p.1 

OAR Box 1112 

Prepped by Ryan Dugan 

Document Number: 

41) ll-C-5b 

Docket Number: 

A-83-22 

Printed 4/16/2008 9:12:07AM Sheet 41 of 97 
_P^2_ 

/ / 

ARGONNE NATIONAL LABORATORY 

9700 South Cass Avenue, Argonne, Illinois 60439 

DRAFT — DO NOT CITE 

ESTIMATING THE RISKS OF 

LEAD-INDUCED HEALTH EFFECTS 

by 

Thomas S. Wallsten* and Ronald G. Whitfield 

Energy and Environmental Systems Division 

Decision and System Sciences 

January 1986 

work sponsored by 

U.S. ENVIRONMENTAL PROTECTION AGENCY 

Office of Air Quality Planning and Standards 

2T- £ ~$~ tr 

*L.L. Thurstone Psychometric Laboratory, University of North Carolina, Chapel Hill 
P.3 

CONTENTS 

ABSTRACT 1 

1 INTRODUCTION 1 

1.1 Overview 2 

1.2 Motivation 3 

1.3 Judgmental Probability Encoding 7 

1.4 Risk Assessment Strategy 9 

1.5 Dose-Response Uncertainty 10 

2 PROBABILISTIC DOSE-RESPONSE RELATIONSHIPS FOR LEAD-INDUCED 

ELEVATED ERYTHROCYTE PROTOPORPHYRIN LEVELS 11 

3 PROBABILISTIC DOSE-RESPONSE FUNCTIONS FOR LEAD-INDUCED 

HEMOGLOBIN DECREMENTS 17 

3.1 Protocol Development 18 

3.2 Protocol Outline 18 

3.3 Conduct of the Sessions • 20 

3.4 Encoding the Judgments 21 

3.5 Representing the Judgments 24 

3.6 The Experts 26 

3.7 Results 28 

3.7.1 Hemoglobin Levels < 11 g/dL, Ages 0-3 Years 28 

3.7.2 Hemoblobin Levels < 11 g/dL, Ages 4-6 Years 32 

3.7.3 Hemoglobin Levels < 9.5 g/dL, Ages 0-3 Years 35 

3.7.4 Hemoglobin Levels <_ 9.5 g/dL, Ages 4-6 Years 38 

3.8 Discussion 38 

4 PROBABILISTIC DOSE-EFFECT AND DOSE-RESPONSE RELATIONSHIPS FOR 

LEAD-INDUCED IQ DECREMENTS 42 

4.1 Protocol Development 46 

4.2 Protocol Outline 47 

4.3 Conduct of the Sessions 48 

4.4 Encoding the Judgments 49 

4.5 Representing the Judgments 50 

4.6 The Experts 52 

4.7 Results 52 

4.7.1 Control Group Mean IQ 53 

4.7.2 Within-Group IQ Standard Deviation 55 

4.7.3 Mean IQ Decrements for the Low SES Group 55 

4.7.4 Mean IQ Decrements for the High SES Group 60 

4.7.5 Change in Percentage of Low SES Group with IQs < 85 60 

4.7.6 Change in Percentage of High SES Group with IQs < 85 63 

4.8 Discussion 66 

t n 
CONTENTS (Cont'd) 

5 ESTIMATED RISKS OF ADVERSE HEALTH EFFECTS UNDER ALTERNATIVE 

AIR-LEAD SCENARIOS 67 

5.1 Exposure Estimates 67 

5.2 Risk Results for EP 73 

5.3 Risk Results for Hemoglobin 78 

5.4 Risk Results for IQ 84 

5.4.1 Expected IQ. Decrement 85 

5.4.2 Increased Probability of Lead-Induced IQ Levels 

Being < IQ* 88 

REFERENCES 95 

APPENDIX A: Fitting Functions to Data on Lead-Induced Elevated 

Erythrocyte Protoporphyrin Levels 96 

APPENDIX B: Hemoglobin 99 

APPENDIX C: Intelligence Quotient 150 

APPENDIX D: Risk Estimates 205 

TABLES 

1.1 Illustrative Risk Output for a Specified Health Effect Given Full 

Information 6 

1.2 Illustrative Risk Output for a Specified Health Effect Given Incomplete 

Information 8 

2.1 Sample Sizes Based on Blood-Lead Level for Piomelli's Data 14 

3.1 Consultants for the Hemoglobin Protocol 19 

3.2 Experts Who Participated in the Hemoglobin Encodings 27 

4.1 Consultants for the IQ Protocol 44 

4.2 Experts Who Participated in the IQ Encodings 45 

5.1 1980 Population Data for Selected U.S. Point Sources of Lead 

Emissions 69 

5.2 Comparative Air Quality at Census Tract Centroids Surrounding 

Modeled Point Sources 70 

5.3 Geometric Mean Blood-Lead Levels for 84-Month Cohorts 74 

I V 
TABLES (Cont'd) 

