EPA747-R-95-010
August, 1996
SEASONAL TRENDS IN
BLOOD LEAD LEVELS IN MILWAUKEE:
STATISTICAL METHODOLOGY
Technical Programs Branch
Chemical Management Division (7404)
Office of Pollution Prevention and Toxics
U.S. Environmental Protection Agency
401 M Street, S.W.
Washington, D.C. 20460
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DISCLAIMER
The material in this document has been subject to Agency technical and policy
review and approved for publication as an EPA report. Mention of trade names, products,
or services does not convey, and should not be interpreted as conveying official EPA
approval, endorsement, or recommendation.
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CONTRIBUTING ORGANIZATIONS
The study described in this report was conducted by the U.S. Environmental
Protection Agency (EPA) and its contractor QuanTech and the Milwaukee Health
Department. The Milwaukee Health Department provided the data and consultation, and
EPA and its contractor entered the data into a database, analyzed the data, and produced
the report.
QuanTech
Quantech (formerly David C. Cox & Associates) provided technical assistance
regarding the data management, and was responsible for the statistical analysis, and for
the overall production of the report.
U.S. Environmental Protection Agency
The U.S. Environmental Protection Agency (EPA) funded the analysis of the data
and was responsible for managing the study, for reviewing study documents, and for
arranging for the peer review of the final report. The EPA Project Leader was Bradley
Schultz. The EPA Work Assignment Manager and Project Officer was Samuel Brown.
Cindy Stroup and Barbara Leczynski provided valuable guidance. Janet Remmers, Dan
Reinhart and Phil Robinson also provided useful comments.
Milwaukee Health Department
The study could not have been done without the assistance and cooperation of the
Milwaukee Health Department. Major contributors included Amy Murphy, Thomas
Schlenker, Mary Jo Gerlach, Kris White, and Sue Shepeard.
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Table of Contents
EXECUTIVE SUMMARY xi
1 INTRODUCTION 1
1.1 PEER REVIEW COMMENTS 1
2 DATA DESCRIPTION 3
2.1 DATA COLLECTION 3
2.2 SUMMARY STATISTICS 5
2.3 DESCRIPTIVE STATISTICS AND FIGURES 6
3 METHODOLOGY 15
3.1 EMPIRICAL SMOOTHING APPROACH 15
3.2 MODELLING 16
3.2.1 Sinusoidal Functions 16
3.2.2 Beta Function 17
3.2.3 Accounting for the Expansion of the Program 18
3.2.4 Accounting for the Effect of Age 19
4 RESULTS 20
4.1 BETA FUNCTION MODELLING RESULTS 20
4.1.1 Unweighted Nonlinear Regression Analysis 20
4.1.2 Weights and the 1991 Procedural Change 24
4.2 SINUSOIDAL FUNCTION MODELLING RESULTS 30
4.2.1 Comparison with Beta Function Modelling Results 30
4.3 AGE'S EFFECT ON SEASONALLY 32
4.4 ADJUSTMENT FACTORS 37
4.4.1 Age and Seasonal Adjustments for Use in Studies of Intervention
Effectiveness in Milwaukee 38
5 DISCUSSION 40
REFERENCES 42
APPENDIX A. TECHNICAL DETAILS 44
APPENDIX B. DATABASE DEVELOPMENT 49
APPENDIX C. GEOGRAPHICAL SUMMARY OF HEALTH DEPARTMENT DATA 51
APPENDIX D. 1990-93 MILWAUKEE PbB MEASUREMENT ADJUSTMENT FACTORS 54
APPENDIX E. 1990-96 MILWAUKEE PbB MEASUREMENT ADJUSTMENT FACTORS 66
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List of Tables
Table 1. Use of Blood Lead Measurements from the Milwaukee Health Department 4
Table 2. First Time Participants in the Milwaukee Blood Lead Screening Program from 1990-
1993 by Year of Measurement 4
Table 3. First Time Participants in the Milwaukee Blood Screening Program from 1990-1993
by Age 5
Table 4. Summary of PROC NLIN Results by Phase ((J>) 21
Table 5. Comparison of Nonlinear Regression Results for (J>=0 26
Table 6. Parameter Estimates and First Order Correlation of Residuals for Weighted
Sinusoidal Model Fit 30
Table 7. Comparison of Sinusoidal and Beta Function Modelling Results 31
Table 8. Testing Symmetry (R=0.5) through the Beta Model 32
Table 9. Estimates from Model Incorporating Age 36
Table C1. Census Counts and Summary of Milwaukee Health Department Blood Lead Data
by Zip Code 53
Table D1. Multiplicative Age Adjustment Factors for 1990-1993 Milwaukee PbB Data 55
Table D2. Seasonal Additive Adjustment Factors Without Procedural Correction for 1990-
March, 1994 Milwaukee PbB Data 56
Table D3. Seasonal Adjustment Factors with Procedural Correction for 1990 - March, 1994
Milwaukee PbB Data 61
Table E1. Seasonal Adjustment Factors for Log Transformed Data from 1990 through
February, 1996 72
Table E2. Seasonal Adjustment Factors for 1990 to February, 1996 Based on an Analysis of
Untransformed Data 79
Table E3. Age Adjustment Factors for 1990 to February, 1996 Milwaukee PbB Data 86
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List of Figures
Figure 1 Mean Monthly Blood Lead Levels and Number of Children Screened Based on
Milwaukee Health Department Data from Sites that Report All Measurements 8
Figure 2 Semi-monthly Arithmetic Mean and 90th Percentile Blood Lead Levels with
Smoothed Estimates 1990-1993 9
Figure 3 Semi-monthly Arithmetic Mean and 90th Percentile Blood Lead Levels with
Functional Form Fit 1990-1993 10
Figure 4 Arithmetic Mean and 90th Percentile Blood Lead Levels for 1990-1993 by Age
Category (n=12,904) 11
Figure 5 Semi-monthly Arithmetic Mean Blood Lead Levels for Males and Females 12
Figure 6 Semi-monthly Smoothed 90th Percentile Blood Lead Levels for Two Age Groups.
13
Figure 7. Semi-monthly Smoothed 90th percentile Blood Lead Levels for Children Under
Three Years of Age 14
Figure 8. Studentized Residuals from Unweighted Analyses of Means 22
Figure 9. Studentized Residuals from Unweighted Analyses of 90th Percentiles 23
Figure 10. Correlogram from Unweighted Analyses of Means 24
Figure 11. Correlogram from Unweighted Analyses of 90th Percentiles 25
Figure 12. Studentized Residuals of 90th Percentiles from Weighted Analyses Using the
Program Expansion Term 27
Figure 13. Studentized Residuals of Means from Weighted Analysis Using the Program
Expansion Term 28
Figure 14. Predicted Values Derived from Fitting 90th Percentiles and Means to the Sinusoidal
and Beta Models 29
Figure 15. Semi-monthly Smoothed 90th Percentile Blood Lead Levels by Age Group (1990
to 1991) 34
Figure 16. Semi-monthly Smoothed 90th Percentile Blood Lead Levels by Age Group (1992
to 1993) 35
Figure 17. Modelled (solid line) and Smoothed (dashed line) 90th Percentile Blood Lead Levels
Using Log Transformed Data from 1990 to 1996 70
Figure 18. Seasonal Adjustment Factors (1990-96) for Log Transformed Data 71
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EXECUTIVE SUMMARY
Most studies on the effectiveness of interventions for reducing children's blood lead
levels (PbB) have not distinguished declines in PbB due to program effectiveness from
seasonal and age-related fluctuations in PbB. In this report, seasonal fluctuations and age
effects in 1990-94 blood lead levels for a northern urban environment are studied, using
data from 13,476 children screened for blood lead in Milwaukee, Wisconsin. The purpose
was to determine whether there were seasonal and age trends, and if so, to estimate the
magnitude of the trends. These estimates can then be used to help interpret studies with
blood lead monitoring data, especially studies on the effectiveness of interventions to
reduce blood lead levels.
The Milwaukee data showed sizeable seasonal and age trends in Milwaukee children's
PbB levels. Blood lead levels were about 40% higher in the summer than the winter, and
about 15-20% higher at ages two to three years than at ages less than one year or ages
five to seven years. Statistical methodology was developed to account for these
fluctuations, so that the effectiveness of intervention programs may be quantified. These
estimates are being used in studies of the effectiveness of lead interventions in Milwaukee.
The methodology was described in considerable technical detail to facilitate analyses of
seasonal and age effects in PbB in other environments.
A tentative result suggests the magnitude of seasonal PbB fluctuations may be greatest
for children less than four years old. Better understanding of the reasons for the trends
might help to better determine mechanisms for reducing childhood lead exposure.
Seasonal fluctuations in PbB are probably greater in cooler environments such as
Milwaukee's, where seasonal changes in exposure to outdoor lead sources and sunlight
are more extreme. At least in the northern U.S., the magnitude of the seasonal and age
trends are large enough so that they must be considered in the design and interpretation
of any blood lead monitoring results.
XI
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1 INTRODUCTION
Many Federal, State, and local programs have been implemented to reduce lead
exposure in children. However, most of the studies of the effectiveness of the
interventions for reducing blood lead (PbB) levels (see Burgoon, etal, 1994 and U.S.EPA,
1995a) have ignored effects of seasonal fluctuations in PbB levels and dependencies of
PbB levels on age. A few studies on abatement effects eliminated the confounding of
seasonal effects but not age effects, by spacing PbB measurements one year apart. For
retrospective studies, the requirement of many repeat measurements one year apart is not
feasible. Thus, quantification of the effects of abatements and other promising intervention
strategies has often not been possible. For example, a study on the effect of educational
and counselling interventions for reducing PbB levels in children (Kimbrough, et al, 1994)
reported that "educating parents proved a very effective tool" for reducing PbB levels, but
did not estimate the decline in PbB levels due to the intervention. Instead, declines in the
Granite City, Illinois children's PbB levels following interventions were simply reported as
being too large to be attributed entirely to seasonal and age effects.
In this report seasonal fluctuations and age effects in 1990-93 PbB levels for a northern
urban environment are studied using data from 13,476 children screened for blood lead
in Milwaukee, Wisconsin. The purpose is to determine whether seasonal and age effects
exist, and if so, to develop simple adjustments to allow for quantification of the effects of
education and abatement programs. Some previous analyses of data from the 1970's and
early 1980's, such as U.S.EPA(1995b), indicated seasonal trends; this analysis sought to
verify and estimate the current trend. Statistical methodology is described in detail to
facilitate analyses of seasonal and age effects in PbB for other environments. Tables with
adjustment factors specific to the 1990-93 Milwaukee PbB data are also included. The
adjustment factors are necessary for planned analyses of the effectiveness of abatement
and lead educational programs in Milwaukee from 1990-93.
1.1 PEER REVIEW COMMENTS
This study was reviewed independently by members of a peer review panel.
Comments which are important for interpreting the study results or which had an important
impact on the report are discussed below.
Some reviewers wanted a clearer description of the Milwaukee Health Department
screening program expansion, and how the expansion may have affected results of the
analysis and validity of the seasonal adjustment factors. In response, portions of the text
were rewritten. Table 1 was added; it delineates the changes and shows how the available
data was used. Also Figure 1 now includes a needle plot showing the number of children
screened for blood lead from 1983-1993. Geographical information was requested, so the
appendices now include Table C1 which shows blood lead level results by zip code.
1
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One of the reviewers was concerned about correlations among residuals from different
time periods. In response, greater emphasis was placed on Figure 12, a residual plot for
90th percentile results which indicated the residuals were not correlated. The analysis of
90th percentiles better describe blood lead levels of children at high risk for lead poisoning
than the analysis of mean blood lead levels which indicated correlation among residuals.
More discussion about this correlation was added to the text.
One of the reviewers thought that the use of the Beta model was not well justified. In
response, figures were added to show that the fit to the model was very good for the 90th
percentiles. The beta model, with a minimum of parameters fit the data as well as
sinusoidal models. The Beta model also allowed for direct assessment of features such
as the potential for abrupt or asymmetric seasonal changes in PbB between winter and
summer. A test for symmetry is now detailed in Section 4.2.1.
Some of the reviewers were concerned about limitations inherent in making
adjustments for removal of seasonal trends. Comments were made that well-designed
randomized trials would likely be a better approach for studies of intervention
effectiveness. In response, text in the Discussion section now more completely discusses
these limitations, and mentions that some seasonal effects might be controlled for in some
well-designed studies. However, formulating well-designed studies for evaluating
effectiveness of interventions is problematic. Furthermore, retrospective studies, which
by definition can not control for seasonality, have certain advantages. First, retrospective
studies usually would include a larger number of children. Second, retrospective studies
would not create artificial circumstances which could lead to invalid conclusions. Finally,
they would not arbitrarily deprive control group children of benefits from interventions
being evaluated.
One of the reviewers was concerned about inferences about the interaction between
age and other effects since the participation in the screening program may be different for
older children (ages greater than three years). Although these are valid concerns, older
children were usually screened for the same reasons as younger children, and only rarely
because of clinical indications. Also, Figure 4 indicates that the relationship between age
and PbB seems consistent from ages 2 to 7.
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2 DATA DESCRIPTION
2.1 DATA COLLECTION
The PbB data is a result of widespread blood lead screening of Milwaukee children,
generally less than seven years old. The screening, occurring in many locations, attempts
to identify children with elevated blood lead levels, so steps can be taken to reduce lead
exposure and lead-related health impacts. The program began in the 1980's with a few
health providers and laboratories reporting blood lead measurements to the Milwaukee
Health Department (MHD). In late 1989, the MHD improved its computerization of its
records. The screening program expanded dramatically in late 1991. From 1992 through
1993 baseline measurements on 10136 children (about 5000 per year) were sent to the
MHD. This corresponds to a coverage of about 50%, since about 10,000 children are born
in Milwaukee per year.
At some of the blood screening locations, all of the results are reported to the local
health department. Although by law all lead screening data is being reported to the local
health department, some sites only reported elevated blood lead levels in the past.
