had to obtain and 

manage data relating to blood-lead levels, environmental exposure, demographic characteristics, 

and programmatic support to state and local childhood lead-poisoning prevention efforts. 

Missing, incomplete, or error-prone data were identified for each data source and steps were 

taken to resolve data problems. Databases were developed to store and later combine each data 

source in a manner that supported the development of predictive models. Master databases that 

integrated multiple data sources were developed to enable efficient access to data required for 

statistical analyses. A data dictionary was prepared to document the various study databases. 

1.2.2 Objective 2 – Conduct Analyses to Identify Predictive Variables and Model 

Children’s Blood-Lead Levels 

The second study objective was to conduct statistical analyses in order to develop models that 

are predictive of risk of childhood lead poisoning within defined geographic areas as a function 

of various different environmental, programmatic, and demographic factors. As part of this 

objective, a National model was developed for predicting risk at the county level based on 

surveillance data from the U.S. Centers for Disease Control and Prevention (CDC), and a local 

model was developed at the census-tract level using blood-lead surveillance data from within the 

Commonwealth of Massachusetts. As part of the model building process at both the national and 

local levels, the various data sources underwent exploratory analyses to investigate data 

distributions, identify relationships between variables, and determine appropriate variables to 

include in subsequent statistical models. Part of the exploratory analyses included an effort to 

identify which environmental, programmatic, and demographic factors were most predictive of 

risk of childhood lead poisoning. Multivariate statistical models then were developed using 

appropriate statistical software to combine the various data sources within a single model that 

accounted for trends in risk of childhood lead poisoning over time within defined geographic 

areas. Model diagnostics were reviewed, and models with the best fit were identified. 

1.2.3 Objective 3 – Develop Visualization Tool to Graphically Model Predicted BloodLead Levels 

The third study objective was to develop an appropriate visualization tool that allows users to 

interact with the results of the statistical model predicting children’s blood-lead levels across the 

United States. This tool provides the user with the flexibility to visually compare the predicted 

blood-lead levels across areas of the country and also to drill down into individual counties or 

census tracts to assess the input data that generated the predicted value. 
 

3 

2.0 STUDY METHODOLOGY 

2.1 General Approach

This pilot study sought to develop models to predict the number of children at risk of elevated 

blood-lead levels for a given geographic area based on a hierarchical combination of 

demographic, environmental, and programmatic information sources. Doing so required looking 

at both the mechanisms of childhood lead risk assessment and control activities at the local level 

as well as at broad trends across the United States. The two main analysis goals correspond to 

developing predictive models at two different levels of geographic specificity, and appear as 

follows: 

1. Broad Coverage (Low-Resolution) Model: This type of model is intended to be able 

to characterize broad trends over time in the prevalence of childhood lead poisoning 

at the county level across the entire United States. This model was based on quarterly 

county-level aggregated surveillance data from the CDC and augmented with 

environmental data from a variety of sources, demographic data from the U.S. 

Census, and programmatic (level of federal funding) information. 

2. High-Resolution Model: This type of model represents the effort to assess the 

relative contribution of various exposure sources associated with elevated blood-lead 

concentrations within select communities. This type of model certainly reflects the 

idea that exposures that contribute to childhood lead poisoning are likely to be 

community specific. This analysis goal was met through modeling census-tract level 

surveillance data within Massachusetts as well as housing unit lead assessment and/or 

control activities. These data sources were augmented with all of the environmental, 

demographic, and programmatic information used in the national model with the 

addition of state programmatic funding levels. 

The primary objective of this pilot study was to utilize combined information from different 

sources at various levels of geographic and temporal specificity to more accurately target 

geographic areas at high risk for not meeting the 2010 goal of eliminating childhood 

lead-poisoning. As such, the study required careful integration of a variety of data sources with 

various characteristics and documentation. Data to support this study were gathered from 

multiple sources, including federal, state and local lead poisoning prevention programs, as well 

as publicly available data that were downloaded from the internet (e.g., census data, EPA’s 

Toxics Release Inventory). 

2.2 Data Management

When each data source was received, the data and supporting documentation were reviewed to 

gain knowledge on the structure, relationship, and quality of the data. Database managers 

worked with the project team to determine the final format for each database, the desired uses of 

the databases; as well as the requirements for maintaining the databases. Based on this 

information, master databases were constructed in SQL server for both the national lowresolution model and for the high-resolution model based on Massachusetts data that integrated 

the various environmental, demographic, and programmatic variables, and facilitated statistical 
 

4 

analyses of the combined data. These datasets were translated directly to SAS datasets for 

statistical analysis, and also were transferred to Microsoft Access for delivery to EPA. The 

Microsoft Access database includes a compact version of each database utilized in the statistical 

analysis, with any extraneous variables removed. In addition, the Microsoft Access database 

includes a copy of the integrated longitudinal dataset used to support the final multivariate 

models developed within this project. 

Throughout the development process, checks for completeness were conducted on all study 

databases, and the project team worked with data-sharing collaborators and EPA to attempt to 

complete missing data as necessary to complete the proposed statistical analyses. Any changes 

to the databases (corrections, additions, deletions, etc.) were documented in appropriate metadata files, and reported to EPA within the data dictionary attached to this report as Appendix H. 

As part of constructing and maintaining these databases, the project team will develop 

appropriate documentation of the combined master databases. 

Standard Operating Procedures (SOPs) were followed to ensure the proper storage, backup, and 

retrieval of datasets created and analyzed for this study. Additional details of these SOPs can be 

found in the Quality Management Plan prepared for this project (Battelle 2007). 

2.3 Descriptive Data Analyses

The analysis began with an assessment of the study sample, i.e., the proportion of counties and 

census tracts in the sample with complete data for both the response variable and the explanatory 

variables. Prior to the fitting of any descriptive statistics to assess the predictive ability of any of 

the explanatory variables, the blood-lead response variables needed to be constructed based on 

the CDC and Massachusetts blood-lead surveillance data. These data sources contain 

information on individual blood-lead testing results on children, and were aggregated into 

quarterly summary statistics (number of children observed, arithmetic and/or geometric mean1

, 

and number of children observed at or above 5, 10, 15, and 25 μg/dL) at the county level (for the 

CDC data) and the census-tract level (for the Massachusetts data). An executable was developed 

to extract these quarterly summary statistics from each county from CDC’s SQL server database 

for children aged 6-36 months, and a similar executable was deployed to create parallel summary 

statistics at the census-tract level for the Massachusetts surveillance data. Because of 

confidentiality restrictions, county/quarter (or census tract/quarter) combinations with fewer than 

5 observations were automatically eliminated from the dataset. Data reported prior to 1995 also 

were eliminated from the analysis database prior to statistical analysis. 

Once the aggregated summary datasets were constructed, they were reviewed for possible 

problems associated with childhood lead poisoning prevention programs not following universal 

reporting protocols (for some localities, data were only transmitted to the CDC National 

Surveillance Database for children with elevated blood-lead concentrations over certain periods 

of time). A screening algorithm was developed to remove these suspect data from the analysis 

dataset – resulting in the elimination of less than 3 percent of the aggregate summary records 

from the National database. The screening algorithm also was applied to the Massachusetts data 

– however no records were eliminated, as Massachusetts was following universal screening and 

 

1

 The CDC reported only the arithmetic mean, while Massachusetts reported both arithmetic and geometric means. 
 

5 

reporting guidelines over the 2000-2006 time period for which they provided data. Additional 

detail on the manner in which the blood-lead response variables were constructed can be found 

in Section 3.1. 

In preparation for developing longitudinal statistical models, univariate summaries of each 

variable as a function of time were generated and comparisons were made of these distributions 

using side-by-side box-plots for continuous data or bar-charts for categorical data. This helped 

verify that the data were clean and ready for analysis and identified cells with sparse data. Such 

descriptive analyses were conducted on each database, to characterize the distributions of all 

observed variables using frequency distributions for categorical variables, and simple summary 

statistics (mean, median, mode, minimum, maximum, and select percentiles) for continuous 

variables. Distributional assumptions also were explored for certain variables, as appropriate, in 

preparation for more sophisticated models. For example, some environmental concentration data 

may depart from normality, and follow a log-normal distribution. In these cases, we additionally 

reported the geometric mean and geometric standard deviation as part of the simple descriptive 

summary. 

The univariate descriptions then were followed by fitting a series of cross-sectional bivariate 

relationships between the blood-lead response variable(s) and each candidate explanatory 

variable. These cross-sectional relationships were explored as a function of time to better 

understand the stability of these relationships, and whether they change over time, so that they 

can be modeled appropriately in the more sophisticated longitudinal analyses. These analyses 

also will help identify which explanatory variables are most predictive of the blood-lead 

response variable. 

In preparation for more sophisticated statistical analyses, such as the Generalized Linear Mixed 

Logistical Regression Model outlined below, relevant stratified analyses were performed to 

investigate interactions discussed in the data analysis plan. For example, the population density 

variable was investigated in this manner, as density may serve as a surrogate to differentiate 

between rural and urban geographic areas in the analyses – and exposure variables may be 

different in these types of areas. Similarly, EPA regions were investigated as a potential 

stratification variable. If variation in the measure of effect is not observed (e.g., odds ratios) 

across the levels of a third variable; however, the third variable can likely be treated as a 

potential confounder in the multivariate model, rather than as an effect modifier. If the odds 

ratios differ markedly—e.g., the effect appears to be protective in one subgroup and hazardous in 

another subgroup—the third variable must be considered as an effect modifier. 

Specific variables within each type were explored using four general approaches – (1) 

histograms or side-by-side box-plots of the candidate explanatory variable, (2) simple regression 

line plots exploring the relationship between predicted risk of lead poisoning and the explanatory 

variable for each of the four specified time periods, (3) distributional summaries of the 

explanatory variable across the three time periods, and (4) statistical modeling of the relationship 

between the explanatory variable and various blood-lead response variables after adjusting for 

the effects of time and seasonality within different regions of the country for the National (LowResolution) model and for the effects of time in the Massachusetts (High-Resolution) Model. 
 

6 

Histograms or Side-by-Side Box-Plots of Potential Explanatory Variables 

Using one record for each quarterly county- or census-tract -level data point, a histogram 

illustrating the distribution of the explanatory variable is presented. A fitted line assists with 

assessing the distribution of each potential explanatory variable (e.g., whether the data are 

approximately normally distributed). Histograms were plotted for potential predictor variables 

that were time invariant. For predictor variables that varied over time within the analysis dataset, 

side-by-side box-plots were used to characterize the distribution over the time periods, using an 

average of the predictor variable across the quarters in which blood-lead concentrations were 

observed within each time-period and area. 

Logit Probability Plots for each Explanatory Variable 

The county-level quarterly proportion of screened children exceeding 10 μg/dL reported by the 

CDC were modeled as a function of each candidate explanatory variable, with separate logit 

curves used to represent each of the time periods. This analysis allows comparison of the 

relationship between the explanatory variable and predicted blood-lead level trends across time 

periods. If the relationship is stable across time, roughly parallel curves are evident. If the effect 

of the variable on blood-lead varies over time, non-parallel (and perhaps intersecting) curves are 

observed. In this case, the longitudinal analyses may need to be adjusted to allow for the effect 

of the covariate to change over time. 

Plots of Predicted GM Blood-Lead Levels and Explanatory Variables 

The census-tract-level quarterly blood-lead data available from Massachusetts were fit to each 

explanatory variable to generate predicted GM blood-lead levels across the range of the 

explanatory variable for each of the time periods. A simple linear regression line plot 

summarizes this analysis with one line for each time period. This analysis allows comparison of 

the relationship between the explanatory variable and predicted blood-lead level trends across 

time periods. If the relationship is stable across time, roughly parallel lines are evident. If the 

effect of the variable on blood lead varies over time, non-parallel (and perhaps intersecting) lines 

are observed. In this case, separate slopes may need to be fit for these variables over different 

periods of time in the more sophisticated longitudinal analyses. 

Distributional Summaries 

The first table presented for each explanatory variable contains a series of summary statistics for 

each of the time periods including sample size, number missing, mean, and standard error. The 

sample size is relative to the number of quarters represented in the analysis dataset; therefore, 

these distributions correspond to the analysis dataset (and not necessarily to the distribution of 

the variable across the nation or state). The distribution of the data for each time period also is 

presented (minimum, median, and maximum and 10th, 25th, 75th, and 90th percentiles). 

Comparing the summary data across time allows assessment of changes in the explanatory 

variable over time for the groups of tracts included in the analysis for each time period. 

Generally, the mix of counties and Massachusetts census tracts included in each of the time 

periods is similar, so that the distribution of the data from each period also is similar. 
 

7 

Statistical Modeling of Relationship between Explanatory Variables and Exceedance of 

Blood-Lead Thresholds for the National (Low-Resolution) Model: 

For each candidate predictor variable being considered for the National (Low-Resolution) 

Model, the following generalized linear mixed models approach was used to model the 

proportion of children exceeding certain thresholds as a function of the predictor variable after 

adjusting for Region-specific intercepts, slopes over time and effects of seasonality: 

ij ij ik k k ij k ij ij i i ij it E Y n = gion ⋅ + ⋅ t + ⋅ Season + X + + ⋅ t 0 1 2 3⋅ 0 1 log ( [ / ]) Re (β β β ) β δ δ v

Where (i indexes county, j indexes time, and k indexes the region of the country), Yij

represents the number of children observed above the blood-lead threshold in the ith

county at time j, nij represents the number of children tested in the ith county at time j, 

tij and Seasonij are fixed effects variables corresponding to a time-trend (in years) and 

seasonality, Xij is the candidate predictor variable being investigated, the beta 

parameters (β) represent a vector of fixed effects, and the delta parameters (δ) 

represent random effects that allow each county to have its own trend over time. The 

Xij predictor variable is mean centered in this series of models, allowing the intercept 

term to be relatively stable across the multiple predictor variables being investigated. 

In this model, it can be assumed that δ0i and δ1i jointly follow a multivariate normal 

distribution with mean zero and covariance matrix 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

Σ = 2

11

2

10

2

01

2

00

σ σ

σ σ . 

 Model 1 follows the above approach – where Yij represents the number of children 

observed with blood-lead concentrations at or above 5 μg/dL, and nij represents the 

total number of children screened within each record (county/quarter). 

 Model 2 follows the above approach – where Yij represents the number of children 

observed with blood-lead concentrations at or above 10 μg/dL, and nij represents the 

total number of children screened within each record (county/quarter). 

 Model 3 follows the above approach – where Yij represents the number of children 

observed with blood-lead concentrations at or above 15 μg/dL, and nij represents the 

total number of children screened within each record (county/quarter). 

 Model 4 follows the above approach – where Yij represents the number of children 

observed with blood-lead concentrations at or above 25 μg/dL, and nij represents the 

total number of children screened within each record (county/quarter). 

In addition to the above models, the project team explored whether the effect of each candidate 

predictor variable on the exceedence proportions varied over time. This was done by exploring 

the interaction between each candidate predictor variable and (1) a linear effect of time, (2) a 

quadratic effect of time, and (3) a 4-level categorical effect of time. 
 

8 

Statistical Modeling of Relationship between Explanatory Variables and Exceedance of 

Blood-Lead Thresholds for the Regional (High-Resolution) Model: 

The Regional (High-Resolution) Models developed for the Massachusetts data at the census-tract 

level of geographic specificity included models for both continuous data (geometric mean) and 

binomial data (exceedence proportions). Therefore, each explanatory variable being considered 

for these models were explored using models for both continuous and binomial data as described 

below: 

Continuous Data: The following mixed models analysis of variance (i.e., a random-effects 

model for continuous data) was used to model the geometric mean (GM) blood-lead 

concentration as a function of a candidate predictor variable: 

Where (i indexes census tract, j indexes time), GMij represents the geometric mean 

blood-lead concentration in the ith census tract at time j, tij is a fixed-effects variable 

corresponding to a time-trend (in years), Xij is the candidate predictor variable being 

investigated, the beta parameters (β) represent a vector of fixed effects, and the delta 

parameters (δ) represent random-effects that allow each county or census tract to have 

their own trend over time. The Xij variable typically is mean centered in this series of 

models, allowing the intercept term to be relatively stable across the multiple 

predictor variables being investigated. In this model, it can be assumed that δ0i and 

δ1i jointly follow a multivariate normal distribution with mean zero and covariance 

matrix

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

Σ = 2

11

2

10

2

01

2

00

σ σ

σ σ , and the residual error also is assumed to follow a normal 

distribution with mean zero and variance . 

 Model 1 follows the above approach – where the responses are weighted equally. 

 Model 2 follows the above approach – where the responses (GM) are weighted by the 

number of children observed (screened) within each record (census tract/quarter). 

Binomial Data: The following generalized linear mixed model (i.e., a random-effects model for 

binomial data) was used to model the proportion of children exceeding certain thresholds as a 

function of a candidate predictor variable: 

ij ij ij ij ij i i ij it E Y n = + ⋅ t + ⋅ Season + X + + ⋅ t 0 1 2 3⋅ 0 1 log ( [ / ]) β β β β δ δ v

Where (i indexes census tract and j indexes time), Yij represents the number of 

children observed above the blood-lead threshold in the ith census tract at time j, nij

represents the number of children tested in the ith census tract at time j, tij is a fixed 

effects variable corresponding to a time-trend (in years), Xij is the candidate predictor 

variable being investigated, the beta parameters (β) represent a vector of fixed effects, 

and the delta parameters (δ) represent random effects that allow each census tract to 

have its own trend over time. The Xij variable also is mean centered in this series of 
 

9 

models, allowing the intercept term to be relatively stable across the multiple 

predictor variables being investigated. In this model, it can be assumed that δ0i and 

δ1i jointly follow a multivariate normal distribution with mean zero and covariance 

matrix 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

Σ = 2

11

2

10

2

01

2

00

σ σ

σ σ . 

 Model 3 follows the above approach – where Yij represents the number of children 

observed with blood-lead concentrations at or above 5 μg/dL, and nij represents the 

total number of children screened within each record (census tract/quarter). 

 Model 4 follows the above approach – where Yij represents the number of children 

observed with blood-lead concentrations at or above 10 μg/dL, and nij represents the 

total number of children screened within each record (census tract /quarter). 

 Model 5 follows the above approach – where Yij represents the number of children 

observed with blood-lead concentrations at or above 15 μg/dL, and nij represents the 

total number of children screened within each record (census tract /quarter). 

 Model 6 follows the above approach – where Yij represents the number of children 

observed with blood-lead concentrations at or above 25 μg/dL, and nij represents the 

total number of children screened within each record (census tract /quarter). 

To allow comparison of the different variables explored within each variable type, tables are 

included in Section 4 that present the log-likelihood statistic from each model run and presented 

in Appendices A and B. Within each variable category, the variable that provided the best fit for 

each of the six models is highlighted in yellow. To ensure compatibility in the likelihood-based 

statistics being used to make comparisons among the different candidate predictor variables, 

missing values for predictor variables were imputed using the mean of the distribution. The 

number of imputed values that were necessary is provided by the nmiss column in the table of 

distributional summaries described above. The project team choose whether to adjust for 

changes in the slope for a candidate predictor variable over time based on a comparison of the 

likelihood statistics after adjusting for the number of degrees of freedom used in the model for 

the effects of the explanatory variable (over time) on the response. Those variables highlighted 

in yellow have the largest likelihood statistic after adjusting for differences in the degrees of 

freedom, and were considered as strong candidate predictors for the multivariate statistical 

models. 

Due to the iterative nature and complexity of the Mixed Models Analysis of Variance and 

Generalized Linear Mixed Modeling Approaches, these models did not always converge. 

Models that failed to converge for a particular predictor variable are discussed in the results 

sections within Appendices D and E, and also are indicated in Tables 4-1 and 4-2, as well as in 

the summary pages of Appendices A and B by blank cells. Cases in which model convergence is 

not attained likely will translate to exclusion of that particular variable when building the 

multivariate model. Note that because of the sparseness of data for children with blood-lead 

levels at or above 25 μg/dL within the Massachusetts data, Model 6 failed to converge across all 

variables. Thus, Model 6 results are not presented or discussed for the Massachusetts models.
 

10 

2.4 Development of Multivariate Statistical Models

2.4.1 Statistical Models for the Broad Coverage – Low-Resolution Model 

This model is being used to characterize broad trends over time in the prevalence of childhood 

lead poisoning across the entire United States. The various surveillance, environmental sources, 

demographic characteristics, and programmatic support data sources were aggregated to the 

county level for all localities with universal screening and reporting. Quarterly estimates of each 

candidate predictor variable were created for each county within the United States, including 

those county/quarter combinations that did not include observed blood-lead response variable 

information (allowing for the extrapolation of the model predictions to geographic areas and 

time-points that were not represented within CDC’s National Surveillance Database). 

In addition to investigating the predictive ability of each potential environmental, programmatic 

and demographic variable as described earlier, various different stratification variables (region of 

the country, population density) and covariates (time trend and seasonality) were investigated. 

As a result, all four multivariate statistical models adjust for a categorical variable that 

differentiates among the risk of childhood lead poisoning within the 10 EPA regions. Within 

each EPA region, a separate intercept, trend over time, and seasonality term (based on fitting 

intercepts for each quarter of time) was included in the multivariate statistical model. For the 

purposes of discussion, it was assumed that the modeling approach will focus on a logistic 

regression model for the proportion of children that have elevated blood-lead concentrations 

(≥10 μg/dL). The temporal nature of declining childhood lead poisoning will be addressed via 

classic concepts of longitudinal data modeling of the low resolution data. Let 

Yij represent the number of children that were detected with blood-lead concentration above 

10 μg/dL from the ith county and jth point in time (quarter), 

nij represent the number of children that had their blood-lead concentration tested from within 

the ith county and jth point in time (quarter), 

Please note that we expect that nij<Nij, where Nij represents the total population of children 

in the ith county and jth point in time. 

tij represent time (in years) corresponding to the Yij response variable, 

Regionik represents the region of the country that the ith county is located within (where 

k==1,...,10 and is representative of the 10 established EPA regions), 

Seasonij represents a series of 4 indicator variables that differentiate between the 4 different 

quarters captured by the j-index, and 

Xij represent a series of predictor variables associated with the Yij response variable. These 

predictor variables may represent air monitoring data, drinking water data, census 

demographic data, programmatic data on federal financial support for lead poisoning 

prevention, and other related information as detailed above that can potentially help predict 

the prevalence of lead poisoning at the county level. 
 