A.l Probability Distributions and Parameters for Piomelli's Data on 

Erythrocyte Protoporphyrin Levels among New York City Children 98 

B.l Summary of Variables Pertaining to the Normal-On-Log-Odds Function 117 

B.2 Encoded Probability Judgments of Experts Regarding Lead-Induced 

Hemoglobin Decrements 120 

B.3 Summary of Functions Fit to the Probabilistic Judgments of Experts 

Regarding Lead-Induced Hemoglobin Decrements 124 

B.4 Summary and Comparison of Judgments and Fitted Functions Concerning 

Lead-Induced Hemoglobin Decrements 129 

C l Encoded Judgements about the Mean IQ of Children Sheltered from 

Lead Exposure 169 

C.2 Encoded Judgements about Population Standard Deviation 170 

C.3 Encoded Judgements about Mean IQ Decrements of Children Exposed 

to Lead 171 

C.4 Parameters of Functions Fit to the Probabilistic Judgments of 

Experts Regarding Mean IQ Levels among Children Sheltered from 

Lead Exposure 177 

C.5 Summary of Functions Fit to the Probabilistic Judgments of Experts 

Regarding Population Standard Deviation for IQ Levels 178 

C.6 Summary of Function Fit to the Probabilistic Judgments of Experts 

Regarding Mean IQ Decrements among Children Exposed to Lead 179 

C.7 Summary and Comparison of Judgments and Fitted Functions Concerning 

Lead-Induced IQ Effects 182 

D.l Upper- and Lower-Bound Estimates of the Geometric Mean Blood-Lead Levels 

Children Living around Selected U.S. Sources of Lead Emissions 206 

D.2 Specification of Distributions for the Risks of Elevated EP Levels 

among Children Ages 0-6 Years 208 

D.3 Summary of Hemoglobin Risk Distributions for Children Aged 0-3 

Years 210 

D.4 Summary of Distributions for Expected IQ Decrement at Age 7 for 

Lower SES Populations of Children 222 

D.5 Summary of Distributions for Increased Probability of IQ^IQ* at Age 7 

for Lower SES Populations of Children 227 
P.6 

FIGURES 

2.1 Mean Response Rate vs. Dose for EP Levels >_ 33 yg/dL and 53 yg/dL 13 

2.2 Median Response Rate and 90% Credible Interval vs. Dose for 

EP = 33 yg/dL 15 

2.3 Median Response Rate and 90% Credible Interval vs. Dose for 

EP = 35 yg/dL 16 

3.1 Dose-Response Functions, Hemoglobin Level ±11 g/dL, 

Ages 0-3 Years 29 

3.2 Comparison of Judgments, Hb 5 11 g/dL, Ages 0-3 Years 31 

3.3 Dose-Response Functions, Hemoglobin Level <_ 11 g/dL, 

Ages 4-6 Years 33 

3.4 Comparison of Judgments, Hb <_ 11 g/dL, Ages 4-6 Years 34 

3.5 Dose-Response Functions, Hemoglobin Level <_ 9,5 g/dL, 

Ages 0-3 Years 36 

3.6 Comparison of Judgments, Hb < 9.5, Ages 0-3 Years 37 

3.7 Dose-Response Functions, Hemoglobin Level <_ 9.5 g/dL, 

Ages 4-6 Years 39 

3.8 Comparison of Judgments, Hb < 9.5, Ages 4-6 Years 40 

4.1 Judgments about Control Group Mean IQ 54 

4.2 Judgments about O,Q 56 

4.3 Judgments about A— for a Lower SES Population 57 

4.4 Comparison of Judgments about A— for a Lower SES Population 59 

4.5 Judgments about A— for a Higher SES Population 61 

4.6 Comparisons of Judgments about A— for a Higher SES Population 62 

4.7 Increased Probability of Having IQ < 85 for a Lower SES Population 64 

4.8 Blood-Lead Level Comparison of Increased Probabilities of Having 

IQ < 85 for a Lower SES Population , 65 

5.1 Response Rate, %, with EP > 33 yg/dL 76 

5.2 Response Rate, %, with EP > 53 yg/dL 77 

5.3 Point Source 5, with Hb < 11 yg/dL 79 V I 
P.7 

FIGURES (Cont'd) 

5.4 Point Source 5, with Hb < 9.5 yg/dL 80 

5.5 Point Source 2, with Hb < 11 yg/dL 81 

5.6 Point Source 2, with Hb < 9.5 yg/dL 82 

5.7 Expected IQ Decrement for Lower SES Children Living around 

Source 5 86 

5.8 Expected IQ Decrement for Lower SES Children Living around 

Source 2 87 

5.9 Increased Probability of Children Living around Source 5 Having 

IQ Levels £ 70 90 

5.10 Increased Probability of Children Living around Source 5 Having 

IQ Levels < 85 91 

5.11 Increased Probability of Children Living around Source 2 Having 

IQ Levels < 70 92 

5.12 Increased Probability of Children Living around Source 2 Having 

IQ Levels < 85 93 

V l l 
P.8 

ESTIMATING THE RISKS OF 

LEAD-INDUCED HEALTH EFFECTS 

by 

Thomas S. Wallsten and Ronald G. Whitfield 

ABSTRACT 

to be completed. 

1 INTRODUCTION 

The Clean Air Act charges the U.S. Environmental Protection Agency (EPA) with 

setting and reviewing both primary and secondary National Ambient Air Quality 

Standards (NAAQS) for selected pollutants. Each primary standard must be set at a level 

sufficient to protect public health with an adequate margin of safety. This report 

presents the results of a risk assessment performed to assist in the review of the primary. 

NAAQS for lead. 

For each review, the scientific basis for revising the primary lead NAAQS is 

presented in an updated document entitled Air Quality Criteria for Lead, hereafter 

referred to as the criteria document (CD). It summarizes and evaluates available 

scientific evidence about the adverse health effects of lead. An EPA staff paper is then 

written, which considers the information in the CD in specifying the elements EPA staff 

members believe to be critical in revising the lead NAAQS. The staff paper is intended 

to bridge the gap between the science presented in the CD and the information needed by 

the EPA Administrator in setting a new ambient standard for lead. Particular attention 

is paid to those areas where judgments must be based on careful interpretation of 

imperfect evidence. Indeed, to provide the required adequate margin of safety, 

uncertainty must be taken into consideration at each step of the process. 
P.9 

Scientific uncertainty was handled in a highly simplified manner when the 1978 

air-lead standard was set. Instead of quantifying uncertainty, deterministic assumptions 

were made that were considered conservative given qualitative assessments of the 

uncertainty associated with available evidence. Calculations based on these assumptions 

resulted in a primary lead NAAQS of 1.5 yg Pb/m° of air. 

Soon thereafter EPA's Office of Air Quality Planning and Standards (OAQPS) 

began exploring methods of risk assessment that incorporated uncertainty in the 

standard-setting process in a formal, defensible, and open manner. This report presents 

the outcome of formal risk assessments regarding three adverse health effects of lead to 

aid the EPA Administrator in determining an adequate margin of safety for the current 

review of the primary lead NAAQS. This work was funded by EPA under an Interagency 

Agreement between EPA and the U.S. Department of Energy. 

Of the many potential adverse health effects associated with exposure to lead, 

EPA's OAQPS selected three for inclusion in this risk assessment: hemoglobin 

decrement, elevated erythrocyte protoporphyrin (EP) levels, and intelligence quotient 

(IQ) decrement. It was decided to limit the population at risk for this risk assessment to 

all U.S. children from birth through their seventh birthdays. Pregnant women (fetus), 

who are particularly sensitive to lead, are not explicitly included in this analysis. 