Samples for the sites reporting only elevated blood lead levels have been excluded, since
this might bias the estimates of seasonality of results. Biases in estimates of average
blood lead levels in the population of children in Milwaukee may also result from a
procedural change in October, 1991, after which all blood analyses directly measured the
lead levels. Prior to October, 1991, some children were screened using FEP (free
erythrocyte protoporphyrin) blood analyses (instead of blood lead). Follow-up blood lead
measurements were made for these children having an elevated FEP level. FEP
measurements were not used for any of the analyses.
Available data for the analyses includes PbB measurements on 25,665 children from
1986 to March, 1994. All PbB measurements in the data set are the baseline
measurements which were made before any intervention by the MHD. For children with
multiple PbB measurements, the data for this seasonality analysis only includes the first
measurement. Blood lead levels from children with prior FEP measurements were also
excluded. The next three paragraphs detail the other exclusion criteria.
By 1990, some sites reported all measurements to the MHD. However, other sites
tended to report only elevated blood lead measurements to the MHD, and data on 9581
children from these sites was excluded (see Appendix for further details). This exclusion
was made to reduce the effect on estimates that would be due to changes in the reporting
of measurements to the MHD.
The analysis, tables, and figures (except Figure 1) excluded pre-1990 data on 2,051
children and 1994 data on 557 children. The pre-1990 data was excluded because it
represented blood lead levels for a small vaguely defined set of children who tended to
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have abnormally high blood lead levels. Data from 1994 was excluded because of
concerns that it may not have been complete.
Table 1 identifies the MHD measurements on 13,746 children that had been used for
this report. Tables 2 and 3 are frequency distributions of these children by year of
measurement and age.
Table 1. Use of Blood Lead Measurements from the Milwaukee Health Department
Description
All recorded baseline
measurements from 1986 to
3/94
Providers report all
measurements
Measurements from
1990 through 1993
Recorded ages from 6 months
to 7 years
Use
Figure 1
All analyses, tables, and figures
except figure 1 , and exceptions
below.
Table 3, Figure 4, Section 4.3
Number of PbB measurements
25,665
25,665 - 9,581
= 16084
1 6084- 2051 (pre90)- 557
(early 94)
= 13,476.
13,476-572
= 12,904.
Table 2. First Time Participants in the Milwaukee Blood Lead Screening Program from 1990-1993 by
Year of Measurement
Year
1990
1991
1992
1993
Total
Number of Observations
1,431
2,466
5,260
4,319
13,476
Percent
10.6
18.3
39.0
32.1
100.0
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Table 3. First Time Participants in the Milwaukee Blood Screening Program from 1990-1993 by Age
Age Category
0.5 - 1 Year
1 - 1 .5 Years
1 .5 - 2.0 Years
2.0 - 2.5 Years
2.5 - 3.0 Years
3.0 - 3.5 Years
3.5 - 4.0 Years
4.0 - 4.5 Years
4.5 - 5.0 Years
5.0 - 5.5 Years
5.5 - 6.0 Years
6.0 - 6.5 Years
6.5 - 7.0 Years
Total
Number of Observations
2,601
4,378
969
690
616
626
720
772
636
461
214
120
101
12,904
Percent
20.2
33.9
7.5
5.3
4.8
4.8
5.6
6.0
4.9
3.6
1.7
0.9
0.8
100.0
Note: 123 children had a missing value forage category due to the date of birth being missing, the ages of
343 children were greater than 7 years, and the ages of 106 children were less than 6 months.
2.2 SUM MARY STATISTICS
Semi-monthly means (aggregated twice a month) and 90th percentiles of
untransfoimed PbB measurements were used for graphing the data and as inputs for the
formal analyses. The 90th percentiles were generally preferred for the purpose of
quantifying effects of interventions for reducing lead exposure of children with higher blood
lead levels. This is because the blood lead levels at the 90th percentile are more similar
to those of children receiving lead interventions than those at the mean, median, or other
measures of central tendancy. Since there are 24 semi-monthly periods per year, and four
years of data, 96 values of means and 90th percentiles for time periods from 1990 through
1993 were statistically analyzed for most analyses. For analyzing effects of age on
seasonality results (described in sections 3.2.4 and 4.3), semi-monthly values were
calculated for each of four age groups from 1990 through 1993 for a total of 4*96=384
means and 90th percentiles.
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The measurements used for calculating the semi-monthly statistics may be thought of
as samples from populations of baseline blood lead levels that would be reported to the
MHD. The populations change as actual blood lead levels change, and as the screening
program coverage becomes more complete. For a semi-monthly period, the actual sample
of measurements depends on a number of factors that include which children are tested
at clinics that report all measurements to the MHD, the timing of the measurements,
measurement errors, and so on.
From 1990 through 1993, the only obvious systematic change in the number of
measurements reported to MHD occurred in late 1991 (see Figure 1). Nevertheless,
subtle changes associated with the expansion of the screening program may have resulted
in gradual systematic changes in the blood lead level summary statistics. These changes
may have had a non-negligible effect on estimates of long term declines in blood lead
levels. In contrast, the gradual changes would have had less effect on estimates
characterizing the seasonality of blood lead levels, because seasonal levels differ
substantially (by about 40%) within a relatively short period of time (between winter and
summer).
2.3 DESCRIPTIVE STATISTICS AND FIGURES
As described in section 2.1, the analyses were based on PbB measurements made
after 1989. Figure 1, shows a striking difference in the characteristics of the 1986 through
1989 versus the post-1989 time series of mean PbB measurements. The excess variation
in mean pre-1990 PbB levels is primarily due to the much smaller number of children
screened before the 1990's. The large drop in observed PbB levels in late 1989 may
partially be a consequence of the expansion of the screening program. It is likely that
before 1990 when there was an even greater need to target children with the highest blood
lead levels, the relatively few participating health care providers may have served children
primarily in areas of the city where blood lead levels tended to be higher. By 1990,
participating primary health providers were more numerous, and areas of the city with
differing blood lead level characteristics may have been more evenly represented among
the children being screened. Although useful for estimating seasonal and age-related
trends, the data here, especially through 1991, is limited in its ability to determine long-
term trends in blood lead levels. The most reliable source for determination of long-term
trends is NHANES II and NHANES III (Pirkle, etal, 1994) which provided data from 1975-
1978 and 1988-1991. These surveys found that blood lead levels had decreased
substantially during the 1980's, but that a significant number of children still had blood lead
contents at levels widely considered as unhealthy.
Figure 2 is a plot of summary PbB levels from 1990-93 aggregated by semi-monthly
period. Open circles and diamonds denote raw means and distribution-free 90th
percentiles for each semi-monthly period. Solid boxes and triangles denote smoothed
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means and 90th percentiles. Smoothing reduces short-term fluctuations caused in part by
variation due to the small number of children sampled each period. The smoothed values
were weighted moving averages over time. For time period t, the smoothed value was
equal to 30% of the raw value at time period t, plus 20% of the sum of the raw values at
time period t-1 (preceding) and t+1 (following), plus 10% of the sum of raw values at time
periods t-2 and t+2, plus 5% of the sum of the raw values at time periods t-3 and t+3.
The smoothed curves in Figure 2 clearly show seasonal fluctuations in PbB
measurements with a peak around July or August and minimum values occurring in the
winter. In the summer, the peaks are easily identified, but for some winters, the PbB
measurements seem almost constant. Especially for 1993, the plot indicates seasonal
fluctuations may be asymmetric. That is, the rise to peak levels may be more gradual and
over a longer period of time than the decline to the lowest winter levels. However, a long-
term decline in lead levels would accentuate the steepness of the seasonal declines in the
fall and winter. Apparent seasonal fluctuations could have also been confounded with
changes associated with the expansion of the screening program. From late September
to early October, 1991, the number of PbB measurements rose from 112 to 235. The
simultaneous sharp drop in PbB levels may have been partially due to the inclusion of
lower risk children into the screening population eligible for the study.
Figure 3 illustrates results from functional form fits for both means and 90th percentiles.
The functional forms were used to clarify issues such as the possible asymmetry of the
data. Details about the functional form fit are provided in section 3.2.2 and Appendix A.
From the fit, peak PbB levels most likely occur in August.
Figure 4 presents plots of mean and 90th percentile PbB levels by age. PbB levels
increased rapidly before the age of 2 years, and then declined gradually thereafter.
Similar results were indicated in at least two other studies. In the Sydney Lead Study
(Cooney, et al, 1989), blood lead levels increased from birth to 18 months and then
declined for ages 18 to 48 months. In the Port Pirie Study (Baghurst, et al, 1992), PbB
levels peaked at age two years. Figure 5, a plot of mean PbB by gender of child, shows
no detectable difference in PbB between males and females.
Figure 6 shows smoothed plots of 90th percentile PbB levels for two different age
groups. The plots suggest substantial seasonality from 1990 to 1993 for children less than
3 years old, but only in 1992 for the older children. The extent to which seasonality
depends on age is uncertain, because of the substantial seasonality shown for all age
groups in 1992. Plots in Figure 7 suggest similar seasonality in PbB for ages 6 months to
1 year, 1-1.5 years, and 1.5-3 years in 1990, 1992, and 1993. In 1991, PbB
measurements had an observed peak in late summer only for children less than one year
old. In 1991, the early peak in PbB measurements for ages 1 -3 years may be due in part
to procedural changes that may have occurred in the blood lead screening program.
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ug/dl
40
30
20
10
N°-°f
Children
800
600
400
200
0
/*!
l*i\ l
A DJ \
A^
V A I
x\
li.. Ihi Illllllllllliiilllll
1986 1987 1988 1989 1990 1991
Note: A denotes the month of August and D denotes the month of December.
1992
1993 1994
Figure 1 Mean Monthly Blood Lead Levels and Number of Children Screened Based on Milwaukee Health Department Data from Sites that
Report All Measurements.
8
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ug/dl
50
40
30
20
10
Jan Apr Jul
1990
Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct
1991 1992 1993
Smoothed Arithmetic Mean
Raw Arithmetic Mean
Smoothed 90th PCT
Raw 90th PCT
Figure 2 Semi-monthly Arithmetic Mean and 90th Percentile Blood Lead Levels with Smoothed Estimates 1990-1993.
9
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ug/dl
50
40
30
20
10
^W^ *VV
^¥w
r*jSi"j3eeer
Jan
Apr Jul
1990
Oct Jan
Apr Jul
1991
Oct Jan Apr
Jul
1992
Oct Jan Apr
Jul
1993
Oct
Functional Form Mean
Raw Arithmetic Mean
Functional Form 90th PCT
Raw 90th PCT
Figure 3 Semi-monthly Arithmetic Mean and 90th Percentile Blood Lead Levels with Functional Form Fit 1990-1993.
10
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ug/dl
50
40
30
20
10
0 6-8 9-12 12-15 15-18 18-21 21-24 24.27 27-30 30-33 33-36 3642 4248 48-54 5440 6046 66-72 72-78 78-84
Age Category (in months)
-• •»- Mean Blood Level -** *- 90th Percentlte Blood Level
Figure 4 Arithmetic Mean and 90th Percentile Blood Lead Levels for 1990-1993 by Age Category (n=12,904).
11
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ug/dl
50
40
30
20
10
Jan Apr Jul
1990
Oct Jan
Apr Jul
1991
SEX
Oct Jan
Female
Apr Jul
1992
Oct Jan
Apr Jul
1993
Oct
Male
Figure 5 Semi-monthly Arithmetic Mean Blood Lead Levels for Males and Females.
12
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ug/dl
50
40
30
20
10
Jan Apr Jul
1990
Oct Jan Apr Jul
1991
Oct Jan
AGE
Less than 3 Years
Apr Jul Oct Jan Apr Jul
1992 1993
-• • •- 3 Years or More
Oct
Figure 6 Semi-monthly Smoothed 90th Percentile Blood Lead Levels for Two Age Groups.
13
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ug/dl
50 :
40 :
so :
20 :
10 :
0
H
m
«•
/ \ 1 ^^ $\ 1 \ J>
e^> / \\M^ \\ /-V\ /A
v ^^ \k^^ /^v
^/ \wv---
\V/ v^
\7
teeT
Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct
1990 1991 1992 1993
AGE ooo % to 1 Year • • • 1 to 1K Years 000 1H to 3 Years
Figure 7. Semi-monthly Smoothed 90th percentile Blood Lead Levels for Children Under Three Years of Age.
14
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3 METHODOLOGY
Empirical smoothing and model fitting approaches were used to characterize seasonal
and long-term trends in the data.
3.1 EMPIRICAL SMOOTHING APPROACH
The empirical smoothing approach included 1) calculating arithmetic means and
empirical percentiles ("raw means and percentiles") of PbB measurements for each half-
month period, 2) smoothing the raw means and percentiles using weighted moving
averages, and 3) plotting both the raw and smoothed statistics against time.
Plots of the raw means and percentiles over time are often sufficient to depict seasonal
and long-term trends of time series. Differences in raw means and percentiles of the PbB
levels are approximately unbiased estimates of differences in baseline blood lead levels
of children covered by the MHD screening program. Thus, the January, 1993 minus the
January, 1992 90th percentile (sample) PbB measurements would on average be equal
to the actual drop from January, 1992 to January, 1993 in the 90th percentile PbB levels
of children covered by the program. Nevertheless, moving averages were calculated,
because sampling variation and random short-term fluctuations can mask trends. In
general, the moving average of a time series yt, is given by:
(1) st = IH.pip]wjyttj;t = p+1, ..., n-p.
Here, the weights wj; j=-p, -p+1 , ..., p, add to 1 , and p is the order of the moving average.
The greater the order and the more similar the weights, the greater the degree of
smoothing, and the greater the reduction in sampling variation and short-term fluctuations.
The weights used here were w0=.3, w.,=.2, w2=.1, w3=.05, and w.j = wr Assuming
independence, the sampling variance for the smoothed statistics would be only about
1 9.5% (or 1 00% * .32+2*(.22+. 1 2+.052)) of the sampling variance of the raw statistics. The
moving average of order 3 helped discern trends occurring over time intervals of a few
months or longer. Graphs of the raw means and percentiles showed that PbB is higher in
the summer than the winter, but may reach a peak in some years as early as April. Graphs
of the smoothed means clearly showed that peak PbB's probably occur sometime in the
summer, perhaps in July or August.
