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OAR Box 1112 

Prepped by Ryan Dugan 

Document Number: 

37) ll-C-3e 

Docket Number: 

A-83-22 

Printed 4/16/2008 9:12:07AM Sheet 37 of 97 
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t* 

I 'AyA, 

a 

PRELIMINARY COMMENTS ON LEAD EXPOSURE 

by 

Ralph L. Keeney, Rakesh K. Sarin, and Robert L. Winkler 

This document is in response to a request to comment on methodologies 

for estimating blood lead concentrations in selected population groups. The 

intent is to make suggestions for developing, implementing, and documenting 

a rational procedure to obtain these desired estimates, rather than to complete 

an effort to provide reasonable estimates. In considering this document, 

it is essential to realize that all of the suggestions are based on a limited 

effort and hence should be considered preliminary. 

The report is organized as follows. Section 1 outlines our intent in a 

general model for the exposure analysis for lead. Section 2 presents sample 

calculations based on information in the Pedco document. Section 3 presents 

general comments on extensions and additional information needed for an actual 

implementation of the exposure analysis. The report is summarized in Section 

4. Two references are frequently cited in this report. The "Pedco document" 

refers to the paper titled "Scenario for analysis" which was sent to us along 

with the May 18, 1984 letter by Dr. Ron Whitfield. The "criteria document" 

refers to the Environmental Protection Agency's four-volume report titled 

"Air quality criteria for lead." 
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Section 1. Exposure Analysis for Lead 

In suggesting possible alternatives for the exposure analysis we defined 

the following objectives: 

1. The output of the exposure analysis should be a meaningful input to 

any subsequent health-risk assessment. 

2. The input requirements of the exposure analysis should be easily 

available (from past studies or experts' opinions) and the exposure model 

should be easily implementable on a microcomputer. 

3. The model should be general enough so that the results for a specified 

population group (e.g., children 1-2 years old) in a given location (e.g., 

Minneapolis) can be easily generated. 

4. The assumptions made in the model should be explicit so that when 

additional information becomes available the model can be updated easily. 

These objectives led us to examine the level of aggregation that the 

exposure model should have. The highest level of aggregation is to work 

directly with blood lead levels, perhaps through a regression model or other 

statistical model with a few appropriate independent variables. The coefficients 

of the model could be obtained from existing studies or inferred from responses 

of experts. At the other extreme, the lowest level of aggregation is to model 

all of the various steps leading to the final blood lead levels. For example, 

in the approach taken by Biller et al , each cohort group is traced through 

a variety of microenvironments on an hour to hour basis, some sort of simulation model is used to predict lead exposure, and a detailed physiological 

model is used to obtain the >• ood lead levels on a day to day basis. 

We believe that an i" : * ediate level of aggregation may be appropriate. 

Our current thought *..s '. would use one month as an averaging time. Since 

the half life of b*l» *-*.'• indicated in the criteria document to be between 20 
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and 40 days, a month may be a reasonable period to consider to examine the 

fluctuations in blood lead levels. 
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Section 2. Sample Calculations for Lead Exposure 

There are two distinct components addressed to calculate lead exposure. 

Submodel 1 concerns lead consumption and Submodel 2 concerns blood lead levels 

given consumption. This section considers both and illustrates the calculations 

necessary to estimate lead exposure using data from the Pedco and criteria 

documents. We describe the approach in simple steps indicating the assumptions 

that are made. More detailed comments on many of the assumptions are found 

in Section 3. 

SUBMODEL 1. LEAD CONSUMPTION 

There are six steps in Submodel 1. We will illustrate calculations using 

one population group of interest, namely black children between 1 and 2 years 

of age who are in poverty and live in homes built after 1950 in the MinneapolisSt. Paul area. 

Step 1. This group, which contains 651 individuals according to the 

Pedco document, should first be divided in terms of the representative air 

quality that they are exposed to as indicated by the location of the air 

quality monitors (map codes A to K). Since the air quality monitors are limited 

in any city, an assumption about the demographic distribution must be made. 

