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OAR Box 1112 

Prepped by RyanDugan 

Document Number: 

17) ll-B-6 

Docket Number: 

A-83-22 

Printed 4/16/2008 9:12:06 AM Sheet 17 of 97 
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UNITED STATES ENVIRONMENTAL PROTECTION AGENCY JJ^ - ft ~£~ 

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''<.*&*• SUBJECT: MODELING THE PERCENT OF CHILDREN WITH HIGH BLOOD LEAD 

LEVELS 

FROM: Joel Schwartz CVc^ (j 

Office of Policy Analysis

 VJp<-Hf 

(j \ flnr, ? I 1985 

TO: Vic Hasselblad 

Allan Marcus 

Jeff Cohen 

The distribution of blood lead levels in U.S. children is a 

broad one, because there is a distribution of exposures those 

children face, a distribution of behavior patterns that affect 

the uptake of that exposure, and a distribution of biological 

absorbtion and excretion rates. Observational data bases, such 

as NHANES II, reflect all of those contributions to the variance 

of the distribution. I believe that the issue we have been 

grapling with on how to determine what air lead standard will 

protect a given percent of children from exceeding some cutoff 

blood lead level is the issue of how to deal with those variance 

components, and how they might change. 

I believe that Vic and Allan's point is that the variance of 

the distribution is partially due to the variance in air lead 

levels; therefore the percent of children at high blood lead 

levels if all areas were at a given ambient standard should be 

estimated in a way that removes that variance. I believe that 

that point is a fair one. My point has been that the technique 

chosen also removes some of the variance in non-air exposure, 

thereby underestimating the variance at uniform air lead, and 

that the assumption that the tail of the distribution is well 

modeled by fitting a lognormal distribution to the overall 

distribution is less robust than some other techniques for 

estimating the size of the tail. I will discuss these further in 

the hopes that we can reach an agreement on the best way to do 

the modeling. 

My first point is that much of the variance associated with 

some of the demographic variables reflects variation in baseline 

exposure, behavior patterns or biological factors, and not air 

lead, and therefore adjusting the distribution for them as a 

technique for removing the variance due to variation in air lead 

levels is excessively conservative. For example, consider race. 

Blacks have higher blood lead levels than whites, however the 

NHANES data indicates that blacks have higher blood lead levels 

than whites even after controlling for degree of urbanization, 

income, residence inside the central city, parents educational 

level, and any other variable that appears to test whether that 

difference is soley due to differential exposure to high urban 

air lead. Indeed, some of those variables also test whether the 

racial difference is due to differential exposure to paint lead. 
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After controlling for all of those factors there is still a 

substantial difference between the races in their blood lead 

levels. Indeed, when we did our gasoline lead regressions, which 

control for the major source of air lead exposure, as well as age 

sex, income , degree of urbanization, region of the country, 

educational level, dietary consumption, etc, blacks still had 

significantly higher blood lead levels. This difference 

reflects true differences in the other factors affecting blood 

lead levels, and therefore should remain as a real factor that 

contributes to the GSD. 

Location is another factor that represents more than just 

difference in air lead exposure. While the estimates of mean 

baseline exposure in the criteria document are reasonable, and 

the best data we have, clearly food lead levels, dust lead, water 

lead, and other factors vary from location to location. One 

important problem with the modeling in the staff paper is that it 

ignores the distribution of city mean baseline levels. Since the 

percent of children at high blood lead levels is nonlinear in the 

mean baseline assumed, adding a distribution in mean blood lead 

levels about the mean baseline quoted in the CD and staff paper 

will in fact change the estimate of the number of children at 

high levels. The probability of exceeding a given blood lead 

level is clearly the product of the probability of the location 

having a mean u, given the grand mean, times the probability of 

having a high blood lead, given u and the gsd within a site. 

Since the product of log normal distributions is lognormal, this 

is equivalent to spreading the gsd by adding the variance of the 

site means to the variance of the within site population. The 

current modeling ignores this by assuming that the baseline in 

every location is the same. 

If I recall what Vic told me correctly, the gsd's quoted in the 

CD removed the variation due to site effects; whereas they should 

only remove the site variations due to air lead variations, and 

leave the site variations due to variations in the baseline 

exposure. 

The NHANES II data can be used to quantify this effect. 

Assuming that degree cf urbanization is a proxy for the distribution of air lead levels (and I argued before that some of the 

variance due to degree of urbanization is due to other factors), 

I regressed the log of blood lead levels on the eight level 

degree of urbanization variable in the NHANES II data . I then 

added the mean back to the residuals and took the mean log 

blood lead level, by site. This is the mean after adjusting all 

the sites to the same population. Table 1 shows the mean, 

standard deviation, and "geometric standard deviation", which is 

exp of the stadard deviation in log space. We can see that there 

is an expected variation in mean blood lead levels for cities of 

the same size. Adding the variance of this distribution to that 

of a distribution with a gsd of 1.39 would give a distribution 

with a gsd of 1.462, which is shown in the last column. 