In theory, the moving average may have also obscured observation of interesting
sudden rises in blood lead levels occurring within a couple of months. In Figure 2, the
moving averages rounded the observed rise in PbB from June to August, 1 993, so that the
August measurement appears as part of a more gradual rise in PbB from January to
August. Although a sudden two-month 20% rise in PbB seems unlikely, the moving
average would have obscured observation of the rise, if it did occur. In general, weights
are chosen to balance the opposing objectives of 1) minimizing deviations between the
15
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smoothed and raw data so that important shorter-term fluctuations are not obscured, and
2) reducing unwanted short-term fluctuations to facilitate better discovery of long-term
trends. Appendix A demonstrates, through a more mathematical description of the
problem, how the chosen weights achieved this balance rather well.
3.2 MODELLING
The graphs of the smoothed statistics led to many questions about the size and timing
of the seasonal fluctuations. Modelling was needed for testing hypotheses (such as
whether the seasonality is symmetric), and to construct meaningful parameter estimates.
Modelling was also used, almost as an exploratory tool as described in section 3.2.3, to
investigate the complicated relationship between age and seasonality in PbB. The
analyses used a novel nonlinear regression approach based on the beta function. As a
check, the data was also fit using a more common sinusoidal function model. Both the
beta and sinusoidal functions models assumed that non-age related patterns in PbB could
be reasonably expressed as the sum of an overall (downward) linear trend and a function
for seasonality.
3.2.1 Sinusoidal Functions
The sinusoidal function model is given in equation 2, where summary PbB levels for
the ith time period, Yh are expressed as a linear function of sine and cosine functions:
(2) Y, = a + P0tj + Ij=[1,p](P1jsin(2njxi) + p2jcos(2njXi)) + e,
Here, t is time in years ranging from t=0 on January 1, 1990 to t=4 on January 1,1994, and
x = the fractional portion of t so that x ranges from 0 on January 1 to 1 on December 31;
e, represents the random error term. The e, would be independent if the e, represent
differences between sampled summary PbB levels and "true" means or percentiles for
populations of PbB levels of Milwaukee children. However, the random errors could be
correlated if the e, also reflected the unpredictability of changing climatic conditions. For
example, June and July PbB levels could be correlated if a hotter-than-normal July often
follows a hotter-than-normal June, and PbB levels rise with temperature.
The random errors might also be correlated if the model (in equation 2) is misspecified.
For example, for the interval from 1990 through 1993, the long-term trend might be
concave (turning downward). Then the random error terms as defined through equation
2 would tend to be positive somewhere in the middle of the time interval, negative
elsewhere, and the correlation would likely be positive.
16
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SAS's PROC REG (SAS, 1990) was used to fit the data to the sinusoidal model, and
higher frequency terms were eliminated using the appropriate F-statistic. The e, were
assumed to be asymptotically normal, and the first-order correlation was calculated to test
the assumption of independence of the successive e,.
3.2.2 Beta Function
The beta function was preferred for modelling fluctuations in PbB levels, because with
a minimum of parameters, it allowed forfeatures suggested by our empirical analysis. The
seasonal component may not be symmetric, and it was noted that during winter months,
lead levels seemed relatively constant. The beta function allows for this relatively constant
low period with a minimum of parameters whereas the sinusoidal function does not. Unlike
the sinusoidal form, the beta function assumes that the peak and minimum PbB level are
reached once each year, and that between the times of peak and minimum PbB levels,
(mean or 90th percentile) PbB levels change monotonically. The beta functional form for
semi-monthly summary lead levels Yh shown in equation 3 with subscripts omitted,
includes components for both linear trend (L) and seasonality (S).
(3) Y = L+S((|>)+e where,
L = a + |3t, and
= A(z/R)TR ((1
Here a, P, A, R, cj), and T are parameters, t=time in years, and z=the fractional portion of
(t-cj)), i.e. IKH)) - int(t-cj))||, so that if cj)=0, z ranges from 0 on January 1 to 1 on December
31 . e is the random error component. $ is the phase parameter ranging from -0.5 to 0.5
(-0.5 < cj) < 0.5). The phase parameter is included to allow the model to fit the seasonal
maximum at the appropriate time of year. The seasonal component equals 0 when z = 0,
and reaches its maximum, A, when z = R. Thus A, (A > 0), is the difference between
maximum and minimum values of the seasonal component. Note that when A=0, the
model suggests there is no seasonal variation. Maximum lead levels occur on the
365(R+c|))th day of the year. R, (0 < R < 1 ), determines whether the seasonal component
is symmetric. If R=.5, the time between maximum and minimum lead levels is one-half
year. If R > .5, the rise to maximum lead levels is more gradual than the decline to
minimum levels. T (T > 0) determines the abruptness of changes in the seasonal
component around the seasonal peak, the 365(R+cJ)) day of the year. Assuming that
maximum lead levels occur during the summer, a large value of T indicates almost
constant lead levels in the winter and most of the spring, a rapid rise to their peak in the
summer, and then a rapid decline to the winter levels. A small value of T indicates less
abrupt changes between peak and minimum lead levels.
Parameters a, P, A, R, and T were estimated through nonlinear regression. The model
was first fit assuming cj)=0 and the e, were independent. The model was then fit using a
17
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range of values for cj) to test whether cj)=0 and to evaluate the sensitivity of inferences to
changes in cj). The independence assumption was checked by calculating a version of a
correlogram from the studentized residuals. The correlogram is a plot of sample
correlations g1; ... , g24 where
(4) gk = (Irtrt+k)/(n-k) t = 1, 2, ... 96-k+1,
and the rt are the studentized residuals. Under the assumption of independence, the
absolute value of the sample correlations would generally be less than 2/n5 (Diggle, 1990).
3.2.3 Accounting for the Expansion of the Program
Two more nonlinear regressions were also considered to account for the greater
coverage of the screening program in 1992 and 1993. First, weights were set equal to the
semi-monthly sample sizes, to account for the possibility that the Var(e,) are approximately
proportional to the sample sizes. The data was also reanalyzed after adding a term to the
model to account for the effect of the program expansion in October, 1991. The term,
denoted by P, is P = 0 if t < 1.79 (corresponding to October 1, 1991); = A otherwise.
The sinusoidal model with the term for the program expansion was thus (omitting subscript
i):
(5) Y = a + p0t + Ij=[1ip](p1jsin(2njx) + P2jcos(2njx)) + P + e
The beta model with term P is:
(6) Y = a + pt + P + S + e
Weighted analyses (with weights equal to the sample sizes) based on the generalized
models of equation 5 and 6 will be referred to as "weighted + P" analyses.
18
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3.2.4 Accounting for the Effect of Age
As shown in Figure 6, both overall PbB levels and seasonality may depend on age.
Equation 7 incorporates age effects into the model, so that
(7) Y = Yk(L+Sk+P)+e where
L = a + pt, and Sk = Ak(x/R)TR ((1-x)/(1-R))T(1-R)
and Yk and Ak are parameters defined for age categories,
k=0: (0.5,1], k=1: (1,1.5], k=2: (1.5,3], and k=3: (3,7) years. The age categories were
chosen so that the age categories are similar with respect to: 1) the number of children
within each category, and 2) the range of mean PbB levels associated with the ages within
age category. From Figure 4, the range of mean PbB levels are about 2.5 ug/dL = (1 1 .5.9)
ug/dl for the ages (0.5, 1 ] years, 2 ug/dL = (13.5-11.5) ug/dL for ages (1,1.5], 1 .25 ug/dL
= (1 4.75-1 3.5) ug/dL for ages (1 .5,3] years, and about 1 .5 ug/dL = (14.5-1 3) ug/dL for ages
(3,7] years.
The Yk are multiplicative age-related factors for overall PbB levels. For example, if Y0=1
and Yi=1 .3, children between 1 and 1 .5 years would have average PbB levels 30% higher
on January 1 than children up to 1 years old. After adjusting for overall lead levels, the Ak,
which represent seasonal differences between high and low PbB levels, are also allowed
to depend on the same age categories. Results from this model (equation 7) are
presented in Section 4.3.
19
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4 RESULTS
4.1 BETA FUNCTION MODELLING RESULTS
4.1.1 Unweighted Nonlinear Regression Analysis
The minimum PbB occurred sometime between late October and early March, because
the basic model of Equation 3 fit the data well (for details see Appendix A, Section A2) for
cj) between -1/6 and 1/6. The date of maximum PbB, sometime between late July and mid-
September, could be more precisely estimated, because lead levels apparently changed
abruptly during the summer and early fall. For a minimum PbB occurring on January 1, the
estimated maximum detrended PbB date (or the date of maximum PbB if the long-term time
trend were removed) was August 13 with a 95% confidence interval (July 25, September
2). For values of § between -1/6 and 1/6, estimated maximum PbB dates ranged from
August 4 to September 4. A, the difference in maximum and minimum lead levels, was
also insensitive to choice of cj). For cj)=0, the estimate of A from monthly mean PbB values
was 3.66 with a 95% confidence interval (2.65, 4.67). For 90th percentile PbB values, the
estimate was 6.70 with a confidence interval (5.22, 8.19). In 1993, the seasonal
component would account for a 38% rise in mean PbB and a 40% rise in 90th percentile
PbB levels from January to August. However, for some cj), the seasonal component was
symmetric whereas for other $ it was not. Assuming a minimum PbB on January 1, the
95% confidence interval for R would be .56 to .67, so that the seasonal component would
be asymmetric. Results for other values of $ are shown in Table 4. Estimates of R ranged
from .425 for a minimum PbB on March 1 to .88 for the minimum occurring on November
1.
Residuals for the unweighted analysis of means and 90th percentiles for cj)=0, are
shown in Figures 8 and 9. Both figures suggest the residuals are generally larger for time
periods before October, 1991 when sample sizes were smaller. Figure 8 also suggests
a positive correlation in residuals for the semi-monthly means. Correlograms are shown
in Figures 10 and 11. Correlations with absolute values above 2/(96)2 = 0.204 are
generally considered significant (see section 3.2.2). From Figure 10, the absolute
correlations for semi-monthly means less than four months apart are significantly greater
than zero. In contrast, it is not clear from Figure 11 whether the 90th percentiles are
correlated. In Figure 11, one sample correlation of 0.23 at 3.5 months was (barely)
significant (exceeded 0.204) and other sample correlations for short time lags (0.5 and 2
months) were nearly significant.
20
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Table 4. Summary of PROC NLIN Results by Phase ((J>)
MEANS DATA
Phase
-5/24
-4/24
-3/24
-2/24
-1/24
0
1/24
2/24
3/24
4/24
5/24
Date of Minimum
PbB
Oct. 16
Nov. 1
Nov. 16
Dec. 1
Dec. 16
Jan. 1
Jan. 16
Feb. 1
Feb. 16
Mar. 1
Mar. 16
R1
C82..94)
(.78..91)
(73,.84)
(.67,78)
(.62,72)
(.56..6T)
(.51, .63)
(.46,.57)
(.41, .53)
C37..48)
Residual SS
287.4
269.4
264.9
265.7
266.9
267.1
267.0
268.3
271.3
274.8
277.9
Fit2
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
MSE = 2.94 (for phase = -3/24)
90th PERCENTILE DATA
Phase
-5/24
-4/24
-3/24
-2/24
-1/24
0
1/24
2/24
3/24
4/24
5/24
Date of Minimum
PbB
Oct. 16
Nov. 1
Nov. 16
Dec. 1
Dec. 16
Jan. 1
Jan. 16
Feb. 1
Feb. 16
Mar. 1
Mar. 16
R
(.82, .94)
(.77..8T)
(72, .81)
(.67,75)
(.61,70)
(.56, .65)
(.52, .60)
(.47, .55)
(.42, .50)
(.37, .45)
(.32, .41)
Residual SS
695.90
661.60
644.66
639.61
639.21
639.08
638.98
639.78
642.13
646.03
650.17
Fit3
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
MSE = 7.10 (for phase = 1/24)
1 Maximum PbB occurs 365*R days after minimum PbB. R=0.5 implies seasonality is symmetric.
21
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2 For means data, fit is acceptable (see Appendix A) if Residual SS < 276.1 = 264.9 + 3.81*2.92.
3 For 90th percentile data, fit is acceptable if Residual SS < 666.1 = 639.0 + 3.81*7.10
22
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Shidentized Re!
r4 \.
Jan Apr Ju| Oct Jan
1990
Apr
1991
Oct Jan Apr Jul Oct
1992
Time Period
Apr Jul Oct
1993
Figure 8. Studentized Residuals from Unweighted Analyses of Means.
23
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Figure 9. Studentized Residuals from Unweighted Analyses of 90th Percentiles.
24
-------
Figure 10. Correlogram from Unweighted Analyses of Means.
25
-------
Figure 11. Correlogram from Unweighted Analyses of 90th Percentiles.
Correlation in residuals for means and 90th percentiles could be a result of correlations
in short-term non-seasonal PbB fluctuations, and/or model misspecification. Short term
non-seasonal fluctuations may include three components. The first component, sampling
variation, would be approximately independent for different time periods. The second
component is generated by unpredictable changes in climate and other factors that affect
exposure and physiology and may cause short-term unpredictable changes in overall
levels of PbB. Most of these unpredictable changes are short-lived, but some could last
for several months, resulting in correlated means and 90th percentile PbB levels. The
third component would include effects of short-term changes linked to the expansion of the
PbB screening program; these changes may affect the types of children whose PbB
measurements are reported to the MHD. Enough children would have to be sampled each
month over a sufficiently extensive time period to be able to detect these correlations;
otherwise the sampling variation would overwhelm the variation from the last two
components.
26
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Model misspecification might have resulted in correlated residuals. This may have
occurred if from 1990-93 the long term trend was not strictly linear (see section 3.2.1).