11 

We introduce the following as a potential baseline model: 

ij ij ik k k ij k ij ij i i ij it E Y n = gion ⋅ + ⋅ t + ⋅ Season + X + + ⋅ t 0 1 2 3⋅ 0 1 log ( [ / ]) Re (β β β ) β δ δ v v

Where the beta parameters (β) represent a vector of fixed effects, and the delta parameters (δ) 

represent random effects that allow each county to have their own trend over time. In this 

model, it can be assumed that δ0i and δ1i jointly follow a multivariate normal distribution with 

mean zero and covariance matrix 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

Σ = 2

11

2

10

2

01

2

00

σ σ

σ σ . 

Counties with larger δ1 parameters estimates represent areas where lead-poisoning has not 

significantly decreased over time. Similarly, the parameter estimates can be used to identify 

those counties with the highest predicted prevalence of childhood lead poisoning at various time 

points in the future. 

In building the multivariate statistical model for the Broad-Based Modeling Objective, the 

project team first evaluated the predictive ability of each candidate predictor variable that was 

considered within the exploratory analyses. For the environmental predictor variables, in 

particular (information from EPA’s 1999 National Air Toxics Assessment, Safe Drinking Water 

Information System, and Toxics Release Inventory), the data were largely concentrated at zero. 

Therefore, a series of zero/one indicator variables that represent county/quarter combinations at 

or above the 95th and 99th percentile of observed values of these environmental predictor 

variables within the analysis dataset also were investigated. 

Once the predictive ability of each candidate variable was established within the exploratory 

analyses described earlier, candidate predictor variables were classified into groups (e.g., 

housing age, income, education, air modeling, programmatic financial support) and then the 

single best predictor variable within each group was selected for possible inclusion within each 

of the six multivariate statistical models being developed. If the selected variable demonstrated a 

relationship with risk of lead poisoning that changes over time (as evidenced by intersecting lines 

in the plots generated in the exploratory analyses), then this interaction was taken into 

consideration within the evaluation of the predictive ability of the candidate variable(s). 

The approach to determining which environmental, programmatic, and demographic variables 

were included in the model followed a backward elimination process – in which each variable 

group’s best predictor variable identified earlier was included in the first model – with variables 

being eliminated from the model when they were not deemed to be highly significant. This 

model building process also was aided by investigation of the selected environmental, 

programmatic, and demographic variables for issues of potential colinearity via investigation of 

correlation matrices and principal components analysis. The resulting multivariate statistical 

models were parsimonious – and in most cases only included variables that were highly 

statistically significant. In a few cases, a variable was left in the model without being highly 

significant – because its elimination caused a large drop in the model log-likelihood (suggesting 
 

12 

that the model is significantly improved with the addition of a variable whose slope is not 

significantly different from zero). 

After the multivariate statistical models were developed, model fit diagnostics were evaluated 

and documented. 

The parameter estimates for the four National Multivariate Statistical Models are provided in the 

results section. The results of these models also were explored in multiple ways. Maps were 

generated to demonstrate observed and predicted proportion of children at or above 10 μg/dL 

within each EPA region for the Years 2000 and 2005 (data were appropriately averaged across 

the four quarters in each of these years prior to mapping). Lists also were generated to identify 

the 150 highest risk counties across the United States at the end of the observation period (2006) 

as predicted by each of the six models, as well as the 10 highest risk counties within each state. 

Finally, the predicted values from these multivariate statistical models (extrapolated to 

county/quarter combinations not represented in the CDC surveillance database) were integrated 

in a unique data visualization tool. The product of this effort is a time-series of maps (or a 

movie) that spatially interpolates risk of childhood lead poisoning as a function of various 

appropriate predictor variables. The visualization tool allows users to interact with the modeling 

results at different levels of temporal and geographic specificity. The tool allows the user to 

select an appropriate response variable (e.g., proportion of children with blood-lead 

concentrations above 5 μg/dL) and play a movie that displays a time-series of maps that displays 

how the predicted (or observed) risk changes over time across the various counties within a 

selected state. The user can zoom in on a rectangular area, to see these results with a higher 

degree of geographic specificity. The user also can stop the movie (or rewind, or fast-forward) 

to isolate specific points in time. By using the mouse, the user also can select a specific county 

and the tool will display the observed and predicted data for that particular county in a separate 

window. The visualization tool was written in C++, and was built in a manner that will allow 

EPA to modify the model and for the project team to quickly import the resulting data from a 

modification into the tool.

2.4.2 Statistical Models for the High-Resolution Model within Massachusetts 

High-resolution models will be utilized to identify the relative contribution of various types of 

exposure sources in elevated risk for childhood lead poisoning within select communities within 

the Commonwealth of Massachusetts. These types of sources include housing factors, broader 

environmental exposure, demographic composition, and programmatic resources. While this 

type of model reflects the idea that exposures contributing to childhood lead poisoning likely are 

community-specific, analysis of the high-resolution models may have certain limitations 

including selection bias and generalizability to other geographic areas. 

The Massachusetts Department of Public Health (MDPH) entered into a limited use data sharing 

agreement with the project team, allowing them to provide blood-lead testing results on 

individual children (aged 6-36 months) and housing inspection data in a format that preserves 

linkages through a housing unit identification variable. These data will be utilized in two 

different modeling approaches. The first modeling approach will seek to develop census tract 

quarterly summary measures similar to the National Model for blood-lead (e.g., exceedance 
 

13 

proportions and geometric means), as well as summary measures for the proportion of housing 

units in each census tract that are known to be in (or out of) compliance with the Massachusetts 

standard of care (for use as a potential explanatory variable). MDPH also has provided the 

project team with summary information regarding HUD and state funding of residential housing 

interventions (lead hazard control and abatement) – which will be used to develop a longitudinal 

summary of current and cumulative per-capita spending on residential intervention within each 

census tract (using various assumptions on the allocation of such dollars). Other explanatory 

variables, such as the U.S. Census, EPA Toxics Release Inventory, 1999 National Air Toxics 

Assessment, and water quality data will be available for use in these models. 

These census-tract level summary data (both response variable and explanatory variables) were 

modeled using a similar approach to what is being proposed for the National (Low-Resolution) 

Model – only the unit of clustering was census tract rather than county. 
 

14 

3.0 DATA SOURCES AND DATABASE DEVELOPMENT 

The main goal of the statistical analysis were to develop a series of predictive models that help 

provide a better understanding of (1) the relative importance of various exposure sources in 

addition to leaded paint in housing and (2) the geographic areas across the United States that 

remain at increased risk for childhood lead poisoning. To do so, blood-lead data were combined 

with various environmental, demographic, and programmatic datasets at different levels of 

geographic specificity and coverage. A description of each of these data sources, as well as 

discussion of how they were combined, is included in this section. 

3.1 Children’s Blood-Lead Measurements

The statistical models are based upon blood-lead levels of children corresponding to the various 

geographic areas studied. To enable national analyses, CDC’s Lead Poisoning Prevention 

Branch provided quarterly summary data from their national surveillance database for children 

aged 6-36 months within each county that had submitted data. These summary measures 

included the number of children screened, percentage of children who exceeded certain bloodlead thresholds, and arithmetic mean blood-lead concentration for state/local grantees with a 

history of universal reporting. 

The intention was to have the models reflect the annual prevalence of childhood lead poisoning 

over time. Thus, the data were summarized so that each child could only be reported once a 

year. An algorithm was developed to select representative screening test(s) for children with 

multiple results with an objective of having children represented in the analysis dataset 

maximally once a year. For a given patient with multiple testing results, the algorithm 

preferentially selected tests confirming elevated blood-lead levels and then selected follow-up 

tests taken beyond nine months of the previously selected test. Screening tests were selected 

when no confirming record was available. 

The response variable consists of quarterly summary statistics from 1995-2005 on the 

distribution of observed blood-lead concentrations in counties across the nation, based on 

information from CDC’s national surveillance database. It should be noted that there likely 

exists significant variation and differences in the sampling and analytical methodologies 

employed in performing childhood blood-lead testing among the different counties that 

contributed to the CDC dataset, and within counties over time. Sampling methods include both 

capillary and venous tests, and different laboratory methods likely are represented within the data 

with varying reporting limits or limits of detection. Variation in reporting limits and limits of 

detection could introduce significant biases into statistical models of any continuous measures of 

blood-lead concentration that could be used in statistical models, such as the geometric or 

arithmetic mean blood-lead concentration. Alternatively, there was agreement among the 

research team and the CDC that measures whether a testing result was found above or below 

certain threshold values (5, 10, 15, and 25 μg/dL) would be more robust to these potential 

reporting and detection biases. Therefore, the National (Low-Resolution) Models focus on the 

proportion of screened children found above these threshold values using a logistic regression 

modeling approach. 
 

15 

After summarizing the test-level data by year, quarter, and county, counties that contained less 

than five test records in a quarter were excluded for confidentiality reasons. The time series of 

summary statistics within select counties were initially investigated to determine appropriate 

exclusion criteria to ensure that the data retained for analysis represented blood-lead 

concentrations that were universally reported (i.e., there were periods of time in which some 

state or local childhood lead poisoning prevention programs only reported elevated blood-lead 

concentrations – and these data needed to be eliminated from the analysis). Thus, the number of 

quarterly summary statistics varied from county to county within the analysis dataset. 

As a prelude to developing the screening algorithm for elimination of data from counties that 

were not following universal reporting protocols, a subset of data from counties with obvious 

non-universal reporting was identified from within the National quarterly aggregate summary 

database. The algorithm was developed based on application to this subset of data prior to being 

utilized on the remainder of the National Surveillance database. The algorithm is based on the 

following: 

Let 

• nij represent the number of children observed in the ith county during the jth quarter 

• P90(ni) represent the 90th percentile of observed nij within the ith county 

• AMij represent the arithmetic mean blood-lead concentration observed in the ith county 

during the jth quarter 

• P50(AMi) represent the 50th percentile of observed AMij within the ith county 

• P10ij represent the proportion of children with blood-lead concentration observed at or 

above 10 μg/dL in the ith county during the jth quarter. 

Then the following 3 exclusion/inclusion criteria are applied sequentially: 

Criterion #1: If nij < Max(P90(ni)/5, 15) and (AMij ≥ 2* P50(AMi) or P10ij≥ 0.75), then 

exclude the data from the ith county during the jth quarter. This exclusion criterion 

essentially eliminates county/quarter combinations with relatively lower screening 

penetration (compared to when peak screening was achieved) and high blood-lead 

concentrations. The rationale for this exclusion criterion is that the periods of time in 

which a lead poisoning prevention program is not conducting universal reporting will 

involve fewer reported testing results that have higher blood-lead concentrations. 

Criterion #2: If nij > 100 and AMij <7, then include the data from the ith county during the 

j

th quarter. This criterion was added to include a small number of county/quarter 

combinations within the testing subset of data that were eliminated by the first exclusion 

criteria but did not appear to be inconsistent with the remainder of data that would be 

included in the analyses. This second criteria was inspected carefully upon application to 

the entire set of quarterly county summary statistics from CDC’s National Surveillance 

database, to ensure that it was reintroducing data into the analysis in a manner consistent 

with the data analysis goals. 

 
 

16 

Criterion #3: If nij < 100 and AMij >10, then exclude the data from the ith county during 

the jth quarter. This third criteria was established to exclude a small amount of data that 

was not captured by the first exclusion criteria (mostly representing counties with a 

median observed blood-lead concentration slightly above 5 μg/dL) 

Within the quarterly county summary statistics from CDC’s National Surveillance database, 

there were 72,466 county/quarter combination-level records. Application of Criterion 1-3 above 

eliminated an total of 2,351 records (3.25%) from the final analysis dataset. 

To enable analyses at a finer level of geographic detail than the county level, the MDPH 

provided blood-lead surveillance data on specific testing results for individual children (with 

confidential identification information excluded) so that data could be summarized and reported 

by census tract. The Massachusetts blood-lead surveillance data represents all children aged 6-

36 months tested from the period 2000-2006. As with the national data, quarterly census-tractlevel records were created for analysis. 

Due to selection bias, it is expected that the CDC National Surveillance dataset as well as the 

Massachusetts surveillance data may show higher proportions of elevated blood-lead 

concentrations than found in the general population. For this reason, the proportion of children 

with elevated blood-lead concentrations as well as the distribution of the potential continuous 

summary measure derived from the surveillance data were compared with those reported by the 

most recent six years of available CDC National Health and Nutrition Examination Survey 

(NHANES). Results of this comparison are presented in Section 7.2. In the future, to account 

for differences between the surveillance and NHANES data, modifications could be made to the 

models to calibrate the surveillance data to better match the national distribution of childhood 

blood-lead concentrations as appropriate (Strauss, 2001a). 

3.2 Demographic Data

 

Demographic information from the 2000 U.S. Census was utilized in both the high- and lowresolution models, with data being acquired at the county level for the entire nation and at the 

census-tract level for Massachusetts. The Census 2000 data gathered by the Census Bureau 

includes over 1,000 variables. To narrow the scope of the project, 43 variables within 9 general 

categories were selected and explored, most of which had been used previously by the project 

team in a CDC-sponsored study to predict risk of elevated blood-lead concentrations at the 

census tract level (Strauss, 2001b). In many cases, the census variables are constructed from 

counts or summary statistics published in the detailed Census 2000 tables. For example, within 

each geographic area, the Census Bureau reported the number of houses that were built before 

1950 and the median income of all households. In order for the analysis to draw comparisons 

from tract to tract and/or county to county, however, the Census variables needed to be 

manipulated in a fashion that depended upon the format of the variable. For example, count 

variables, such as the number of housing units built before 1950, were changed to percentages. 

Summary statistic variables describing income on the other hand, may be standardized within 

state to adjust for between-state differences in the cost of living. Table 3-1 supplies the list of 

the variables investigated within the nine categories and notes how they were calculated. 
 

17 

Table 3-1. Initial Variables for Analysis Created From the 2000 Census 

Variable 

Group Census Variable* Format Calculation Analyzed Variable 

Persons Count Land Area 

(Units = .001 km2

) 

Population Density 

Density Housing units Count Land Area 

(Units = .001 km2

Housing Density 

White population Count Persons Pct White 

Black population Count Persons Pct Black 

Indian, Eskimo, and Aleut 

population 

Count Persons Pct American Indian and 

Alaskan Native 

Asian Pacific population Count Persons Pct Asian 

Other Race population Count Persons Pct Other Race 

Native Hawaiian and Other 

Pacific Islander population 

Count Persons Pct Native Hawaiian and 

Other Pacific Islander 

Multiple Race population Count Persons Pct Multiple Race 

Race 

Hispanic population Count Persons Pct Hispanic 

Children Less than or Equal 

to 6 Years Old 

Count Persons Pct le 6 years 

Age Median Age* Statistic Median age of persons 

Median Age of Children Less 

than or Equal to 6 Years Old* 

Statistic Median age of persons LE 

6 years 

Family 

Structure 

Single Parent* = Single Male 

with Children + Single 

Female with Children 

Count Household with 

Children Less than or 

equal to 18 years old = 

Married Couple with 

children + Single Male 

with Children + Single 

Female with Children 

Pct Single Parent 

Less than a 9th grade 

Education 

Count Persons 18 years old 

and over 

Pct less than 9th grade 

Less than high school* = #13 

+ persons with 9th to 12th 

grade education without 

obtaining a high school 

diploma 

Count Persons 18 years old 

and over 

Pct no HS degree 

Less than college* = #14 + 

persons with high school 

diploma, but no college 

experience 

Count Persons 18 years old 

and over 

Education Pct no college 

Less than college degree* = 

#15 + persons that attended 

college without obtaining a 

college diploma 

Count Persons 18 years old 

and over 

Pct no college degree 
 

18 

Table 3-1. (continued) 

Variable 

Group Census Variable* Format Calculation Analyzed Variable 

Household Median Income Statistic Standardized Median 

Income for Households 

Family Median Income Statistic Standardized Median 

Income of Families 

Per Capita Income Statistic Standardized per capita 

income of persons 

Households without earnings Count Households Pct No Earnings 

Households without wages Count Households Pct No Wage or Salary 

Income 

Households that obtain public 

assistance Count Households Pct With Public Assistance 

Persons below poverty level Count 

Persons for whom 

poverty status is 

determined 

Pct Persons Below Poverty 

Persons who are less than or 

equal to five years old that are 

below poverty level* 

Count 

Persons who are less 

than or equal to five 

years old for whom 

poverty status is 

determined 

Pct Persons Below Poverty 

of Age LE 5 Below 

Families with total income 

below the poverty level Count Families Pct Families Below Poverty 

Poverty 

Level 

Families with total income 

below the poverty level that 

have children under 5 years 

old. 

Count Families with children 

under five years old 

Pct Poverty of Families 

with Children LT 5 

Vacant Count Housing Units Pct Vacant 

Housing Units Built before 

1940 Count Housing Units Pct Pre 1940 Housing 

Housing Units Built before 

1950 Count Housing Units Pct Pre 1950 Housing 

Housing Units Built before 

1960 Count Housing Units Pct Pre 1960 Housing 

Housing Units Built before 

1970 Count Housing Units Pct Pre 1970 Housing 

Housing Units Built before 

1980 Count Housing Units Pct Pre 1980 Housing 

Median Year that Housing 

Units were Built Statistic Median Year Built 

Housing 

Units 

Median Year that Housing 

Units were Built - Calculated 

by the Project Team 

Statistic Calculated Median Year 

Built 
 

19 

Table 3-1. (continued) 

Variable 

Group Census Variable* Format Calculation Analyzed Variable 

Housing Units that are rented Count Occupied Housing Units Pct Renter Occupied 

Occupied Housing Units Built 

before 1940 Count Occupied Housing Units Pct Pre 1940 Occupied 

Housing 

Occupied Housing Units Built 

before 1950 Count Occupied Housing Units Pct Pre 1950 Occupied Housing 

Occupied Housing Units Built 

before 1960 Count Occupied Housing Units Pct Pre 1960 Occupied 

Housing 

Occupied Housing Units Built 

before 1970 Count Occupied Housing Units Pct Pre 1970 Occupied 

Housing 

Occupied Housing Units Built 

before 1980 Count Occupied Housing Units Pct Pre 1980 Occupied Housing 

Occupied 

Housing 

Units 

Median Year that Occupied 

Housing Units were Built Statistic Median Year Built - 

Occupied Only 

Median Rent Statistic Standardized Median 

Housing Gross Rent 

Value Value of Owner Occupied 

Housing Units Statistic Standardized Median Housing Unit Value 

*Variables that were created by combining different pieces of information from the 2000 Census 

Income and Poverty 

Median income per household, family, and person were calculated. Additionally, the proportion 

of households that do not receive any wages, do not receive any earnings, and do receive public 

assistance were investigated. The census defines earnings and wages as follows: 

• “Earnings” represent the amount of income received regularly before deductions for 

personal income taxes, Social Security, bond purchases, union dues, Medicare 

deductions, etc. 

• “Wages” include total money earnings received for work performed as an employee 

during the calendar year 1999. It includes wages, salary, Armed Forces pay, 

commissions, tips, piece-rate payments, and cash bonuses earned before deductions were 

made for taxes, bonds, pensions, union dues, etc. 

Similar to the income variables described above, the poverty level of individuals and families 

within each county were summarized as the variables Percent Persons and Percent Families 

Below the Poverty Level. In order to focus on the poverty level of the children within each 

county, however, Percent Persons Five Years and Under and Percent Families with Children 

Under Five Years Below Poverty Level variables were created. Note that in calculating the 

various percentages for each of the variables, the denominator changes. Also note that for some 

of the multivariate models presented later in the report, some of the income variables may have 

been rescaled to represent income in thousands of dollars, to allow the parameter estimates for 

the regression models to be discernable within the first 3 significant digits. 
 

20 

Race 

The Census Bureau presents five general race groups; (1) White, (2) Black, (3) Indian, Eskimo, 

and Aleut, (4) Asian Pacific and (5) Other, each of which was included and explored separately. 

Additional variables were included on percent of Native Hawaiians and Other Pacific Islanders, 

percent of the population reporting multiple races (Percent Multiple Races), and percent of the 

population reporting that they are Hispanic (Percent Hispanic). 

Housing Cost

Two variables were constructed to investigate housing cost – Median Rent and Median Housing 

Value. Median Housing Value includes the value of all housing units (owned and rented). Both 

of these variables were standardized to account for state-to-state differences in the cost of living. 

Note that for some of the multivariate models presented later in the report, some of the housing 

cost variables may have been rescaled to represent housing costs in thousands of dollars, to allow 

the parameter estimates for the regression models to be discernable within the first 3 significant 

digits. 

Occupancy

Occupied housing units are more likely to have lead paint removed than vacant homes. Thus, the 

percent of housing units that are vacant potentially indicates the level of care taken to maintain 

buildings within the area. Buildings that are not occupied are more likely to accumulate dust or 

debris to which the children of an area may be exposed upon reoccupancy. Percent of vacant 

housing units was explored for those reasons. Similarly, the standard of care could be different 

between rental properties and owner-occupied properties. Thus, the percent of rental units in an 

area also was explored. The percent of occupied housing units that are rented, rather than 

owned, was calculated by dividing the number of rented occupied housing units within an area 

by the total number of occupied housing units. 