We use a naive assumption for this illustration that the 651 children are 

evenly distributed across the monitors in terms of exposure. Thus, we can 

say that approximately 60 children in our population group are exposed to the 

air quality indicated by the monitor corresponding to each map code. Note 

that this calculation does not require that a population group actually live 

in the vicinity of the location of an air quality monitor. We only require 

an assumption that a given location has the same air quality as the air quality 

indicated by a particular monitor. A more realistic assumption might be to 
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assign a higher proportion of the population in poverty to locations near 

either a smelter or a battery plant (e.g., map codes F or K). Additional 

demographic information would be valuable in this regard. 

The inhalation levels of lead will depend on the number (or proportion) 

of people exposed to various air quality levels in each of the months. In 

our example, this distribution for each month is given from the quarterly 

information in the Pedco document. For the first month, the concentration 

3 

ranges from 0.22 to 1.64 yg/m . 

For our subsequent illustration we will only use 60 children exposed to 

map code A air quality. The lead concentration exposure from air for these 

children for 12 months of 1981 is, respectively, 0.41, 0.41, 0.41, 0.37, 0.37, 

0.37, 0.37, 0.37, 0.37, 0.56, 0.56, and 0.56, measured in yg/m3 (see Pedco 

Table 2). 

Step 2. Based on the air quality exposure in Step 1, the total amount 

of lead inhaled per day is calculated. For a given month this daily amount 

will remain constant and thus it is an average amount for the month. We make 

the following assumptions: 

• the ratio of indoor to outdoor air quality (Table 7-7 in the 

criteria document) is 0.5 

3 

• the amount of air inhaled is 10 m /day 

• the indoor and outdoor time are 20 hours/day inside and 4 hours/ 

day outside 

• seasonal factors (e.g., both the indoor/outdoor activity division 

and the indoor/outdoor air quality ratio may vary by season) 

are ignored for the purposes of our simple example. 

The average lead inhaled per day can now be calculated. For the 60 children 

in our example, this calculation for month 1 is 
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3 3 

Lead inhaled (yg/day) = 10 m /day[(20 hrs. inside x 0.41 yg/m air quality 

x 0.5 inside/outside air quality ratio) 

+ (4 hrs. outside x 0.41)]/24 hrs. 

= 2.4 yg/day. 

The results for all 12 months of 1981 are, respectively, 2.4, 2.4, 2.4, 2.1, 

2.1, 2.1, 2.1, 2.1, 2.1, 3.2, 3.2, and 3.2 yg/day. 

Step 3. In this step we estimate the amount of lead ingested in the 

form of dusts. The categories of dusts are household dusts, soil dusts, street 

dusts, and occupational dusts. The dust lead concentration will correlate 

to some extent with air lead concentration but additionally will depend on 

family gardens, interior lead paint, distance from the residence to a smelter, 

etc. We recommend that a few convenient (from the standpoint of data collection) 

categories be used to arrive at the dust lead concentration that a population 

is exposed to. In our example we assume the base case from Table 7-23 of 

the criteria document. We also assume the amount of dust ingested is the 

same as in Table 7-23 for the 60 children. Thus, the calculation for the 

dust lead consumed is as follows: 

Type of dust 

Household dust 

Street dust 

Occupational dust 

Dust lead 

concentration 

yg/g 

300 

90 

150 

Dust inges 

g/day 

0.05 

0.04 

0.01 

ted 

Dust lead 

consumed 

yg/day 

15 

4.5 

1.5 

21.0 

(Note that the original Table 7-23 has an inconsistency in the street dust 

calculation since 90(0.04) =3.6. This inconsistency should be resolved, but 

we do not have sufficient information to resolve it.) 
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Using information from Table 7-25 of the criteria document, notice that 

for the 60 children living in the households near a smelter (represented by 

map codes F and G), there may be an increase in dusts to 25,000 yg/g, and 

for the children living in houses built before 1950, the household dusts will 

rise to 2000 yg/g because of interior lead paint. There will be similar 

increases due to family gardens, occupation, etc. 