Nonlinearity in observed trends could be due to either nonlinear trends in summary values
of PbB levels of all Milwaukee children, or nonlinear effects linked to the screening
program's expansion. As discussed in the next section, the observed correlations seem
partially attributable to the effects of an abrupt expansion of the MHD screening program
in October, 1991.
27
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4.1.2 Weights and the 1991 Procedural Change
The results described in the previous section suggested that a weighted regression
analysis would be appropriate, since the residuals tended to be larger before the program
expanded in October, 1991. Weights were set equal to semi-monthly sample sizes, a
proper choice if sampling error accounted for almost all of the random fluctuations. A
weighted+P regression analysis was also performed to account for a possible October,
1991 shift in the types of children included in the screening program. Residuals from the
weighted+P fit to the 90th percentile data are shown in Figure 12. The plot shows no
obvious pattern, indicating that under the model with the expansion term (see equation 6),
the random error components for the 90th percentiles may be independent. Thus, the
weighted+P analysis apparently yields valid confidence intervals for parameters R and A
characterizing the seasonal variation of 90th percentile blood lead levels.
Residuals for the weighted+P fit to the means data, shown in Figure 13, show a slight
quadratic trend. The trend in the means residuals may be due to a nonlinear trend in
mean PbB values of all Milwaukee children. Alternatively, nonlinear changes in the
observed mean PbB values may be partially attributable to changes in the types of children
covered by the program. It is not clear why the long-term trend seems linear for 90th
percentiles, but may be nonlinear for the means data. It is possible that the difference in
trends may be partially attributable to MHD interventions which target children at high risk
of lead poisoning.
Parameter estimates resulting from the unweighted regression, the weighted (without
the expansion term), and the weighted + P regression analyses are shown in Table 5
under the assumption that cj)=0. The first two columns of Table 5 compare parameter
estimates from weighted and unweighted regression analyses. The choice of weights
causes negligible to about 10% changes in estimates of slope, A (the difference between
seasonal maximum and minimum PbB), and R (defines time of maximum PbB). The last
column shows confidence intervals from weighted + P analyses. The estimate of A was
substantially and significantly different from 0 only for the 90th percentile data. The
similarity between the three sets of confidence intervals for A and R shows that the
uncertainty about proper weighting of the data and treatment of the effects of 1991
procedural changes may have had only a minimal effect on the results.
Table 5. Comparison of Nonlinear Regression Results for (fr=0
MEANS DATA
28
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Parameter
Intercept2
Slope3
Amplitude2
R
T
A2
Confidence Interval
Unweighted
(16.2,18.3)
(-.120.-.095)
(2.65,4.67)
(.564..671)
(0.80,8.62)
Weighted
(16.4,18.2)
(-.124.-.100)
(3.26,4.80)
(.601, .671)
(2.36,9.73)
Weighted + P1
(16.5,18.3)
(-.125.-.086)
(3.13,4.74)
(.601, .674)
(2.24,9.71)
(-1.63,. 665)
90th PERCENTILE DATA
Parameter
Intercept
Slope
Amplitude
R
T
A
Confidence Interval
Unweighted
(24.9,27.8)
(-.153.-.114)
(5.21,8.19)
(.564,. 646)
(2.65,9.64)
Weighted
(24.3,27.0)
(-.146.-.109)
(5.95,8.31)
(.596,.654)
(4.18,10.9)
Weighted + P1
(24.8,27.2)
(-.105.-.050)
(5.25,7.49)
(.602..661)
(4.06,10.4)
(-5.34.-2.11)
1Weighted analysis using model with procedural term.
2|jg/dL
3ug/dl_ per semi-monthly time period
4Point estimate of slope for 90th % from weighted + P = -.0777
5Point estimate of procedural discontinuity in 90th % = -3.727
29
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Figure 12. Studentized Residuals of 90th Percentiles from Weighted Analyses Using the Program
Expansion Term.
30
-------
31
-------
Studentlzed
Residual In
ug/dl
3
-1
Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct
1990 1991 1992 1993
Figure 13. Studentized Residuals of Means from Weighted Analysis Using the Program Expansion
Term
32
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ug/dl
40
30
20
10
Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct
1990 1991 1992 1993
* * * Sinusoidal 90th PCT o o o Beta 90th PCT
-•—•—•- Sinusoidal Mean 000 Beta Mean
Figure 14. Predicted Values Derived from Fitting 90th Percentiles and Means to the Sinusoidal and
Beta Models
33
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4.2 SINUSOIDAL FUNCTION MODELLING RESULTS
The model of equation 8 provided an adequate fit to the 90th percentile data. As was
the case with the beta function, residuals resulting from the sinusoidal fit to the means data
were somewhat correlated.
(8)
i = a + p0t, + p1sin(2nxi) + p2cos(2nXi) + P, + 6;
Higher frequency sine and cosine terms (see equation 2) contributed little to the overall
fit. Parameter estimates from a weighted analysis are shown in Table 6.
Table 6. Parameter Estimates and First Order Correlation of Residuals for Weighted Sinusoidal Model
Fit.
Parameter
Intercept1 (a)
Slope2 (3n)
Sine1 (3.)
Cosine1 (37)
A1
First order correlation
Means
19.2
-.106
-1.53
-1.29
-0.50
0.07
90th Percentiles
28.7
-.0786
-2.46
-2.10
-3.83
0.34
1|jg/dL
2ug/dl_ per semi-monthly time period
4.2.1 Comparison with Beta Function Modelling Results
Table 7 compares sinusoidal and beta function modelling estimates of the 1) slope, 2)
the difference between seasonal maximum and minimum PbB, 3) the date corresponding
to 365*R, the date of maximum (detrended) PbB. The weighted (weights equal to the
number of children) mean square errors (MSE), a statistic that indicates how closely the
model fit the data, are also given. Plots of the predicted mean and 90th percentile blood
lead values are shown in Figure 14. Both Table 7 and Figure 14 show similar results from
the Beta and sinusoidal models. This may be an indication that the two models will yield
reasonable results if 1) PbB levels change monotonically between peak and minimum
levels, 2) seasonal fluctuations are not highly asymmetrical, and 3) changes in PbB around
the peak level are not too abrupt.
Although the choice of model (sinusoidal or beta) had only a minimal impact on these
estimates, the beta functional model is a recommended tool for other PbB analyses
because it can: 1) more directly assess asymmetry, and 2) more flexibly account for abrupt
34
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seasonal changes. Table 8 illustrates how the beta model can be used to test whether the
seasonal effect is symmetric, or if R=0.5. Parameter estimates and a weighted version
(weights equal to the sample sizes) of the residual sum of squares (RSS) for R constrained
to equal 0.5 (using the weighted+P approach for 90th percentiles) is given in the first
column. The same are then shown for R unconstrained in the second column. Results of
an F test, shown at the bottom of the table, indicate that there is insufficient evidence to
reject the hypothesis that the seasonality is symmetric. Note that the parameter estimates
in both columns of the table are virtually identical.
Abruptness and asymmetry of seasonal fluctuations could depend on climate and other
factors. It would be much more difficult to test the symmetry of the seasonality using the
sinusoidal model.
Table 7. Comparison of Sinusoidal and Beta Function Modelling Results1
MEANS DATA
Parameter
Slope2
A3
Date of Maximum PbB
Weighted4 MSE
Slope
A
Date of Maximum PbB
Weighted MSE
Sinusoidal Model Estimate
-0.106
4.00
8/21
265
90th PERCENTILE DATA
-0.078
6.47
8/21
532
Beta Function Model Estimate
-0.101
3.94
8/21
266
-0.078
6.37
8/18
525
1Weighted+P analysis
2ug/dl_ per semi-monthly period
3Absolute difference between maximum and minimum seasonal PbB levels (ug/dL)
4Weights equal to number of children; denominator equals 96-6=90 for sinusoidal model, 96-7=89 for Beta
model
35
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Table 8. Testing Symmetry (R=0.5) through the Beta Model
Results for 90th Percentiles
Parameter
Intercept
Slope
A
A
R
T
*
Weighted RSS
Estimate
R=0.5
26.0
-0.775
6.36
-3.75
0.5
7.42
0.11
46830
R unconstrained
26.0
-0.775
6.37
-3.73
0.56
7.43
0.06
46760
F-statistic = (46830-46760)7(46760/89) = 0.14
4.3 AGE'S EFFECT ON SEASONALITY
Results from this section will show that the seasonality and overall level of PbB may
depend on age in a fairly complicated way. Parameter estimates for the model of equation
6 (section 3.2.3) are shown in Table 9. Note from the intercept estimates that winter PbB
levels increase with age, but the seasonal difference between highest and lowest PbB
levels is greatest between ages 1 to 3 years. For children aged 1.5 to 3 years in 1993,
there was an estimated 38% increase in PbB levels from January 1 to peak levels in
August. This compares to a 30% increase for the youngest, a 41 % increase for 1 to 1.5
year olds, and only a 15% increase for children over 3. Estimated percent increases in the
90th percentile PbB's were (from youngest to oldest) 30%, 48%, 37%, and 3%. The
difference in the size of the overall seasonal trend from 1990 to 1993 by age group is
striking. In fact, the observed seasonal trend for children over 3 years old was not
significant. Summer PbB levels were actually higher for the 1 to 3 year olds than for older
children.
However, as Figures 15 and 16 show, conclusions about the dependency of the
seasonality on age require caution. Only PbB measurements for ages 1.25 to 2.5 were
consistently higher in the summer than the winter from 1990 through 1993. Similar
"seasonal" patterns can be observed in 1991 to 1993 PbB measurements for ages 0.75
to 1.25 years, and 1992-1993 PbB measurements for ages 0.5 to 0.75 years. For ages 2.5
36
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to 4 years, "seasonal" patterns can be observed in 1992 to 1993, but not in 1990 or 1991.
For ages 4 to 7 years, PbB was higher in the summer than the winter in 1992, perhaps in
1993, but not in 1990 or 1991.
The lack of any discernable pattern in PbB measurements for some age groups in 1990
and 1991 may be largely due to sampling variation. (For children less than 9 months data
was so limited the graph was omitted.) Conversely, observed patterns in the empirical
data that suggest seasonality may be the result of short-term random fluctuations in PbB,
sampling variation, or aberrations due to pre-1992 procedural changes affecting the
reporting of PbB measurements. The inconsistent patterns in the PbB data for older
children only demonstrate the need for analyses of data beyond 1993. The additional data
would be helpful to determine whether patterns observed in older children in 1992 are
evidence of real seasonality in PbB levels, or merely an aberration caused by random
fluctuations and sampling variation. If the additional data would show substantially less
seasonality for older children, adjustments described later in Section 4.4.1 could then be
modified to account for the dependency of seasonality on age.
37
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ug/dl
55
50
45
40
35
30
25
20
15
10
Jan
Apr Jul
1990
Oct
Jan
Apr Jul
1991
0.75 to 1.25 Years (n=1 842)
1.25 to 2.5 Years (n^21)
2.5 to 4.0 years (n^18)
4.0 to 7.0 Years (n=431)
Figure 15. Semi-monthly Smoothed 90th Percentile Blood Lead Levels by Age Group
(1990 to 1991)
38
-------
ug/dl
32
28
24
20
16
12
Jan
Apr Jul
1992
.
*
Oct
Jan
AGE
0.50 to 0.75 Years (n=399)
0.75 to 1.25 Years (n=3825)
1 .25 to 2.5 Years (n=1 631 )
Apr Jul Oct
1993
o 2.5 to 4.0 years (n=1 444)
0 4.0 to 7.0 Years (n=1 873)
Figure 16. Semi-monthly Smoothed 90th Percentile Blood Lead Levels by Age Group
(1992 to 1993)
39
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40
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Table 9. Estimates from Model Incorporating Age
MEANS DATA
Parameter
Intercept
(PbB on 1/1/90)
Slope2
Seasonal
Difference4
R
T
p4
Y
Age Group (in Years)
(.5, 1]
15.2
-.073
3.0
.623
5.0
-1.8
1.007
0,1.5]
16.51
-.0793
4.45
1.09
d.5,3]
19.1
-.092
4.86
1.26
>3
19.8
-.096
1.9
1.31
90th PERCENTILE DATA
Parameter
Intercept
Slope
Seasonal
Difference
R
T
P
Y
Age Group (in Years)
(.5, 1]
23.8
-.061
5.9
.605
5.2
-5.0
1.005
(1,1.5]
25.0
-.064
8.9
1.05
(1.5,3]
30.9
-.079
8.9
1.30
>3
31.9
-.082
0.7
1.34
c^ = 15.2*1.09
2ug/dl_ per semi-monthly period
3Equals3Y1 =-.073*1.09
4|jg/dL
^qualsA^ =4.04*1.09
638% increase from January, 1993 levels
7Fixed
41
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4.4 ADJUSTMENT FACTORS
Several methods for seasonal adjustment of data were considered for analyses of
abatement and educational outreach programs. Adjustments were based on results for
90th percentiles (instead of means), because the 90th percentiles better describe the PbB
levels of children targeted by the intervention programs. Adjustments could be additive
or multiplicative. For example, by defining additive seasonal adjustments s, for each of 24
bimonthly time periods, the adjusted PbB, Y*, of a measurement Y taken during time period
i would be Y* = Y + s,. For multiplicative adjustments, Y* = Y*s,. For our data, "average"
PbB levels were only about twice as large during the summer of 1 990 as compared to the
winter of 1993, so either type of seasonal adjustment would yield similar results. Our
model fitting procedures assumed that the effects of seasonality were additive.
Multiplicative adjustments would have been indicated if the studentized residuals had
been larger for higher predicted PbB measurements. The graph of the studentized
residuals from the weighted + P analysis of 90th percentiles, shown in Figure 1 1 , indicates
no change in the size of residuals from 1990 to 1993, despite the decline in PbB. Thus,
additive adjustments seem adequate.