1.1 OVERVIEW 

To the extent possible, details of the methods and results of the risk assessments 

are presented in appendixes rather than in the body of this report. Nevertheless, readers 

will obtain a good understanding of the risk assessments from the main text. Section 1.2 

presents the motivation for the particular form of the risk assessments that were carried 

out. Section 1.3 discusses the role of judgmental probability encoding in the risk 

assessment. Section 1.4 summarizes the overall risk assessment strategy, while Sec. 1.5 

discusses dose-response uncertainty. 
P.10 

Section 2 treats the dose-response uncertainty for lead-induced elevated EP 

levels. Because relatively complete data are available, judgmental probability encoding 

was unnecessary in considering lead-induced changes in EP level. Sections 3 and 4 focus 

on dose-response uncertainty for lead-induced hemoglobin and IQ decrements, 

respectively. Judgmental probability encoding was required in these cases; the encoding 

procedures are described in the respective sections prior to the summaries of the results. 

Section 5 discusses possible blood-lead* (PbB) distributions and their levels of 

uncertainty under alternative NAAQS. The uncertainty for each health effect is then 

combined with that for each alternative PbB distribution to yield derived risk 

estimates. The report concludes with four appendixes. 

1.2 MOTIVATION 

The purpose of a risk assessment for lead health effects is to estimate 

probability distributions over fractions of the population at risk that would suffer 

specific, well-defined health effects under alternative primary NAAQS for lead. The 

probabilities must be estimated in a formal, defensible manner that is open to public 

scrutiny. They will generally reflect two sources of uncertainty, one deriving from the 

characteristics of the data and the other from a lack of knowledge. The former type of 

uncertainty reflects measurement and sampling error, and probabilities are generally 

calculated by means of standard statistical procedures. Although this type of 

uncertainty can be altered by means of experimental manipulations, it cannot be 

eliminated completely in any finite study. 

The latter type of uncertainty reflects the paucity, incompleteness, and indirect 

nature of much of the available data. For example, it is frequently necessary to draw 

inferences about a health effect in a specific population on the basis of epidemiological 

•Blood lead is generally used as the index of lead exposure in health studies and is used in 

this way in this assessment. 
or clinical data on different populations under varying or different exposure conditions, 

or from laboratory data on other species or on in vitro preparations. This type of 

uncertainty is judgmental, and no statistical techniques exist for quantifying it. It can, 

however, be quantified using appropriate procedures to encode subjective probabilities. 

Different experts will assess the uncertainty differently, depending on their faith in the 

implicit or explicit theories required for extrapolation from the data to the effect in 

question and on their perception of the distance over which the extrapolation must be 

made. Therefore, it is necessary that the procedures accommodate and represent a 

possible divergence of judgments. The level of this type of uncertainty, as well as the 

degree of divergence among experts, can be reduced, and conceivably even eliminated, 

by increasing the amount of available knowledge. 

Conducting a risk assessment in which these two types of uncertainty are 

distinguished provides one means for responding to a challenge issued by William 

Ruckleshaus in a speech given at Princeton University when he was EPA Administrator. 

He stated: 

If I am going to propose controls that may have serious economic and 

social effects, I need to have some idea of how much confidence should 

be placed in the estimates of risk that prompted those controls 

(Ruckleshaus, 1984, p. 158). 

In the same talk, he went on to propose some principles for reasonable discussions about 

risk: 

First, we must insist on risk calculations being expressed as 

distributions of estimates and not as magic numbers that can be 

manipulated without regard to what they really mean. We must try to 

display more realistic estimates of risk to show a range of 

probabilities. To help do this, we need new tools for quantifying and 

ordering sources of uncertainty, and for putting them in perspective. 
P.12 

Second, we must expose to public scrutiny the assumptions that 

underlie our analysis in management of risk (Ruckleshaus, 1984, p. 158). 

If there were complete information relevant to a given health effect in a 

population, then the statistical uncertainty could be represented by a single probability 

distribution for each alternative NAAQS under consideration. A hypothetical example of 

a risk assessment output of this type is given in Table 1.1.* For example, in this 

hypothetical situation, the probability is 0.01 that fewer than 0.5% of the population will 

suffer the health effect, the probability is 0.05 that fewer than 1% of the population will 

suffer it, and so forth. (Equivalently, the probability is 0.99 that more than 99.5% of the 

population will not suffer the health effect, 0.95 that more than 99% will not suffer it, 

etc.) Alternative NAAQS 4 provides the greatest degree of protection. 

Presumably, output of this sort would be helpful to the EPA Administrator in 

selecting a standard that in his or her judgment would protect the public health with an 

adequate margin of safety. For example, if he or she determined that the intent of the 

Clean Air Act is met by protecting 99.5% of the population at risk with probability 0.99, 

then alternative 1 would be selected. If the intent is met by protecting 99.5% of the 

population with probability 0.95, then alternative 2 is the appropriate one. Of course, 

this example is highly simplified because multiple health effects will generally be of 

interest, and populations can be defined in various ways. However, it illustrates the role 

that formal risk analysis can play in the standard-setting process. 

Generally, the information relevant to a particular health effect associated with 

an environmental agent will be indirect and incomplete, and experts will differ with 

regard to the associated judgmental uncertainty. The extent of agreement across 

experts is a measure of how firm the probability estimates are, and is useful information 

in setting the standard. 

One way of representing the extent of agreement is to propagate the encoded 

probabilities of each expert through the entire analysis, which results in a family of 
P.13 

TABLE 1.1 Illustrative Risk Output for a Specified 

Health Effect Given Full Information 

Response 

R0 

0.5% 

1.0Z 

1.5% 

Rate 

Probabi 

1 

0.01 

0.05 

0.41 

lity (Res ponse Rate 

NAAQS Alternative 

2 

0.06 

0.11 

0.53 

3 

0.19 

0.23 

0.6A 

± v 

4 

0.38 

0.60 

0.75 
P.14 

7 

distributions under each alternative NAAQS. A hypothetical example in this case is 

shown in Table 1.2. Under alternative 1, for example, there is a 0.01 to 0.02 probability 

that fewer than 0.5% of the population will suffer the health effect. The closer together 

are the distributions in a family, the more firm are the probability estimates. 

In setting the NAAQS, the degree of firmness in the estimates can be taken into 

account in any of a number of ways. For example, one criterion might be that 99.5% of 

the population be protected with a probability whose lower bound is no less than 0.01 or 

with a probability estimated to be 0.02 in at least, for example, 75% of the risk 

distributions. 

On a less formal level, the probability encoding of each expert can be 

accompanied by a discussion of the relevant data. Summaries of these discussions can be 

an important supplement to the probability distributions and provide guidance on their 

use. 

The risk assessments in this report yield outputs similar to those in Table 1.2 plus 

associated discussions. However, while endeavoring to make the outputs fully 

interpretable, we do not presume to suggest the criteria that should govern their use in 

the standard-setting process. 