If the lead concentration is correlated with air quality, then the monthly 

averages of the dust lead consumed will vary over the period. 

Step 4. We now compute the lead ingested from food and milk. This consumption may be assumed constant for some well-defined categories (e.g., rural 

vs. urban, poor vs. non-poor, child vs. adult, male vs. female). For our 

example the lead ingested from food and milk will be 28.7 yg/day (Table 7-18 

of the criteria document). 

Step 5. The amount of lead ingested from water and beverages can also 

be assumed to be constant for some well-defined categories. We use Table 7-21 

in the criteria document to assume that the 60 children in our example consume 

11.2 yg/day of lead from this source. 

Step 6. The amount of lead inhaled per day and ingested per day can now 

be obtained. In our example the amount of lead inhaled/day for each of the 

12 months is given in Step 2. The amount of lead ingested will be 60.9 yg/day 

which is obtained by adding the results in Steps 3, 4, and 5. This is assumed 

to remain constant throughout the year for this example calculation. 

SUBMODEL 2. BLOOD LEAD CONTENT 

So far we have illustrated calculations (in Steps 1-6) for the daily 

amount of lead inhaled and ingested for the 12 months in a year. It is assumed 

that within a month there is no variation in the inhalation or ingestion 

amounts. At this point we suggest two alternatives to compute blood lead 
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8 

levels (yg/dl) for each of the 12 months. Before we discuss these alternatives, 

we provide a general observation that the degree of uncertainty in the data 

reported in the criteria document is sufficient to warrant the explicit use 

of expert opinion to complement the data used for the modeling. In Submodel 1, 

the data are reasonably sufficient so that the explicit quantification of the 

judgments of experts can be kept at a minimum, although such information can 

still be very useful. We also suggest that for some health effects it may be 

desirable to encode experts by providing them with some initial conditions 

about a population group and the lead inhalation and lead ingestion amounts 

calculated in Steps 1-6. We now discuss two alternative approaches that relate 

the lead inhalation and the lead ingestion with the blood lead levels. 

Physiological Modeling Approach 

In this approach we will assume that the blood lead is in daily equilibrium 

with other compartments and the blood lead levels fluctuate only monthly (thus, 

there will be 12 blood lead levels for an individual in a year). A diagrammatic 

representation of this model is given in Figure 2. 

By making assumptions about the deposition rates and absorption rates as 

shown in the figure, we can calculate the total lead absorption (yg/day) for a 

member of a population group. A sample calculation for the 60 children in our 

example will be as follows: 

[2.4yg (daily inhalation) x 0.35 (deposition in lower airways) 

x 1 (absorption rate)] + [(60.9 + 0.15 x 2.4) (daily ingestion) 

x 0.1 (absorption rate)] 

=6.95 yg/day. 

Note that this number may be considerably higher if the absorption rates given 

in Table 10-3 of the criteria document are used. Thus, the above calculation 
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is a sample calculation and the numerical figure may not be realistic. 

If we assume a 50% excretion rate, then a daily retention of 3.47 yg/day 

will be predicted for each of the 60 children. 

We now have to make several assumptions about the intercompartmental 

transport of lead, the half-life of blood lead (e.g., 30 days), the time it 

takes to reach a new equilibrium with an increase or decrease in lead intake, 

and the blood volume. We can then compute on a month to month basis the new 

blood lead levels. This part of the model cannot be constructed from the 

information in the criteria document. We believe, however, that with a modest 

amount of information from experts, it is possible to build a simple model 

that can provide reasonable estimates of average monthly blood levels. 