Adjustments could be calculated as simple differences in raw statistics, or based on
model fitting results. Advantages of adjustments based on raw differences are their
simplicity and "unbiasedness", but "raw" adjustments are often unstable. For 90th
percentiles denoted by z0 for the reference period and z, for period i, the simple adjustment
would be s, = ZQ-Z,.
Adjustments based on model fitting results would be s, = YO - Y,, where perhaps
Yi = a + pt, + Pi + s^).
Model-based adjustments would tend to be more stable, because the models are
calibrated using all available data, as opposed to data from only the ith and reference
periods. Model-based adjustments are recommended when data is limited, and the
variance of raw estimates is very large. However, model fitting introduces an additional
potential source of bias caused by model misspecification. Although for our data, results
were almost identical for the beta and the sinusoidal models, adjustments would
sometimes be highly dependent on the choice of model.
Moving averages often offer a reasonable compromise between adjustment strategies
based on model fitting and raw statistics. Seasonal adjustments shown in Appendix D are
based on the moving average of order 3 described earlier in Section 3.1 . Data used for
the adjustment are within 3 periods of the adjusted period, yet the sampling variance may
be less than 20% of the sampling variance for the raw summary statistics. Adjustments
based on higher order moving averages would have been recommended if there had been
42
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more sampling variation. Moving averages require the assumption that second derivatives
(which describe the rates at which the slope of a function changes) of "true" seasonal and
time trends are sufficiently small.
4.4.1 Age and Seasonal Adjustments for Use in Studies of Intervention
Effectiveness in Milwaukee
Multiplicative age and additive seasonal adjustments used in a study of intervention
effectiveness (U.S. EPA, 1996) in Milwaukee are given in Appendix D. For that study, the
adjusted PbB values were "equivalent" PbB values for ages 1.75 to 2 years for
measurements made in January, 1993.
The adjusted PbB measurement, y*, for a child in age group k during time period i with
PbB measurement y was calculated using the formula:
(9) y =(y+A,)*Mk.
Here, Mk is the multiplicative age adjustment factors (for the kth age group); A, is the
additive seasonality adjustment factor (for the ith time period). The age and seasonal
adjustment factors are shown in the last columns of Tables D.1 andTable D.2 respectively.
For example, to calculate the adjusted measurement corresponding to a March 7, 1992
measurement of 20ug/dl_ for a 1.4 year old child, note that the age adjustment factor (from
Table D. 1) is 1.083, and the seasonality adjustment factor (from Table D.2) is 1.42. The
adjusted PbB would be (20+1.42)*1.083 = 23.2.
Note that the seasonality adjustment precedes the age adjustment, and that the final
adjustments depend to a small extent on the ordering. For the age adjustment to precede
the seasonality adjustment, the seasonality adjustments would have had to be modified
to represent the seasonal fluctuations for ages 1.75 to 2 years. The absolute difference
in summer and winter PbB levels between ages 1.75 and 2 years might be greater than
for other age groups. This is because seasonal differences seem proportional to average
PbB levels, and PbB levels tend to peak around age 2 years.
The multiplicative age adjustment factors are inversely proportional to the arithmetic
mean PbB's based on data from 1990-1993. The additive seasonality adjustment factors
are based upon moving averages of the "detrended" 90th percentile PbB's. Here,
detrended means that the linear long-term trend had been removed from the semi-monthly
90th percentiles before the moving averages had been calculated. The reason for this was
to assure that the adjustments would only reflect changes in PbB due to seasonality. The
"detrending" was designed to filter out other effects (such as effects related to the
screening program expansion). The long-term trend was removed by first fitting the
1990-93 90th percentiles to the Beta function model, equation 3, with $=0. From the
model fit, the estimate of the downward trend was 0.1335ug/dl_ per semi-monthly time
43
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period. Thus, the time series was detrended by adding 0.1335*i to the 90th percentile PbB
measurements for time periods i = 1 ... 99. The time series was then smoothed using the
moving average with weights .3, .2, .1, and .05. The additive seasonality adjustment
factors, A,, were then set equal to the smoothed values minus the smoothed value for i=73
(for the first half of January, 1993).
It is difficult to determine a "best" method for filtering out all of the long-term (non-
seasonal) effects on PbB from the seasonal adjustment factors. A control group should
be used in studies of intervention effectiveness for reducing lead exposure, so that
changes in adjusted blood lead levels due to the non-seasonal factors (that can not be
filtered out) would affect both study and control groups. An alternative set of seasonal
adjustment factors are given in Table D.3. A desirable feature of these adjustment factors
is the lack of any discontinuity due to the effect of procedural changes in October, 1991.
For these adjustment factors, the time series of semi-monthly PbB values was detrended
using the results from the weighted+P analysis given in the third column of table 3. The
detrending was accomplished by first adding .0777*i to the 90th percentiles to remove the
long-term trend. Then 3.727 was added for time periods after September, 1991 to remove
the effect of procedural changes in October, 1991. Smoothing and the A, were then
calculated as described in the previous paragraph.
44
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5 DISCUSSION
The Milwaukee data showed sizeable seasonal and age trends in Milwaukee children's
PbB levels. Blood lead levels were about 40% higher in the summer than the winter, and
about 15-20% higher at ages two years than at ages one year and five years. The
seasonal fluctuations have been attributed to complex physiological changes linked to
increased exposure to lead or increased sunlight in the summer. Exposure may increase
in the summer because of factors that include increased outdoor playing time, more
opening and closing of windows, increased hand-to-mouth activity, and drier leaded dust
that more easily enters homes. In Milwaukee, the age effect, related to factors such as
increased hand-to-mouth activity of two year olds, was similar to the age effect observed
in at least two other studies, the Sydney Lead Study (Cooney, et al, 1989), and the Port
Pirie Study (Baghurst, et al, 1992).
Inconsistent results on seasonality in PbB from many small studies (see McCusker,
1979) suggest that seasonal patterns in PbB differ by location and/or climate. The
Milwaukee data shows substantial seasonal fluctuation in PbB, so these trends must be
recognized in similar northern urban environments. Seasonal fluctuations in PbB are
probably largest in cooler environments such as Milwaukee's where seasonal differences
in outdoor play and exposure to sunlight are more extreme. The Milwaukee results
contrast with suggestions of some researchers that early evidence of seasonal trends
(Blanksma et al, 1969; Guinee, 1972) are no longer relevant because of the phaseout of
leaded gasoline (see U.S.EPA, 1995a).
The MHD data set has limitations that must be noted. The MHD data is routinely
collected health department data, and was not subject to the types of data quality checks
had the data been collected for other purposes. Also, the data is not reliable for estimating
long-term trends before 1992, since blood lead screening was much more limited before
1992. Thus, evaluating long-term trends in PbB was beyond the scope of this study (see
NHANES III, Pirkle, et al, 1994). Nevertheless, the changes in PbB associated with the
expansion of the screening program would have had less effect on estimates
characterizing the seasonality of blood lead levels, because seasonal levels differ
substantially within a short period of time (between summer and winter).
Other studies should help refine our understanding of the factors that may cause
complex seasonal and age-related patterns. Further study is suggested by a tentative
result suggesting that the magnitude of seasonal PbB fluctuations may depend on age.
For 1990, 1991, and 1993, the seasonal fluctuations in PbB levels, although substantial
for ages 1-3 years, were limited for ages 4 to 7.
A model based on the beta function, developed to analyze the complex seasonal
patterns in PbB levels (see U.S.EPA, 1995b), should have broad application. Unlike
traditional methods, the beta function model allows for direct assessment of features such
45
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as the potential for abrupt or asymmetric seasonal changes in PbB between winter and
summer levels. Statistical literature includes discussion of other time series with possible
asymmetric rises and falls such as the Canadian Lynx data (Campbell and Walker, 1977)
and sunspots data (Morris, 1977). Although evidence for asymmetry was limited in the
Milwaukee data, it is necessary to be able to test for such features in PbB data from other
environments, where seasonal characteristics in PbB levels may differ.
Both empirical and model-based results indicated that seasonal and age related trends
could influence results from studies of the effectiveness of interventions for lowering PbB
in children. Although these trends might sometimes be controlled for in well-designed
prospective studies, adjustment factors would be needed for trend removal in retrospective
studies. However, retrospective studies have several advantages. First, they allow for
adequate sample sizes, a major consideration because of the large variability in PbB
levels. Second, they do not create artificial circumstances which could lead to invalid
conclusions. They also do not arbitrarily deprive control group children of benefits from
the interventions being evaluated.
Seasonal and age-related adjustment factors were calculated through a four-stage
process. First, 90th percentiles were calculated to summarize PbB levels for each of the
96 semimonthly periods between 1990 and 1993. Second, the 90th percentile PbB values
were fit to a model so that long-term trends in PbB could be removed. The seasonal
adjustments were then based on the moving averages of the detrended 90th percentile
PbB values. Finally, age adjustments were calculated as simple ratios of arithmetic means
using predefined age categories. 90th percentiles were chosen as the summary statistics
for the semi-monthly periods, because of their applicability to populations of children
subject to PbB interventions. Since age and seasonal trends likely depend on many
factors related to geographic location, type of environment (urban or rural), and time
period, the adjustment factors shown in Appendix D are specific to Milwaukee from 1990
to 1993. Nevertheless, the four-step procedure, with appropriate modifications, should be
applicable to many other PbB data sets, so that the effects of abatement and educational
interventions in other locations may also be quantified.
46
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REFERENCES
Baghurst P, long S, McMichael A, Robertson E, Wigg N, Vimpani G (1992). "Determinants
of blood lead concentrations to age 5 years in a birth cohort study of children living in the
lead smelting city of Port Pirie and surrounding areas." Archives of Environmental Health,
203-210.
Blanksma L, Sachs HK, Murray EF, O'Connel MJ (1969). "Incidence of high blood lead
levels in Chicago children." Pediatrics 44:661-667.
Burgoon D, Rust S, Schultz B (1994). "A summary of studies addressing the efficacy of
lead abatement," in Lead in Paint, Soil, and Dust: Health Risks, Exposure Studies, Control
Measures, Measurement Methods, and Quality Assurance, ASTM STP 1226, Michael E.
Beard and S.D. Allen Iske, Eds., American Society for Testing and Materials, Philadelphia.
Campbell MJ and Walker AM (1977). "A survey of statistical work on the MacKenzie River
series of annual Canadian lynx trappings for the years 1821-1934, and a new analysis."
Journal of the Royal Statistical Society, A 140:411-31.
Cooney GH, Bell A, McBride W, Carter C (1989). "Low-level exposures to lead: The
Sydney Lead Study." Developmental Medicine and Child Neurology, 31:640-649.
Diggle P (1990). Time Series, Oxford University Press, Oxford.
Guinee VF (1972). "Epidemiologic studies of lead exposure in New York City." Int.
Symposium on Environmental Health Aspects of Lead, Amsterdam, Oct. 2-6, 1972.
Kimbrough R, LeVois M, Webb D (1994). "Management of children with slightly elevated
blood lead levels." Pediatrics, 93: 188-191.
McCusker J. (1979). "Longitudinal changes in blood lead level in children and their
relationship to season, age and exposure to paint or plaster." American Journal of Public
Health. 69: 348-52.
Morris J (1977). "Forecasting the sunspot cycle." Journal of the Royal Statistical Society,
A, 140:437-447.
Pirkle JL, Brody DJ, Gunter EW, Kramer RA, Paschal DC, Flegal KM, and Matte TD.
(1994). "The Decline in blood lead levels in the United States: The National Health and
Nutrition Examination Surveys (NHANES)," JAMA 272, 284-291.
SAS/STAT User's Guide, Version 6 (1990), SAS Institute, Gary, NC, 2:1135-1194.
47
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Seber GAP, Wild CJ (1989). Nonlinear Regression. Wiley.
United States Environmental Protection Agency (1996). "Effect of in-home educational
intervention on children's blood lead levels in Milwaukee." Report EPA 747-R-95-009.
United States Environmental Protection Agency (1995a). "Review of studies addressing
lead abatement effectiveness." Report EPA 747 R-95-006.
United States Environmental Protection Agency (1995b). "Seasonal rhythms of blood-lead
levels: Boston, 1979-1983." Report EPA 747-R-94-003.
48
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APPENDIX A. TECHNICAL DETAILS
49
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A1. Inputs to PROC NLIN and Properties of Estimates
SAS's PROC NLIN and the Newton-Raphson option were used for most1 of the
nonlinear regression beta function model fits. Details about the algorithm are provided in
the SAS/STAT User's Guide, Volume 2.
If the random errors e, are independent and identically distributed with finite variance
a2, then the resulting parameter estimates of a, (3, A, R, and T are consistent with
asymptotic normal distributions. If in addition, the e, are also normally distributed, then
upon satisfaction of certain regularity conditions, the estimates are maximum likelihood
estimates. Details are provided in Seber and Wild (1989).
Inputs into PROC NLIN include starting values for the parameter estimates, a model
statement, bounds for some of the parameters, and first and second partial derivatives of
E(Y) with respect to the parameters. The model, without a phase component, is:
E(Y) = a + pt + A(x/R)TR ((1-x)/(1-R))T(1-R).