Family Structure

The Census Bureau does not supply a unique variable that indicates the number of single parent 

households within an area. Therefore, this variable was created by combining Census variables 

as follows: 

M = Number of Households with a male householder (no wife present) whose own 

children are under 18 years old 

F = Number of Households with a female householder (no husband present) whose own 

children are under 18 years old 

T = M + F + Number of married couples with own children under 18 years. 

The Percent of Single Parent Households variable used represented (M+F)/T. 

Housing Age

During the 1950s, as the United States started to become aware of the consequences associated 

with the exposure of lead in paint, the use of lead paint within homes began to decrease. In 

1977, however, the use of lead paint in homes became illegal. Thus, the years during which the 

housing units were built within each area is important to characterize; older homes are more 

likely to contain lead paint than newer homes. A number of variables related to housing age by 

county were investigated to identify those that best predict children’s blood-lead levels. Census 
 

21 

data on the full population of housing units as well as the population of occupied housing units 

were investigated. Note that for some of the multivariate models presented later in the report, the 

median age of house variable was centered at 1950 to provide stability to the intercept term in 

the models.

Children’s Age 

The Census Bureau does not report all data by single years of age. More typically the agency 

reports the total number of people that fall into various age categories. The variable, “Pct LE 6 

years” was created to identify the number of children within each geographic area less than or 

equal to six years of age at the time of the 2000 Census. Additionally, the median age of the 

total population and of those less than or equal to six years old was calculated by taking a 

weighted average of the midpoint of each age category (the counts are used as the weights). 

Education 

A series of variables pertaining to the proportion of adults with various levels of education were 

created as follows: 

L9 = Number of people older than 18, that have less than a 9th grade education 

L12 = Number of people older than 18, that have 9th though 12th grade experience, but 

do not have a high school diploma 

12 = Number of people older than 18, that obtained a high school diploma or GED 

C = Number of people older than 18, that have some college experience but did not 

receive a college degree 

T = Number of People that are over than 18 years old 

Percentage variables were created from the L9 through C variables by dividing them by the total 

number of people over 18 years old. Exploratory analyses were conducted upon the four 

percentage variables. 

Population Variables 

Because both counties and census tracts vary with respect to spatial area and population, and 

previous work suggests that risk of childhood lead poisoning differs between rural and urban 

areas, a population density variable was used as a potential explanatory variable or effect 

modifier in the statistical models. Population density was explored in two ways. The first 

divides the number of people within the tract by the amount of land area measured in .001 square 

kilometers. The second divides the number of housing units by the amount of land area 

measured in .001 square kilometers. Housing units include the following: a house, an apartment, 

a mobile home, a group of rooms, or single room that is occupied as separate living quarters. 

3.3 Environmental Data

Environmental data acquired for this project include air and groundwater monitoring data 

aggregated at the county level for the low-resolution model and at higher resolutions for the 

Massachusetts analyses. In cases where the data were available for a limited number of airmonitoring stations or drinking water samples available for the region(s) being investigated, geospatial modeling techniques might be used as appropriate to develop predictions across the entire 

region. Existence of industrial sources of lead within each county and census tract, as indicated 
 

22 

by the Toxics Release Inventory (TRI), also were included as an environmental data source. 

Each of theses data sources are discussed in further detail below. 

3.3.1 Concentrations of Lead in Air 

EPA maintains a number of ongoing air monitoring programs that collect data over time on 

concentrations of various criteria air pollutants, air toxics, constituents of particulate matter, and 

other airborne chemicals. Each of these monitoring programs have multiple air monitoring 

stations that are deployed throughout the country to meet various goals associated with the Clean 

Air Act and other federal and state regulations and programs. For example, some of the 

monitoring stations are placed in close proximity to industrial sources of pollution and major 

populations centers, while other stations are placed in remote areas to assess background 

chemical concentrations. While many of these monitoring sites provide information on the 

concentration of lead in air over time, a quick assessment of the spatial coverage of these 

monitoring networks suggested that making use of these data would be problematic for this study 

due to time and resource constraints. Lead concentrations in air from the monitoring networks 

are not available in the majority of counties that will be covered in the low-resolution model, or 

the census tracts that will be covered in the high-resolution models – as shown at the following 

EPA Website (http://www.epa.gov/airtrends/lead.html). 

Rather than using air monitoring data as described above, the study used modeled predictions of 

concentrations of lead in air from EPA’s 1999 National Scale Air Toxics Assessment – in which 

county and census-tract-level predictions are available throughout the entire country based on the 

use of predictive models. Documentation for the 1999 National Scale Air Toxics Assessment, as 

well as the predicted air concentration data can be found at 

http://www.epa.gov/ttn/atw/nata1999/tables.html. The predictions were generated using the 

Assessment System for Population Exposure Nationwide, or ASPEN. This model is based on 

the EPA’s Industrial Source Complex Long Term model (ISCLT), which simulates the behavior 

of the pollutants after they are emitted into the atmosphere. ASPEN uses estimates of toxic air 

pollutant emissions and meteorological data from National Weather Service Stations to estimate 

air toxics concentrations nationwide. 

The ASPEN model takes into account important determinants of pollutant concentrations, such 

as: 

• rate of release 

• location of release 

• the height from which the pollutants are released 

• wind speeds and directions from the meteorological stations nearest to the release 

• breakdown of the pollutants in the atmosphere after being released (i.e., reactive decay) 

• settling of pollutants out of the atmosphere (i.e., deposition) 

• transformation of one pollutant into another (i.e., secondary formation). 

The model estimates toxic air pollutant concentrations for every county and census tract in the 

continental United States; however, these data are only available for 1999. Both the BroadBased National Model and the High-Resolution Model within Massachusetts considered the 

integration of information from the ASPEN Model. The National Model investigated the 
 

23 

median, average, and 95th percentile predicted air lead concentration within each county, while 

the High-Resolution Model only considered the average predicted air lead concentration within 

each census tract. Within the National Model, the median, average and 95th percentile predicted 

air-lead concentrations were mostly distributed near zero. For this reason, zero/one indicator 

variables were created to indicate that the observed value of these ASPEN Model predictions 

were observed at or above the 95th and 99th percentile within the analysis dataset for potential use 

within the predictive models. In addition, EPA collaborators identified a subset of 20 counties 

with observed elevated air-lead concentrations, and an indicator variable was used to assess 

whether these 20 counties had higher risk of childhood lead poisoning in the predictive models. 

The second air-lead variable investigated is based on predictions from the HAPEM5 (Hazardous 

Air Pollutants Exposure Model, Version 5) model. According to the EPA website, “the 

HAPEM5 model has been designed to predict the ‘apparent’ inhalation exposure for specified 

population groups and air toxics. Through a series of calculation routines, the model makes use 

of census data, human activity patterns, ambient air quality levels, climate data, and 

indoor/outdoor concentration relationships to estimate an expected range of ‘apparent’ inhalation 

exposure concentrations for groups of individuals.”2

 Because air quality concentrations in 

indoor environments can be quite different than those in the outdoor environment, an exposure 

model generally is employed to predict the apparent inhalation exposure. The Air Exposure 

(HAPEM5) model variable captures the predicted exposure data from this model. 

The third air-lead variable considered, Air Hazard Quotient (HQ), is derived from the 1999 

National Scale Air Toxics Assessment data. This variable represents lifetime exposure for 

children at the centroids of each census tract or county. Lifetime exposure is calculated based on 

considering annual exposures and yearly activity patterns. The HAPEM5 and HQ air-lead 

variables were only considered within the context of the High-Resolution Model within 

Massachusetts. 

3.3.2 Toxic Release Inventory Variables 

EPA’s Toxics Release Inventory (TRI) catalogs various sources of lead, based on information 

provided by industrial facilities. This data source was used to generate county- and census-tractlevel estimates of the total amount of lead and/or lead-containing compounds that are released by 

industrial facilities into the environment via air, surface water, or underwater injection. 

Although the above-described ASPEN modeling results are based on the (airborne) emissions 

data and how they would theoretically translate into average ambient air-lead concentrations, the 

data from the TRI are available for multiple years and for other types of emissions (such as 

surface water). Thus, this information has the potential to add predictive power to the models. 

Three types of TRI variables were utilized – total compounds, lead only, and total lead. Within 

each type, five pollution variables were explored – total lead in the air, lead in fugitive air, lead 

from smokestacks, lead in surface water, and lead in water by injection. Thus, 15 total TRI data 

variables were evaluated. 

 

2 http://epa.gov/ttn/atw/nata1999/ted/teddraft.html 
 

24 

Within the National Model, the distributions of the TRI emissions variables were mostly 

concentrated near zero. For this reason, additional zero/one indicator variables were created to 

indicate that the observed value of these TRI emissions were observed at or above the 95th and 

99th percentile within the analysis dataset for potential use within the predictive models. 

3.3.3 Water Quality Data 

The plumbing system inside a home and the service line from the street to the home may contain 

lead and can contribute to drinking water contamination. To address this potential source, EPA 

obtained data from their Safe Drinking Water Information System that includes the 90th 

percentile result of tap water lead levels for public water systems. Public water suppliers must 

monitor at customer’s taps every 6 months. Public water systems can reduce monitoring to 

annually, triennially, or every 9 years (if granted a monitoring waiver) if the 90th percentile value 

from previous monitoring is at or below the action level of 15 parts per billion. The number of 

customer’s taps, or monitoring sites, that a system is required to sample is based on the 

population served by the system. Further, systems are required to select sites that are most likely 

to have the highest lead levels (i.e., older homes, homes with copper pipes with lead solder or 

homes served by a lead service line). Therefore, the 90th percentile value of samples collected 

during a monitoring period is not reflective of individual exposure to lead in drinking water. 

Data available from this monitoring program include 90th percentile water lead values for public 

drinking water systems serving greater than 3,300 persons (systems serving less than 3,300 

persons are required to report the 90th percentile level only if they exceed the action level), the 

population size served by each facility, the start and end date for the monitoring period, and the 

county in which the facility is located. These data were used to construct a population-size 

weighted average 90th percentile water-lead concentration variable within each county/quarter 

combination. However, it is important to note that most public water systems do not remain 

within county lines. Large water systems may serve multiple counties or a county may be served 

by several small public water systems. 

Because there were some county/quarter combinations with no observed data from EPA’s Safe 

Drinking Water Information System, an indicator variable was developed to indicate whether the 

county/quarter included a monitored facility (or not) – allowing an intercept to be fit among 

those county/quarters with no drinking water monitoring, and a slope estimate to be fit for the 

effect of the weighted average 90th percentile drinking water-lead concentration among reported 

facilities. 

EPA’s Safe Drinking Water Information System data were not geocoded to the census-tract 

level, and therefore these data were only available for use in supporting the Broad-Based 

National Model at this time. 

3.4 Programmatic Data

Most of the explanatory variables being explored in this project are considered risk factors for 

childhood lead poisoning. Among factors that might mitigate these risks, it was anticipated that 

the level and characteristics of programmatic support from either federal, state, or local sponsors 

may contribute toward meaningful reductions in the prevalence of childhood lead poisoning. 

The level of financial support available within each county served as a proxy for programmatic 
 

25 

support in the low-resolution (National) models. In the high-resolution models run for 

Massachusetts, information from housing inspections also were explored within the statistical 

models. The following sections detail the specific characteristics of the variables used within the 

models. 

3.4.1 Programmatic Funding Variables 

The goal of this variable is to construct a longitudinal history of current and cumulative 

per-capita dollars allocated to each county and census tract to combat childhood lead poisoning. 

For use in both the national and state models, data were obtained from HUD’s Office of Healthy 

Homes and Lead Hazard Control on grants funded since the inception of the Lead-Based Paint 

Hazard Control Grant Program in 1992. Data also were obtained from CDC’s Lead Poisoning 

Prevention Branch on their program’s grant funding approximately three weeks prior to the end 

of this project, and therefore these data were only able to be integrated into the Massachusetts 

models due to time constraints. 

Four variables were generated from these data and analyzed – current and cumulative funding 

allocated to each county or census tract to combat childhood lead poisoning, both Standardized 

by number of children per tract and Not Standardized. The Standardized variable is a funding 

per child variable while the Not Standardized versions are funding for geographic area variables. 

For the high-resolution model in the Commonwealth of Massachusetts, information on withinstate funding levels was obtained and analyzed. Within-state funding data were available down 

to the township level. The state, HUD, and CDC funding data also were combined to create 

Total Funding variables, including both current and cumulative levels and both Standardized and 

Not Standardized versions. The total funding variables also were only investigated as part of the 

Massachusetts analyses. 

Becuase there may be delays in the effects of programmatic funding on risk of lead poisoning, 

time-lagged versions (at 6-, 12-, 18-, 24-, 30-, and 36-months) of the programmatic funding 

variables in the National Model also were investigated. 

3.4.2 EPA Region 

The EPA region was investigated as a potential predictor of children’s blood-lead levels to 

determine if that high-level geographic indicator should be included as a stratification variable in 

the national multivariate models.

3.4.3 Housing Inspection Data (Massachusetts) 

The Commonwealth of Massachusetts maintains an extensive database on all lead-based paint 

inspections conducted over time (dating back to the early 1990s). The MDPH provided a 

database that contains a single record for each inspection, with the following information: 

housing-unit id, census tract, date of inspection, and result of inspection (whether the housing 

unit was found to be in compliance with Massachusetts standards). The database contains 

records on over 200,000 housing units – with many housing units having multiple inspections 
 

26 

over time. Note that for units with multiple records, time periods in which the units were both in 

and out of compliance with the Massachusetts standards were identified. 

These data can be used in the Massachusetts high-resolution models in two ways. First, a 

longitudinal summary measure of the proportion of housing within each census tract that was 

known to be in compliance with the Massachusetts standards was developed. It was anticipated 

that within a census tract, as this proportion increases over time, the risk of childhood lead 

poisoning will decrease. Second, due to the fact that individual blood-lead records from 

Massachusetts with linkable housing-unit identification variables were available, a determination 

could be made regarding whether a housing unit was in compliance at the time of the blood-lead 

test for each child in the database (with potential outcomes of the determination being yes, no, 

and unknown). 

The first approach described above is consistent with the methods for exploring aggregated 

summary blood-lead information over time within each census tract. The second approach 

allows utilization of some predictive information at the individual child level. This information 

may help improve prediction, and also may help assess what information might be lost when 

transitioning from individual-level data to aggregate summary data in the analyses. 

Unfortunately, due to time and resource constraints, only the first method was explored within 

this project. Thus, the three measures listed below were calculated using four different methods. 

The three measures are: 

• P - represents the Proportion of Housing Units within a census tract that are assumed to 

Meet the Massachusetts Standard of Care at any given time 

• F - represents the Proportion of Housing Units within a census tract that are assumed to 

Not Meet the Massachusetts Standard of Care at any given time 

• N - represents the Proportion of Housing Units within a census tract with Housing 

Inspection Information at any given time. 

As noted, the measures were generated in four different ways, each handling the longitudinal 

information in a slightly different manner. The four measures, numbered in the model results 

from 1 to 4, are listed below. 

1. Naïve Method 1 – Create a longitudinal history for each housing unit inspected, and 

treat the first inspection observation as being representative for time periods 

preceding that inspection. 

2. Naïve Method 2 – Create a longitudinal history for each housing unit inspected, and 

assume missing information for time period preceding the first test on each unit. 

3. Naïve Method 3 – Create a longitudinal history for each housing unit inspected, and 

treat the first inspection observation as being representative for time periods 

preceding that inspection if the housing unit failed, and assume missing information 

for time period preceding the first test if the unit passed. 

4. MDPH Approved Method – Create a longitudinal history for each housing unit, with 

different rules for the treatment of the time-period preceding the first test based on (a) 

the housing inspection result and (b) the reason for ordering the inspection. 
 

27 

Note that for housing units with multiple inspections, each housing inspection result is assumed 

to be representative of the house (either pass or fail) until the next result. The last result is 

carried forward over time (e.g., if the last observed inspection on a house passed in November of 

1998 – that particular house is assumed to be meeting the Massachusetts standard of care over all 

subsequent time periods in the dataset). If multiple inspections occur on the same house within a 

particular quarter (3-month interval), the maximum result (with pass being coded as a 1, and fail 

being coded as zero) is used to represent the house. The 0/1 results are then summed across all 

observed housing units within each census tract over time (quarters). The summed results are 

then divided by the number of housing units reported within each census tract from the 2000 

Census. 

While all of the above described housing inspection variables were investigated in the 

exploratory data analyses, only the P4, F4, and N4 variables associated with the MDPHapproved method of constructing the longitudinal history within each housing unit observed was 

considered within the context of the multivariate models. 

3.5 Data Linkages

The primary objective of this pilot study was to utilize combined information from different 

sources at various levels of geographic and temporal specificity to more accurately target 

geographic areas at high risk for not meeting the 2010 goal of eliminating childhood lead 

poisoning. As such, work on the study required careful integration of a variety of data sources 

with various characteristics and documentation. Data to support this study were gathered from a 

variety of sources, including federal, state, and local lead poisoning prevention programs, as well 

as publicly available data downloaded from the internet (e.g., Census data, EPA’s Toxics 

Release Inventory), as detailed in the previous sections. 

Upon receipt of each data source, the data and supporting documentation was reviewed to gain 

knowledge on the structure, relationship, and quality of the data. Database managers worked 

with the project team (including collaborators providing data to the project, as well as EPA) to 

determine the final format for each database, desired uses of the databases, as well as the 

requirements for maintaining the databases. Based on this information, separate master 

databases were constructed for the national model and for the high-resolution Massachusetts 

model that integrate the various environmental, demographic, and programmatic variables, and 

facilitate statistical analyses of the combined data. These databases were constructed by 

combining data from a variety of formats including MS SQL Server, MS Access, Excel, ACSII, 

Access, ArcView, and SAS® electronic databases. In order to combine the various data sets, 

they were merged on key fields, including state, county, census tract, and time period. The data 

being used for analyses of a particular geographic level (e.g., county) are comparable because 

they are representative of that geographic area. 

Throughout the development process, checks for completeness were conducted on all study 

databases, and the project team worked with data-sharing collaborators and EPA to attempt to 

complete missing data as necessary to support the proposed statistical analyses. Any changes to 

the databases (corrections, additions, deletions, etc.) were documented in appropriate metadata 

files. Documentation of the combined master databases is included in Appendix H. 
 

28 

Standard Operating Procedures (SOPs) were followed to ensure the proper storage, backup, and 

retrieval of datasets created and analyzed for this study. The various databases were backed up 

to tape nightly via automated backup routines, and were only accessible to members of the 

project team. CD-ROM backups were made on a regular basis to serve as a safeguard in case the 

backup system failed for any reason. 

Microsoft Access and SQL server were the primary software tools used for data management. 

The SAS® System was the primary statistical data analysis tool used on this project. ArcView 

software was used to translate results into maps, as seen in Appendices F and G. 

The data utilized for the study were maintained in a manner that preserved the confidentiality of 

all the data and prevented its unauthorized release. As data files were received from EPA, the 

original data (e.g., data with personal identifiers) were handled as though they were classified as 

confidential business information (CBI) under the Toxic Substances Control Act (TSCA), even 

though EPA may not specifically classify these data as “CBI.” The data files were not shared 

with anyone outside of the project team. 
 

29 

4.0 EXPLORATORY DATA ANALYSES 

Because the goal of this study was to develop a series of statistical models that predict the risk of 

childhood lead poisoning at the geographic level across multiple response variables (proportion 

of children screened at or above 5, 10, 15 and 25 ug/dL), all potential predictor variables first 

were explored individually to determine their predictive ability. Results from these bivariate 

analyses were assessed to identify the set of variables to include in the multivariate model that 

predicts how the risk of childhood lead poisoning changes over time among the various census 

tracts and counties included in the analysis. 

This section of the report provides the results of the series of exploratory analyses described in 

Section 2.2, which were performed to assess the potential predictive power of various candidate 

demographic, environmental, and programmatic variables for potential use in the multivariate 

models. These exploratory analyses initiated with an assessment of the study sample, i.e., the 

proportion of counties in the sample with complete and reliable data for both the response 

variable and the explanatory variables. 

Each candidate predictor variable was reviewed with particular attention focusing on the manner 

in which the county-level predictor variables would be merged with the quarterly summary 

blood-lead information prior to fitting the statistical models. In preparation for developing 

longitudinal statistical models, univariate summaries of each predictor variable as a function of 

time were produced. Comparisons of these distributions were made using side-by-side box-plots 

for continuous data or bar-charts for categorical data. This helps verify that the data are clean 

and ready for analysis and helps identify cells with sparse data. Such descriptive analyses were 

conducted on each predictor variable database to characterize the distributions of all observed 

variables using frequency distributions for categorical variables, and simple summary statistics 

(mean, median, mode, minimum, maximum, and select percentiles) for continuous variables. 

The univariate descriptions then were followed by fitting a series of cross-sectional bivariate 

relationships between the blood-lead response variable(s) and each candidate explanatory 

variable. These cross-sectional relationships were explored as a function of time to better 

understand the stability of these relationships, and whether they change over time, so that they 

can be modeled appropriately in the more sophisticated longitudinal analyses. These analyses 

also help identify which explanatory variables are most predictive of the blood-lead response 

variable. 

4.1 Relationship between National Blood-Lead Data and Explanatory Variables

The response variable for the national data analysis consisted of quarterly summary statistics 

from 1995-2005 on the distribution of observed blood-lead concentrations in counties across the 

nation, based on information from CDC’s National Childhood Lead Poisoning Surveillance 

Database. The time series of summary statistics within select counties were initially investigated 

to determine appropriate exclusion criteria to ensure that the data retained for analysis 

represented blood-lead concentrations that were universally reported (i.e., there were periods of 

time in which some state or local childhood lead poisoning prevention programs only reported 

elevated blood-lead concentrations – and these data needed to be eliminated from the analysis). 
 