Correlational Approach 

In this approach the relationships obtained from the observational and 

experimental studies reported in Chapter 11 of the criteria document are used 

to correlate blood lead with the inhaled lead and ingested lead. The models 

for inhaled lead and ingested lead will be discussed separately. 

Inhaled Lead. As shown in Figure 3, we need a relationship between blood 

lead level (y) and inhalation lead amount (z). The studies have provided 

data on the relationship between y and air lead concentration (x), say y = f(x). 

For example, f may be linear with a slope of 1.97 + 0.39 for children and 

1.64 + 0.22 for adults. In our Steps 1 and 2 we have established a relationship 

between z and x, say z = g(x). It is therefore possible to derive a relationship between y and z, say y = h(z). 

We recommend that expert opinion be sought to establish the relationship 

between y and z. Of course, the results of experimental and observational 

studies should be used to provide a benchmark. This approach may be easier 
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10 

to implement than seeking expert opinion on the relationship y = f(x). This 

is because there are many more intervening variables that influence f as 

compared with h. 

In our example the contribution of inhaled air to blood lead will be 

0.82 yg/dl (assuming f is linear with a slope of 2). 

Ingested lead. The blood lead contribution by ingestion is divided into 

food and water and dust ingestion. A relationship between lead intake and 

blood lead level must be established. If we assume a linear relationship 

bewteen blood lead level and dietary level intake with a slope of 0.06 (see 

the criteria document, page 11-160), then for our example the incremental 

blood lead contribution will be computed as 

0.06 x (28.7 + 11.2) = 2.4 yg/dl 

since food and water intakes were 28.7 and 11.2 yg/day, respectively, from 

Steps 4 and 5. 

Finally, the relationship between soil and dust lead and blood lead is 

used to compute the incremental blood lead contribution from this source. 

Again, if we assume the linear relationship with a slope of 1.8 yg/dl (see 

the criteria document, page 11-161), then from Step 3 we use the dust lead 

concentration of 540 yg/g or 0.54 mg/g and thus the blood lead contribution 

will be 

1.8 x 0.54 = 0.972 yg/dl. 

The total blood lead concentration for each of the 60 children in our 

example will be 

0.82 (inhalation contribution) +2.4 (food and beverage contribution) 

+ 0.972 (dust contribution) = 4.192 yg/dl. 
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11 

Notice that the dust lead concentration is a variable with a large range. 

If we assume 2000 yg/g concentration (which may be reasonable for an inner 

zone of the city), then the blood lead concentration for the 60 children will 

be predicted to be 6.82 yg/dl. 

In order to get the estimates of the percentage of blood lead levels 

for the indicated population group of blacks aged 1-2, additional calculations 

similar to those above need be completed. First, a set of calculations for 

each of the air quality monitors B through K needs to be completed, assuming 

60 individuals in each group. Next, similar calculations for the other blacks 

aged 1-2, indicated in Table 1 of the Pedco document, need to be completed. 

These groups are seven individuals in poverty in pre-1950 housing, 56 individuals 

not in poverty in pre-1950 housing, and 1935 individuals not in poverty in post1950 housing. The resulting blood lead concentrations of these three groups 

need to be combined with the information from the 651 individuals in poverty 

living in post-1950 housing to provide the required blood lead distributions 

for blacks aged 1-2. 

The sample calculations presented in this section utilize point estimates 

of the various parameters in the model. To get a more realistic distribution 

of blood lead levels for particular groups, uncertainty about the parameters 

should be incorporated explicitly into the analysis. To illustrate this notion, 

consider one parameter, the amount of time spent indoors per day. We used an 

estimate of 20 hours per day indoors in our calculations. However, the average 

number of hours spent indoors will vary within the group of 60 children. Suppose 

that this variation could be represented by the following probability distribution: 