1.3 JUDGMENTAL PROBABILITY ENCODING 

We wish to emphasize that subjective probability encoding is unnecessary 

whenever adequate, direct data are available. However, more often than not, such data 

are not available, and the only alternatives to encoding judgmental probabilities will be 

to treat the added uncertainty qualitatively, which currently cannot be done in a rigorous 

manner, or to ignore it altogether, which is indefensible. 

For encoded judgmental probabilities to be useful, they must meet two criteria. 

The first is subtle, and itself judgmental, but is nevertheless very important; namely, 

judgments must be obtained from respected experts who span the range of respected 
P.15 

TABLE 1.2 Illustrative Risk Output for a Specified Health 

Effect Given Incomplete Information 

Response 

R 0 

0.5% 

1.0% 

1.5% 

Rate 

Probability (Res 

1 

0.01-0.02 

0.01-0.05 

0.29-0.41 

ponse Rate < 

NAAQS Alternative 

2 

0.02-0.06 

0.04-0.11 

0.40-0.53 

3 

0.11-0.19 

0.15-0.23 

0.53-0.64 

R0) 

4 

0.26-0.38 

0.49-0.60 

0.68-0.75 
P.16 

opinion. Although it would appear to be difficult to establish what the range of opinion is 

and who the appropriate experts are, in practice the relevant issues tend to be debated 

frequently and publicly enough that such decisions are possible. 

For the present risk assessments, EPA's OAQPS selected the experts whose 

judgments were to be encoded. Although their names are included with the assessment, 

their individual judgments and discussions are identified by code letter only. Thus, users 

of the risk assessments can decide whether the full range of opinion is represented, and 

the individual experts can feel free to give their best responses without worrying that 

they may involve themselves in endless arguments or discussions with others who may 

disagree. 

The second criterion is that an individual's encoded probability judgments must 

be stable over time (barring new information), coherent in a well-defined way, and 

accurately represent his or her uncertainty. Research relating to these issues has been 

reviewed by Wallsten and Budescu (1983), and an experiment specifically addressing them 

in the present context was performed by Wallsten et al. (1983). The techniques used in 

the present work were based on this foundation but also relied on pilot work described in 

Whitfield and Wallsten (1984). 

1.4 RISK ASSESSMENT STRATEGY 

The strategy employed in this analysis is most easily understood by first assuming 

that no uncertainty is involved. In this case, one first specifies the dose-response curve 

for each selected health effect of lead. For a well-defined population, well-defined 

exposure conditions, and a well-defined physiological or behavioral effect, a doseresponse curve plots the percentage of the population exhibiting the effect as a function 

of dose level. This function is assumed to be unaffected by alternative air-lead 

scenarios. However, the alternative scenarios do determine the distribution of dose 

levels in the population. Thus, one can combine the dose-response function for a health 
P.17 

10 

effect with the dose distribution under each alternative scenario to yield the percentage 

of the population that would suffer the effect under that alternative scenario. In reality, 

there is uncertainty at each step, and it must be incorporated into the analysis in a 

manner providing final outputs of the form shown in Table 1.1 or 1.2. 

1.5 DOSE-RESPONSE UNCERTAINTY 

In addition to the two types of uncertainty discussed in Sec. 1.2, there is 

ambiguity regarding the level of an effect that should be considered adverse and for 

which a dose-response function would be of interest. This issue was dealt with in the 

present work by simply selecting two levels of the relevant variable for each health 

effect and estimating a dose-response function for each. The levels were selected so as 

to span the range that arguably delimits normal from adverse consequences. 

It must be emphasized that a population dose-response function exists for a given 

effect under specified conditions. When relatively complete data are available regarding 

the dose-response function of interest, the population values are still uncertain because 

of sampling and measurement error. Because this was the case with elevated EP levels, 

a straightforward application of the appropriate probability distributions to the data 

yielded the desired results (see Sec. 2). However, when the data regarding the doseresponse function of interest are incomplete or indirect, then there is judgmental 

uncertainty associated with extrapolation (see Sec. 1.3). This was the case with both the 

hemoglobin and IQ decrements. Because unique factors were associated with each of 

these instances, the procedures and models employed for quantifying the uncertainty 

were different. 
P.18 

11 

2 PROBABILISTIC DOSE-RESPONSE RELATIONSHIPS FOR LEAD-INDUCED 

ELEVATED ERYTHROCYTE PROTOPORPHYRIN LEVELS 

Piomelli et al. (1982) examined PbB and EP levels from 2004 New York City 

children ages 2 to 12 years, who had been screened to account for the effects of iron 

deficiency and other confounding variables. Empirical dose-response curves were 

presented for two levels of EP elevation; in each case, the percentage of the sample with 

EPs above the critical level was plotted as a function of PbB level. Our consultants felt 

that the population from which the sample was drawn was sufficiently close to the 

population of interest (children up to their seventh birthdays) that extrapolation was not 

necessary. The data were used directly.* 

Because of the very careful procedures employed by Piomelli et al. (1982), it is 

necessary to consider only sampling, and not measurement, error. Each of the points on 

a dose-response function is based on a number of observations (N) , of which X exhibit 

the health effect and the remainder (N - X) do not. These data provide an estimate P of 

the true population proportion P suffering the health effect at the PbB level in 

question. Of course, uncertainty is associated with the estimate because of sampling 

error. In classical probability theory, this uncertainty is handled by using the binomial 

distribution with parameters P, X, and N to calculate confidence intervals around P as an 

estimate of P, or more generally to calculate a probability distribution over P. Thus, the 

output is a probability distribution over the percentage of the population affected at 

each observed PbB level. 

The Bayesian approach is to calculate a posterior probability distribution over P, 

given the data and a prior distribution over P. When the prior distribution is represented 

as a beta distribution with parameters a and b, then the posterior distribution is also 

•Similar data were collected by Hammond et al. (1985) on a sample from a different 

population of children. The dose-response functions were very similar to those obtained 

by Piomelli et al. (1982), but certain nonindependencies in the data due to their 

longitudinal nature made them unsuitable for the present purpose. 
P.19 

12 

beta, but with parameters a + X and b + (N - X). A conservative strategy is to assume a 

diffuse prior state of information characterized by a = b = 0 (Winkler, 1972). In this case, 

the resulting probability distribution over the fraction of the population affected at a 

given PbB level is very close to that calculated in the classical manner. Technically, 

however, the interpretation is different, and the Bayesian approach used is the one most 

suitable for our purposes. Further details are provided below and in App. A. 