The first derivative with respect to A is:
d(E(Y))/dA = (x/R)TR ((1
Let F = exp((ln x - In R)TR + (ln(1 -x)-ln(1 -R))T(1 -R)). Then the first derivative with respect
to T is:
d(E(Y)/dT) = AF(R ln(x/R) + (
1 A MATLAB program was written to generate the results shown in Table 8.
50
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The other first and second derivatives can be gleaned from the programming code for
the unweighted fit:
proc nlin method=newton data=avlead;
parms aO=17.3 a1=-.11 a2=5 a3=.6 a4=5;
temp = (x/a3)**(a3*a4)*((1-x)/(1-a3))**(a4*(1-a3));
model y=aO + (a1*t) + a2*temp;
bounds a3>=0, a4>=0, a3<=1;
der.aO = 1;
der.al = t;
der.a2 = temp;
temp2= log(x/(1 -x))+log((1 -a3)/a3);
der.aS = a2*temp*a4*temp2;
temp3=a3*log(x/a3)+(1 -a3)*log((1 -x)/(1 -a3));
der.a4 = a2*temp*temp3;
der.aO.aO = 0;
der.aO.a1 = 0;
der.aO.a2 = 0;
der.aO.a3 = 0;
der.aO.a4 = 0;
der.al.a1 = 0;
der.al.a2 = 0;
der.a1.a3 = 0;
der.al.a4 = 0;
der.a2.a2 = 0;
der.a2.a3 = temp*a4*temp2;
der.a2.a4 = temp*temp3;
dfda3=tem p*a4*tem p2;
der.a3.a3 = a2*a4*(temp/(a3*(a3-1))+dfda3*temp2);
dfdt=temp*temp3;
der.a3.a4 = a2*temp2*(temp+a4*dfdt);
der.a4.a4 = a2*temp3*dfdt;
output out=preds p=yhat r=yresid;
51
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A2. Incorporating Phase
The model
Y = a + p(t) + S((|>) + e
was fit by comparing the residual sums of squares of repeated fits using a range of values
for cj). An approximate 95% confidence interval for $ would include all values of $ for
which the residual sum of squares is no greater than RSS* + 3.81 *MSE*. Here, RSS* and
MSE* are the residual sums of squares and mean square error values minimized with
respect to cj), and 3.81 is the critical value corresponding to a=.05 for the chi-square
distribution with 1 df.
Referring to table 5, RSS* for 90th percentiles « 639.0 and MSE*» 7.1 = 639/90, so the
95% confidence interval for $ would include all values for which RSS < 666.1 = 639.0 +
3.81*7.1. This approach allowed observation of how assumptions about § affected
estimates of other parameters.
A3. Properties of the Nonlinear Regression Estimates
If the random errors e, are independent and identically distributed with finite variance
a2, then the parameter estimates of a, (3, A, R, T, P, are, upon satisfaction of regularity
conditions (see Seber and Wild), consistent with asymptotic normal distributions. If in
addition, the e, are also normally distributed, then the nonlinear regression estimates are
maximum likelihood estimates.
A4. Mathematical Justification for Moving Average Weights
The theoretical material in this section is from Diggle, 1990. Let |j(tj) be a moving
average for the time series y(t|). Weights for a moving average might be chosen to
minimize the quantity Q(a), where
Q(a) = I (y, - M(t|))2 + a J(M"(t))2 dt.
The summation term, "the residual sum of squares", measures the closeness of the fit
between the moving average and the original time series. The integral term measures the
smoothness of the moving average, a determines the tradeoff between goals of obtaining
a very smooth fit and minimizing the residual sum of squares.
If data are equally spaced at unit time intervals (as ours is), then Q(a) would be
approximately minimized when
(8) Wj = .5*h-1(K((i+.5)/h)+K((i-.5)/h)), where h=a25, and
52
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K(u) = .5 exp(-|u|/2-1) sin(.25n + |u|/2-1).
The weights of the 3-order moving average are within .05 of the weights given in (8)
for a=1. For larger values of a, Q(a) would be minimized by a higher order moving
average.
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APPENDIX B. DATABASE DEVELOPMENT
54
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The Milwaukee Health Department (MHD) provided the data described in this report
from the health department's lead case tracking system called "STELLAR". One of
STELLAR's data files, LAB.BAS, contains records for each blood lead level reported to the
health department. Each time a child's blood lead level was reported, all the children's
blood lead levels in LAB.BAS were reviewed by MHD staff, and additional entries to the
STELLAR data files were made when necessary. LAB.BAS also includes the
corresponding date of measurement, the sample type, the child's name and date of birth,
the child identifier, the address identifier, and the medical provider. As of July 1994, there
were 75,084 records in this file.
Medical providers and laboratories send data on children's blood lead levels to the
MHD. Providers include primary care physicians, public health clinics, HEADSTART
centers, and Women Infant and Children centers (WICs). Some providers reported all
measurements and some only reported elevated levels. A list of all possible providers was
created from the LAB file and each was called to verify the procedure used. All
HEADSTART and WICs but only half of the clinics and physicians reported all
measurements. Therefore, a final list of providers that reported all measurements was
created and used in the creation of the database. The data analyzed for this report only
includes measurements from providers who reported all measurements regardless of level.
The database used for the analysis was created by first sorting the LAB file by the child
identifier and sampling date. The first measurement in chronological order for each child
was maintained in the database. Measurements were deleted if the corresponding
provider name was not among those listed as reporting all measurements. The final
database has 16,084 observations: 2,051 measurements occurring before January 1,
1990,13,476 measurements occurring between January 1,1990 and December 31,1993,
and 557 measurements after December 31, 1993.
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APPENDIX C. GEOGRAPHIC SUMMARY OF HEALTH DEPARTMENT DATA
56
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Table C.1 summarizes blood lead data for each Milwaukee zip code which according
to the 1990 U.S. Census had at least 2500 children less than 7 years old. U.S. Census
population figures for each zip code are given in the first column. The table compares the
Census data to the number of children who had blood lead measurements taken for first
time (the number of children screeened).
Estimates of coverage of the MHD screening program are given in the last column.
The coverage of the MHD (screening) program for 1992-93 can be defined as the
proportion of children who were are born in Milwaukee from 1992 through 1993 who have
or will be tested for blood lead before their seventh birthday. The number of children born
during 1992-93 would have been about 2/7 times the number of children less than seven
years old in 1990. The number of children born in 1992-93 who would be screened by
their seventh birthday would be approximately equal to the number of children tested for
blood lead for the first time from 1992-93 under the following two assumptions. First, the
number of children screened reached equilibrium by 1992. Second, the age distribution
of the children screened was about the same for each year by 1992. A crude estimate of
coverage for each zip code was calculated as the ratio of the the number of children
screened during 1992-93 divided by 2/3 * (1990 Census population for ages up to 7
years).
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Table C1. Census Counts and Summary of Milwaukee Health Department Blood Lead Data by Zipcode1
Zipcode
53204
53205
53206
53207
53208
53209
53210
53212
53215
53216
53218
53221
53225
Total3
1990 U.S Census
Population
Ages 0-7 Years
6558
2611
7092
4504
6925
5506
4806
5736
5709
4332
4775
3066
2837
74739
Mean PbB
(UQ/dL)
1990-93
11.5
14.0
15.0
9.3
14.7
10.6
15.4
14.9
10.6
11.5
9.1
8.2
7.5
Number Screened
1990-91
459
176
504
73
414
237
514
489
207
225
160
53
38
1992-93
1406
371
1180
343
825
540
742
1198
713
533
470
183
177
Coverage2
1992-93
75%
50%
58%
27%
42%
34%
54%
73%
44%
43%
34%
21%
22%
1 Includes only zipcodes with >2500 children less than 7 years old.
2 Equals number screened during 1992-93 divided by (2/7)*population
3 Over all zipcodes
58
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APPENDIX D. 1990-93 MILWAUKEE PbB MEASUREMENT ADJUSTMENT
FACTORS
(These factors are not appropriate for other PbB data sets).
59
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Table D1. Multiplicative Age Adjustment Factors for 1990-1993 Milwaukee PbB Data
Age Category (Years)
.5-75
.75-1
1-1.25
1.25-1.5
1.5-1.75
1.75-2.0
2.0-2.25
2.25-2.5
2.5-2.75
2.75-3.0
3.0-3.5
3.5-4.0
4.0-4.5
4.5-5.0
5.0-5.5
5.5-6.0
6.0-6.5
6.5-7.0
Other1
Number
519
2082
3585
793
605
364
408
282
318
298
626
720
772
636
461
214
120
101
466
Arithmetic Mean(|jg/dL)
9.14
11.41
12.43
13.28
13.60
14.34
14.75
14.17
14.21
14.29
13.38
13.76
13.02
12.84
12.30
12.51
12.33
12.23
10.75
Adjustment Factor
1.568
1.256
1.154
1.080
1.054
1.000
0.972
1.012
1.009
1.004
1.072
1.042
1.101
1.117
1.165
1.146
1.163
1.173
1.334
Includes 123 without any recorded birthdate, 106 with ages less than 6 months, and 237 with ages greater
than 7 years.
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Table D2. Seasonal Additive Adjustment Factors Without Procedural Correction for 1990-March, 1994
Milwaukee PbB Data
Year 1990
Time
Period
Starting
Date
Jan 1, 90
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th
Percentile
PbB
22.6
24.5
23.2
27.0
27.3
34.0
22.2
23.0
30.0
28.3
32.7
28.5
34.2
30.7
30.6
25.5
24.0
31.0
32.0
27.2
24.0
22.7
25.4
24.5
Detrended
90th
Percentiles1
12.987
15.021
13.854
17.788
18.221
25.055
13.388
14.322
21.455
19.889
24.422
20.356
26.189
22.823
22.856
17.890
16.523
23.657
24.791
20.124
17.058
15.891
18.725
17.958
Smoothed
Detrended
Series2
14.116
14.782
15.886
17.078
18.226
18.815
17.743
17.892
19.330
20.589
21.997
22.716
23.109
22.528
21.471
20.440
20.178
21.157
21.241
20.124
18.753
17.906
17.805
17.943
Adjustment
Factors Without
Detrending3
-6.175
-6.766
-7.771
-8.850
-9.865
-10.320
-9.115
-9.130
-10.435
-11.560
-12.835
-13.420
-13.680
-12.965
-11.775
-10.610
-10.215
-11.060
-11.010
-9.760
-8.255
-7.275
-7.040
-7.045
Adjustment
Factors4
3.324
2.658
1.554
0.362
-0.786
-1.375
-0.303
-0.452
-1.890
-3.149
-4.557
-5.276
-5.669
-5.088
-4.031
-3.000
-2.738
-3.717
-3.801
-2.684
-1.313
-0.466
-0.365
-0.503
61
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Table D2 (continued) - Year 1991
Time
Period
Starting
Date
Jan 1,91
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th
Percentile
PbB
25.1
23.0
25.3
21.0
26.2
24.6
28.4
25.0
27.2
34.5
27.0
28.5
30.0
27.6
25.0
30.9
30.3
29.7
21.4
22.3
22.0
18.0
18.0
17.8
Detrended
90th
Percentiles1
18.692
16.725
19.159
14.992
20.326
18.859
22.793
19.526
21.860
29.293
21.927
23.560
25.194
22.927
20.461
26.494
26.028
25.561
17.395
18.428
18.262
14.395
14.529
14.462
Smoothed
Detrended
Series2
17.877
17.835
17.834
18.027
18.876
19.784
20.948
21.716
22.915
24.253
23.977
23.830
23.884
23.412
23.601
24.224
24.073
22.781
20.490
18.683
17.237
15.920
15.344
15.352
Adjustment
Factors Without
Detrending3
-6.845
-6.670
-6.535
-6.595
-7.310
-8.085
-9.115
-9.750
-10.815
-12.020
-11.610
-11.330
-11.250
-10.645
-10.700
-11.190
-10.905
-9.480
-7.055
-5.115
-3.535
-2.085
-1.375
-1.250
Adjustment
Factors4
-0.437
-0.395
-0.394
-0.587
-1.436
-2.344
-3.508
-4.276
-5.475
-6.813
-6.537
-6.390
-6.444
-5.972
-6.161
-6.784
-6.633
-5.341
-3.050
-1.243
0.203
1.520
2.096
2.088
62
-------
Table D2 (continued) - Year 1992
Time
Period
Starting
Date
Jan 1,92
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th
Percentile
PbB
20.9
17.0
19.4
18.0
19.0
20.0
18.0
16.0
19.1
24.0
21.1
24.0
22.0
25.0
24.0
25.0
24.0
24.0
21.0
22.0
18.0
19.0
18.0
17.0
Detrended
90th
Percentiles1
17.696
13.929
16.463
15.196
16.330
17.463
15.597
13.730
16.964
21.997
19.231
22.264
20.398
23.531
22.665
23.798
22.932
23.065
20.199
21.332
17.466
18.599
17.733
16.866
Smoothed
Detrended
Series2
15.566
15.519
15.763
15.921
16.020
16.188
16.107
16.355
17.704
19.237
20.221
21.139
21.758
22.386
22.865
22.948
22.782
22.065
21.099
20.132
19.016
18.349
17.933
17.536
Adjustment
Factors Without
Detrending3
-1.330
-1.150
-1.260
-1.285
-1.250
-1.285
-1.070
-1.185
-2.400
-3.800
-4.650
-5.435
-5.920
-6.415
-6.760
-6.710
-6.410
-5.560
-4.460
-3.360
-2.110
-1.310
-0.760
-0.230
Adjustment
Factors4
1.874
1.921
1.677
1.519
1.420
1.252
1.333
1.085
-0.264
-1.797
-2.781
-3.699
-4.318
-4.946
-5.425
-5.508
-5.342
-4.625
-3.659
-2.692
-1.576
-0.909
-0.493
-0.096
63
-------
Table D2 (continued) - Year 1993
Time Period
Starting
Date
Jan 1, 93
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th
Percentile
PbB
18.0
18.0
15.4
15.0
14.0
16.0
17.0
16.0
17.2
20.0
18.0
19.0
21.0
19.3
19.0
22.0
24.4
20.2
16.6
18.4
18.0
15.5
16.0
19.4
Detrended 90th
Percentiles1
18.000
18.134
15.667
15.401
14.534
16.668
17.801
16.935
18.268
21.202
19.335
20.469
22.602
21.036
20.869
24.003
26.536
22.470
19.003
20.937
20.670
18.304
18.937
22.471
Smoothed
Detrended
Series2
17.440
17.014
16.337
15.931
15.874
16.398
17.171
17.775
18.678
19.642
20.120
20.709
21.362
21.746
22.329
23.113
23.341
22.420
21.218
20.567
20.090
19.514
19.387
19.141
Adjustment Factors
Without
Detrending3
0.000
0.560
1.370
1.910
2.100
1.710
1.070
0.600
-0.170
-1.000
-1.345
-1.800
-2.320
-2.570
-3.020
-3.670
-3.765
-2.710
-1.375
-0.590
0.020
0.730
0.990
1.370
Adjustment
Factors4
0.000
0.426
1.103
1.509
1.566
1.042
0.269
-0.335
-1.238
-2.202
-2.680
-3.269
-3.922
-4.306
-4.889
-5.673
-5.901
-4.980
-3.778
-3.127
-2.650
-2.074
-1.947
-1.701
64
-------
Table D2 (continued) - Year 1994
Time Period
Starting
Date
Jan 1,94
Jan 16
Feb 1
Feb16
Mar 1
90th
Percentile
PbB
13.0
13.0
14.0
17.0
35.0
Detrended
90th
Percentiles1
16.204
16.338
17.471
20.605
38.738
Smoothed
Detrended
Series2
18.209
18.828
20.261
23.373
28.164
Adjustment
Factors Without
Detrending3
2.435
1.950
0.630
-2.384
-7.098
Adjustment
Factors4
-0.769
-1.388
-2.821
-5.933
-10.724
1Detrended by subtracting .1335*(73-i) from 90th percentiles.