Average hours 

inside per 

24 

22 

20 

18 

16 

day Probability 

0.2 

0.2 

0.3 

0.2 

0.1 
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12 

Carrying out the calculations of the average lead inhaled per day for each 

of the five possible values of the average number of hours spent inside per 

day, we arrive at the following distribution for the average amount of lead 

inhaled: 

Average lead 

inhaled (yg/day) 

2.05 

2.22 

2.39 

2.56 

2.73 

Probability 

0.2 

0.2 

0.3 

0.2 

0.1 

Thus, instead of having a single figure for the average amount of lead inhaled 

per day, we have a distribution. Given our assumptions, we would estimate 

that 20% of our group of children would inhale an average of 2.05 yg/day, 20% 

would inhale an average of 2.22 yg/day, and so on. 

In a similar manner, uncertainty about any of the parameters in the model 

could be introduced and included in the analysis. The calculations required 

are of the same nature as in our simple example without uncertainty. The 

number of calculations required will increase rapidly as uncertainty about 

more parameters is introduced, but this can be handled readily on a computer. 

The intent of the sample calculations in this section is to illustrate the 

level of aggregation that we recommend and to show the types of calculations 

that are involved. In the next section we discuss the assumptions in more 

detail and indicate what sort of additional information might be helpful in 

extending the model. 
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•13 

Section 3. Comments about lead exposure calculations 

This section elaborates on many of the assumptions necessary to calculate 

lead exposure. The comments will be placed in an order corresponding to the 

order in which the assumptions were necessary in the sample calculations in 

Section 2. 

DISTRIBUTION OF LEAD CONCENTRATIONS IN AIR 

Lead concentrations are only measured at selected monitors, yet one is 

concerned about exposure everywhere. Thus, assumptions are necessary about the 

lead concentrations in air everywhere. The example calculations assumed that 

the 11 monitors each represented 1/11 of the total area of exposure. However, 

two of those monitors were near battery facilities and two near lead smelters. 

We would expect that the proportions of total areas near such facilities would 

be less than 2/11 in each case. It would, therefore, seem reasonable to make 

judgments, based on data, about the percentage of the total exposure area with 

characteristics similar to each of those represented by the 11 monitor sites. 

It is important to recognize that this assumption must always be made either 

implicitly or explicitly. To assume that the monitors are completely representative of the air quality of an entire area of concern is simply one of the 

many possible assumptions about air lead concentrations. 

DEMOGRAPHIC DISTRIBUTION OF POPULATION EXPOSED 

The next key assumption would match individuals in a given population 

group with different air exposure levels. The illustration assumes that the 

651 children in the group of concern were evenly exposed to lead air concentrations representative of the 11 monitor sites. In fact, demographic data 

may indicate that certain population groups may be more likely to live in 

inner cities, and hence perhaps near battery plants or lead smelters, than 
14 

in the suburbs, which would presumably have different lead air concentrations. 

Such demographic information could be utilized in proportioning a population 

group among the lead air concentrations over the area of concern. 

PERSONAL FACTORS AFFECTING LEAD EXPOSURE 

There are a number of personal factors affecting inhaled lead exposure, 

as indicated in Step 2 of the example in Section 2. They concern the ratio 

of indoor to outdoor air quality, the amount of air inhaled, the time spent 

indoors and outdoors, and the dependence of these on seasonal factors. In the 

example calculation, we assumed these factors were the same for each of the 

individuals of the population group of concern and that they did not vary with 

the seasons. However, we could clearly make assumptions about the percentage 

of a given population spending different amounts of time indoors and outdoors 

and varying this with seasons. We could also assume a distribution on the 

ratio of indoor to outdoor air quality. The results of such assumptions, 

which could be based on various data sources, would be a probability distribution for the monthly averages of daily lead inhaled for each population group 

of interest. 

