OAR Box 1112 

Prepped by Ryan Dugan 

Document Number: 

15) ll-B-4 

Docket Number: 

A-83-22 

Printed 4/16/2008 9:12:06 AM Sheet 15 of 97 

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P.2 

^ APR 2 2 1985 

Subject: Draft Staff Paper on Lead 

From: Joel Schwartz 

Office of Policy Analysis 

To: Jeff Cohen 

Office of Air Quality Planning and Standards 

As I mentioned in our phone conversation yesterday, I think that 

we can improve the modeling of the percent of children at risk as 

a function of geometric mean blood lead level that is currently 

contained in the draft staff paper. This memorandum repeats the 

problems with the current approach that I discussed with you, 

and, I hope, offers a simple solution to them. 

The overriding source of the problems is that the distribution of 

blood lead levels in children is reall y the sum of two 

distributions, one from general exposure to air lead, food lead, 

etc., and one from very high exposure to lead paint or other high 

concentration sources. Since the sum of log normal distributions 

is not in fac t log normal, one would expect this to introduce 

error s into the fit of the distribution at high levels. Since 

one would not expect the blood lead levels of lead paint exposed 

children to fall proportionately as the mean blood lead level 

falls, (i.e. their blood lead levels will not fall by 4 or 5 

ug/dl from a reduction in air lead that produces an average 1 

ug/dl fall) the underestimate of the fatness of the tail would be 

expected to increase as the mean blood lead level fell. 

This theoretical point is supported by the data as well. For 

example, CDC and NCHS in their analysis of the NHANES II data 

divided the sample into two periods, before and afte r the rate of 

change of blood lead levels increased. For the second period the 

geometric standard deviation of both black and white children's 

blood lead levels was approximately 1.43. However, the GSD that 

correctly predicted the percent of children above 3 0 ug/dl was 

1.54, i.e. the extreme tail is fatte r than predicted by the GSD 

that best fits the entir e distribution. Moreover, the 

difference in thes e GSD's was larger in the second period, when 

mean blood lead levels were lower, than it was in the first 

period. So the error increase s as the mean blood lead level 

falls. Since OAQPS intends to se t the standard on the basis of 

protecting 99.5% (or 99.2% or 99.8%) of U.S. children from being 

above some critical level, we will be setting the standard in 

precisely the tail of the cumulative distribution function where 

we know both that the GSD systematically underpredicts the number 

of children at high blood lead levels, and where we know that the 

error appears to change with the mean blood lead level. 

As an ancillary point, while I think that Alan Marcus's estimates 

of the GSD for a homogeneous sub-population of children are quite 

correct, they are not the appropriate GSD's to use for your 

goal. Since the standard is being se t by looking at ALL 

children and trying to pick a standard that will keep e.g. 99.5% 
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of ALL children below the critica l level, the appropriate GSD to 

use in any cas e is the GSD for all children. This was 1.47 in 

the NHANES II survey. This is not a trivial point. The Criteria 

document's calculation of the GSD is adjusted, by anova, for the 

effects of age, race, sex, and income. That is, it gives a value 

that one would expect if all children were the same race, had the 

same family income, etc . However, the broadening of the 

distribution due to the broad distribution of family incomes in 

the United State s is a real one. Poorer people do get more 

exposure to lead. Therefore, if our goal is to keep 99.5% of 

real U.S. children below some critical effects level, we must use 

the real distribution. To put this in bette r perspective , the 

NHANES data (Vital and Health Statistics, serie s 11, no. 223) 

indicate s that 4 percent of U.S. children were above 30 ug/dl and 

9.1% of them were above 25 ug/dl in the NHANES II survey. Using 

the reported geometric mean blood lead leve l for those children, 

and the higher of the homogeneous GSD's (1.39), the predicted 

number of children exceeding 3 0 ug/dl or 2 5 ug/dl respectively 

are 1.68 % and 5.8.. Thus the error involved is substantial. 

Even using the actual GSD of 1.47 for NHANES II children gives a 

prediction of 3.46% above 30, versus the actual 4%. This 

reflects the fa t tail discussed earlier . None of this is to say 

that the calculations of the GSD's for homogeneous groups done in 

the Criteri a Document ar e wrong, they just ar e not the 

appropriate ones to use if we are targeting 99.5% of the nonhomogeneous population of U.S. children. Note that one does not 

have to be dealing with the whole U.S. population to ge t such 

high GSD's. the GSD for children in urban areas with populations 

over one million is 1.46, for black children with family incomes 

under $6000 is 1.47, etc. 

We dealt with this problem in the gasoline lead rule by using 

logisti c regression analysis of the percent of children above 

e.g. 30ug/dl to predict that percentage, rather than just moving 

the mean and using a constant GSD. This approach is superior 

conceptually, and also is partially nonparametric, in that it 

makes no assumption about the shape of the distribution curve, 

but merely fits the tail area at the appropriate cutoff to a 

logisti c function of the variable of interest. I think that the 

same approach to your problem will also give a bette r fit. In 

addition, regression analysis is more robust than other 

techniques, such as rollback modeling. 