30 

Thus, the number of quarterly summary statistics varied from county to county within the 

analysis dataset. 

The national blood-lead data were categorized into four time periods – (1) January 1, 1995 to 

December 31, 1999; (2) January 1, 2000 to December 31, 2001; (3) January 1, 2002 to December 

31, 2003, and (4) January 1, 2004 to December 31, 2005 – so that change over time could be 

evaluated. Using the specified four time periods split the dataset of quarterly county-level 

records into roughly similar sizes. Presented below are the exploratory analysis results for the 

demographic, environmental, and programmatic variables investigated. Detailed figures and 

tables containing results are included in Appendix A. A detailed discussion of the results seen in 

Appendix A is contained in Appendix D. 

To allow comparison of the different variables explored within each variable type, Tables 4-1 

through 4-4 present the log-likelihood statistic from each single covariate model presented in 

Appendix A for each of the four blood-lead threshold values, respectively. Each explanatory 

variable was investigated in four different ways with respect to how the effect of the variable 

might vary over time within the longitudinal analysis dataset: 

1. Investigate the explanatory variable on its own, assuming that the effect remains stable 

over time. 

2. Investigate the explanatory variable with a linear interaction with time, assuming that the 

effect of the variable on risk of childhood lead poisoning either increases or decreases 

linearly over time (on the logit scale). 

3. Investigate the explanatory variable with a quadratic interaction with time, assuming that 

the effect of the variable on risk of childhood lead poisoning either increases or decreases 

as a quadratic function in time (on the logit scale). 

4. Investigate the interaction between the explanatory variable and four select time periods, 

which is helpful for diagnosing whether the effect remains stable (or changes) over time – 

but is not particularly useful for the final multivariate model where the application of the 

model might be to forecast how risk of lead poisoning might extend into future years. 

Within each variable category, the variable that provided the best fit across the four time 

variables is indicated with a double asterisk (**). For example, within the income category, the 

Categorical time variable achieved the best fit for seven of the eight income variables in the 

model of proportion of children with blood-lead levels above 5 μg/dL. Within that category, 

Percent No Household Wage achieved the best model fit across the 8 income variables. Those 

variables (indicated with the double asterisk) were the most likely to become candidate 

predictors for the multivariate statistical models. 
 

31 

Table 4-1. Summary of Exploratory Analysis Fit as shown by -2 Log Likelihoods for 

Pr(PbB >= 5 μg/dL) Models 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

Median_Family_Income 235522.9 233514.6 

Median_HH_Income 235495.9 233439 

Median_Per_Capita_Income 235600.3 234626.6 233735.4 

Pct_HH_No_Earnings 235611.3 235601.3 234404.8 233260.3 

Pct_HH_No_Wage 235579.7 235567.8 234323.0** 233183.8* 

Pct_LT_Poverty 235763.3 234363.2 233608.5 

Pct_Family_Income_LT_Poverty 235761.5 235744.8 234446.2 233751.1 

Income 

Pct_LE_5Yrs_LT_Poverty 235794.2 234373.9 

Pct_Asian 235769 235681.3 234627.7 234511.6 

Pct_Black 235867.4 234612.0** 

Pct_White 235915.1 235259.3 233688.1 

Pct_NHOPI 235888.9 235536.9 235918.5 

Pct_Other_Race 235862.1 235848.1 235559.1 235250.1 

Pct_Multi_Race 235817.2 234679.6 234595 

Race 

Pct_Hispanic 235851.8 233502.6* 

Housing Median_Rent 235265.4 235189.1 234046.8** 233401.0* 

Cost Housing_Value 235571.9 235562.9 235128.2 234857.9 

Pct_Rented 235913.4 235887.7 Occupancy Pct_Vacant 235884.8 235872.2 235427.2** 234479.4* 

Single 

Parent Pct_Single_Parent 235878.1 235884 234527.9** 233660.7* 

Median_Yr_Built 235421.5 235483.4 234415.3 

Median_Yr_Occ_Built 235412.7 235432.6 234214.3 233119.1 

Pct_Built_Pre_1940 235268.9 235277.3 233803.4 233243.7 

Pct_Built_Pre_1950 235241.8 233574.5 232990.3 

Pct_Built_Pre_1960 235344.5 235357.7 233484.5** 232839.7* 

Pct_Built_Pre_1970 235449 235463.1 233650.7 232904.6 

Pct_Built_Pre_1980 235487.1 235503 233834.3 232946.2 

Pct_Occ_Built_Pre_1940 235277.5 235285.1 233834 233291 

Pct_Occ_Built_Pre_1950 235233.3 235245.1 233601.1 233030.9 

Pct_Occ_Built_Pre_1960 235359.2 233499.6 232866.4 

Pct_Occ_Built_Pre_1970 235458.6 235471.3 233666 232928.4 

Home Age 

Pct_Occ_Built_Pre_1980 235495.4 235510.7 233840.8 232959.7 

Pct_LE_Six 235827.7 235829.8 234448.4** 233449.9 Children Num_LE_Six 235905.5 235924.2 227590.8* 

Pct_LT_9th_Grade 235850.1 235848.4 234398.6 233744 

Pct_No_HS_Degree 235715.8 234321.2 233411.6 

Pct_No_College 235509.4 234237.9 Education 

Pct_No_College_Degree 235556.5 235505.7 234226.0** 233106.0* 

Total_Housing_Units 235906.3** 235922.2 

Population Total_Pop 235908.5 235928.6 228102.6* 

Housing_Density 235920.4 235925.8 235699.2 
 

32 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

air_avg 235905.9 235906.7 235836 

air_med 235905 235905.5 235921 

air_p95 235907.6 235909.8 235815.6** 235735.7* 

air_avg_p95 235906.4 235909.6 233727.0* 

air_med_p95 235907.2 235135.4** air_med_p95 235914.4 

air_p95_p95 235911.9 235918.5 236090.1 235244.7 

air_avg_p99 235906.2 

air_med_p99 235903.5 235766.3** 235718.3 

Air Lead 

air_p95_p99 235905.8 235695.8 

TRI Compounds air_fug 235943.8 235684.6 235325.2 

TRI Compounds air_tot 235922.9 235940.6 235199.3 

TRI Compounds air_stk 235921.5 235940.7 235406.7 235355.6 

TRI Compounds under_inj 235925.3 235968.5 235986.4 

TRI Compounds water_surf 235921.3 235942.9 235910.3 235912.1 

TRI Lead Only air_fug 235927.2 235312.9 235155.4 

TRI Lead Only air_tot 235929.4 235955.8 235385.1 235169.4 

TRI Lead Only air_stk 235928.7 235955.2 235437.5 

TRI Lead Only under_inj 235928.5 235985.8 235997.1 

TRI Lead Only water_surf 235926.6 235952.3 235942.9 

TRI Lead Total air_fug 235927.3 235950.7 235244.9** 234850.4* 

TRI Lead Total air_tot 235930 235957.3 235036 

TRI Lead Total air_stk 235955.9 235478.1 235321.1 

TRI Lead Total under_inj 235928.4 235956.1 235984.3 235999.2 

TRI Lead Total water_surf 235926.7 235933 

tri_as1_p95 235909 234966.5 235011.7 

tri_as2_p95 235912.6 235917.9 234262.7 

tri_as3_p95 235907.5 235910.7 

tri_af1_p95 235914 235919.2 235132.3 235125.1 

tri_af2_p95 235910.9 235916.8 234837.1 233669.7 

tri_af3_p95 235915.8 234396.5 233058.4 

tri_at1_p95 234716.4 234606.5 

tri_at2_p95 235911.7 235915.7 233993.9 232572.7 

tri_at3_p95 235910.2 233685.3** 232564.5* 

tri_ws1_p95 235919.1 235370.9 235422 

tri_ws2_p95 235908.1 235915.4 233861.9 233253.8 

tri_ws3_p95 235908 

tri_ui1_p95 235904.1 235904.1 234661.9 233559.3 

tri_ui2_p95 235904.1 235904.1 234661.9 233559.3 

tri_ui3_p95 235904.1 235904.1 234661.9 233559.3 

tri_as1_p99 235908.5 235519.5 

tri_as2_p99 235908.3 235914.4 235104.8 

tri_as3_p99 235906.6 235912 

tri_af1_p99 235906.1 235735.5 

tri_af2_p99 235907.5 235912.6 234680 234116.8 

tri_af3_p99 235905.7 235128.3 234668.4 

tri_at1_p99 235909.1 235711.7 235364.2 

TRI 

tri_at2_p99 235915.6 234704.6 
 

33 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

tri_at3_p99 235907.7 235913.8 235213.9 234780.2 

tri_ws1_p99 235907 235912.3 235863.4 235847.8 

tri_ws2_p99 235907.6 235913 235667.2 235712.8 

tri_ws3_p99 235907.6 235913.9 235706.5 235748.5 

 

tri_ui2_p99 235904.1 235904.1 234661.9 233559.3 

tri_ui3_p99 235905 235910.1 235921.5 235887.1 

 CDC_cur_lag6 235415.6 234816.9 234090.5 

 CDC_cur_lag12 235427.3 235275.1 234678.5 233854.6 

 CDC_cur_lag18 235270.6 234599.8 233781.8* 

 CDC_cur_lag24 235847 235039.4 234566.7 

 CDC_cur_lag30 235897.1 235246 

 CDC_cur_lag36 235727.6 235050.5 234702.5 234162.9 

 HUD_cur_lag6 235914 235833.5 235432.4 235494.8 

 HUD_cur_lag12 235761.9 235691.3 235358.3 235381.6 

 HUD_cur_lag18 235762.7 235673.8 235437.5 235352.7 

 HUD_cur_lag24 235707.6 235525.1 235434.3 235211.7 

 HUD_cur_lag30 235672.8 235487.1 235445.4 235175.9 

 HUD_cur_lag36 235626.3 235273 234912.4 

 CDC_cum_lag6 235611.1 234603.5 234200.7 233952.6 

 CDC_cum_lag12 235762.8 234668.8 234304.8 

 CDC_cum_lag18 235859.9 234760.3 234472.7 234162.5 

 CDC_cum_lag24 235898.2 234851.6 234646.1 

 CDC_cum_lag30 234933.1 234793.8 234433.2 

 CDC_cum_lag36 235883 234920.4 234824.7 234466.2 

Funding HUD_cum_lag6 235908.5 234878.9 234725.3 234382.8 

 HUD_cum_lag12 235924.3 234413.4 

 HUD_cum_lag18 235961.9 235051 234650.3 

 HUD_cum_lag24 235952.8 235099.6 234558.3 234503.5 

 HUD_cum_lag30 235897.3 235132.9 234450.4 234499.3 

 HUD_cum_lag36 235794 235148.6 234334.5 

 tot_cur_lag6 235918.7 235841.5 235210 235306.5 

 tot_cur_lag12 235727.4 235169.7 235194.9 

 tot_cur_lag18 235799.2 235654.7 235245.5 235101.6 

 tot_cur_lag24 235742.9 235439.1 235226.8 234897.9 

 tot_cur_lag30 235657.8 235355.1 235216.4 234839.7 

 tot_cur_lag36 235546.3 235043.1 235054.3 234518.3 

 tot_cum_lag6 235928.9 234463 

 tot_cum_lag12 234735 234380.2 234067.2 

 tot_cum_lag18 235958 234825.3 234340.7 234123.9 

 tot_cum_lag24 235944.2 234876.7 234168.7 

 tot_cum_lag30 235888.1 234190.6 234192.1 

 tot_cum_lag36 235774.3 234937.9 234115.8** 234217.6 

HUD_cur 252824.5 252845.5 252876.3 

HUD_cum 252864.5 252670.1 252673.7 252679.3 

CDC_cur 252679.7 252170.2 251830.5 251799.9 

CDC_cum 252586.4 252213.5 252226.6 252202.3 
 

34 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

Current – HUD+CDC 235788 235296.1 235214.1 Funding Cumulative – HUD+CDC 235940.8 234583.8 234050.2 

Screening screen_penetration 232188 232220.8 231442.3** 230769.8* 

** Variable factor(s) showed best fit when adjusted for degrees of freedom and were thus chosen to represent 

parameter category in multivariate analysis. 

* Variable factors showed best fit; however, were not included in multivariate analysis because the time 

categorical variable had less than ideal prediction properties. 

Table 4-2. Summary of Exploratory Analysis Fit as shown by -2 Log Likelihoods for 

Pr(PbB >= 10 μg/dL) Models 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

Median_Family_Income 252403.4 252372.3 251685 251406 

Median_HH_Income 252382.8 251605.3 251222.3 

Median_Per_Capita_Income 252486.2 252425 251792.5 251439.9 

Pct_HH_No_Earnings 252446.7 252444 251506.4 251091 

Pct_HH_No_Wage 252363.4 252336.2 251373.8** 250935.7 

Pct_HH_Public_Assist 252779.8 252806.7 251403.6 250521.9 

Pct_LT_Poverty 252743.7 252763.4 251392.3 250602.3 

Pct_Family_Income_LT_Poverty 252715.7 252736.5 250516 

Income 

Pct_LE_5Yrs_LT_Poverty 252839.5 252848.3 250483.1* 

Pct_Asian 252668.4 252569.2 252369.5 250374.8 

Pct_Black 253025.3 253012.9 252123.9 251966.4 

Pct_White 252930.5 252888 252285.1 

Pct_NHOPI 252837.9 253276.4 252846.7 

Pct_Other_Race 252775.6 252727.4 252540.6 252403.1 

Pct_Multi_Race 252788.2 252745.4 251886.2** 

Race 

Pct_Hispanic 252813.9 248350.1* 

Median_Rent 252008.3 251790.4 251043.0** 250455.8* Housing Cost Housing_Value 252392.2 252324.9 252139.5 

Pct_Rented 253049.2 252943.3** 251135.1* Occupancy Pct_Vacant 252968.6 252990.6 252368.7 

Single Parent Pct_Single_Parent 253124 253084.3 251927.9** 251596.8* 

Median_Yr_Built 252361 252361 252263.4 252227.6 

Median_Yr_Occ_Built 252391.1 252391.8 251439.8 250974.6 

Pct_Built_Pre_1940 252030 251996.7 251206.9 

Pct_Built_Pre_1950 252006.6 251977.8 251082.9 250788.7 

Pct_Built_Pre_1960 252250.6 252241.6 251073.7** 250590.1* 

Pct_Built_Pre_1970 252433.4 252431.3 251254.4 250672.3 

Pct_Built_Pre_1980 252481.8 251344.2 250756.3 

Pct_Occ_Built_Pre_1940 252035.3 252001.6 251398 

Pct_Occ_Built_Pre_1950 252020.3 251992 251106 250805.4 

Pct_Occ_Built_Pre_1960 252267.3 251103.2 250611.8 

Pct_Occ_Built_Pre_1970 252477.8 252477.2 250713.2 

Home Age 

Pct_Occ_Built_Pre_1980 252508.2 252502 251371.5 250782.6 

Pct_LE_Six 252767 252725.9 251597.1** 251003.9* Children Num_LE_Six 252881.3 252835.7 
 

35 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

Pct_LT_9th_Grade 252734.3 252691.3 251568.3 249792.4* 

Pct_No_HS_Degree 252574.1 252551.1 251197.8 250216.7 

Pct_No_College 252279.4 252216.7 251090.4** 250602.5 Education 

Pct_No_College_Degree 252237.3 251142.9 250691.1 

Total_Housing_Units 252895.2 252818.7 251937 243207.7 

Population Total_Pop 252890.7 252834.7 251907.9** 242397.1* 

Housing_Density 252854.6 252838.1 252786.9 252547.2 

air_avg 252880.2 252861.4 252906.8 252015.3 

air_med 252884.8 252867.1 253026.4 251966.2* 

air_p95 252876.9 252863.8 252740.9** 252187.9 

air_avg_p95 252912.5 252878.3 249593.0* 

air_med_p95 252910 252728.4** 252883.7 

air_p95_p95 252885 253156.2 

air_avg_p99 252841.7 252844 252840.5 252814.5 

air_med_p99 252839.7 252842.6 252819.6 252786.5 

Air Lead 

air_p95_p99 252848.7 252852.6 252832.5 

TRI Compounds air_fug 252867.9 252889.1 252914 252314.2 

TRI Compounds air_tot 252889.4 252901.7 252880.6 252313.3 

TRI Compounds air_stk 252884.9 252894.2 252815.7 252454.4 

TRI Compounds under_inj 252862.5 252885.6 252919.1 

TRI Compounds water_surf 252864.1 252885.1 252884.7 

TRI Lead Only air_fug 252869.4 252894.4 252747.2 252624.6 

TRI Lead Only air_tot 252884.3 252905.2 252653.5** 252138.6 

TRI Lead Only air_stk 252882.2 252900.4 252707.7 252298.7 

TRI Lead Only under_inj 252866.5 252889.9 252907.5 252931.1 

TRI Lead Only water_surf 252866.8 252892.3 252900.6 

TRI Lead Total air_fug 252871.7 252896.1 252798.3 252475 

TRI Lead Total air_tot 252891.5 252909.9 252702.6 252031.8* 

TRI Lead Total air_stk 252890.3 252905.6 252699.8 252203.4 

TRI Lead Total under_inj 252867.1 252889.4 252904.5 252929.7 

TRI Lead Total water_surf 252868.4 252893.9 252897.6 

tri_as1_p95 252887.8 252864.5 252435.7 

tri_as2_p95 252886.8 247577.4 

tri_as3_p95 252922.4 252903.3 251601.7 248106.4 

tri_af1_p95 252923.9 252910.9 252833 252941.9 

tri_af2_p95 252864.3 252862.8 252237.8 248140.5 

tri_af3_p95 252883.1 252872.3 251998.1 248650.8 

tri_at1_p95 252886.9 252855.8 252210.2 

tri_at2_p95 252911.6 251677.1 247510.1* 

tri_at3_p95 252893.2 251553.2 248305.6 

tri_ws1_p95 252904.6 252880.2 253019.4 252996.8 

tri_ws2_p95 252885.1 251407.9** 

tri_ws3_p95 252892.3 252895.8 251422.9 248164.1 

tri_ui1_p95 252840.1 252840.1 251871.5 251377.4 

tri_ui2_p95 252840.1 252840.1 251871.5 251377.4 

tri_ui3_p95 252840.1 252840.1 251871.5 251377.4 

Tri 

tri_as1_p99 252856.4 
 

36 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

tri_as2_p99 252864.7 252768.7 252011.1 

tri_as3_p99 252867.3 252867.6 252781.5 

tri_af1_p99 252855.1 252872.8 

tri_af2_p99 252866.8 252862.5 252719 251667.2 

tri_af3_p99 252851.4 252852.6 252743.1 251999.2 

tri_at1_p99 252844.8 252850.4 252865.3 252235.8 

tri_at2_p99 252869.5 252869.6 252035.9 

tri_at3_p99 252863.2 252860.2 252780.2 252047.7 

tri_ws1_p99 252864.6 252865.7 252817.4 252839.7 

tri_ws2_p99 252853.8 252857.9 252679.5 252740.5 

tri_ws3_p99 252858.5 252859.9 252756.3 

tri_ui1_p99 252840.1 252840.1 251871.5 251377.4 

tri_ui2_p99 252840.1 252840.1 251871.5 251377.4 

tri_ui3_p99 252842.9 252851.7 252822.1 252824.4 

 CDC_cur_lag6 252593.4 252079 251795.6 

 CDC_cur_lag12 252468.6 251799 251576.9** 251723.5 

 CDC_cur_lag18 252652.5 252011.3 251869.8 

 CDC_cur_lag24 252698.2 252155.7 251983.6 251948.3 

 CDC_cur_lag30 252579.9 252298.4 252201.5 

 CDC_cur_lag36 252861.4 252659.6 

 HUD_cur_lag6 252848.9 252867.7 252599.3 252883.1 

 HUD_cur_lag12 252836 252839.2 252674.2 252823 

 HUD_cur_lag18 252857.7 252873.7 252693.1 252856.3 

 HUD_cur_lag24 252847.7 252847.4 252785.4 252804.8 

 HUD_cur_lag30 252821.7 252849.1 252709.2 

 HUD_cur_lag36 252800.2 252769.4 252762.3 252713.8 

 CDC_cum_lag6 252638.8 252230.7 252255.1 

 CDC_cum_lag12 252277.9 252311.3 252258.1 

 CDC_cum_lag18 252387.7 252319.1 

 CDC_cum_lag24 252817.8 252422.6 252451.6 252377.5 

Funding CDC_cum_lag30 252840.3 252479.6 252498.3 252424.6 

 CDC_cum_lag36 252836.1 252501 252515.7 252446.4 

 HUD_cum_lag6 252859.8 252650.4 252640.5 

 HUD_cum_lag12 252856.9 252607.7 252639.5 252615.3 

 HUD_cum_lag18 252856.7 252636 252602.2 

 HUD_cum_lag24 252852.4 252583.7 252612.3 252582.4 

 HUD_cum_lag30 252853.1 252570.4 252586.8 252559.1 

 HUD_cum_lag36 252556.3 252544.6 252520.3 

 tot_cur_lag6 252840.8 252857 252532.5 252837.6 

 tot_cur_lag12 252848.3 252826.7 252615.3 252765.8 

 tot_cur_lag18 252863.6 252859.5 252627.1 252788.9 

 tot_cur_lag24 252855.8 252803.6 252686.2 252715.8 

 tot_cur_lag30 252838.7 252608.6 252773.5 

 tot_cur_lag36 252796.7 252732.3 252677.3 252653.3 

 tot_cum_lag6 252863.1 252551.2 252577.9 252560.4 

 tot_cum_lag12 252861 252531.9 252565.2 

 tot_cum_lag18 252858.7 252530.3 252565.1 252537.4 
 

37 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

tot_cum_lag24 252518.4 252551.1 252528.4 

tot_cum_lag30 252854.9 252510.3 252535.2 252515.6 

tot_cum_lag36 252855.1 252503 252491.2 

HUD_cur 252824.5 252845.5 252876.3 

HUD_cum 252864.5 252670.1 252673.7 252679.3 

CDC_cur 252679.7 252170.2 251830.5 251799.9 

CDC_cum 252586.4 252213.5 252226.6 252202.3 

Current – HUD+CDC 252812.9 252831.6 252573.5 252837 

Funding 

Cumulative – HUD+CDC 252861.2 252590.5 252602.3 252591.5 

Screening screen_penetration 243704.7 243043.2** 243416.3 

** Variable factor(s) showed best fit when adjusted for degrees of freedom and were thus chosen to represent 

parameter category in multivariate analysis. 