The next line carries the analysis further, by first 
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TABLE 1 

LOG MEAN 

2.665 

2.666 

LOG SD 

0.189 

0.183 

GSD TOTAL GSD 

1.208 1.462 

1.200 1.458 

controlling for degree of urbanization, income, and race, before 

taking the site means. Again there is a noticable residual 

variance in the means of locations with the same population, 

racial mix and income levels. Adding that variance to that of a 

population with a gsd of 1.39 would give a new gsd of 1.458. 

The above calculations demonstrate that there is a variation 

in mean blood lead levels among cities, and that correcting for 

demographic proxies for air lead exposure leaves a residual 

variation in site means due to variations in non-air exposure. 

This is an approximation to the distribution of mean blood lead 

levels across sites with the same air lead exposure. Estimating 

a childs likelihood of having an elevated blood lead level, or 

the percent of children above a certain blood lead level at a 

given air lead level cannot ignore this variation in background 

level. 

CASE 

Site Means, Controlling 

For Degree of Urbanization 

Site Means, Controlling 

for Urbanization, Race 

and Income 

There are likely to be differences in baseline exposure that are 

a function of degree of urbanization, since higher population 

density will increase the soil contamination from other sources 

than air (e.g. old batteries, industrial facilities etc.). 

Similarly some of the racial and income differences in blood lead 

levels are certainly not due to airlead exposure. On the other 

hand, these proxies may not completely control for air 

variations. It would clearly be better to remove the airlead 

variance directly. 

To do this I repeated the gasoline lead regressions, and used 

them to remove the variance due to gasoline lead exposure, which 

is about 85% of air lead exposure. By ajusting every individuals 

blood lead level to what it would be at zero gasoline lead 

exposure, we arrive at a good estimate of the distribution of 

blood lead levels due to baseline exposure variations, biological 

differences, etc. To account for the remaining 15% of air lead 

exposure, the resulting gsd can be reduced by 15% of the change 

in the gsd in going from the unadjusted distribution to the one 

expected at zero gasoline lead. Using the gsd from this analysis 

incorporates differences due to variations in baseline exposure 

among locations, races, etc, which must be incorporated to 

correctly predict the effect of of additional exposure to air 

lead on the percent of children that will have high blood lead 

levels. To maintain the distribution as log normal, the gasoline 

regression was done using a dependent variable of log blood lead. 
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The regression is shown in the appendix. Then each individuals 

log blood lead was reduced by the gaslead regression coefficient 

times their gasoline lead exposure, and a weighted univariate was 

performed on the resulting distribution. The results are shown 

on the first line of table 2. The estimated gsd is 1.428. Moreover, the principal reason that this gsd is higher than those in 

the CD is the natural variation in the baseline exposure among 

sites with similar demographic characteristics, not the variation 

in demographic characteristics between sites. To illustrate 

this, the second line in table 2 shows the same results, after 

adjusting by regression for the effect of degree of urbanization. 

Even if all children lived in towns with the same degree of 

urbanization, they would have a gsd of 1.414. To illustrate this 

further, the next two lines show the mean and gsd of location 

means at zero gasoline lead with and without adjusting for degree 

of urbanization. (The mean reflects zero gaslead, but not zero 

stationary source lead, the gsd reflects our correction for both 

factors.) 

TABLE 

LOG MEAN 

1.99 

2 

LOG SD 

0.360 

GSD 

1.428 

CASE 

Controlling for 

Airlead (zero airlead) 

Controlling for 1.989 0.346 1.414 

Airlead and Degree of 

Urbanization 

Location Mean 1.935 0.187 1.46 * 

Controlling for 

Airlead 

Location Mean 1.978 0.161 1.44* 

Controlling for 

Airlead and 

Urbanization 

Note: site means differ from overall means because the sites had 

different populations, which is controlled for in the overall mean. 

* assuming a GSD of 1.39 after controlling for sites, and adding 

the site variance due to non air sources back in. 

In summary, it appears that the best estimate for the GSD for 

children six and under, if the air lead was zero, is 1.428. To 

calculate the percent of children with blood lead levels above 

the lowest effect level, we should use this GSD and look at the 

effect of increasing everyones airlead exposure to 0.50, etc. 

This will give the percent of children expected to exceed that 

level if every location is at the ambient standard. 

I still like the idea of doing logistic regressions to see how 
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the percent of children above a given level changes. Regression 

is a more robust technique than fitting distributions, and it can 

also be corrected to eliminate the variance due to airlead 

exposure. I will try to do that soon and send you the results. 
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REGRESSION RESULTS 

LOG BLOOD LEAD, CHILDREN SIX AND YOUNGER 

VARIABLE 

INTERCEPT 

GASLEAD 

URBANIZATION 

RACE 

SEX 

INCOME 

AGE 

COEFFICIENT 

2.256 

0.1624 

-0.0265 

0.2129 

-0.0307 

-0.1219 

-0.0185 

t-STATISTIC 

36.01 

17.67 

-10.44 

11.24 

2.35 

-12.69 

-4.974 

P-VALUE 

0.0001 

0.0001 

0.0001 

0.0001 

0.0187 

0.0001 

0.0001 

NOTE: Regression was run in WLS, not SURREGR, since this gives 

the identical coefficients, and we already know the significant 

variables.