Figure 2.1 presents the dose-response data for two EP levels (Piomelli et al., 

1982), and Table 2.1 presents the sample-size data. The two EP levels (33 yg/dL and 53 

yg/dL) were each considered as adverse. Expressions can be determined for the mean 

dose-response curves that are shown. These expressions, listed in App. A, are functions 

of PbB level and what Piomelli et al. call "natural frequencies" for the occurrence of EP 

levels above 33 yg/dL and 53 yg/dL, and involve the normal probability distribution 

function. 

As discussed above, the beta distribution is the proper distribution to use to 

describe uncertainty about the true population proportion suffering from elevated EP 

levels. However, for PbB levels above 5 yg/dL and below 50 yg/dL, sample sizes are 

large enough that the normal distribution can be used to closely approximate beta 

distributions for both EP levels. Table A.l in App. A summarizes the probabilistic doseresponse functions that were derived. 

Figures 2.2 and 2.3 show median dose-response relationships and 90% credible 

intervals for the 33 yg/dL and 53 yg/dL EP levels, respectively. For all cases in which a 

normal approximation is adequate, median and mean response rates are identical, and 

confidence intervals are symmetrical about the median values. The median value is that 

response rate at which it is equally likely that the actual rate is above or below it. There 

is a probability of 0.05 that the population response rate is below the credible interval 

range and a probability of 0.05 that it is above it. 
P.20 

13 

cn 99H 

In 95-

<1> o 

* " w . Al 

Q_ 0) 

•V) > 

90H 

75-

50-| 

25^ 

? 10* 

> 

D 

JZ 

5-4 

H 

10 20 30 40 

Blood-Lead Level (yiig/dL) 

50 

FIGURE 2.1 Mean Response Rate vs. Dose for EP Levels > 33 yg/dL and 53 yg/dL 

(Source: Adapted from Piomelli et al., 1982) 
I I '.» 11 II -p I* JH""*-*-

P.21 

14 

TABLE 2.1 Sample 

Sizes Based on 

Blood-Lead Level 

for PiomeUi's Data 

PbB 

(yg/dL) 

0-10 

10-20 

20-30 

30-40 

40-98 

No. of 

Children 

131 

1177 

544 

109 

43 

Source: Seaman, 

personal communication (1985). 
15 

99-

rj) 

^. 95-

2% 90" 

C§AI 

tn 75-

C > 

^ o> 25-

> 

D 10* 

H 

90% 

Credible 

Interval 

Median 

10 20 30 40 50 

Blood-Lead Level (jug/dL) 

FIGURE 2.2 Median Response Rate and 90% Credible Interval vs. Dose for 

EP = 33 yg/dL 
16 

P.23 

99-

3. 95-

2% 90" 

C?AI 

• » 75 " 

c > 

*i

 50

-

Q)LlJ 

CC rj) 25. 

• — 

J 10-

fc* 5-

/ 90% 

/ /) Credible 

Interval 

Median 

10 20 30 40 50 

Blood-Lead Level (/xg/6L) 

FIGURE 2.3 Median Response Rate and 90% Credible Interval vs. Dose for 

EP = 53 yg/dL 
P.24 

17 

3 PROBABILISTIC DOSE-RESPONSE FUNCTIONS FOR 

LEAD-INDUCED HEMOGLOBIN DECREMENTS 

Data are very incomplete regarding dose-response functions for lead-induced 

hemoglobin decrement in the full population of U.S. children prior to the seventh 

birthday. Therefore, it was necessary to encode experts' subjective probabilities about 

the population response rates at each of several PbB levels. Encoded probabilities have 

to meet two criteria. One is that they be internally consistent by specific criteria that 

will be specified shortly. The other is that they are satisfactory to the experts in the 

sense that they agree that the encodings properly represent their judgments. 

Only a finite number of PbB levels can be presented for encoding; in this study 

the number was about six. However, it is necessary to interpolate between levels to use 

the judgments in the risk assessments. Such interpolations can be made by fitting a 

suitable probability distribution to the encoded values. The distribution must fit the 

judgments by a reasonable mathematical criterion, but equally importantly, the expert 

must agree that the function is accurate. 

To meet all these requirements and to follow the recommendations developed by 

Wallsten et al. (1983), we developed a protocol for the probability encodings and then 

met with each expert on two occasions separated by about one month. Judgments were 

encoded during the first session, and functions were fit to them prior to the next visit. 

The judgments and functions were reviewed during the second session, and changes were 

made that were deemed necessary by the expert. When required, there was additional 

follow-up through the mail and by phone. 

Section 3.1 describes the protocol development, and Sec. 3.2 outlines the 

protocol itself. The manner in which the encoding sessions were conducted, the 

probability encoding methods, and the procedures for fitting functions to the encoded 

judgments are described in Sees. 3.3, 3.4, and 3.5, respectively. Section 3.6 indicates 

whose judgments were encoded, Sec. 3.7 summarizes the results, and Sec. 3.8 provides 

some summary discussion. 
P.25 

18 

3.1 PROTOCOL DEVELOPMENT 

The consultants listed in Table 3.1 aided us in developing the hemoglobin 

probability encoding protocol. Their assistance took many forms, including discussing the 

literature with us, guiding us in reading key studies, and carefully commenting on 

numerous drafts of the protocol. 

After studying relevant portions of the CD and discussing them at length with a 

subset of our consultants, who for the most part were the authors of those portions, we 

prepared a first draft of the protocol. This draft was shown to those experts as well as 

to others who were drawn from the population of people whose judgments might be 

encoded. We worked with these experts, structuring the problem in the manner we would 

if we were going to encode their judgments, and revised the protocol accordingly. 

In this fashion, the protocol went through a number of drafts. If all the 

respondents viewed the problem in the same way, this way was specified in the 

protocol. If they differed or indicated that others might differ from them, we allowed 

the individual to individualize the scenario, subject only to the constraints that the 

obtained judgments could map into the rest of the model and be comparable across 

experts. The protocol was ultimately structured such that the consultant health experts 

considered it reasonable and indicated that they would feel comfortable providing the 

desired probabilistic judgments. 

The protocol was tested by using it to encode the judgmental probabilities of two 

members of the EPA staff familiar with the effects of lead. The test was considered 

successful and is reported in Whitfield and Wallsten (1984). 

3.2 PROTOCOL OUTLINE 

The full protocol is presented in App. B; only a general outline is provided here. 