* Variable factors showed best fit; however, were not included in multivariate analysis because the time 

categorical variable had less than ideal prediction properties. 

Table 4-3. Summary of Exploratory Analysis Fit as shown by -2 Log Likelihoods for 

Pr(PbB >= 15 μg/dL) Models 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

Median_Family_Income 292772.5 292744.3 292659.9 292689.4 

Median_HH_Income 292732.9 292590.8 292579.8 

Median_Per_Capita_Income 292812.2 292732.2 292766.8 

Pct_HH_No_Earnings 292772.9 292756 292428.7 

Pct_HH_No_Wage 292673.9 292612.3 292449.8** 292310.0* 

Pct_HH_Public_Assist 293171.5 293226 292889.5 292588 

Pct_LT_Poverty 293148.6 293226.2 292933.3 292609.9 

Pct_Family_Income_LT_Poverty 293112.9 292898.4 292547.8 

Income 

Pct_LE_5Yrs_LT_Poverty 293290.6 293338.3 292997.4 292700.3 

Pct_Asian 292966.2** 293176.7 292343.9 

Pct_Black 293610.6 293556.2 293324.7 293411.1 

Pct_White 293448.5 293343.9 293334.4 293311.7 

Pct_NHOPI 293217.4 293230 293216.3 

Pct_Other_Race 293165.6 293130.1 293088.7 293085.7 

Pct_Multi_Race 293181.3 293035.3 292946.7 

Race 

Pct_Hispanic 293237.8 293524.2 292091.3* 

Housing Median_Rent 292358.3 292076.9 291971.3** 292091.4 

Cost Housing_Value 292727.1 292691.2 292732.6 292573.7 

Pct_Rented 293905.5 293533.3** Occupancy Pct_Vacant 293703.2 293721.5 293765 293491.3* 

Single 

Parent Pct_Single_Parent 293863 293781.9** 

 Median_Yr_Built 292980.6 292980.6 293008.9 292998.6 

 Median_Yr_Occ_Built 292999.8 293001.5 292856.3 292749.7 

Home Age Pct_Built_Pre_1940 292381.9 292335.9 292195.2 292161 

 Pct_Built_Pre_1950 292404.2 292364.6 292078.8 

 Pct_Built_Pre_1960 292815.6 292525.3 292400.7 
 

38 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

 Pct_Built_Pre_1970 293100 293103.4 292826.6 292669 

 Pct_Built_Pre_1980 293086.5 293089.8 292851.2 292684.6 

 Pct_Occ_Built_Pre_1940 292356.8 292313.7 292177 292138.7 

Home Age Pct_Occ_Built_Pre_1950 292357.3 292139.4** 292071.1* 

 Pct_Occ_Built_Pre_1960 292842.2 292546.1 292418.1 

 Pct_Occ_Built_Pre_1970 293160.9 292884 292725.2 

 Pct_Occ_Built_Pre_1980 293111.9 292711 

Pct_LE_Six 293214.5 292911.5** 292859.9 Children Num_LE_Six 293389 293281.3 293584.6 290311.1* 

Pct_LT_9th_Grade 293199.4 293131.7 293000.2 292491.7 

Pct_No_HS_Degree 292960 292951 292701.2 292376 

Pct_No_College 292557.4 292434.4 292260.2** 292152.4* Education 

Pct_No_College_Degree 292613.7 292501.1 292328.1 292254.9 

Total_Housing_Units 293444.1 293298.7 293466.2 

Population Total_Pop 293417.4 293297.9 293561.7 290521.5* 

Housing_Density 293273.5 293267.2** 293232.3 

air_avg 293392.7 293361.7 293366.1 

air_med 293410.8 293382.5 293418.4 292995.5* 

air_p95 293378.4 293353.2 293316.8** 293112.1 

air_avg_p95 293522.6 293462.9 293467.7 292547.1* 

air_med_p95 293524.1 293509.8** 292580.3* 

air_p95_p95 293421.4 293566.7 292731.7 

air_med_p99 293289.2** 293293.8 293304.7 293262.7 

air_avg_p99 293312.1 293284.2 

air_med_p99 293289.2** 293293.8 293304.7 293262.7 

Air Lead 

air_p95_p99 293307 293306.7 

TRI Compounds air_fug 293312 293329.5 293358.7 

TRI Compounds air_tot 293391.4 293416.4 

TRI Compounds air_stk 293379.4 293373.4 293382.6 293324 

TRI Compounds under_inj 293280.9** 293325.9 

TRI Compounds water_surf 293302.9 293322.7 293339.6 

TRI Lead Only air_fug 293303.9 293327.8 293305.4 293302.9 

TRI Lead Only air_tot 293317.6 293193.9* 

TRI Lead Only air_stk 293339.1 293351.3 293337.7 293240.5 

TRI Lead Only under_inj 293317.4 293358.1 

TRI Lead Only water_surf 293295.9 293321.1 293362.7 

TRI Lead Total air_fug 293334.7 293331 

TRI Lead Total air_tot 293361.2 293369.8 293351.5 293196.7 

TRI Lead Total air_stk 293364.2 293370.5 293355.6 293251.3 

TRI Lead Total under_inj 293315.8 293344.4 293356.7 

TRI Lead Total water_surf 293300.6 293326 293350.3 293369 

tri_as1_p95 293431.9 293374.3 293326.2 293354.1 

tri_as2_p95 293447.9 

tri_as3_p95 293468.1 293184.4 292325.9 

tri_af1_p95 293511.4 293486.3 293488.2 293535.3 

tri_af2_p95 293346.9 293341.6 292046.2* 

Tri 

tri_af3_p95 293406.8 293388.9 293217 292195.8 
 

39 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

tri_at1_p95 293445.5 293386 293309.2 

tri_at2_p95 293490.2 293434.4 293188.8 

tri_at3_p95 293524.3 293473.4 293159 292314 

tri_ws1_p95 293384.9 293682.5 

tri_ws2_p95 293397.5 293388.1 293081.1** 292172.3 

tri_ws3_p95 293449.3 293433.9 293122.9 292238.7 

tri_ui1_p95 293260.7 293260.7 293101.5 

tri_ui2_p95 293260.7 293260.7 293101.5 

tri_ui3_p95 293260.7 293260.7 293101.5 

tri_as1_p99 293300.7 293299.9 293278.9 

tri_as2_p99 293334.1 293325.5 

tri_as3_p99 293352.7 293342.5 293339.9 293153 

tri_af1_p99 293317.7 293328.2 293169 

tri_af2_p99 293341.5 293329 293303.8 293016 

tri_af3_p99 293319.2 293311.8 293303.8 293101.5 

tri_at1_p99 293295.1 293296.7 293129.5 

tri_at2_p99 293359.2 293347.3 293169.3 

tri_at3_p99 293332.6 293315.4 293315.4 293153.9 

tri_ws1_p99 293338.4 293329.3 293345.2 

tri_ws2_p99 293304.9 293222.9 293282 

tri_ws3_p99 293308.9 

tri_ui1_p99 293260.7 293260.7 293101.5 

tri_ui2_p99 293260.7 293260.7 293101.5 

tri_ui3_p99 293269.5 293293.4 293282.9 

 CDC_cur_lag6 293205.3 292977.5 292865.8 292890.8 

 CDC_cur_lag12 293218.4 292865.8 292774.0** 292863.8 

 CDC_cur_lag18 293255.1 292878.1 292799.5 292857.9 

 CDC_cur_lag24 293274.7 292961.8 292890.1 292900.2 

 CDC_cur_lag30 293176.8 293015.4 293003.6 

 CDC_cur_lag36 293290.1 293206.1 293076.1 293048.7 

 HUD_cur_lag6 293284.6 293128.1 293287.2 

 HUD_cur_lag12 293253.2 293249.9 293149.3 293242.7 

 HUD_cur_lag18 293258.5 293268.9 293117.4 

Funding HUD_cur_lag24 293253.7 293257.1 293203.1 293251.9 

 HUD_cur_lag30 293238.4 293251.9 293106.6 293268.9 

 HUD_cur_lag36 293208.4 293194.5 293190.6 293186.5 

 CDC_cum_lag6 293422.1 293214.4 293231.5 293238 

 CDC_cum_lag12 293393.4 293207.1 

 CDC_cum_lag18 293368.7 293212.7 293218.9 

 CDC_cum_lag24 293218.2 293214.6 

 CDC_cum_lag30 293218 293228.4 293207.6 

 CDC_cum_lag36 293310.8 293205.4 293218.2 293193.2 

 HUD_cum_lag6 293239.4 293145.3 

 HUD_cum_lag12 293234.4 293120.8 293146.5 293150.1 

 HUD_cum_lag18 293243.7 293134.7 293163.9 293150.3 

 HUD_cum_lag24 293257.1 293145.3 293148.9 

 HUD_cum_lag30 293267.1 293164.4 293133.9 
 

40 

Parameter 

Category Variable Name X Only Linear Time 

Quadratic 

Time 

Categorical 

Time 

 HUD_cum_lag36 293278.3 293149.3 293146.1 293110.8 

 tot_cur_lag6 293267.9 293280.2 293102.1 293268.2 

 tot_cur_lag12 293260.9 293241.6 293127.1 293218.6 

 tot_cur_lag18 293262.4 293261.9 293237.1 

 tot_cur_lag24 293257.8 293239.6 293160.8 293215.4 

 tot_cur_lag30 293245.2 293258.1 293049.9 293252.3 

 tot_cur_lag36 293206.8 293151.9 293164.7 

 tot_cum_lag6 293257.7 293107.8 293124.1 

 tot_cum_lag12 293100 293123.9 293133.9 

Funding tot_cum_lag18 293257.7 293114.6 293142.1 293138.5 

 tot_cum_lag24 293267.9 293154.5 293141.8 

 tot_cum_lag30 293275.4 293128.8 293153.2 

 tot_cum_lag36 293284.2 293130.5 293142.3 293117.5 

HUD_cur 293269.1 293287.6 293172.6 293293 

HUD_cum 293156.9 293156.8 293193.2 

CDC_cur 293240.8 292881.8 292906.9 

CDC_cum 293450.7 293231.1 293246.3 293256.8 

 Current – HUD+CDC 293267.6 293284.9 

 Cumulative – HUD+CDC 293135.6 293170.4 

Screening screen_penetration 286744.8** 

** Variable factor(s) showed best fit when adjusted for degrees of freedom and were thus chosen to represent 

parameter category in multivariate analysis. 

* Variable factors showed best fit; however, were not included in multivariate analysis because the time 

categorical variable had less than ideal prediction properties.

Table 4-4. Summary of Exploratory Analysis Fit as shown by -2 Log Likelihoods for 

Pr(PbB >= 25 μg/dL) Models 

Parameter 

Category Variable Name X Only Linear Time Quadratic Time 

Categorical 

Time 

Median_Family_Income 364225.4 364192.5 364302.8 364426 

Median_HH_Income 364098.6 364048 364139.1 364252.5 

Median_Per_Capita_Income 364504.4 364426.7 364532.3 364681.7 

Pct_HH_No_Earnings 363967.7 363893.9** 364071.9 364002.6 

Pct_HH_No_Wage 363920.7 363960.8 363949.4 

Pct_HH_Public_Assist 364638.9 364705.3 364637.4 

Pct_LT_Poverty 364611.6 364741.3 364847.1 364616.8 

Pct_Family_Income_LT_Poverty 364541.7 364696 364777.3 364527.4 

Income 

Pct_LE_5Yrs_LT_Poverty 364863.6 364929.7 

Pct_Asian 364527.2 364399.3** 364394.5* 

Pct_Black 365490.4 365511.8 

Pct_White 365248.9 365038.9 365365.2 

Pct_NHOPI 364794.8 364856 364770.1 

Pct_Other_Race 364698 364678.7 

Pct_Multi_Race 364801.9 364772.8 364831.2 364838.6 

Race 

Pct_Hispanic 364789.2 364703.1 

Housing Median_Rent 363769.6 363524.9** 363876.3 
 

41 

Parameter 

Category Variable Name X Only Linear Time Quadratic Time 

Categorical 

Time 

Cost Housing_Value 364228.4 364217.5 364266.9 364326.7 

Pct_Rented 366003.6** 366069.6 366361.5 Occupancy Pct_Vacant 366381.1 366351.7 366647.4 366332.7 

Single 

Parent Pct_Single_Parent 365919.4 365878.4** 365993.3 366022.9 

Median_Yr_Built 364858.6 364893.4 364874.1 364997.8 

Median_Yr_Occ_Built 364890.1 364927.1 365077.9 365041.9 

Pct_Built_Pre_1940 363573.4 363524.8 363636.7 363617.9 

Pct_Built_Pre_1950 363716.9 363694.8 363795.8 363754.9 

Pct_Built_Pre_1960 364677.4 364715.4 364720.3 

Pct_Built_Pre_1970 365255 365322.4 365404.2 365310.9 

Pct_Built_Pre_1980 365157.7 365231.3 365333.9 365231.9 

Pct_Occ_Built_Pre_1940 363502.8** 363615.6 363591.1 

Pct_Occ_Built_Pre_1950 363710.5 363694.8 363795.4 

Pct_Occ_Built_Pre_1960 364710.4 364754.6 

Pct_Occ_Built_Pre_1970 365363.2 365429.2 365509.7 365420.4 

Home Age 

Pct_Occ_Built_Pre_1980 365200.7 365373.4 365276 

Pct_LE_Six 364874.1 364787.6** 365003.5 Children Num_LE_Six 365297.1 

Pct_LT_9th_Grade 364694.7 364636.7 364676.4 364634.3 

Pct_No_HS_Degree 364365.8 364490.3 364359.9 

Pct_No_College 363888.4 363710.1** 363897.3 363941.3 Education 

Pct_No_College_Degree 364172.5 363983.5 364160.7 

Total_Housing_Units 365469.1 365116.6 

Population Total_Pop 365377.3 365172.2 

Housing_Density 364890.0** 364908.1 364921.6 364925.2 

air_avg 365109.3 365098.9 365098.8 365022.8* 

air_med 365149.3 365142.8 

air_p95 365066.7 365050.9** 365053.1 365028.1 

air_avg_p95 365506.4 365342.9 

air_med_p95 365605.6** 365444.5* 

air_p95_p95 365231.4 365186.4 365205.3 

air_med_p99 364910.2** 364934.1 364912.5* 

air_avg_p99 364950.2 364949.7 364959 364957.4 

air_p95_p99 364974.5 364974.2 364984.1 

TRI Compounds air_fug 365029.5 365019.8 365019.4 

 TRI Compounds air_tot 365254.2 365215.5 365259.6 

 TRI Compounds air_stk 365170.3 365147.7 365176.2 365183.3 

 TRI Compounds under_inj 364946 364964.8 365107.4 

 TRI Compounds water_surf 364940.3 364958 364980.3 364994 

Tri TRI Lead Only air_fug 364920.3 365037.8 

 TRI Lead Only air_tot 364918.4 364960.3 364976.7 

 TRI Lead Only air_stk 364950.5 364975.5 364992.6 365001.8 

 TRI Lead Only under_inj 364931.6 364947.7 364984.2 364995.3 

 TRI Lead Only water_surf 364934.6 364960.9 365008.7 

 TRI Lead Total air_fug 364905.3** 364928.5 364977.9 

 TRI Lead Total air_tot 364996.6 365013.8 365014.8 
 

42 

Parameter 

Category Variable Name X Only Linear Time Quadratic Time 

Categorical 

Time 

 TRI Lead Total air_stk 365012.9 365029.9 365049.1 365054.7 

 TRI Lead Total under_inj 364926.7 364942.8 364980 364990.4 

 TRI Lead Total water_surf 364946.9 364973.4 365004.6 365022.5 

tri_as1_p95 365325.7 365249.4 365249.7 

tri_as2_p95 365223.1 365193.4 365152.7 

tri_as3_p95 365559.3 365489.7 365459.1 365423.2 

tri_af1_p95 365498 365506.5 365620 

tri_af2_p95 365113.2 365113.5 365005.7 

tri_af3_p95 365283.2 365267 365225.7 365145.6 

tri_at1_p95 365406.5 365320.9 365306.8 365423.7 

tri_at2_p95 365435.5 365358.5 365319.4 365270.2 

tri_ws1_p95 365307.8 365270.9 365266.6 

tri_ws2_p95 365239.4 365230.3 365195 

tri_ws3_p95 365338.3 365316.1 365285.3 

Tri tri_ui1_p95 364871.7 364871.7 365011.6 364990 

tri_ui2_p95 364871.7 364871.7 365011.6 364990 

tri_ui3_p95 364871.7 364871.7 365011.6 364990 

tri_as1_p99 364965.4 364961.3 364961.2 364964.3 

tri_as2_p99 365027.6 365021.2 365024.1 364974.7 

tri_as3_p99 365079.1 365059.8 365067.5 365020.9 

tri_af1_p99 365068 365051.1 

tri_af2_p99 365053.7 365042.3 365038.6 364985.1 

tri_af3_p99 365022.6 365006.5 365010.2 364974 

tri_at1_p99 365048.8 365036.8 365050 364994.8 

tri_at2_p99 365034.9 365011.9 365019.8 365005.5 

tri_at3_p99 364999.7 364972.1 364983 

tri_ws1_p99 364994.9 364977.9 364985.8 364990.4 

tri_ws2_p99 364991.4 364981.6 364976.5 

tri_ws3_p99 364951.1 364993.6 

tri_ui1_p99 364871.7 364871.7 365011.6 364990 

tri_ui2_p99 364871.7 364871.7 365011.6 364990 

tri_ui3_p99 364867.2 364864.5** 364857.2* 

 CDC_cur_lag6 365029.5 364956.9 364956.9 364945.6 

 CDC_cur_lag12 365008.6 364858.7 364871.8 364857.2 

 CDC_cur_lag18 364967 364840.3 364881.1 364852 

 CDC_cur_lag24 364989 364897 364960.1 

 CDC_cur_lag30 364937.9 364919.4 364963.5 364906.9 

 CDC_cur_lag36 364893.3 364894.9 364991.3 364904.2 

 HUD_cur_lag6 364916 364927.7 364808.6 364920 

Funding HUD_cur_lag12 364889.1 364804.6 364900.9 

 HUD_cur_lag18 364869.8 364768.1** 

 HUD_cur_lag24 364850.4 364863.1 364824 364891.8 

 HUD_cur_lag30 364824.3 364841.4 364789.4 

 HUD_cur_lag36 364796.1 364782.8 364802.3 364768.8* 

 CDC_cum_lag6 365040.7 365009.7 365084.8 365040 

 CDC_cum_lag12 365006.7 365000.8 365059.1 365027.3 

 CDC_cum_lag18 364981.8 365047.7 365021.5 
 

43 

Parameter 

Category Variable Name X Only Linear Time Quadratic Time 

Categorical 

Time 

 CDC_cum_lag24 364957 364993.3 365033.1 365011.9 

 CDC_cum_lag30 364934.4 364984.2 365017.3 

 CDC_cum_lag36 364920.3 364978 365004.7 

 HUD_cum_lag6 364860.6 364793.5 364808.3 364816.4 

 HUD_cum_lag12 364850.7 364788 364807.5 

 HUD_cum_lag18 364851.8 364791.1 364810.2 364794.2 

 HUD_cum_lag24 364867.1 364816.1 364790.5 

 HUD_cum_lag30 364877.2 364807.6 364803.6 364772.6 

 HUD_cum_lag36 364892.6 364826.6 364809.5 364775.8 

 tot_cur_lag6 364930.2 364941.5 364842.7 364926.8 

 tot_cur_lag12 364840.7 364900 

 tot_cur_lag18 364862.5 364872.6 364795.3 364887.3 

Funding tot_cur_lag24 364862 364873 364853.4 

 tot_cur_lag30 364830.9 364848.9 364794.7 364868.3 

 tot_cur_lag36 364793.7 364783.3 364816.2 364776.2 

 tot_cum_lag6 364890.4 364819.5 364839.4 364845.2 

 tot_cum_lag12 364876.1 364814 364833.9 364836.1 

 tot_cum_lag18 364873.5 364819 364837.1 364830.7 

 tot_cum_lag24 364884.2 364833.1 364846 364832.5 

 tot_cum_lag30 364889.6 364839.5 364821.7 

 tot_cum_lag36 364902.3 364849.2 364829.3 

HUD_cur 364930.7 364948 364886.1 364936.8 

HUD_cum 364883.2 364815.7 364835.9 

CDC_cur 365027.8 364962.7 364969.9 364980.6 

CDC_cum 365081.4 365028.2 365131.3 365060.7 

 Current – HUD+CDC 364946.5 364966.1 364919.2 

 Cumulative – HUD+CDC 364843 364865.1 364864.6 

Screening screen_penetration 360376 360256.7** 360321.8 

** Variable factor(s) showed best fit when adjusted for degrees of freedom and were thus chosen to represent 

parameter category in multivariate analysis. 