EXPOSURE FROM LEAD CONCENTRATIONS IN DUST 

The example assumed that all individuals in the population group of 

interest were exposed to the same amount of lead concentrations in dust and 

that they consumed the same amount of lead per day as a result. We might expect 

that the lead concentrations in dust would be correlated with the lead concentrations in air. Specifically, for instance, the lead concentrations in dust 

at school playgrounds near very busy streets may be much higher than elsewhere. 

These types of considerations could be taken into account along with the 

proportion of the population group of interest spending time in such locations 
15 

in order to calculate inhalation of lead in dust. Other factors, such as 

whether the parents in a household work in a lead smelter or a battery plant, 

for instance, greatly affect the lead dust in the home, as does the proximity 

of the home td such facilities. By making assumptions about the proportion of 

a given population living with different characteristics, such as proximity 

to these facilities, we could again calculate a probability distribution for 

the average daily lead consumed for a given population group. 

EXPOSURE TO LEAD DUE TO FOOD AND WATER 

In the example calculation, we assumed that all individuals in a given 

group had the same amount of lead ingested due to food and water consumption. 

By assuming a distribution for food and water consumed for a given population 

group, we would again get a probability distribution for the amount of lead 

in those products consumed. Specifically, for instance, we might expect that 

individuals eating a lot of home-grown vegetables and fruits, who also live 

near facilities emitting lead, would have much higher ingestion levels of lead. 

PERSONAL HABITS AND LEAD EXPOSURE 

One of the key personal habits affecting lead exposure is the cleanliness 

of the home. This is particularly important for small children who would crawl 

on the floor, pick up the dust on their hands, and then stick their hands in 

their mouths. Another personal habit particularly relevant to small children 

is pica. If children live in houses with lead paint on the interior walls 

or if they eat soil that happens to be relatively high in lead content, then 

naturally the amount of lead ingested increases significantly. By making 

assumptions about the proportion of a given population group with these 

personal habits, we can calculate distributions for lead exposure. 
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16 

DEPOSITION AND ABSORPTION RATES 

Assumptions must be made about the percentage of lead in air deposited 

in the lower air ways and the upper air ways, the amount of deposition in the 

upper air ways that is eventually ingested, and the respective absorption 

rates for deposition in the lower air ways and for ingested lead. Point estimates 

of each of these rates were utilized in the sample calculation. The data may 

indicate a distribution ofrates may be more appropriate for any given population 

group. The appropriateness of such assumptions should be carefully appraised 

by experts. If a distribution is used, this would result in a distribution 

of lead absorption for any given population. 

RETENTION AND EXCRETION RATES 

The same types of comments as above pertain to the excretion and retention 

rates for lead in the blood. 

LEAD EQUILIBRIUM IN THE BODY 

Assumptions are necessary about where lead is "stored" in the body and 

the amount that is stored. The criteria document has a good deal of physiological 

information on this, although expert opinion would be very helpful to complement 

that data. If point estimates are made of variables such as the manner in which 

lead is taken from the blood and stored in the bones, we will get point estimates of the blood lead concentrations for any given set of absorption rates 

in the previous information leading to blood lead. However, one may wish to 

make probabilistic assumptions, based on physiological data and expert 

judgment, about the physiological properties of a given population group with 

respect to storage of lead in the body. If so, probabilistic distribution of 

blood lead concentrations would result for any given set of variables leading 

to initial blood lead absorption. 
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17 

RELATIONSHIPS BUILT ON CORRELATED DATA 

With the correlational approach, the sample calculations assumed linear 

deterministic relationships between blood lead and inhaled lead and between 

blood lead and ingested lead from food and water sources and from dust sources. 

Although there is much uncertainty about the data, these relationships are 

deterministic. More appropriate models may account for the uncertainties 

inherent in our information about these relationships, which are perhaps 

partially due to inherent differences between the physiology of different 

individuals in a given population group. 