Section 1, the introduction, indicates what we were attempting to do and why. Sections 
P.26 

19 

TABLE 3.1 Consultants for the Hemoglobin Protocol 

Consultants Affiliation 

Dr. Julian Chisolm John F. Kennedy Institute 

Johns Hopkins University 

Mr. Jeff Cohen OAQPS,a U.S. EPA 

Dr. Anita Curran Westchester County 

Dept. of Health 

Mr. Thomas Feagans OAQPS, U.S. EPA 

Dr. Lester Grant Environmental Criteria 

Assessment Office, U.S. EPA 

Mr. John Haines OAQPS, U.S. EPA 

Dr. Paul Hammond Dept. of Environmental Health 

University of Cincinnati 

Mr. Robert Kellam OAQPS, U.S. EPA 

Dr. Paul Mushak Department of Pathology 

University of North Carolina 

Office of Air Quality Planning and Standards. 
P.27 

20 

2-5 specify the parameters of the problem, so that the dose-response functions are well 

defined. Section 6 raises various points in the literature for discussion. Sections 7 and 9 

discuss the process of probability encoding. Section 8 deals peripherally with hemoglobin 

decrement and raises issues concerning possible adverse health effects associated with 

elevated EP levels. 

More specifically, Sec. 2 defines adverse hemoglobin levels as 9.5 g/dL and 

11 g/dL, thereby bracketing the range of interest. Thus, judgments were encoded for two 

sets of dose-response functions. Section 3 defines the population at risk for encoding as 

all United States children from conception through their seventh birthday. However, the 

experts were given the option of considering separately the age groups 0-3 and 4-6 years 

if they thought for any reason that the two groups would have different dose-response 

functions. Therefore, experts who exercised this option had their probabilistic judgments 

encoded for four dose-response relationships. 

Section 6 elicits discussion from the expert on relevant theories and data. This 

step helped ensure that the problem was structured properly, that the expert consciously 

reviewed his or her knowledge prior to providing probability judgments, and that a 

possible basis for understanding any discrepant judgments was provided. 

Sections 7 and 9, which cover the probability encoding, were derived from our 

prior work on encoding probability judgments about dose-response functions (Wallsten et 

al., 1983). Section 7 provides suggestions on how to minimize biases in probability 

encoding, whereas Sec. 9 discusses the intended probability encoding procedure. 

3.3 CONDUCT OF THE SESSIONS 

All sessions were conducted during the winter of 1984-1985. Sections 1-8 of the 

protocol were sent to each expert before the scheduled review. The protocol was then 

used to guide discussion and interaction during the sessions. 
P.28 

21 

Approximately one to three hours was spent at the beginning of the first session 

discussing the material in Sees. 2-6 of the protocol. The concepts in Sec. 7 were then 

discussed and illustrated, after which the probability encoding began. (The experts were 

not required to read Sec. 9 of the protocol; it simply constituted a record of what we 

were doing.) The actual encoding took about four to six hours. 

The second session took place four to six weeks after the first session and lasted 

from two to four hours. It included a review of the summaries of the previous session, 

which had been sent in the mail; additional probability encoding as necessary; and 

discussion of the material in Sec. 8 of the protocol. 

3.4 ENCODING THE JUDGMENTS 

Probability encoding began in session 1 after the relevant literature and the 

factors determining the dose-response function had been thoroughly discussed with the 

expert. The intention was to encode probability judgments for possible response rates at 

PbB levels of 5, 15, 25, 35, 45, and 55 yg/dL. Higher PbB levels were employed with one 

expert. 

To determine useful points in the dose-response space for encoding probabilities, 

each expert was first asked to supply broad "99% confidence interval" ranges for possible 

response rates at each of the PbB levels. We helped the expert determine these ranges 

by posing suitable questions. For example, after a range was specified, we asked whether 

the expert could construct a plausible explanation if some day it were found that the true 

value fell outside that range. 

For most of the experts, probabilities were encoded using a probability wheel. 

For this purpose, the range of possible response rates for each PbB level was divided into 

five equal intervals for detailed encoding at six points. For example, if the response-rate 

range at a particular PbB level was 0.2-0.7, subsequent encodings were recorded at 0.2, 
P.29 

22 

0.3, 0.4, 0.5, 0.6, and 0.7. If during the encoding process it became apparent that other 

points either inside or outside the range were important, they were incorporated. 

Blood-lead levels were presented for encoding in a random order; for a particular 

PbB level, response rates were also presented in a random sequence. Probabilities were 

encoded for all response rates at a given PbB level before moving on to the next PbB 

level. 

The probability wheel used for the encoding is radially divided into two sectors of 

adjustable relative areas — one orange and one blue. The wheel can be spun so that it 

randomly stops with either sector under a pointer. For a particular response rate R at a 

given PbB level L, the wheel was set at some relative area of blue, and the expert was 

asked to consider the following question: 

Is it more probable that the true response rate at blood-lead level L is 

less than R, or that a random spin the wheel would stop with the 

pointer on blue? 

Thus, the expert was asked to weigh two probabilities and decide which was greater. The 

expert's answer determined whether the proportion of blue was increased or decreased, 

and the question was posed again. This procedure was continued until the wheel was set 

such that the expert considered it equally likely that the wheel would randomly land on 

blue as that the true response rate was less than R for PbB level L. The relative area of 

blue was then provisionally taken as the judged cumulative probability F(R|L). The 

procedure was repeated for the required response rates until an entire cumulative 

probability distribution over R for 0 < R < 1.0 had been encoded for a PbB of L. 

If after a period of time the expert did not become comfortable with the 

probability wheel, an encoding method based on successive intervals and hypothetical 

bets was used. In this case, a cumulative subjective probability of F(R|L) = 0.50 was first 

encoded by having the expert specify a population response rate R for the PbB level 

under consideration such that if a bet were made such that the payoff depended on 
P.30 

23 

whether the true response rate turned out to be above or below R, the expert would be 

indifferent as to which bet he held. In other words, the expert specified a response rate 

such that in his or her judgment it was equally likely that the true rate is above as below 

it. Frequently, it turned out that the expert was not indifferent between the two sides of 

the bet and that with a little more effort it was possible to find a response rate at which 

he or she was. 