2Smoothed values of column 3 using weights .3, .2, .1, .05.
Adjustment factors if 90th percentiles had not been detrended.
4Equals 17.44 (smoothed value at t=73) - column 3 values.
5Uses 1994 90th percentile semi-monthly PbB values.
65
-------
Table D3. Seasonal Adjustment Factors with Procedural Correction for 1990 - March, 1994 Milwaukee PbB
Data
Year 1990
Time Period
Starting Date
Jan 1, 90
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile
PbB
22.6
24.5
23.2
27.0
27.3
34.0
22.2
23.0
30.0
28.3
32.7
28.5
34.2
30.7
30.6
25.5
24.0
31.0
32.0
27.2
24.0
22.7
25.4
24.5
Detrended 90th
Percentiles1
17.006
18.983
17.761
21.639
22.016
28.794
17.072
17.950
25.027
23.405
27.883
23.760
29.538
26.116
26.093
21.071
19.649
26.726
27.804
23.082
19.960
18.737
21.515
20.693
Smoothed
Detrended
Series2
18.087
18.721
19.784
20.929
22.021
22.554
21.427
21.520
22.902
24.105
25.458
26.120
26.458
25.821
24.708
23.621
23.304
24.226
24.254
23.082
21.655
20.752
20.595
20.678
Adjustment
Factors3
3.080
2.446
1.383
0.238
-0.854
-1.387
-0.260
-0.352
-1.735
-2.938
-4.291
-4.953
-5.291
-4.654
-3.541
-2.454
-2.137
-3.060
-3.087
-1.915
-0.488
0.415
0.572
0.489
66
-------
Table D3 (continued) - Year 1991
Time Period
Starting Date
Jan 1,91
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile
PbB
25.1
23.0
25.3
21.0
26.2
24.6
28.4
25.0
27.2
34.5
27.0
28.5
30.0
27.6
25.0
30.9
30.3
29.7
21.4
22.3
22.0
18.0
18.0
17.8
Detrended 90th
Percentiles1
21.370
19.348
21.726
17.504
22.781
21.259
25.137
21.814
24.092
31.470
24.047
25.625
27.203
24.880
22.358
28.336
27.814
27.291
22.796
23.774
23.551
19.629
19.707
19.584
Smoothed
Detrended
Series2
20.555
20.458
20.401
20.538
21.331
22.184
23.292
24.004
25.147
26.430
26.097
25.895
25.893
25.366
25.498
26.252
26.418
25.816
24.587
23.470
22.340
21.154
20.522
20.474
Adjustment
Factors3
0.612
0.709
0.766
0.629
-0.164
-1.017
-2.125
-2.837
-3.980
-5.263
-4.930
-4.728
-4.726
-4.199
-4.331
-5.085
-5.251
-4.649
-3.420
-2.303
-1.173
0.013
0.645
0.693
67
-------
Table D3 (continued) - Year 1992
Time Period
Starting Date
Jan 1,92
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile
PbB
20.9
17.0
19.4
18.0
19.0
20.0
18.0
16.0
19.1
24.0
21.1
24.0
22.0
25.0
24.0
25.0
24.0
24.0
21.0
22.0
18.0
19.0
18.0
17.0
Detrended 90th
Percentiles1
22.762
18.940
21.418
20.095
21.173
22.251
20.328
18.406
21.584
26.562
23.739
26.717
24.795
27.872
26.950
28.028
27.105
27.183
24.261
25.338
21.416
22.494
21.572
20.649
Smoothed
Detrended
Series2
20.632
20.530
20.718
20.820
20.863
20.976
20.838
21.031
22.324
23.801
24.729
25.592
26.155
26.727
27.150
27.178
26.955
26.183
25.161
24.138
22.966
22.244
21.772
21.319
Adjustment
Factors3
0.535
0.637
0.449
0.347
0.304
0.191
0.329
0.136
-1.157
-2.634
-3.562
-4.425
-4.988
-5.560
-5.983
-6.011
-5.788
-5.016
-3.994
-2.971
-1.799
-1.077
-0.605
-0.152
68
-------
Table D3 (continued) - Year 1993
Time Period
Starting Date
Jan 1, 93
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile
PbB
18.0
18.0
15.4
15.0
14.0
16.0
17.0
16.0
17.2
20.0
18.0
19.0
21.0
19.3
19.0
22.0
24.4
20.2
16.6
18.4
18.0
15.5
16.0
19.4
Detrended 90th
Percentiles1
21.727
21.805
19.282
18.960
18.038
20.116
21.193
20.271
21.549
24.426
22.504
23.582
25.659
24.037
23.815
26.893
29.370
25.248
21.726
23.603
23.281
20.859
21.436
24.914
Smoothed
Detrended
Series2
21.167
20.685
19.952
19.490
19.378
19.846
20.563
21.111
21.959
22.866
23.289
23.822
24.419
24.747
25.275
26.002
26.175
25.198
23.941
23.233
22.701
22.069
21.886
21.584
Adjustment
Factors3
0.000
0.482
1.215
1.677
1.789
1.322
0.604
0.056
-0.792
-1.699
-2.122
-2.655
-3.252
-3.580
-4.108
-4.836
-5.008
-4.031
-2.774
-2.066
-1.534
-0.902
-0.719
-0.417
69
-------
Table D3 (continued) - Year 1994
Time Period
Starting Date
Jan 1
Jan 16
Feb 1
Feb16
Mar 1
90th Percentile
PbB
13.0
13.0
14.0
17.0
35.0
Detrended 90th
Percentiles1
18.592
18.670
19.747
22.825
40.901
Smoothed
Detrended
Series2
20.569
21.160
22.546
25.616
30.375
Adjustment
Factors3
0.598
0.007
-1.379
-4.449
-9.208
1Detrended by adding .0777*(i-73) and 3.727 fort>42.
2Smoothed values of column 3 using weights .3, .2, .1, .05.
3Equals 21.167 (smoothed value at i=73) - column 3 values.
sizes (n=120).
70
-------
APPENDIX E. 1990-96 MILWAUKEE PbB MEASUREMENT ADJUSTMENT
FACTORS
(These factors are not appropriate for other PbB data sets).
71
-------
In response to one of the peer reviewer's comments a set of seasonality adjustments
was calculated for log(PbB) values, and zipcode information for the screened children was
incorporated into the trend analysis. During peer review, additional Milwaukee Health
Department blood lead data became available through February, 1 996. Seasonality trends
were reevaluated with the new data, and adjustment factors were calculated for the
extended time period January 1 , 1 990 through February 1 5, 1 996. The basic methodology
for calculating these new adjustment factors is as before. Methodological details are
given in the following text. The new adjustment factors are given in Tables E1 though E3.
Step-bv-Step Details of the Adjustment Process
Seasonal adjustment factors for the log transformed data were calculated through a six-
step procedure.
First, the log transformed data were adjusted to account for differences associated with
the address zip codes of the screened children. This adjustment was done through an
analysis of variance (ANOVA). The dependent variable was the log (PbB) value; the
(three) independent classification variables were based on 1 ) the six bimonthly periods of
the year (e.g., January - February, March -April, etc.), 2) (ten) half-year time intervals (first
half of 1990, ..., last half of 1995), 3) zip codes (zip codes with less than 1000 children
were combined). Each child's adjusted log(PbB) value was then set equal to the log(PbB)
value minus the least squares mean value corresponding to the child's zip code.
Second, the 90th percentile values were calculated for each semi-month period from
January 1, 1990 through December 31, 1995.
Third, the 90th percentile values were fit using the model:
where t = time in years (for January 1, 1990, t=0).
A,(t) = 4t for t < 0.25; A,(t) = 1 for t > 0.25.
A2(t) = 2t for t < 0.5; A2(t) = 1 for t > 0.50.
A3(t) = (4/3)t for t < 0.75; A3(t) = 1 for t > 0.75.
A4(t) = tfort<1; A4(t) = 1 fort>1.
A5(t) = 0.8t if t<1 .25; A5(t) = 1 for t > 1 .25.
A6(t) = (2/3)t for t < 1 .5; A3(t) = 1 for t > 1 .5.
A7(t) = (4/7)t for t<1 .75; A4(t) = 1 for t > 1 .75
A8(t) = 0.5t if t<2; A5(t) = 1 for t > 2.
72
-------
This is just an elaboration of the Beta model described in Section 3.2.2 and 3.2.3. Without
the last five terms on the right-hand side, equation (11) is identical to equation (6) in
Section 3.2.3. The quadratic term (P2ti2) was included to better account for nonlinearity in
the long-term trend. The last four terms are included to account for medium-term
nonseasonal fluctuations in the observed PbB values associated with the expansion of the
screening program between January 1, 1990 and December 31, 1991.
The fourth step is "detrending" the time series by subtracting out the components
associated with the linear trend, Ph and the last five terms in equation 9. The fifth step is
calculating a moving average of the detrended time series. Finally, the adjustment factors
are set equal to the smoothed value at time t=73 (corresponding to January 1,1993) minus
the smoothed value for the time period when the child's blood sample was collected.
The same procedure was used to calculate adjustment factors directly from the
untransformed data, but with two exceptions. First, the PbB values were never adjusted
using zip code information. Second (obviously), the log transformation was never used.
The next paragraph describes the procedure for calculating age adjustment factors for
the log transformed data.
First, the log transformed data were adjusted to account for differences associated with
the address zip codes of the screened children, and also differences associated with
trends in PbB values over time. This adjustment was done through the analysis of
variance (ANOVA) described above. Each child's adjusted log(PbB) value was first set
equal to the log(PbB) value minus the least squares mean value corresponding to the
child's zip code. Each zip code adjusted value was then adjusted for the time trend by
subtracting the least squares value associated with the six month time interval (when the
child's blood sample was collected). Average adjusted log(PbB) values were then
calculated for thirteen predefined age categories. For each age category, the age
adjustment was then set equal to the average for the age category minus the average for
a reference category (1.75 through 2.0 years).
Multiplicative age adjustments for unadjusted data were calculated by simply applying
the exponential function to the adjustments for the log transformed data.
As described in Section 4.4.1, untransformed data could be adjusted directly using the
formula (equation 9, Section 4.4.1):
y* = (y+A,)*Mk.
Here, Mk is the multiplicative age adjustment factors shown in Table 3 (for the kth age
group); A, is the additive seasonality adjustment factor from Table 2 (for the ith time
period).
73
-------
The seasonal and age adjusted log transformed data would be equal to the log
transformed data plus the sum of the corresponding age (Table 3) and seasonality
adjustments (Table 2). Examples for using the tables follow:
Example 1: Suppose Pbb value on September 1, 1992 is 25.
Thenlog(Pbb) = 3.219.
log(Pbb) (adjusted for seasonality from Table 1)
= 3.219-0.241 =2.978.
Seasonally adjusted Pbb = exp(2.978) = 19.6. (This represents the
equivalent Pbb value for a measurement made January 1, 1993 using the
adjustments that were based on the log transformed values).
Example 2: Suppose Pbb value on September 1, 1992 is 25.
Adjusted PbB = 25-5.729 = 19.3.
(This represents the equivalent Pbb value for
measurement made in Jan., 1993 based on the analysis of
the untransformed values).
Note that the adjustments from Tables E.1 and E.2 do not yield identical results.
Adjustments from Table E.1 are being used for a retrospective analysis of paint
abatements in Milwaukee.
74
-------
40
35
30
25
20
15
10
1990
1991 1992 1993
Time Sample Collected
1994
1995
Figure 17. Modelled (solid line) and Smoothed (dashed line) 90th Percentile Blood Lead Levels Using
Log Transformed Data from 1990 to 1996
-------
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
1990 1991
1992 1993 1994
Time Sample Collected
199
Figure 18. Seasonal Adjustment Factors (1990-96) for Log Transformed Data
-------
Table E1. Seasonal Adjustment Factors for Log Transformed PbB Data from 1990
through February, 1996.