To implement this approach for your problem I took the NHANES II 

data, divided it into seventeen quarters, and for each quarter 

took the mean of the log of the blood leads for children aged six 

and under, and also computed the percent of those children who 

were above 15ug/dl, 20ug/dl, and 25ug/dl. All of these 

calculation s were weighted. I then performed logistic 

regressions on how those percentages varied with the means. This 

direc t estimatio n technique avoids the GSD problem and 

automatically incorporates the actual data on children above 

thes e targe t levels, avoiding the error s of the GSD approach 

noted above. The regressions were weighted by the siz e of the 

sample in each quarter, and were done using maximum likelihood 
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estimator s in Pro c Nlin. The results ar e shown below. 

LOGISTIC REGRESSION 

DEPENDENT VARIABLE: PROBABILITY OF BEING OVER 

2 5 ug/dl 

PARAMETER 

INTERCEPT 

MEAN LN(LEAD) 

COEFFICIENT 

-16.20 2 

5.053 

STANDARD ERROR 

1.757 

0.636 

t-STATISTIC 

9.22 

7.94 

PARAMETER 

INTERCEPT 

MEAN LN(LEAD) 

LOGISTIC REGRESSION 

DEPENDENT VARIABLE: PROBABILITY OF BEING OVER 

2 0 ug/dl 

COEFFICIENT 

-15.50 6 

5.242 

STANDARD ERROR 

1.123 

0.409 

t-STATISTIC 

13.81 

12.33 

PARAMETER 

INTERCEPT 

MEAN LN(LEAD) 

LOGISTIC REGRESSION 

DEPENDENT VARIABLE: PROBABILITY OF BEING OVER 

15 ug/dl 

COEFFICIENT 

-13.41 8 

4.998 

STANDARD ERROR 

0.818 

0.304 

t-STATISTIC 

16.40 

16.44 

Usin g thes e regressio n result s we ca n calculat e the mean blood 

lea d leve l tha t correspond s t o a give n choic e o f critica l lead 

leve l and a give n fractio n o f th e populatio n t o be held below 

tha t critica l level . Fo r example , if th e critica l leve l i s 20 

ug/d l and th e critica l fractio n i s 99.5% o f th e children , we hav e 

t he following. 

log(p/l-p) = 15.506 + 5.242*mean log(lead) 

f o r the 99.5% leve l p = .005, and p/(l-p) = .00502 5 yielding 

-5.293 3 = -15.50 6 + 5.246«mean ln(lead) 

which ca n obviousl y be solve d fo r th e geometri c mean blood lead 

level . To tes t th e results , I predicte d th e percen t of children 

abov e 2 5 ug/d l usin g this techniqu e and usin g a constan t GSD of 

1.39 . The two predicte d value s of th e percen t of children abov e 

thes e level s wer e regresse d on th e actua l observations. The Rsquar e o f th e logisti c prediction s wa s higher , indicating , a s 
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- . , .>••» . 

expected, a bette r fit to the data. I think that this technique 

is more accurate and should be used to replace the table on 

page 78 and the numbers in the next few following pages that give 

the mean blood lead levels that are associated with various 

choices of p and of critical effects level. 

I do have two quick comments to make on the rest of the Staff 

Paper. While the gasoline lead regressions that we did are not 

directly relevant to your work, they do provide considerable 

suppor t fo r the judgment tha t you reached regarding the 

significance of the non-direct inhalation pathways. Since these 

results were presented to CASAC at the last criteria document 

review and were reviewed favorably, I think that it would be 

useful to cit e them. The regressions indicated that gasoline 

lead, an airborne source of lead, was a large contributor to 

blood lead levels. Further, while it is only possible to make 

qualitative estimate s of airborne lead levels at that time, the 

siz e effec t indicated by the gasolin e lead regressio n 

coefficients, in the NHANES data, the New York City data, and the 

Chicago data, suggest that the direct inhalation component was no 

more than 25% of the total. These results are similar to those 

of Carol Angle, and since they were derived using different data 

and different techniques, that similarity is striking. It might 

be worthwhile mentioning this. Moreover, the regressions 

indicate that about 8 ug/dl of average blood lead was coming from 

gasoline lead in 1976 -1980. The average air monitor reading at 

that time was below 1 ug/cu. m , although the average monitor was 

site d too high and therefore underestimated exposure. Even 

correcting for that would appear to give a ratio of 7-8, which is 

above the high end that you mention in the staff paper. While 

this calculatio n is inherentl y rough, I believ e tha t it 

qualitatively supports using the high end of the ratio's that you 

discussed, and that this ratio deserve s some attention in setting 

your margin of safety. 

Secondly, while the blood pressure work is discussed in the 

health appendix, it is not discussed in the body of the paper or 

with respec t to the setting of the standard. If the assessment 

in the current version of the corrigenda to the criteria document 

is accepted by CASAC without substantial change, I think that 

will need to be changed.