* Variable factors showed best fit; however, were not included in multivariate analysis because the time 

categorical variable had less than ideal prediction properties. 

4.2 Relationship between Local Blood-Lead Data and Explanatory Variables

Many of the variables investigated for the National (Low Resolution) model also were explored 

for the local modeling using Massachusetts data. All of the census data were used in both 

models, although at the census-tract level rather than at the county level. The various 

demographic, environmental, and programmatic variables were explored using the same 

techniques as the national data, which were described in Section 2.2. Detailed figures and tables 

containing exploratory results are included in Appendix B. A detailed discussion of the results 

seen in Appendix B is contained in Appendix E. Table 4-5 presents the log-likelihood statistics 

that resulted from the bivariate modeling. Variables presenting the best model fit within each 

variable category are highlighted in yellow. 
44 

Table 4-5. Summary of Log-likelihood Ratios from each Model Fit to all Potential Explanatory Variables, 

Variable Category Variable Model 1 Model 2 Model 3 Income Median Family Income ($) 51727.2 48154.7 86501.8 Income Median Household Income ($) 51689.2 48114.6 86375.5 Income Median Per Capita Income ($) 51917.2 48345.5 86812.3 Income Percent No Household Earnings 52020.1 48445.8 86853.4 Income Percent No Household Wage 52039.6 48467.3 86858.3 Income Percent Household on Public Assistance 51963.8 48385.7 86854.4 Income Percent Below Poverty Line 51974.1 48389.9 86778.4 Income Percent Family Income Below Poverty Line 51991.3 48412.1 86847.5 Income Percent Less than 5 Years in Poverty 52025.2 48446.0 86924.8 . Race Percent Amer. Indian and Alaskan Native Alone 52259.2 48692.5 87120.6 Race Percent Asian Alone 52264.2 48699.0 87139.8 . Race Percent Black Alone 52170.1 48599.1 87051.0 Race Percent White Alone 52123.5 48547.4 86960.9 Race Percent Native Hawaiian and Other Pacific Islander Alone 52273.4 48706.6 87135.6 Race Percent Other Race Alone 52202.6 48633.4 87055.1 Race Percent Multiple Races 52042.2 48470.6 86889.1 Race Percent Hispanic 52181.3 48609.2 87019.6 Housing Costs Median Rent ($) 52004.0 48440.1 86942.8 Housing Costs Housing Value ($) 52094.5 48520.9 87032.6 Occupancy Percent Rented 52006.7 48421.1 86681.5 Occupency Percent Vacant 52186.5 48617.5 87003.7 Single Parent Percent Single Parent 51747.7 48155.6 86542.8 Home Age Year Built 51949.7 48360.5 86621.1 Home Age Year Occupied Unit Built 51966.8 48377.9 86641.4 Home Age Percent Built Before 1940 51923.9 48335.3 86505.1 Home Age Percent Built Before 1950 51897.9 48308.1 86483.1 Home Age Percent Built Before 1960 51959.8 48374.0 86653.5 Home Age Percent Built Before 1970 52052.3 48469.4 86806.3 Home Age Percent Built Before 1980 52073.4 48490.9 86850.4 Home Age Percent Occupied Units Built Before 1940 51931.0 48342.4 86512.2 Home Age Percent Occupied Units Built Before 1950 51910.8 48321.2 86497.8 Home Age Percent Occupied Units Built Before 1960 51975.9 48389.9 86675.0 
45 

Variable Category Variable Model 1 Model 2 Model 3 Home Age Percent Occupied Units Built Before 1970 52070.4 48486.2 86829.5 Home Age Percent Occupied Units Built Before 1980 52083.6 48501.0 86860.0 Children Percent Less than 6 Years of Age 52280.4 48713.7 87126.9 . Children Number Less than 6 Years of Age 52243.2 48678.2 86913.2 Education Percent Less than 9th Grade 52006.5 48435.7 86828.7 Education Percent without High School Degree 51852.7 48279.9 86709.8 Education Percent without any College 51787.2 48218.2 86729.0 Education Percent without College Degree 51822.1 48251.2 86759.6 Population Total Housing Units 52286.9 48720.8 87090.7 Population Total Population 52223.0 48660.6 86909.7 Population Housing Density 52272.6 48697.2 87068.2 Air Air Dispersion (ASPEN) Model 52275.1 48708.3 87136.9 Air Air Exposure (HAPEM5) Model 52273.1 48706.3 87134.9 Air Air Hazard Quotient (HQ) 52272.3 48705.5 87134.0 HUD Funding Current HUD Funding ($ per Child) 52290.9 48722.4 87140.4 HUD Funding Cumulative HUD Funding ($ per Child) 52287.3 48723.3 87163.4 HUD Funding Current State Funding ($ per Child) 52162.4 48582.7 87014.3 HUD Funding Cumulative State Funding ($ per Child) 52200.7 48617.7 87044.0 HUD Funding Current CDC Funding ($ per Child) 52288.3 48720.8 87151.7 HUD Funding Cumulative CDC Funding ($ per Child) 52292.6 48725.0 87136.0 HUD Funding Current Total Funding ($ per Child) 52282.8 48711.9 . . HUD Funding Cumulative Total Funding ($ per Child) 52292.2 48721.9 87145.9 . HUD Funding Current HUD Funding ($ per Census Tract) 52302.9 48737.1 87167.5 HUD Funding Cumulative HUD Funding ($ per Census Tract) 52306.8 48740.4 87097.6 . HUD Funding Current State Funding ($ per Census Tract) 52232.2 48659.5 87178.1 HUD Funding Cumulative State Funding ($ per Census Tract) 52210.6 48638.3 87222.7 HUD Funding Current CDC Funding ($ per Census Tract) 52297.5 48729.5 87162.7 . HUD Funding Cumulative CDC Funding ($ per Census Tract) 52303.7 48737.2 87121.6 HUD Funding Current Total Funding ($ per Census Tract) 52303.1 48735.6 87173.9 HUD Funding Cumulative Total Funding ($ per Census Tract) 52300.1 48732.3 87179.7 
46 

Variable Category Variable Model 1 Model 2 Model 3 TRI TRI Compounds (Total Air) 52295.5 48728.8 87153.5 TRI TRI Compounds (Fugitive Air) 52287.7 48720.7 87146.1 TRI TRI Compounds (Stacks) 52295.6 48728.9 87154.3 TRI TRI Compounds (Water Surface) 52285.5 48718.8 87147.0 TRI TRI Lead Only (Total Air) 52291.0 48724.0 87153.1 

TRI Lead Only (Fugitive Air) 52289.6 48722.6 87151.4 

TRI TRI Lead Only (Stacks) 52291.7 48725.0 87153.7 TRI TRI Lead Only (Water Surface) 52274.4 48708.5 87138.1 TRI TRI Total Lead (Total Air) 52295.8 48729.0 87155.2 TRI TRI Total Lead (Fugitive Air) 52291.5 48724.6 87154.0 TRI TRI Total Lead (Stacks) 52295.6 48728.9 87154.3 TRI TRI Total Lead (Water Surface) 52285.4 48718.6 87147.4 Housing Inspection P1: Proportion of Housing Units Passing MA Standard of Care: 

Naïve Method 1 

52214.0 48643.0 87070.2 

 F1: Proportion of Housing Units Failing MA Standard of Care: 

Naïve Method 1 

52108.5 48548.2 86916.6 

 N1: Proportion of Housing Units Assessed: Naïve Method 1 52131.7 48554.8 86963.0  P2: Proportion of Housing Units Passing MA Standard of Care: 

Naïve Method 2 

52240.8 48671.5 87101.3 

 F2: Proportion of Housing Units Failing MA Standard of Care: 

Naïve Method 2 

52199.5 48645.5 87046.4 

 N2: Proportion of Housing Units Assessed: Naïve Method 2 52208.4 48641.6 87066.2  P3: Proportion of Housing Units Passing MA Standard of Care: 

Naïve Method 3 

52240.8 48671.5 87101.3 

 F3: Proportion of Housing Units Failing MA Standard of Care: 

Naïve Method 3 

52108.5 48548.2 86916.6 

 N3: Proportion of Housing Units Assessed: Naïve Method 3 52160.8 48586.2 86996.1  P4: Proportion of Housing Units Passing MA Standard of Care: 

MDPH Method 

52240.5 48671.1 87098.8 

 F4: Proportion of Housing Units Failing MA Standard of Care: 

MDPH Method 

52106.5 48545.8 86919.8 

 N4: Proportion of Housing Units Assessed: MDPH Method 52160.3 48585.5 86994.8 . 
 

47 

5.0 STATISTICAL MODELING RESULTS 

As described in Section 2.3, for each statistical model within each of the two broad model types 

(Low and High Resolution) the variables that led to the best model fits were initially included in 

a multivariate statistical model and assessed jointly to determine which variables were predictive 

of children’s blood-lead levels. If higher order interactions with time were not significant within 

the multivariate model and did not negatively impact the fit of the model upon removal, they 

were subsequently removed. As results of each model run were reviewed, some variables were 

dropped from the model if they were not significant predictors of the outcome variable and were 

not improving the fit of the model by being included. Thus, each model was run and results were 

assessed multiple times until a final model was reached. The sections below present the final 

model results for the national risk models (Section 5.1) and the local risk models for 

Massachusetts (Section 5.2). Maps of the predicted results are included in Section 6 and in 

Appendix G. 

5.1 Low-Resolution Modeling Results

Table 5-1 presents the full set of variables included in the final multivariate models for Models 1 

through 4. Across all four models, the time and space variables were important predictors of the 

various outcomes. The same three variables related to time and space were included in all four 

models: 

• EPA region 

• the interaction between EPA region and a continuous measure of time (in years, 

centered at the year 2000) 

• the interaction of EPA region and quarter of the year with the 3rd quarter (JulySeptember) associated with the highest predicted lead levels. 

Notes on the other variable types explored and a summarization of the set of variables included 

in the final models are presented below. 

• Income – Percent of Units with No Household Wages was included in Models 1 to 3 with 

all interactions with time included. Percent of Units with No Household Earnings was 

included in all Model 4 although the interaction with time squared was dropped. 

• Race – Percent Black was included in Model 1, Percent Multiple Races in Model 2, and 

Percent Asian in Models 3 and 4, although the interaction with time squared was dropped 

in Model 3 and both interactions were dropped in Model 4. The best-fitting race 

variables were included in Models 1 through 5. 

• Housing Cost – Median Rent was only included in all models and all interaction terms 

appeared to be strong predictors. 

• Occupancy – Percent Vacant was included in Model 1 and Percent Rented in the other 

three. The interaction with time squared was dropped in Models 2 and 4. 

• Single Parent Status – The percent of single parent households was included in all 

models with the interaction with time squared was dropped in Models 3 and 4. 

• Housing Age – Percent Built Pre-1960 was included in Models 1 and 2, Percent Built Pre1950 in Model 3, and Percent Built Pre-1940 in Model 4. 
 

48 

• Children’s Age – The percent of children less than six years old was included in all 

models, although the p-values for each term in Model 2 are high. 

• Education Level – Percent Without a College Degree was included in all models, 

although the interaction with time squared was dropped in Model 3 and both interaction 

terms were dropped in Model 4. 

• Population – Total Housing Units was included in Model 1 without either interaction 

with time. Total Population was included in Model 2 with both interactions. Housing 

Density was included in Models 3 and 4, although the interaction terms were dropped 

from Model 4. 

• Air Lead – Median Air Lead, 99th Percentile was included in Models 1, 2, and 4, although 

the interaction terms were dropped from Models 3 and 4. Air Lead 9th Percentile was 

included in Model 2. 

• TRI –TRI Lead Total Air, 95th Percentile was included in Model 1 with all interaction 

terms. TRI Lead Water Surface 95th Percentile was included in Models 2 and 3 with both 

interaction terms. TRI Lead Underwater Injection 95th Percentile was included in Model 

4 but the interaction with time squared was dropped. 

• Drinking Water – The two Mean Water Lead Concentration variables were included in 

each model, although the interaction with time squared was dropped in Model 3 and both 

interactions were dropped in Model 4. 

• Funding – Total Cumulative Funding 36-month Time Lag was included in Model 1 with 

both interactions with time. Current CDC Funding 12-month Time Lag was included in 

Models 2 and 3 with both interaction terms. Current HUD Funding 12-month Time Lag 

was included in Model 4 with all terms being significant. 

• Screening – Screening penetration was included in each model, although the interaction 

with time squared was dropped in Models 2 and 4. 

Thus, in Model 4 for probability of blood-lead level ≥ 25, most of the interactions with time 

squared were dropped from the model and a number of the interactions with time were dropped 

as well. Note that when the interaction with time and/or time squared were significant or 

improved the model, the lower order terms were kept in the model even if a particular term had a 

p-value above 0.05. 

Tables 5-2 through 5-7 present the parameter estimates from each of the four multivariate 

national models. The standard error and p-value associated with each predictor also is included. 

Estimates also are presented for the three variance components that were included in the national 

models – 2

δ 0 σ , 2

, δ 0 δ 1 σ , and 2

δ 1 σ (related to the random intercept (δ0i) and slope (δ1i) terms. 

Following each table are two figures that provide information on the fit of the final models. The 

first, a histogram of the residuals from the final model fit, helps determine whether or not it is 

reasonable to assume that the random errors in a statistical process can be assumed to be drawn 

from a normal distribution. Figures 5-1, 5-3, 5-5, and 5-7 contain the residual histograms of the 

observed-predicted probabilities from each of the four logistic regression models. Please note 

that for these four histograms – the model was actually applied on the logit scale. However, 

because the logit is undefined for observed proportions at zero and one, the histograms were 

applied to the original scale of measure. 
 

49 

The second set of figures plot the observed values versus the predicted values for each model. If 

the multivariate model fitted is appropriate, predicted values obtained from regressing the 

observed values on the multivariate model’s predicted values when plotted against observed 

values, one would expect all the points to be very close to the 45° line. Figures 5-2, 5-4, 5-6, and 

5-8 contain these comparison plots for each of the four national models, respectively. The plots 

were conducted on both the observed probability and logit probability scales, with observed data 

points at zero and one censored in the logit scale plots. 

In general, these plots suggest that the models are performing well. A weighted regression line 

(blue line) fit to the observed versus predicted plots shows a very high R2 value in most of the 

models that mirrors the 45° line (shown in red) for the majority of the data. One trend observed 

in these plots that is important to consider is that the Broad-Based National Models tend to 

under-predict for county/quarter combinations with higher proportions that exceed the 5, 10, 15 

and 25 μg/dL threshold values. Further exploration may be necessary to determine whether these 

higher values represent county/quarter combinations with fairly sparse data (i.e., few 

observations) – which might explain why they would have been less influential because the 

models are influenced by the number of observations associated with each observed value. For 

the higher blood-lead threshold categories, the model appears to over-predict the lower observed 

proportions – suggesting the possibility of a regression to the mean effect. 
 

50 

Table 5-1. Summary of Variables Included in Final National Multivariate Model 

Variable Type Model 1 Model 2 Model 3 Model 4 

Region Region Region Region 

Area and Time Time*Region Time*Region Time*Region Time*Region 

Region*Quarter Region*Quarter Region*Quarter Region*Quarter 

Income Percent of Units No 

HH Wages 

Percent of Units 

No HH Wages 

Percent of Units 

No HH Wages 

Percent of Units No 

HH Earnings 

Race Percent Black 

Percent Multiple 

Races Percent Asian Percent Asian 

Housing Cost Median Rent Median Rent Median Rent Median Rent 

Occupancy Percent Vacant Percent Rented Percent Rented Percent Rented 

Family 

Structure 

Percent Single Parent Percent Single 

Parent

Percent Single 

Parent

Percent Single 

Parent

Housing Age Percent Built Pre1960 

Percent Built Pre1960 Percent Occupied 

Built Pre-1950 

Percent Occupied 

Built Pre-1940 

Children’s Age Percent < Six Years 

Old 

Percent < Six 

Years Old 

Percent < Six 

Years Old 

Percent < Six Years 

Old 

Education Percent without 

College Degree 

Percent No College Percent No College Percent No College 

Population Total Housing Units Total Population Housing Density Housing Density 

Air Lead Median Air Lead, 

99th percentile 

Air Lead, 95th

percentile 

Median Air 99th

percentile 

Median Air 99th

percentile 

TRI TRI Lead Total Air, 

95th percentile 

TRI Lead Water 

Surface 95th, 

percentile 

TRI Lead Water 

Surface 95th, 

percentile 

TRI Lead UI 95th, 

percentile 

Mean Water Lead 

(water=1) 

Mean Water Lead 

(water=1) 

Mean Water Lead 

(water=1) 

Mean Water Lead 

Drinking Water (water=1) 

Lead Mean Water Lead 

(water=2) 

Mean Water Lead 

(water=2) 

Mean Water Lead 

(water=2) 

Mean Water Lead 

(water=2) 

Funding 

Total Cumulative 

Funding 36-month 

Time Lag 

Current CDC 

Funding 12-month 

Time Lag 

Current CDC 

Funding 12-month 

Time Lag 

Current HUD 

Funding, 12-month 

Time Lag 

Screening Screening Penetration Screening 

Penetration 

Screening 

Penetration 

Screening 

Penetration 

 

52 

-0.84 -0.72 -0.6 -0.48 -0.36 -0.24 -0.12 0 0.12 0.24 0.36 0.48 0.6 0.72 0.84

0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

22.5

Percent

Residuals from Model-3 (P5)

Figure 5-1. Histograms of Residuals from Fitted National Multivariate Model 1 Predicted (P5) 

0.0

0.2

0.4

0.6

0.8

1.0

Observed (P5) 

0.0 0.2 0.4 0.6 0.8 1.0

Figure 5-2a. Plot of National Multivariate Model Predicted Values versus Observed with 

Fitted Regression Line and 45° Reference Line for Proportion of Children 

with BLL ≥ 5 μg/dL Predicted (P5 - Logit Scale) 

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

Observed (P5 - Logit Scale) 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Figure 5-2b. Plot of National Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children 

 with BLL ≥ 5 μg/dL (Logit Scale) 

R2 from Fitted Regression= 0.840 

R2

 from Fitted Regression=0.857 

 

54 

-0.2775 -0.1875 -0.0975 -0.0075 0.0825 0.1725 0.2625 0.3525 0.4425 0.5325 0.6225

0

5

10

15

20

25

30

Percent

Residuals from Model-4 (P10)

Figure 5-3. Histograms of Residuals from Fitted National Multivariate Model 2 Predicted (P10) 

0.0

0.2

0.4

0.6

0.8

Observed (P10) 

0.0 0.2 0.4 0.6 0.8

Figure 5-4a. Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with BLL ≥ 10 μg/dL. Predicted (P10 - Logit Scale) 

-8

-6

-4

-2

0

2

Observed (P10 - Logit Scale) 

-8 -6 -4 -2 0 2

Figure 5-4b. Plot of National Multivariate Model Predicted Values versus Observed with Fitted 

 Regression Line and 45° Reference Line for Proportion of Children with BLL ≥ 10 μg/dL 

 (Logit Scale) 

R2

 from Fitted Regression= 0.867 

R2

 from Fitted Regression= 0.896 

 

56 

-0.148 -0.108 -0.068 -0.028 0.012 0.052 0.092 0.132 0.172 0.212 0.252 0.292 0.332

0

10

20

30

40

50

Percent

Residuals from Model-5 (P15)

Figure 5-5. Histograms of Residuals from Fitted National Multivariate Model 3 Predicted (P15) 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Observed (P15) 

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Figure 5-6a. Plot of National Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children 

 with BLL ≥ 15 μg/dL. Predicted (P15 - Logit Scale) 

-9

-7

-5

-3

-1

1

Observed (P15 - Logit Scale) 

-9 -7 -5 -3 -1 1

Figure 5-6b. Plot of National Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children 

 with BLL ≥ 15 μg/dL (Logit Scale) 

R2

 from Fitted Regression= 0.867 

R2

 from Fitted Regression= 0.821 

 

58 

-0.0525 -0.0275 -0.0025 0.0225 0.0475 0.0725 0.0975 0.1225 0.1475 0.1725 0.1975

0

10

20

30

40

50

60

70

80

90

Percent

Residuals from Model-6 (P25)

Figure 5-7. Histograms of Residuals from Fitted National Multivariate Model 4 Predicted (P25) 

0.00

0.07

0.14

0.21

0.28

0.35

Observed (P25) 

0.00 0.07 0.14 0.21 0.28 0.35

Figure 5-8a. Plot of National Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children 

 with BLL ≥ 25 μg/dL. Predicted (P25 - Logit Scale) 

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

Observed (P25 - Logit Scale) 

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

Figure 5-8b. Plot of National Multivariate Model Predicted Values versus Observed with 

 Fitted Regression Line and 45° Reference Line for Proportion of Children 

 with BLL ≥ 25 μg/dL (Logit Scale) 

R2

 from Fitted Regression= 0.726 

R2

 from Fitted Regression= 0.744 
 

59 

5.2 High-Resolution Modeling Results

The Massachusetts final multivariate models were constructed similarly to the national models. 

One basic difference in the Massachusetts models is that there was no EPA region. Thus, there 

was no area variable included other than census tract. As in the national model, time period and 

quarter were significant predictors; however, in the Massachusetts model they are not interacted 

with an area variable. Table 5-6 presents the full set of variables included in the final 

multivariate models for Models 1 through 5. Model 6 was not fit for the Massachusetts data 

because of the scarcity of data above 25 μg/dL. 