Year 1990
Time Period
Starting Date
Jan 1, 90
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
3.043
3.060
3.081
3.121
3.272
3.431
3.127
3.174
3.179
3.135
3.494
3.249
3.536
3.217
3.282
3.242
3.174
3.265
3.289
3.307
3.168
3.003
3.088
3.187
Smoothed 90th
Percentiles
3.060
3.080
3.119
3.164
3.224
3.251
3.217
3.208
3.212
3.251
3.316
3.339
3.351
3.312
3.273
3.253
3.237
3.249
3.247
3.223
3.173
3.124
3.123
3.143
Adjustment
Factors
0.046
0.077
0.090
0.097
0.089
0.114
0.146
0.098
0.038
-0.057
-0.180
-0.259
-0.300
-0.263
-0.227
-0.210
-0.195
-0.210
-0.200
-0.159
-0.091
-0.025
-0.006
-0.008
77
-------
Table E1 (continued) - Year 1991
Time Period
Starting Date
Jan 1,91
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
3.161
3.203
3.159
3.146
3.164
3.216
3.394
3.296
3.250
3.461
3.156
3.324
3.288
3.258
3.121
3.375
3.241
3.289
3.048
3.002
2.977
2.881
2.914
2.858
Smoothed 90th
Percentiles
3.159
3.171
3.170
3.178
3.202
3.241
3.292
3.301
3.308
3.316
3.285
3.276
3.272
3.249
3.247
3.256
3.235
3.187
3.107
3.030
2.973
2.929
2.907
2.897
Adjustment
Factors
0.011
0.052
0.106
0.151
0.181
0.195
0.133
0.050
-0.032
-0.113
-0.157
-0.222
-0.252
-0.223
-0.215
-0.218
-0.191
-0.137
-0.304
-0.191
-0.098
-0.017
0.041
0.087
78
-------
Table E1 (continued) - Year 1992
Time Period
Starting Date
Jan 1,92
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
2.953
2.835
2.914
2.905
2.951
2.868
2.809
2.847
2.924
3.158
3.065
3.098
3.029
3.157
3.072
3.146
3.169
3.135
2.934
2.968
2.817
2.790
2.845
2.865
Smoothed 90th
Percentiles
2.897
2.894
2.899
2.903
2.896
2.879
2.876
2.904
2.964
3.032
3.066
3.079
3.088
3.103
3.114
3.120
3.114
3.067
2.996
2.934
2.875
2.846
2.846
2.841
Adjustment
Factors
0.101
0.096
0.082
0.070
0.068
0.077
0.072
0.036
-0.032
-0.107
-0.149
-0.170
-0.186
-0.209
-0.226
-0.239
-0.241
-0.201
-0.137
-0.081
-0.028
-0.006
-0.013
-0.014
79
-------
Table E1 (continued) - Year 1993
Time Period
Starting Date
Jan 1, 93
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
2.923
2.787
2.595
2.601
2.560
2.637
2.702
2.806
2.723
2.873
2.784
2.928
2.969
2.940
3.005
2.958
3.091
3.068
2.737
2.839
2.804
2.769
2.751
2.806
Smoothed 90th
Percentiles
2.821
2.757
2.679
2.635
2.625
2.650
2.701
2.745
2.779
2.820
2.852
2.897
2.935
2.959
2.987
2.993
2.996
2.956
2.878
2.836
2.805
2.765
2.729
2.672
Adjustment
Factors
0.000
0.058
0.129
0.168
0.172
0.141
0.085
0.035
-0.004
-0.050
-0.087
-0.137
-0.180
-0.209
-0.242
-0.252
-0.260
-0.225
-0.151
-0.113
-0.087
-0.050
-0.019
0.036
80
-------
Table E1 (continued) - Year 1994
Time Period
Starting Date
Jan 1,94
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
2.431
2.472
2.578
2.609
2.455
2.576
2.577
2.618
2.766
2.779
2.789
3.143
2.926
2.993
2.814
2.958
3.010
3.045
2.868
2.806
2.652
2.751
2.652
2.741
Smoothed 90th
Percentiles
2.587
2.545
2.547
2.545
2.544
2.569
2.604
2.652
2.732
2.796
2.871
2.942
2.952
2.946
2.937
2.946
2.962
2.939
2.882
2.808
2.748
2.712
2.685
2.658
Adjustment
Factors
0.117
0.154
0.149
0.149
0.146
0.117
0.080
0.029
-0.054
-0.121
-0.199
-0.272
-0.285
-0.281
-0.275
-0.285
-0.303
-0.282
-0.227
-0.155
-0.097
-0.062
-0.037
-0.011
81
-------
Table E1 (continued) - Year 1995
Time Period
Starting Date
Jan 1, 95
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
2.563
2.586
2.525
2.591
2.346
2.549
2.571
2.560
2.485
2.606
2.742
2.901
2.899
2.837
2.812
2.782
2.800
2.900
2.792
2.757
2.747
2.989
2.867
2.723
Smoothed 90th
Percentiles
2.619
2.576
2.548
2.522
2.499
2.514
2.536
2.549
2.583
2.647
2.732
2.808
2.842
2.839
2.827
2.815
2.816
2.820
2.812
2.807
2.820
2.843
2.824
2.774
Adjustment
Factors
0.027
0.069
0.096
0.122
0.144
0.128
0.105
0.091
0.058
-0.007
-0.092
-0.168
-0.202
-0.199
-0.187
-0.174
-0.175
-0.178
-0.170
-0.164
-0.176
-0.198
-0.178
-0.127
82
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Table E1 (continued) - Year 1996
Time Period
Starting Date
Jan 1, 96
Jan 16
Feb 1
90th Percentile PbB
2.720
2.738
2.596
Smoothed 90th
Percentiles
2.721
2.651
2.556
Adjustment
Factors
-0.072
-0.001
0.096
83
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Table E2. Seasonal Adjustment Factors for 1990 to February, 1996 Based on Analysis of
Untransformed Data.
Year 1990
Time Period
Starting Date
Jan 1, 90
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
23.0
25.0
23.4
27.0
27.2
34.1
22.3
23.0
30.0
28.4
32.9
30.4
35.7
30.0
31.6
26.1
24.2
31.0
32.0
27.4
24.0
23.2
26.1
24.8
Smoothed 90th
Percentiles
23.985
24.518
25.416
26.395
27.350
27.800
26.600
26.615
28.025
29.340
30.850
31.760
31.965
30.965
29.760
28.475
27.910
28.670
28.565
27.355
25.920
25.150
25.050
25.145
Adjustment
Factors
0.062
0.341
0.256
0.091
-0.050
0.316
1.679
1.173
-0.727
-2.531
-4.529
-5.926
-6.487
-5.712
-4.733
-3.671
-3.328
-4.310
-4.376
-3.285
-1.967
-1.314
-1.331
-1.541
84
-------
Table E2 (continued) - Year 1991
Time Period
Starting Date
Jan 1,91
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
27.0
23.0
25.3
21.0
26.5
23.0
28.0
25.0
28.1
33.8
27.6
28.2
31.0
30.3
24.9
31.4
30.4
32.0
21.9
23.0
22.0
18.0
18.0
16.0
Smoothed 90th
Percentiles
25.010
24.570
24.130
24.010
24.480
25.070
26.200
27.105
28.310
29.550
29.355
29.240
29.510
29.130
28.960
29.355
29.145
27.845
25.280
23.100
21.190
19.395
18.405
18.045
Adjustment
Factors
-1.108
0.044
1.197
2.031
2.275
2.400
1.273
-0.343
-2.257
-4.206
-4.718
-5.310
-5.728
-4.937
-4.354
-4.336
-3.712
-1.998
-7.171
-4.711
-2.520
-0.443
0.830
1.474
85
-------
Table E2 (continued) - Year 1992
Time Period
Starting Date
Jan 1,92
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
20.0
17.1
20.7
19.0
19.0
20.0
18.0
16.0
20.0
24.0
21.0
24.0
23.0
24.0
24.0
25.0
24.0
24.0
21.1
22.0
18.0
19.0
18.0
17.0
Smoothed 90th
Percentiles
18.340
18.620
19.130
19.250
19.025
18.935
18.650
18.800
20.100
21.450
22.200
23.000
23.450
23.750
24.100
24.105
23.810
23.020
21.930
20.820
19.560
18.755
18.200
17.650
Adjustment
Factors
1.270
0.888
0.277
0.056
0.182
0.173
0.361
0.114
-1.282
-2.727
-3.572
-4.465
-5.007
-5.399
-5.840
-5.935
-5.729
-5.027
-4.024
-3.001
-1.826
-1.106
-0.635
-0.168
86
-------
Table E2 (continued) - Year 1993
Time Period
Starting Date
Jan 1, 93
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
18.0
18.0
15.0
15.0
14.0
16.0
17.0
16.0
17.0
20.4
18.0
19.0
20.0
19.0
21.0
22.0
25.0
21.0
16.2
18.4
18.0
16.0
16.3
20.2
Smoothed 90th
Percentiles
17.400
16.800
15.950
15.450
15.300
15.700
16.370
16.840
17.630
18.470
18.730
19.140
19.620
20.150
21.000
21.610
21.690
20.530
18.940
18.125
17.590
16.945
16.730
16.280
Adjustment
Factors
0.000
0.519
1.288
1.709
1.780
1.302
0.556
0.010
-0.856
-1.770
-2.103
-2.586
-3.138
-3.738
-4.658
-5.338
-5.486
-4.393
-2.870
-2.120
-1.650
-1.069
-0.917
-0.529
87
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Table E2 (continued) - Year 1994
Time Period
Starting Date
Jan 1,94
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
12.3
13.0
14.0
16.0
13.0
14.0
14.0
16.0
19.0
18.2
18.0
27.0
21.7
23.2
20.0
20.0
23.0
25.0
21.0
17.0
17.0
16.0
14.0
18.0
Smoothed 90th
Percentiles
14.960
14.245
14.240
14.215
14.150
14.450
15.110
16.170
17.790
18.945
20.470
22.130
22.260
22.050
21.710
21.555
22.010
21.850
20.500
18.650
17.350
16.200
15.550
15.350
Adjustment
Factors
0.730
1.384
1.330
1.296
1.303
0.946
0.230
-0.885
-2.559
-3.768
-5.345
-7.057
-7.238
-7.078
-6.787
-6.681
-7.183
-7.069
-5.765
-3.960
-2.704
-1.597
-0.989
-0.830
88
-------
Table E2 (continued) - Year 1995
Time Period
Starting Date
Jan 1, 95
Jan 16
Feb 1
Feb16
Mar 1
Mar 16
Apr 1
Apr 16
May 1
May 16
Jun 1
Jun 16
Jul 1
JuM6
Aug 1
Aug 16
Sep 1
Sep16
Oct 1
Oct16
Nov 1
Nov16
Dec 1
Dec 16
90th Percentile PbB
13.0
14.0
14.0
13.0
10.0
15.0
12.6
14.0
11.0
14.0
15.0
21.0
21.0
17.0
18.9
16.0
19.0
20.1
16.0
17.0
16.0
19.0
17.0
16.8
Smoothed 90th
Percentiles
14.550
13.900
13.550
12.880
12.660
12.970
13.030
13.070
13.460
14.580
16.250
18.095
18.790
18.480
18.325
17.940
18.110
18.075
17.470
17.210
17.145
17.330
17.195
16.810
Adjustment
Factors
-0.071
0.539
0.851
1.483
1.666
1.320
1.225
1.150
0.727
-0.426
-2.128
-4.004
-4.729
-4.448
-4.321
-3.964
-4.160
-4.151
-3.571
-3.335
-3.293
-3.500
-3.387
-3.022
89
-------
Table E2 (continued) - Year 1996
Time Period
Starting Date
Jan 1, 96
Jan 16
Feb 1
90th Percentile PbB
17.0
15.7
14.0
Smoothed 90th
Percentiles
16.150
14.940
13.480
Adjustment
Factors
-2.382
-1.191
0.252
90
-------
Table E3. Age Adjustment Factors for 1990-February, 1996 Milwaukee PbB Data
Age Category (Years)
0.5-0.75
0.75-1
1.0-1.25
1.25-1.5
1.5-1.75
1.75-2
2 - 2.25
2.25-2.5
2.5-3
3-4
4-5
5-6
6-7
Adjustment for Log (PbB)
Values
0.812
0.279
0.096
0.039
-0.028
0
-0.018
-0.033
0.039
0.107
0.169
0.207
0.262
Multiplicative Adjustment for
Untransformed Data
2.252
1.322
1.101
1.040
0.972
1.000
0.982
0.968
1.040
1.113
1.184
1.230
1.300
91
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50272-101
REPORT DOCUMENTATION 1 REPE°ART74N°R,5,10
4. Title and Subtitle
SEASONAL TRENDS IN BLOOD LEAD LEVELS IN MILWAUKEE
7. Author(s)
Pawel, D.J; Foster, C.; Cox, D.C.
9. Performing Organization Name and Address
QuanTech, Inc.
1911 North Fort Myer Drive, Suite 1000
Rosslyn, Virginia 22209
12. Sponsoring Organization Name and Address
U.S. Environmental Protection Agency
Office of Pollution Prevention and Toxics
Washington, DC 20460
3. Recipient's Accession No.
5. Report Date
August 1996
6.
8. Performing Organization Rept. No.
10. Project/Task/Work Unit No.
1 1 . Contract (C) or Grant (G) No.
68-D3-0004
13. Type of Report & Period Covered
Technical Report
14.
15. Supplementary Notes
In addition to the authors listed above, Jill LeStarge of Quantech was a major contributor to the study.
16. Abstract (Limit: 200 words)
Most studies of the effectiveness of the interventions for reducing children's blood lead levels (PbB) have not
distinguished declines in PbB due to program effectiveness from seasonal and age-related fluctuations in PbB. In this
report, seasonal fluctuations and age effects in 1990-93 blood lead levels for a northern urban environment are studied,
using data from 13,476 children screened for blood lead in Milwaukee, Wisconsin. The Milwaukee data showed
sizeable seasonal and age trends in Milwaukee children's PbB levels. Blood lead levels were about 40% higher in the
summer than the winter, and about 15-20% higher at ages two to three years than at age less than one year or ages
five to seven years. Statistical methodology was developed to account for these fluctuations, so that the effectiveness
of intervention programs may be quantified. The methodology was described in considerable detail to facilitate
analyses of seasonal and age effects in PbB in other environments. Seasonal fluctuations in PbB are probably greater
in cooler environments such as Milwaukee's, where seasonal changes in exposure to outdoor lead sources and sunlight
are more extreme. A tentative result suggests the magnitude of the seasonal PbB fluctuations may be greatest for
children less than four years old.
17. Document Analysis a. Descriptors
Lead exposure reduction, children, blood lead levels, seasonality
18. Availability Statement
19. Security Class (This Report)
Unclassified
20. Security Class (This Page)
Unclassified
21. No. of Pages
102
22. Price
(SeeANSI-Z39.18)
OPTIONAL FORM 272 (4-77)
(Formerly NTIS-35)
71
92
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