Having determined the response rate corresponding to a subjective probability of 

0.50, the expert was then asked to imagine that in fact the necessary research had been 

done, that the true response rate was now known, and that it was greater than the value 

he had just indicated. (On half the occasions at this point, he or she was to imagine that 

the true response rate was less than that earlier specified.) Given that the true rate was 

greater than that which had been indicated, a new response rate R was to be specified 

for a new bet such that the expert would be indifferent as to whether his payoff 

depended on the true population response rate being above or below it. Once such a 

value was determined, this corresponded to a subjective probability of F(R|L) = 0.75. In 

this manner, response rates corresponding to subjective probabilities of 0.25, 0.50, and 

0.75 were encoded. Response rates corresponding to subjective probabilities of 0.01 and 

0.99 were also determined by imagining bets with 1:99 and 99:1 odds. 

After the cumulative probability distribution over response rate was encoded for 

a given PbB level, regardless of the encoding method employed, the distribution was 

graphed and shown to the expert for discussion. Any inconsistencies were pointed out 

and resolved. Such inconsistencies appeared as dips in the graphs, which should rise 

monotonically as the response rate goes from 0 to 1 (see Wallsten et al., 1983, for 

details). 

The implications of the encoded distributions were also discussed. For example, 

for R, > Rj, F(RJ|L) = 0.25 and F(R-|L) = 0.75. These probabilities imply that the expert 

considers the true response rate equally likely to fall inside the (R-, R-) interval as 
P.31 

24 

outside it. If the expert disagreed with this or any of several other implications, 

adjustments were made. When the expert was satisfied that the encoded distribution 

represented his probabilistic judgment, another PbB level was selected and the process 

was repeated. 

When distributions had been encoded for all selected PbB levels, they were 

plotted on a graph and discussed with the expert. If two distributions crossed at any 

point, this inconsistency was resolved (see Wallsten et al., 1983, for details). When the 

expert was satisfied that the entire set of distributions represented his or her 

probabilistic judgments, the encoding was finished. 

Following the first session, the encoded judgments were fit by distributions in a 

manner described in Sec. 3.5. Summaries of these fits and the encoded judgments, along 

with explanatory text, were sent to the expert prior to the second visit. During the 

second visit, all of the materials were reviewed, additional probability encoding was 

carried out as necessary, and the expert was asked to indicate whether the fitted 

distributions correctly represented his or her judgments. In a few instances, function 

fitting was carried out later, and further discussion was continued by letter and 

telephone. 

As seen in App. C, the fitted functions were very close to the encoded 

probabilities. When an expert finally felt that the probabilities correctly represented his 

or her judgments, he or she felt that the fitted functions did as well. 

3.5 REPRESENTING THE JUDGMENTS 

Calculating risk required fitting a distribution to the assessed points. Because 

the probabilistic judgments about the dose-response relationships are generally "s"-

shaped over the closed [0,1] interval, as demonstrated in Wallsten et al. (1983) and 

Whitfield and Wallsten (1984), it can be difficult to represent them with simple 

mathematical functions. One particularly useful function that is relatively easy to work 
P.32 

25 

with is the normal-on-log-odds distribution function, which is obtained by fitting a 

normal distribution to the natural log of the odds implied by the population response rate 

R. Thus, the following relationships can be defined: 

X = Y*-— , for 0 < X < « 

Y = ln(X), for -<"> < Y < =° 

where X is the odds variable and Y is the log of the odds variable. The variable Y is 

assumed to be normally distributed with mean y and variance o . If Y is normally 

distributed, then X is log-normally distributed, and the distribution induced on R is called 

a normal-on-log-odds distribution. Although the normal-on-log-odds distribution cannot 

be expressed in a closed form, all probabilities of interest can be easily derived from the 

normal distribution over Y, as discussed in App. B. 

A separate normal-on-log-odds distribution function was fit to the elicited 

cumulative distribution functions (CDFs) or the probability judgments over response rate 

R, at each PbB level L-, where j = 1, ..., m. This fitting was done by deriving leastsquares estimates of the parameters y.- and o:, denoted by y; and OJ, for the normal 

distribution applied to the log-odds transformed variable Y, as described in App. B. 

These distributions, each with separate least-squares estimates for y- and o:, are referred 

2 

to as the best-fitting normal-on-log-odds distributions. The standard regression r 

statistic, which compares actual judgments to those predicted by the fitted function, 

assesses how well the derived distribution represents the probability judgments at a given 

PbB level. 

As presented fully in App. B, the normal-on-log-odds distribution described the 

1 2 

encoded judgments very well, with r values generally exceeding 0.95. (An r value of 

1.0 indicates a perfect fit.) Nevertheless, goodness of fit was sacrificed to a small 
P.33 

26 

degree by fitting an expert's probability judgments with a family of equal-variance 

normal-on-log-odds distributions. Such a procedure ensures that the derived distributions 

at two different lead levels never cross one another, not even at the extremes. Crossing 

would imply that exceeding a specified response rate is judged more probable at bloodlead level L, than at Ln, where L« is greater than Lj. 

Equal-variance normal-on-log-odds distributions were derived by (1) obtaining a 

least-squares estimate of the standard deviation pooled over lead levels, o' , (2) setting 

all the a', equal to o' , and (3) finding new least-squares estimates of the means, y' (see 

J P J 

App. B). The result is a set of normal-on-log-odds distributions, one for each blood-lead 

level LJ, that have a common variance and differ only in the mean. Their goodness of fit 

can also be assessed by calculating r between observed and predicted judgments. 

Because for each PbB level L;, probability judgments were elicited over virtually 

the entire [0,1] interval, and these judgments exhibited no inconsistencies (i.e., 

crossings), the fit of the equal-variance normal-on-log-odds distributions was generally 

close to that of the best-fitting normal-on-log-odds distributions. Because the equalvariance distributions cannot give rise to inconsistencies, these representations of an 

expert's judgments are preferred for estimating risk. They were in fact accepted by each 

expert, with a slight adjustment required for Expert D. 

3.6 THE EXPERTS 

The individuals listed in Table 3.2 were selected in the fall of 1984 by 

EPA/OAQPS for participation in the study as experts. All of them agreed to participate, 

with the understanding that their judgments would be kept anonymous. Results are 

therefore presented for Experts A through E, the codes being randomly assigned to the 

names listed in Table 3.2. 
27 

TABLE 3.2 Experts Who Participated in the Hemoglobin 

Encodings 

P.34 

Expert Affiliation 

Dr. Julian Chisolm 

Dr. Bernard Davidow 

Dr. Paul Hammond 

Dr. Sergio Piomelli 

Dr. John Rosen 

John F. Kennedy Institute 

Johns Hopkins University 

New York City Board of Health 

Dept. of Environmental Health 

University of Cincinnati 

Columbia University 

New York City Lead Poisoning 

Prevention Program 

Montefiore Hospital and 

Medical Center 
P.35 

28 

3.7 RESULTS 

The qualitative discussions about the effects of lead are summarized in App. B. 