Among the demographic variables, housing cost, occupancy, family structure, and housing age 

were significant predictors in all five models. Median Rent was the selected housing cost 

variable in all five models. For occupancy, Percent Rented was the selected variable in four of 

the five models. Percent of Single Parent Households is the family structure variable in all 

models. Three housing age variables were included across the five models, but Percent Built 

Pre-1950 was the included variable in Models 1 to 3. 

Race and Income variables were included in four of the five final models. Median Household 

Income and Percent Multiple Races were the two variables used in all four models. Children’s 

Age, Education, and Population each had a variable included in one of the final models. Number 

of Children less than or equal to six years old and Total Population were included in Model 3. 

Percent Without 9th Grade Education was included in Model 4. 

Unlike the national models, none of the environmental variables were included in the final 

multivariate models for Massachusetts. On the other hand, the housing inspection data from 

Massachusetts were predictive and included in all of the final models. The percentage of units 

passing the Massachusetts standard of care (calculated using the MDPH method) was included in 

all five models. Additionally, the percentage of units failing the Massachusetts standard of care 

(calculated using the MDPH method) was included in Models 4 and 5. 

The selected programmatic funding variable was included in Models 1, 2, and 5. Current State 

Funding ($ per Child) was used in the GM models and Cumulative CDC Funding ($ per tract) 

was used in Model 5. 

As with the national models, parameter estimates and associated standard errors and p-values are 

presented for all models in Table 5-7. Figures 5-9 to 5-18 contain the histograms of residuals 

and plots of observed versus predicted values that allow assessment of the various model fits. 

These plots suggest that models 1-3 are performing well, with Models 4 and 5 providing a 

somewhat suboptimal fit (perhaps due to fewer children being observed above the 10 and 15 

μg/dL threshold values in Massachusetts). The weighted regression line fit to the observed 

versus predicted plots (shown in blue) also demonstrates a systematic degradation in model 

performance from Models 3 through 5, with the R2

 value diminishing as the blood-lead threshold 

value increases. Similar to the National Models, the High-Resolution Multivariate Models in 

Massachusetts tend to under-predict for census-tract/quarter combinations with higher geometric 

mean blood-lead concentrations and higher exceedance proportions. Further exploration may be 

necessary to determine whether these higher values represent county/quarter combinations with 
 

60 

fairly sparse data (i.e., few observations) – which might explain why they would have been less 

influential in Models 2 through 6, which are influenced by the number of observations associated 

with each observed value. 

Appendix F presents predictions of areas of the country estimated to have the highest children’s 

blood-lead levels. These predictions were generated by averaging predicted values across the 

four quarters of 2006. Table F-1 lists the 150 counties/townships in the United States with the 

highest predicted GM blood-lead levels (using Model 2) and proportion of children above 5, 10, 

15, and 25 μg/dL. Table F-2 lists the 10 counties in each state with the highest levels of those 

same five outcomes. Table F-3 lists the 150 Massachusetts census tracts with the highest 

predicted GM blood-lead levels. Figure F-1 provides a map of these 150 Massachusetts census 

tracts. 
61 

Table 5-6. Summary of Variables Included in Final Massachusetts Multivariate Model 

Variable Type Model 1 Model 2 Model 3 Model 4 Time Time Period, Quarter Time Period, Quarter Time Period, Quarter Time Period, Quarter Income Median Household Income Median Household Income Median Household Income Median Household Income Race Percent Multiple Race Percent Multiple Race Percent Multiple Race Percent Multiple Race Housing Cost Median Rent Median Rent Median Rent Median Rent Occupancy Percent Rented Percent Rented Percent Rented Percent Rented Family Structure Percent Single Parent Percent Single Parent Percent Single Parent Percent Single Parent Housing Age Percent Built Pre-1950 Percent Built Pre-1950 Percent Built Pre- 1950 Percent Occupied Built Pre-1940 Children's Age Number less than 6 years old Education Percent without 9th Grade education Population Total Population 

P4 - % Passing Standard of Care, MDPH Method 

P4 - % Passing Standard of Care, MDPH Method 

P4 - % Passing Standard of Care, MDPH Method 

P4 - % Passing Standard of Care, MDPH Method 

Housing Inspection F4 - % failing 

standard of care, MDPH Method 

Funding Current State Funding ($ per Child) Current State Funding ($ per Child) 
 

62 

Table 5-7. Massachusetts Multivariate Model Estimates 

Model Effect Levels Estimate Standard 

Error 

PValue 

Intercept _ 2.290 0.033 <.0001

Time _ -0.088 0.002 <.0001

1 -0.187 0.007 <.0001

2 -0.143 0.007 <.0001

3 0.130 0.006 <.0001 Quarter (Season) 

4 0.000 . . 

Median Household Income _ -0.008 0.001 <.0001

Percent Multiple Races _ 3.909 0.536 <.0001

Median Rent ($): _ -0.032 0.005 <.0001

Percent Rented Units _ -0.568 0.069 <.0001

Percent Single Parent Households _ 0.702 0.096 <.0001

Percent Units Built Before 1950 _ 0.849 0.047 <.0001

p4 _ -0.983 0.166 <.0001

Current State Funding _ 0.028 0.006 <.0001

2

0 σ δ

0.229 . 

2

, 0 1 σ δ δ

-0.026 . 

2

1 σ δ

0.004 . 

1 

(Geometric 

Mean) 

2 σ Error

0.191 . 

Intercept _ 2.249 0.033 <.0001

Time _ -0.087 0.002 <.0001

1 -0.185 0.006 <.0001

2 -0.137 0.006 <.0001

3 0.127 0.006 <.0001 Quarter (Season) 

4 0.000 . . 

Median Household Income _ -0.008 0.001 <.0001

Percent Multiple Races _ 3.826 0.531 <.0001

Median Rent ($): _ -0.032 0.005 <.0001

Percent Rented Units _ -0.561 0.069 <.0001

Percent Single Parent Households _ 0.735 0.096 <.0001

Percent Units Built Before 1950 _ 0.866 0.046 <.0001

p4 _ -0.933 0.164 <.0001

Current State Funding _ 0.031 0.006 <.0001

2

0 σ δ

0.218 . 

2

, 0 1 σ δ δ

-0.024 . 

2

1 σ δ

0.004 . 

2 

(Weighted 

Geometric 

Mean) 

2 σ Error

3.986 . 
 

63 

Model Effect Levels Estimate Standard 

Error 

PValue 

Intercept _ -2.312 0.054 <.0001

Time _ -0.146 0.003 <.0001

1 -0.195 0.010 <.0001

2 -0.117 0.010 <.0001

3 0.187 0.009 <.0001 Quarter (Season) 

4 0.000 . . 

Median Household Income _ -0.010 0.001 <.0001

Percent Multiple Races _ 3.420 0.610 <.0001

Median Rent ($): _ -0.044 0.006 <.0001

Percent Rented Units _ -0.724 0.083 <.0001

Percent Single Parent Households _ 0.817 0.119 <.0001

Percent Units Built Before 1950 _ 1.468 0.056 <.0001

Number Residents Less than Six Years of Age _ 0.000 0.000 0.0114 

Total Population _ 0.000 0.000 0.0292 

p4 _ -0.649 0.218 0.0029 

2

δ 0 σ 0.129 0.007 

2

, δ 0 δ 1 σ -0.008 0.001 

3 

(Proportion 

of Children 

with Blood 

Lead ≥ 5 

μg/dL) 

2

δ 1 σ 0.004 0.000 

Intercept _ -4.235 0.052 <.0001

Time _ -0.136 0.005 <.0001

1 -0.282 0.022 <.0001

2 -0.130 0.021 <.0001

3 0.247 0.020 <.0001 Quarter (Season) 

4 0.000 . . 

Median Household Income _ -0.010 0.001 <.0001

Percent Multiple Races _ 4.326 0.781 <.0001

Median Rent ($): _ -0.057 0.009 <.0001

Percent Rented Units _ -0.562 0.119 <.0001

Percent Single Parent Households _ 0.697 0.159 <.0001

Percent Occupied Units Built Before 1980 _ 1.758 0.083 <.0001

Percent Residents with Less than Ninth Grade 

Education 

_ -0.581 0.279 0.0372 

f4 _ 1.802 0.504 0.0004 

p4 _ -1.339 0.321 <.0001

2

0 σ δ

0.175 0.016 

2

, 0 1 σ δ δ

-0.013 0.003 

4 

(Proportion 

of Children 

with Blood 

Lead ≥ 10 

μg/dL) 

2

1 σ δ

0.004 0.001 
 

64 

Model Effect Levels Estimate Standard 

Error 

PValue 

Intercept _ -6.278 0.144 <.0001

Time _ -0.093 0.008 <.0001

1 -0.307 0.042 <.0001

2 -0.093 0.040 0.019 

3 0.332 0.036 <.0001 Quarter (Season) 

4 0.000 . . 

Median Rent ($): _ -0.049 0.010 <.0001

Percent Vacant Units _ 1.039 0.335 0.0019 

Percent Single Parent Households _ 1.002 0.169 <.0001

Percent Occupied Units Built Before 1980 _ 1.187 0.168 <.0001

f4 _ 4.047 0.677 <.0001

p4 _ -1.476 0.440 0.0008 

Cumulative CDC Funding _ 0.000 0.000 0.0127 

2

0 σ δ

0.249 0.035 

2

, 0 1 σ δ δ

-0.020 0.008 

5 

(Proportion 

of Children 

with Blood 

Lead ≥ 15 

μg/dL) 

2

1 σ δ

0.004 0.002 
 

65 

-1.875 -1.275 -0.675 -0.075 0.525 1.125 1.725 2.325 2.925 3.525 4.125 4.725

0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Percent

Residuals from Model-1 (GM)

Figure 5-9. Histograms of Residuals from Fitted Massachusetts Multivariate Model 1 Predicted (GM) 

0

1

2

3

4

5

6

7

8

Observed (GM) 

012345678

R2 from Fitted Regression = 0.697 

Figure 5-10. Plot of Massachusetts Multivariate Model Predicted Values versus 

 Observed with Fitted Regression Line and 45° Reference Line for 

 Unweighted Geometric Mean Response 
 

66 

-1.8 -1.35 -0.9 -0.45 0 0.45 0.9 1.35 1.8 2.25 2.7 3.15 3.6 4.05 4.5 4.95

0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Percent

Residuals from Model-2 (Weighted GM)

Figure 5-11. Histograms of Residuals from Fitted Massachusetts Multivariate Model 2 Predicted (Weighted GM) 

0

1

2

3

4

5

6

7

8

Observed (Weighted GM) 

012345678

R2 from Fitted Regression = 0.700 

Figure 5-12. Plot of Massachusetts Multivariate Model Predicted Values versus 

 Observed with Fitted Regression Line and 45° Reference Line for Weighted 

 Geometric Mean Response
 

67 

-0.34 -0.26 -0.18 -0.1 -0.02 0.06 0.14 0.22 0.3 0.38 0.46 0.54 0.62

0

2.5

5.0

7.5

10.0

12.5

15.0

Percent

Residuals from Model-3 (P5)

Figure 5-13. Histograms of Residuals from Fitted Massachusetts Multivariate Model 3 Predicted (P5) 

0.00

0.12

0.24

0.36

0.48

0.60

0.72

0.84

Observed (P5) 

0.00 0.12 0.24 0.36 0.48 0.60 0.72 0.84

Figure 5-14a. Plot of Massachusetts Multivariate Model Predicted Values versus 

 Observed with Fitted Regression Line and 45° Reference Line for 

 Proportion of Children with BLL ≥ 5 μg/dL. Predicted (P5 - Logit Scale) 

-5

-4

-3

-2

-1

0

1

2

Observed (P5 - Logit Scale) 

-5 -4 -3 -2 -1 0 1 2

Figure 5-14b. Plot of Massachusetts Multivariate Model Predicted Values versus 

 Observed with Fitted Regression Line and 45° Reference Line for 

 Proportion of Children with BLL ≥ μg/dL (Logit Scale) 

R2 from Fitted Regression = 0.579 

R2

 from Fitted Regression = 0.531 
 

68 

-0.12 -0.09 -0.06 -0.03 0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.3 0.33 0.36

0

5

10

15

20

25

30

35

Percent

Residuals from Model-4 (P10)

Figure 5-15. Histograms of Residuals from Fitted Massachusetts Multivariate Model 4 Predicted (P10) 

0.0

0.1

0.2

0.3

0.4

Observed (P10) 

0.0 0.1 0.2 0.3 0.4

Figure 5-16a. Plot of Massachusetts Multivariate Model Predicted Values versus 

 Observed with Fitted Regression Line and 45° Reference Line for 

 Proportion of Children with BLL ≥ 10 μg/dL Predicted (P10 - Logit Scale) 

-6

-5

-4

-3

-2

-1

0

Observed (P10 - Logit Scale) 

-6 -5 -4 -3 -2 -1 0

Figure 5-16b. Plot of Massachusetts Multivariate Model Predicted Values versus 

 Observed with Fitted Regression Line and 45° Reference Line for 

 Proportion of Children with BLL ≥ 10 μg/dL (Logit Scale) 

R2

 from Fitted Regression = 0.269 

R2

 from Fitted Regression = 0.312 
 

69 

-0.039 -0.015 0.009 0.033 0.057 0.081 0.105 0.129 0.153 0.177 0.201 0.225 0.249 0.273

0

10

20

30

40

50

60

Percent

Residuals from Model-5 (P15)

Figure 5-17. Histograms of Residuals from Fitted Massachusetts Multivariate Model 5 Predicted (P15) 

0.0

0.1

0.2

0.3

Observed (P15) 

0.0 0.1 0.2 0.3

Figure 5-18a. Plot of Massachusetts Multivariate Model Predicted Values versus 

 Observed with Fitted Regression Line and 45° Reference Line for 

 Proportion of Children with BLL ≥ 15 μg/dL. Predicted (P15 - Logit Scale) 

-5

-4

-3

-2

-1

0

Observed (P15 - Logit Scale) 

-5 -4 -3 -2 -1 0

Figure 5-18b. Plot of Massachusetts Multivariate Model Predicted Values versus 

 Observed with Fitted Regression Line and 45° Reference Line for 

 Proportion of Children with BLL ≥ 15 μg/dL (Logit Scale) 

R2 from Fitted Regression = 0.113 

R2

 from Fitted Regression = 0.119 
 

70 

6.0 GRAPHICAL PRESENTATION OF MODELING RESULTS 

In addition to the discussion of the final multivariate modeling results in Section 5, it is 

informative to be able to view the results visually. Two methods were utilized for graphical 

presentation of the results – mapping and via use of an interactive software tool. Section 6.1 

presents a subset of the maps generated, while Sections 6.2 and 6.3 discuss the interactive 

software tool. 

6.1 Maps of Observed and Predicted Blood-Lead Outcomes

Mapping is an informative method to graphically present the results of the multivariate models. 

Figure 6-1 contains maps displaying the observed levels of GM blood-lead levels in 2000 and 

2005 based on CDC’s national surveillance data, and the comparable predicted GM blood-lead 

levels in 2000 and 2005. A key difference is that maps of observed levels contain many counties 

with missing data either because they do not submit childhood lead surveillance data to CDC or 

they have too few test records to be included in the analysis, while the maps of predicted levels 

covers all counties in the country. Appendix G contains detailed maps from the national level 

models of GM blood-lead levels and proportion of children with BLLs ≥ 10 μg/dL. 

Because it is difficult to view many of the individual counties within the U.S.-level maps, 

regional-level maps also were produced. Figure 6-2 contains examples of these for EPA Region 

V. Comparable maps for all regions are included in Appendix G. With darker colors 

representing areas of higher lead levels, it appears that lead levels are declining across EPA 

Region V from the 2000 to 2005 time period. Figure 6-3 contains maps of observed and 

predicted proportion of children’s blood-lead levels in Massachusetts at the census-tract level. 

The Boston area is enlarged to better show the tracts in that area. 

6.2 Visualization Tool Development

In addition to generating maps, a software tool was developed to provide a flexible way for users 

to quickly view data for particular areas and to obtain information that led to the results being 

viewed. To do this, the project team utilized existing technology developed through internal 

research and modified this technology to meet the needs of this study. The software sews 

together a series of static maps so that they can be viewed dynamically. This allows users to 

view a movie of changes in surfaces over time and space. 

The software is written in C++. Users interact with the software via a Windows GUI that is 

implemented using Microsoft Foundations Classes (MFC). The 3-dimensional graphics within 

the tool were implemented using an Open Graphics Library (OpenGL). 
71 

Figure 6-1. Observed and Predicted Proportion of Children with Blood-Lead Levels ≥ 10 μg/dL in the Uni

 by County, 2000 and 2005 

Predicted Proportion of Blood-Lead Levels >/= 10 ug/dL

2005

United States September 2007

LEGEND

0 - 0.00990.01 - 0.02490.025 - 0.04990.05 - 0.0749

0.075 - 0.09990.10 - 0.24990.25 +No data

Proportion of PbB Levels >/= 10 ug/dL

0 180 360 540 90

Miles

0 490 980 245

Miles

0 130 260 65

Miles

Predicted Proportion of Blood-Lead Levels >/= 10 ug/dL

2000

United States September 2007

LEGEND

0 - 0.00990.01 - 0.02490.025 - 0.04990.05 - 0.0749

0.075 - 0.09990.10 - 0.24990.25 +No data

Proportion of PbB Levels >/= 10 ug/dL

0 180 360 540 90

Miles

0 475 950 237.5

Miles

0 130 260 65

Miles

Observed Proportion of Blood-Lead Levels >/= 10 ug/dL

2005

United States September 2007

LEGEND

0 - 0.00990.01 - 0.02490.025 - 0.04990.05 - 0.0749

0.075 - 0.09990.10 - 0.24990.25 +No data

Proportion of PbB Levels >/= 10 ug/dL

0 175 350 525 87.5

Miles

0 460 920 230

Miles

0 125 250 62.5

Miles

Observed Proportion of Blood-Lead Levels >/= 10 ug/dL

2000

United States September 2007

LEGEND

0 - 0.00990.01 - 0.02490.025 - 0.04990.05 - 0.0749

0.075 - 0.09990.10 - 0.24990.25 +No data

Proportion of PbB Levels >/= 10 ug/dL

0 170 340 510 85

Miles

0 470 940 235

Miles

0 130 260 65

Miles
 

72 

Figure 6-2. Observed and Predicted Proportion of Children with Blood-Lead Levels ≥ 10 

μg/dL in Region V by County, 2000 and 2005 

Predicted Proportion of Blood-Lead Levels >/= 10 ug/dL

2005

US EPA Region 5

September 2007

0 50 100 150 25

Miles

LEGEND

0 - 0.0099

0.01 - 0.0249

0.025 - 0.0499

0.05 - 0.0749

0.075 - 0.0999

0.10 - 0.2499

0.25 +

No data

Proportion of PbB Levels >/= 10 ug/dL

Predicted Proportion of Blood-Lead Levels >/= 10 ug/dL

2000

US EPA Region 5

September 2007

0 50 100 150 25

Miles

LEGEND

0 - 0.0099

0.01 - 0.0249

0.025 - 0.0499

0.05 - 0.0749

0.075 - 0.0999

0.10 - 0.2499

0.25 +

No data

Proportion of PbB Levels >/= 10 ug/dL

Observed Proportion of Blood-Lead Levels >/= 10 ug/dL

2005

US EPA Region 5

September 2007

0 50 100 150 25

Miles

LEGEND

0 - 0.0099

0.01 - 0.0249

0.025 - 0.0499

0.05 - 0.0749

0.075 - 0.0999

0.10 - 0.2499

0.25 +

No data

Proportion of PbB Levels >/= 10 ug/dL

Observed Proportion of Blood-Lead Levels >/= 10 ug/dL

2000

US EPA Region 5

September 2007

0 50 100 150 25

Miles

LEGEND

0 - 0.0099

0.01 - 0.0249

0.025 - 0.0499

0.05 - 0.0749

0.075 - 0.0999

0.10 - 0.2499

0.25 +

No data

Proportion of PbB Levels >/= 10 ug/dL
73 

Figure 6-3. Observed and Predicted Proportion of Children with Blood-Lead Levels ≥ 10 μg/dL in Massach

Tract, 2000 and 2005

Observed Proportion of Blood-Lead Levels >/= 10 ug/dL

2000

Massachusetts February 2007

LEGEND

0 - 0.00990.01 - 0.02490.025 - 0.04990.05 - 0.0749

0.075 - 0.09990.10 - 0.24990.25 +No data

Proportion of PbB Levels >/= 10 ug/dL

0 10 20 30 5

Miles

Observed Proportion of Blood-Lead Levels >/= 10 ug/dL

2005

Massachusetts 

LEGEND

0 - 0.00990.01 - 0.02490.025 - 0.04990.05 - 0.0749

0.075 - 0.09990.10 - 0.24990.25 +No data

Proportion of PbB Levels >/= 10 ug/dL

0 10 

5

Predicted Proportion of Blood-Lead Levels >/= 10 ug/dL

2005

Massachusetts 

LEGEND

0 - 0.00990.01 - 0.02490.025 - 0.04990.05 - 0.0749

0.075 - 0.09990.10 - 0.24990.25 +No data

Proportion of PbB Levels >/= 10 ug/dL

0 10 

5

Predicted Proportion of Blood-Lead Levels >/= 10 ug/dL

2000

Massachusetts February 2007

LEGEND

0 - 0.00990.01 - 0.02490.025 - 0.04990.05 - 0.0749

0.075 - 0.09990.10 - 0.24990.25 +No data

Proportion of PbB Levels >/= 10 ug/dL

0 10 20 30 5

Miles
 

74 

The software visualizes the observed values and the predicted values for the response variable of 

each model (6 national models, 5 Massachusetts models). The software interpolates the 

predicted values spatially within each state using a squared inverse distance algorithm; it 

interpolates linearly in time. The predicted values are defined for each county. There are two 

visualization modes: (1) a spatial surface moving in time, and (2) a time series. The tool was 

built in a flexible way so that it can be easily adapted to accept updated data. 