ADDITIVE RELATIONS FOR BLOOD LEAD CONCENTRATIONS 

The sample calculation assumed that the contribution to blood lead from 

inhaled air, food and water sources, and dust sources were additive. This 

may be a significant assumption and should be carefully appraised by the 

experts. The criteria document alludes to the possibility that there are 

natural mechanisms to reduce the blood lead content (e.g., by storing lead 

in bone) when exposure to lead is high. If such is the case, the additive 

approach to blood lead would tend to overestimate the likelihood of high concentrations of blood lead and underestimate low concentrations because of the 

compensatory actions of the body. The development of reasonable models of 

these compensatory relationships would likely heavily rely on the judgment 

of experts. 

CALCULATIONS OF DISTRIBUTIONS OF BLOOD LEAD 

Given all the discussion about assumptions in the section, one could see 

that the calculations of distributions for blood lead for a given population 

group could be very time-consuming. Basically, if uncertainties are accounted 

for in each of the variables that are important for influencing blood lead 
P.19 

18 

distributions in a given population group, the number of calculations is very 

large. However, as illustrated by the sample calculation, these calculations 

are not complex. It would be reasonable to have these calculations done on a 

small computer designed for very easy input of probability distributions on 

the variables. Prior to that, we would suggest that a sensitivity analysis 

of importance of those variables for blood lead concentrations be conducted 

using that computer model. This would likely reduce the amount of data 

necessary to get reasonable distributions for blood lead concentrations in a 

given population group. 

Adjustment for Changes in Ambient Lead Levels 

The discussion of our approach to lead exposure has been based entirely 

on the use of historical data regarding actual ambient lead levels. Changes 

in standards or in other factors (e.g., the use of leaded gasoline) would be 

expected to cause changes in ambient lead levels. This in turn would cause 

changes in exposure which would be reflected in different distributions of 

blood lead levels. In order to make appropriate adjustments in the analysis, 

we would need to make some assumptions concerning expected changes in ambient 

lead levels. For instance, what if ambient lead levels are reduced to the 

point where the largest quarterly mean reported by any of the 11 monitors is 

3 

exactly equal to 1.0 yg/m ? At one extreme, all quarterly means below 1.0 

3 3 

yg/m might remain the same and all means above 1.0 yg/m would be reduced to 

3 

1.0 yg/m . Another possibility is that all quarterly means, whether below or 

3 

above 1.0 yg/m , would be reduced to some degree. Once an assumption is made 

about the changes in the quarterly means, the analysis can proceed as before. 

It is important, however, that careful thought be given to possible changes 

in ambient lead levels. If the change is to a new standard, past data will 

not be available, and it will be necessary to rely on expert judgments about 

potential modifications in ambient lead levels. 
19 

The Role of Additional Information 

It is clear that the information in the criteria document provides an 

excellent starting point for an analysis of lead exposure. However, the information is not complete in the sense that it does not provide data regarding 

all population groups of potential interest, all locations, all possible 

combinations of relevant factors, and so on. Furthermore, in many cases it 

provides point estimates for parameters of Interest but does not provide a 

distribution to reflect the uncertainty about these parameters or the variability 

in these parameters within a particular population. Thus, for a complete 

analysis more information is needed. Perhaps a detailed analysis of past 

studies will provide some additional information, and any future data collection 

could be aimed at issues of particular interest for a lead exposure analysis. 

We believe that it is also important to obtain and use information from experts. 

Expert judgments regarding variability within a population in terms of different 

parameters, regarding adjustments necessary for changes in standards, and 

regarding other factors can be very valuable in an exposure analysis. It is 

important that any relevant data be included in the analysis and that the 

experts familiarize themselves with such data before providing their own judgments to augment the data. In areas where the data or the information from the 

experts seem shaky, it would be useful to conduct a sensitivity analysis. In 

general, of course, sensitivity analysis is useful in pinpointing aspects of 

the model that are particularly crucial in terms of their impact on the final 

output. This would be an indication of the aspects of the problem crucial in 

terms of impact on final blood lead levels. 
P.21 

20 

Section 4. Summary and Discussion 

As noted in the introduction, our intent is to make suggestions for 

developing, implementing, and documenting a rational procedure to obtain estimates of blood lead concentrations in selected population groups. Given the 

limited effort involved, the suggestions should be considered preliminary in 

nature. 