Figures 6-4 and 6-5 are screen shots from the visualization tool. Figure 6-4 provides an example 

of a response surface generated by the tool to illustrate predicted blood-lead levels across a 

geographic area. In this example, the area is the state of Illinois. Figure 6-5 provides an 

example of a method the visualization provides to plot predicted blood-lead levels in a given 

geographic area over time. 
 

75 

Figure 6-4. Response Surface of Predicted Geometric Mean Blood-Lead Concentration 

Across the State of Illinois from the Visualization Tool 
 

76 

Figure 6-5. Time Series Plot of Observed and Predicted Geometric Mean Blood-Lead 

Concentration in Cook County Illinois from the Visualization Tool 
 

77 

7.0 DISCUSSION AND FUTURE WORK 

The goal of this study was to determine whether tools could be developed to differentiate 

geographic areas (counties and census tracts), based on their predicted risk of containing children 

with elevated blood-lead levels. Statistical models were developed that link CDC’s childhood 

blood-lead surveillance data to demographic predictor variables available in the 2000 U.S. 

Census. While earlier chapters of this report focus on the development and performance of these 

statistical models, this chapter provides a discussion of the factors that should be considered 

when using the models, and some preliminary ideas for improvement. 

7.1 Major Findings

The results of this study suggest that longitudinal predictive models can be developed at the 

county level across the nation based on the use of quarterly summary information from CDC’s 

National Surveillance Database, and at the census-tract level within states that have a long 

history of universal screening and reporting, such as Massachusetts. These models can be used 

to describe how risk of childhood lead poisoning changes over time within different regions of 

the country, as well as within small geographic areas within states (e.g., counties) and even 

smaller geographic areas within counties (e.g., census tracts). They can be used to predict the 

risk of childhood lead poisoning in counties (or census tracts) with little or no surveillance data, 

and also can be used to identify those counties (or census tracts) that are at highest risk at the end 

of the period of observation (see Appendix F for a list of the 150 counties across the country at 

highest risk predicted by each of the six models, as well as the top 10 counties within each state). 

The statistical model chosen (a random-effects model with separate intercepts and slopes 

estimated within each county or census tract) also allows ranking of geographic areas based on 

the rate of decline over time after accounting for the fixed-effects variables of the model 

(although only among those areas that provided adequate surveillance data). Within the context 

of the Broad-Based National Model, these random effects would allow us to identify those 

counties that are experiencing a more rapid reduction in risk of childhood lead poisoning over 

time (to identify best practices) and those counties that are experiencing a significantly less rapid 

decline over time (to identify areas in need of additional attention and resources for combating 

lead poisoning), after already accounting for the demographic, programmatic, and environmental 

factors included in the multivariate model. 

Within the context of the series of Broad-Based National Models, the data suggest that there are 

significant differences in the distribution of childhood blood-lead concentrations among the 

different regions of the country, and that the manner in which these distributions change over 

time and are impacted by seasonality also is regionally specific. After accounting for these 

regional differences, a number of demographic, environmental, and programmatic variables were 

found to be highly predictive of childhood blood-lead concentrations among the different 

response variables modeled within this project. The specific variables that were found to be 

predictive within the multivariate models varied based on the response variable; however, there 

were certainly some variables that were found to be selected in multiple models. In addition to 

various census demographic variables that were identified in previous risk modeling efforts (e.g., 

age of housing, percent single parent families, race/ethnicity), it was found that variables 

constructed from EPA’s Safe Drinking Water Information System, time-lagged programmatic 
 

78 

funding information from HUD and/or CDC, and variables associated with high lead emmisions 

or predicted air concentrations were selected within the National (Low Resolution) multivariate 

statistical models. 

Within the context of the High-Resolution Model developed using data from the Commonwealth 

of Massachusetts, the project team also found a highly significant downward trend in the risk of 

childhood lead poisoning among the five models developed. Due to a very small number of 

children observed at or above 25 μg/dL within Massachusetts over the 2000-2006 period of 

observation – this sixth model was not included. After accounting for the long-term reduction 

over time and seasonality using similar methods that were employed in the Broad-Based 

National Model, we found that only the demographic and programmatic variables were 

predictive of the risk of childhood lead poisoning at the census-tract level. Of particular interest 

were the variables that described the proportion of housing units within each census tract that 

were found to be in compliance and out of compliance with the Massachusetts Standard of Care. 

In all five of the multivariate models, the risk of childhood lead poisoning was significantly 

reduced as the proportion of housing units in compliance increased within a census tract. In 

addition, for the last two models (which predicted proportion of children at or above 10 and 15 

μg/dL), the risk of childhood lead poisoning increased significantly as the proportion of housing 

units out of compliance increased within a census tract. 

7.2 Comparison Between Results and NHANES

Due to selection bias associated with surveillance data, it is expected that the CDC National 

Surveillance dataset as well as the Massachusetts surveillance data may show higher proportions 

of elevated blood-lead concentrations than found in the general population. For this reason, the 

proportion of children with elevated blood-lead concentrations as well as the distribution of the 

potential continuous summary measure derived from the surveillance data were compared with 

those reported by the most recent six years of available CDC National Health and Nutrition 

Examination Survey (NHANES). Results of this comparison are presented graphically in Figure 

7-1 – suggesting that there is a highly significant difference between the NHANES and CDC’s 

National Surveillance Database with respect to the proportion of children observed at or above 5 

μg/dL (with lesser differences observed for the proportion of children observed at or above 10, 

15, and 25 μg/dL). In future work on this project, EPA might consider methods for calibrating 

the Surveillance data to better match the National Distribution of childhood blood-lead 

concentrations using methods similar to those employed by Strauss, et. al. 2001a. 
 

79 

Legend: NHANES

National Surveillance

Prob(Blood Lead >= 15)

0.0

0.1

0.2

0.3

0.4

0.5

time

1994 1996 1998 2000 2002 2004 2006

Legend: NHANES

National Surveillance

Prob(Blood Lead >= 25)

0.0

0.1

0.2

0.3

0.4

0.5

time

1994 1996 1998 2000 2002 2004 2006

Legend: NHANES

National Surveillance

Prob(Blood Lead >= 5)

0.0

0.5

1.0

1.5

2.0

2.5

time

1994 1996 1998 2000 2002 2004 2006

Legend: NHANES

National Surveillance

Prob(Blood Lead >= 10)

0.0

0.1

0.2

0.3

0.4

0.5

time

1994 1996 1998 2000 2002 2004 2006

Figure 7-1. Comparison of National Surveillance Data to NHANES Data 
 

80 

7.3 Data Issues

The models that were developed as part of this project are based on data sources that have both 

strengths and limitations. In this section, four potentially limiting aspects of the data are 

considered – biases from the geocoding process, biases inherent in the surveillance data, 

reporting limits in surveillance data, predicting within-area relationships with ecological models, 

and use of Census data from 2000. 

7.3.1 Biases from Geocoding 

The quarterly summary statistics from CDC’s National Surveillance Database utilized in these 

analyses were available at the county level of geographic specificity. CDC based this 

summarization on county FIPS codes reported by its grantees. This field is quite well reported in 

CDC’s CBLS database. The Massachusetts surveillance data was summarized and analyzed at 

the census-tract level, with the geocoding of address data within the Massachusetts data being 

conducted by MDPH staff. While there is no reason to suspect lack of data quality within the 

Massachusetts surveillance data, experience shows that the process of geocoding can introduce 

some subtle biases into surveillance data. Thus, the following section is offered as a guide for 

EPA to consider for future modeling efforts in which state or local surveillance data are 

geocoded to the census-tract level: 

The geocoding process is highly dependent on the quality of address data recorded by the local 

lead poisoning prevention programs with whom the blood-lead information originated. Several 

factors could prevent an address from being successfully geocoded, such as: 

• Erroneous, illegible, or purposefully misleading address information being provided to 

the childhood lead poisoning prevention program 

• Address data that contain either a P.O. Box or Rural Route as part of the street address, 

which typically cannot be successfully geocoded 

• Errors in data entry. 

While these problems with address data are likely to occur in all programs with a non-trivial 

frequency, there may be a systematic bias that programs introduce (albeit unintentionally) when 

correcting address data. It is likely that address data errors are identified and corrected with 

higher frequency for children who have an elevated blood-lead level and require follow up. 

Given the potential bias introduced through the geocoding process, further research may be 

worthwhile to determine whether there are reasonable approaches that could be used to adjust the 

models for this bias. 

7.3.2 Reporting Limits in Surveillance Data

Other naturally occurring biases in the surveillance data may influence the degree to which 

models are representative of the true trends in childhood lead poisoning. For example, within the 

context of the Broad-Based National Model, there may be differences between states and 

localities in the manner in which childhood blood-lead testing results are reported to CDC. 

Sections 2 and 3 included a discussion about a screening algorithm that was applied to the 
 

81 

surveillance data to supress county/quarter data combinations for areas that were not conducting 

universal reporting of blood-lead testing results. Additional scrutiny of these data by CDC and 

other members of the lead poisoning prevention community may reveal other county/quarter 

combinations that were not identified through the screening algorithm that should be excluded 

from these analyses. We are confident that the overall impact of including these data in the 

current work will not severely bias the fixed-effects parameter estimates in the series of 

generalized linear mixed models developed in this project. 

7.3.3 Selection Bias in Surveillance Data

Selection bias is perhaps the most serious bias that is yet left unaccounted for in the models that 

have been developed, and may have severe impact on their predictive ability. Surveillance data 

are observational by nature, and are not designed to be representative of the general population. 

There are many competing forces that influence whether or not a child is screened at an 

appropriate age, and recorded in the blood-lead surveillance database. Some have hypothesized 

that surveillance data in the urban environment are representative of the affluent (who have 

private health insurance) and the poor (who receive Medicaid or other medical assistance), while 

under-representing the working poor (who may have no health insurance, and no mechanism for 

receiving appropriate preventive medical testing). While this may be true in general, many 

outstanding lead poisoning prevention programs currently are extending outreach, education, and 

screening services to areas with historically high incidence of childhood lead poisoning. These 

programs generally provide assistance to all members of the community, regardless of 

entitlement status. While these services are typically offered in high-risk urban areas with the 

infrastructure of a federally funded (CDC and/or HUD) or state-funded lead poisoning 

prevention program, they typically are less available in similar high-risk rural areas without 

similar infrastructure. In addition to outreach, education and screening activities, many 

childhood lead poisoning prevention programs (or partnering housing agencies) receive funding 

from HUD’s Office of Lead Hazard Control to conduct environmental investigations and reduce 

lead hazards in the residential environment. Many of these activities generate targeted screening 

of children living in deteriorated, older housing – which also is a non-trivial source of selection 

bias in the surveillance data. 

An important question for EPA to address is how selection bias is likely to influence the relative 

rankings of counties within a region or census tracts within a more localized area, as well as the 

predictive ability of the models themselves. 

7.3.4 Limitations of Ecological Models for Predicting Within-Area Relationships 

The models that were developed within this project are ecological models that describe quarterly 

distributional summary statistics within geographic areas as a function of predictor variables 

assessed within those same geographic areas. It also may be the case that some of these 

predictor variables have significant variation within a county (or census tract) – and that this 

within-area variation is highly predictive of risk of childhood lead poisoning within these 

geographic areas. Unfortunately, the data limitations within this study (for both the blood-lead 

response variables as well as many of the predictor variables) prohibit us from ascertaining these 

important person-level relationships. This type of relationship can be established only by linking 
 

82 

individual blood-lead concentration data with individual-level environmental, demographic, 

and/or programmatic information (which usually is not available). 

Within the context of the High-Resolution Massachusetts Model – it may be possible to link 

individual blood-lead records with the longitudinal housing inspection information to assess the 

loss of information associated with going from an individual-level model to an area-based 

ecological model. This type of assessment could be introduced in later stages of this project. 

7.3.5 Use of 2000 Census Data and Other Time Invariant Data as Predictors 

One potential criticism of the modeling effort is that we are linking blood-lead surveillance data 

collected between 1995 and 2006 to census data that were collected in 2000. Is the demographic 

information collected in 2000 likely to remain unchanged over the course of time? The answer 

probably depends on the variable under consideration. For example, age of housing in census 

tracts or proportion of housing built prior to 1950 is not likely to change dramatically in census 

tracts, unless there is a lot of demolition or new construction occurring. On the flip side, average 

income is likely to change substantively over time. 

Even though the demographic information contained in the 2000 Census is likely to change over 

time, the more important question is what effect will that change have on our model predictions? 

While the models likely would be improved with the use of more current census data for use as 

predictors, we do not believe that the use of older (less current) information will result in poor or 

inaccurate prediction. In fact, for the purpose of predicting current or future trends in childhood 

lead poisoning, we are more concerned with the age of the surveillance data that are being used 

as the response variable in this modeling exercise than with the age of the predictor variables. 

Similar arguments can be made for the use of static air modeling data, and averaged information 

from EPA’s Toxics Release Inventory. 

7.4 Model Validation Issues

The risk index models developed as part of this project may require validation before being used 

by childhood lead poisoning prevention programs throughout the country. The following four 

issues might be considered by EPA as being important to address as part of this validation 

exercise: 

1. Within counties and/or census tracts that contribute blood-lead information to the 

models, how representative is the screened population of children (on which the 

models are based) of the general population of children? 

2. Within counties and/or census tracts that do not contribute much information to the 

models (e.g., counties with low screening penetration), how well does the model 

perform at predicting relative risk and blood-lead distributions? 

3. Can risk index models based on historical blood-lead data from 1995 through 2005 

accurately predict risk and blood-lead distributions in future years (e.g., can it be used 

to forecast towards the federal 2010 goal)? 
 

83 

4. Can the High-Resolution Model developed in Massachusetts be generalized to predict 

risk and blood-lead distributions in other states across the Nation (or even within EPA 

Region 1)? 

If EPA is to provide childhood lead poisoning prevention programs with a risk characterization 

tool based on these models, a comprehensive validation should be pursued to address the above 

four issues. 

Validation of the Surveillance Data 

The first issue is related to the quality of the data supporting model development. For example, 

if CDC’s surveillance data are biased toward inclusion of high-risk children (as shown in the 

comparisons to NHANES), the risk index models also will be biased and tend to over-predict 

children at high risk. Note that if the bias is consistent among all counties and census tracts (i.e., 

it over-represents high risk children everywhere), the model predictions for the proportion of 

children in each blood-lead category likely will be biased, while the ability for risk indices to 

differentiate between high- and low- risk areas will be preserved. If the biases occur differently 

in different areas, non-trivial adjustments to the model would need to be pursued prior to use by 

childhood lead poisoning prevention programs. 

Because the unit of analysis in the development of the Broad-Based National Model is at the 

county level, the goal of a validation exercise would be to determine whether the distribution of 

children’s blood-lead concentrations that are included in the surveillance data for a sample of 

census tracts are representative of the general population of children found within those census 

tracts. One possible approach, would be to develop a field testing validation survey, in which a 

stratified random sample of counties are selected for a short-term outreach campaign in which 

eligible children are sampled in a representative manner. Stratification variables to be 

considered would be Rural/Suburban/Urban, predicted level of risk from the model, and possibly 

levels of socio-economic status. Obviously, development of such a survey would be costly, 

difficult to implement, and likely beyond the scope of this project. Alternatively, CDC might be 

able to reveal the specific counties that participated in various waves of NHANES – with 

comparisons being made in those specific counties. Access to the identification of the specific 

counties from which NHANES study subjects were sampled (within the NHANES analysis 

dataset) would provide this project with the best foundation to address the serious biases 

identified in Section 7.2 and calibrate the model to ensure that it is more reflective of the U.S. 

population. 

Validation of the Models in Areas with Low Screening Penetration 

This second issue relates to the performance of the risk index models in predicting both relative 

risk and the number of children in different blood-lead categories in the census tracts that 

historically had low screening penetration. Due to the fact that there is little to no data in these 

geographic areas to determine the fit of the risk index models, some field studies similar to the 

one described in the previous section would need to be conducted to address this issue. The 

major difference between the two field studies is that the census tracts chosen for this validation 

exercise would be tracts in which the screening penetration is low. 
 

84 

A similar approach could be used to conduct this field validation exercise in which a stratified 

sample of counties would be identified for the study, and a representative sample of children’s 

blood-lead levels would be obtained within those census tracts using an intense, brief outreach 

effort. The counties again would be chosen using a stratified random sampling approach, to 

obtain a sample of tracts that represents a combination of high-, medium- and low-risk areas in 

the rural, suburban, and urban environments. This is an area for potential future collaboration 

with CDC and perhaps some of their lead poisoning prevention grantees. 

Validation of the Models in Predicting Future Blood-Lead Concentrations 

Validation of this third issue can be performed to a certain extent using data that are already 

available as part of the modeling process. For example, in the national model where data are 

available from 1995 through 2005, data for a state or set of states can be removed for one or 

more years and the missing data predicted by the model. If all 2005 data were removed, models 

would be developed using the data from 1996 through 2004, and then the “future” predictive 

ability of those models can be assessed by applying them to the data from 2005. 

Validation of the Models in Predicting Blood-Lead Concentrations in Other Geographic Areas 

The last type of validation involves the determination of synergies (or lack thereof) in prediction 

between the Broad-Based National Model and the High-Resolution Model. Conceptually, we 

should be able to aggregate the modeling predictions from multiple census tracts within a county 

from the low-resolution model and match the county-level predictions from the Broad-Based 

National Model. Due to the fact that the National Model and Massachusetts Models were 

developed independently, using different data sources for the surveillance data (CDC and 

MDPH), and utilizing different predictor variables – these synergies may not exist. 

Further work on integrating the Broad-Based National Model with the High-Resolution Model 

(or multiple high resolution models if EPA is successful at expanding this project to include 

multiple additional programs) can be done by fitting these two types of models jointly under the 

concept of hierarchical linear modeling. This type of model, while more sophisticated and 

computer-intense, can be developed using specialized software under a Monte-Carlo Markov 

Chain Bayesian formulation. 

7.5 Other Recommendations for Immediate Future Work

The previous sections within Chapter 7 focus on various important issues related to the 

development of models to predict risk of childhood lead poisoning at the geographic level, 

including calibration to the nationally representative trends over time observed in NHANES, 

assessment of the potential impact of a variety of important biases and other data quality issues, 

and various model validation exercises that can be explored. EPA also has been including other 

state and local lead poisoning prevention programs as part of the project conference calls in 

anticipation of developing additional High-Resolution Models as part of follow-up work to this 

project. While these are all worthy tasks to pursue as part of future work, there are some 

additional analyses that the project team would recommend pursuing on the Broad-Based 

National Model as well as the High-Resolution Model within Massachusetts prior to approval of 

this report as a final report. These activities include the following: 
 

85 

• Broad-Based National Model 

o CDC grantee relationship managers may have insight into data quality issues 

(such as the previously discussed laboratory minimum reporting values, and not 

following universal reporting guidelines) for specific geographic areas and 

periods of time. Additional scrutiny of these data could be used to improve the 

quality of the blood-lead response data that serves as a basis for these models. 

The maps and visualization tool should help foster this review of the data. 

o In addition to the above data review –further investigation into using urban vs. 

rural status as a potential effect modifier in the analyses also is recommended. 

Differentiating between urban and rural areas can be conducting in numerous 

ways, including: 

 Determining whether the county is part of a Metropolitan Statistical Area 

within the 2000 US Census 

 Identification of the counties that contain the U.S. top 100 (or 200) cities 

based on population size 

 Use of a population density score (with a cut-off value). 

Use of this variable as a potential effect modifier might include fitting separate 

intercepts and slopes for the effects of time and seasonality within the different 

regions of the country, as well as the potential for using different environmental, 

programmatic, and demographic predictor variables in these two area types in the 

multivariate predictive models. 

o Once the proper way of handling the potential effect modifier for rural versus 

urban areas – the exploratory analyses that assess the predictive ability of each 

candidate environmental, programmatic, and demographic variable could be refit 

in a manner consistent with the baseline effects that will be included in the model. 

Thus – rather than assessing the predictive ability of a candidate variable after 

adjusting for the downward trend of time, it should be assessed after adjusting it 

for region, region*time, region*seasonality, and potentially region*urban/rural. 

High-Resolution Model in Massachusetts 

• Due to the fact that we know that Massachusetts followed universal screening and 

reporting guidelines during the entire period of observation (2000-2006), and the fact that 

these data have been used previously to support federally funded research projects – there 

is less concern about some of the previously mentioned data quality issues. This does not 

mean that the Massachusetts data are not potentially biased or flawed, as there are still 

probable selection biases and potential geocoding biases that were introduced into the 

analysis dataset that supports the High-Resolution Model. Our collaborators at the 

Massachusetts Department of Public Health are invited to review and comment on this 

work, and add their insight and experience in making recommendations on additional 

ways of handling the various data sources that were integrated into this model. 

• It also is recommended that comparisons be made between the observed and predicted 

data from the Broad-Based National Model for counties in Massachusetts (based on the 

input data received from CDC) with the observed and predicted data from the High-
 

86 

Resolution Model (based on the input data received from MDPH) by aggregating the 

observed and predicted census tract data within Massachusetts to the county level. 

• Finally, pursuit of some additional analyses of the individual-level data from MDPH is 

recommended – by linking individual blood-lead testing results on children over time to 

the housing inspection results (as well as other census-tract level predictors that were 

used in the current High-Resolution Model). This will help identify the degree of 

information loss experienced by pursuit of the ecological models of aggregate summary 

data. 
 

87 

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