The first important question in the development of a model for exposure 

analysis concerns the appropriate level of aggregation. We feel that without 

substantially more data (which would be difficult and expensive to collect), 

it is counterproductive to disaggregate too much, into a large number of "small" 

steps or submodels. On the other hand, relating blood levels directly to air 

lead levels, with perhaps a few other variables included in the model, might 

represent too high a level of aggregation, although It might be worthwhile 

to attempt such an analysis for the sake of comparison. We recommend an 

intermediate level of aggregation, where the process is broken down into a few, 

but not too many, submodels. Specific details of the submodels might differ 

from our preliminary analysis with sample computations, but that degree of 

aggregation seems to be reasonable. 

The emphasis in this report has been on presenting a general approach to 

an exposure analysis for lead, not on spending our limited effort on an actual, 

detailed analysis. The sample calculations in Section 2 are designed to illustrate the level of aggregation we currently feel is appropriate. These 

calculations are based on limited information using mainly point estimates of 

various parameters. Except for the single illustration using indoor activity 

time, uncertainty about the parameter values and variability among the members 

of a population have not been considered in the calculations. 
21 

In Section 3 we indicate how the simple approach in Section 2 can be 

extended to generate more realistic estimates of blood lead concentrations. 

An important aspect of the extension is the explicit consideration of uncertainty 

about the parameter values and variability among the members of a population. 

This gives rise to probability distributions for the parameters and ultimately 

to a distribution of blood lead concentrations for any selected population 

group. A key issue here concerns the sources of information from which the 

probability distributions are determined. In some cases data already available 

may be used to arrive at distributions. In other cases, it will be necessary 

to solicit expert judgments and to base the distributions on any available 

data and on the judgments. A complete analysis should be dynamic in nature, 

with the nature of the available data and the experts' judgments possibly 

causing modifications in the level of aggregation and in other details of the 

model. 

In conclusion, we recommend that the experts from EPA who have worked on 

exposure analysis should first scrutinize the validity of our submodels and 

determine which parameter values can be reasonably assumed to be deterministic. 

Appropriate experts (demographers, health experts, etc.) can then be consulted 

to define ranges or probability distributions for some critical parameters. 

A simple computer program can then be written to obtain blood lead concentrations 

in selected population groups in a given city or locality using our proposed 

approach or its modified version. 
P.23 

Air quality, location, age, age of housing 

xk 

Submodel 1 

LEAD CONSUMPTION 

¥ 

Daily inhalation and ingestion of lead by 

sources (food, drinks, dust) averaged over a month 

ik i 

Submodel 2 

BLOOD LEAD CONTENT 

V 

Monthly average blood lead level 

Figure 1. General structure of model with intermediate 

level of aggregation 
Daily 

inhalation 

Daily 

ingestion > 

Month 1 

Exhaled 50% 

Deposition in 

Lower Airways 35% 

Equilibrium level 

of lead from 

previous month 

~ ' " " T absorptsipn Deposition in |7*> ,,

 r .

. .,„. rate IOC 

Upper Airways 15% 

2k 

Total Lead 

Ingested 

3E 

Total Lead absorption 

absorption 

fate 10-30% 

\ 

T*-

Excretion rate 

50-60% 

Lead 

Excreted 

V 

Lead 

Retained 

I 

Figure 2. Physiological model 
P.25 

a ir lead concentration in /•g/m (x) 

z - g(x) 

(steps 1-2) 

y = f(x) 

(criteria document) 

lead inhalation in /vg/day (z) blood lead level in /**-g/dl (y) 

Figure 3. Relationship between air lead and blood lead