The detailed quantitative results, including the encoded judgments, parameter values for 

the fitted functions, and goodness-of-fit measures are also given in App. B. This section 

uses the functions fit to each individual's probabilistic judgments to summarize the 

quantitative results. The functions accurately represent the underlying encoded values, 

both because goodness of fit was excellent and because each expert endorsed the output 

of the respective functions as representing his judgments. 

Recall that probabilistic judgments were encoded about dose-response functions 

for lead-induced hemoglobin decrements among U.S. children aged 0-6 years. 

Hemoglobin levels of 9.5 g/dL and ILO g/dL were considered, and the experts were given 

the option of dividing the population of children into age groups of 0-3 and 4-6 years. 

Results are presented separately for the four conditions obtained by crossing the two 

hemoglobin levels with the two age groups. ' 

Experts A, D, and E believe that dose-response relationships are different for the 

two age groups and therefore provided four distinct sets of probabilistic judgments. 

Expert C believes that a single dose-response function applies to children in the 0-6 age 

range and therefore provided a single set of probabilistic judgments for each hemoglobin 

level. Expert B felt uncomfortable with the notion of judgmental probability encoding 

and therefore did not supply any judgments. His qualitative comments are presented in 

Sec. B.4 of App. B. 

3.7.1 Hemoglobin Levels < 11 g/dL, Ages 0-3 Years 

Figure 3.1 summarizes the judgments of Experts A, C, D, and E regarding the 

dose-response function for hemoglobin levels less than or equal to 11.0 g/dL in U. S. 

children age 0-3 years. (With Expert Cs concurrence, his judgments for age 0-6 are 

reproduced in both the 0-3 and 4-6 age groups.) Each person's judgments are shown in a 

separate panel. 
M 

o 

a 

pi PJ 

d 

o co 

I 

re cn "8 

n 

o 

S 

*•*•• 

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B 

fi 

I-*-* 

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< 

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| A oq 

a 

r 

(V 

u 

o 

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5 

Pr (Hb < 11 g/dL) Pr (Hb < 11 g/dL) 

Pr (Hb < 11 g/dL) 

Pr (Hb < 11 g/dL) 

o 

-_^ _* O l " Kl tn 04 

m 

**. Ul 

w Ul 

1 r 

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\ .V". •» 

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\ \ \ \ N V '• X '• V \ \ \ •. \ * '• \ 

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P.37 

30 

The graphs are analogous to the usual dose-response functions found in the 

literature, except, of course, that they are based on probabilistic judgments rather than 

on direct data. The dark, central curve in each panel shows the median judged doseresponse curve for each expert. In other words, for a given panel, according to that 

expert, at each blood lead level there is a 0.50 probability that the true response rate is 

above the indicated value and a 0.50 probability that the true response rate is below it. 

The two lighter lines on either side of the median curve contain the central 50% 

credible interval. Thus, according to the expert in a particular panel, at each blood lead 

level there is a 0.25 probability that the true response rate is below the lower light 

curve, a 0.50 probability that it is between the two light curves, and a 0.25 probability 

that it is above the upper one. In a similar manner, the dashed and dotted pairs of curves 

contain central 90% and 98% credible intervals, respectively. 

The more tightly packed the family of functions are in a panel, the less 

uncertainty an expert indicates in his judgments. Thus, Figure 3.1 gives a rather 

complete representation of each expert's probabilistic judgments. 

Figure 3.2 is less complete, but provides a convenient means of comparing 

judgments across experts. The axes are the same as in Figure 3.1. The vertical bars at 

each lead level represent each expert's central 90% credible interval for response rate, 

and the dot within each bar indicates the median judgment at that lead level. 

Note first that there is substantial overlap in the judgments of experts C, D, and 

E. This is true despite the fact that expert Cs judgments are for the full 0 to 6 age 

range, while those of the others are restricted to age 0-3. The judgments of expert A 

tend to differ from those of C, D, and E. 

Considering the overlapping judgments of C, D, and E first, note that none 

suggests a threshold. According to their median judgments, the best estimate of 

response rate is between 4% and 9% at PbB = 5 yg/dL, rising to between 22% and 28% at 

PbB = 55 yg/dL. 
50 

40 

VI 

JD 

30H 

JD 

o 

O 

10 

T 

•?T i 

TT 

TT 

T 

t i t 

H I 

it T 

* I 

I 1 1 

1 

• ii 

l to 

i :Ti ?] 

i i i— i I • 1 1 •——i 1 i i— i 1 r—i— i 1 i i— i 1 1 r-—"i 1—i—i— i 1 i' i III I 1— i • 

ACD E ACD E ACD E ACO E A C D t ACO E ACD E ACD C 

5 fig/dL 15 fig/dL 25 fiq/dl 35 /xg/dL 45 fiq/dl 55 /*g/dL 65 i*g/dL 75 fiq/dl 

Blood-Lead Level 

FIGURE 3.2 Comparison of Judgments, Hb < 11 g/dL, Ages 0-3 Years 
P.39 

32 

Expert C expresses the least uncertainty in his judgment about dose-response 

function, and Expert E expresses the most, although in all cases, variance in the 

judgments increases with PbB within the range considered (cf. the 90% credible intervals 

represented by the vertical bars in Figure 3.2). Thus, considering the 90% credible 

intervals for experts C, D, and E, response rate is greater than a value between 12% and 

28% at PbB = 5 yg/dL, with probability 0.05. Response rate then rises, and exceeds a 

value between 40% and 62% at PbB = 55 yg/dL, also with probability 0.05. 

Expert A's judgments differ from those of Experts C, D, and E. According to his 

judgments, blood leads less than about 45 yg/dL do not cause hemoglobin levels to dip 

below 11 g/dL in this age group. At PbB = 45 yg/dL, the most likely response rate is 3%, 

and this rises to a most likely rate of 16% at PbB = 75 yg/dL. Furthermore, with 

probability 0.05, the response rate at PbB = 45 yg/dL is greater than 15%, and with the 

same probability it is greater than 50% at PbB = 75 yg/dL. Although our primary interest 

is in blood leads less than or equal to 55 yg/dL, we inquired about the higher levels here 

to provide a fuller picture of Expert A's judgments. 

3.7.2 Hemoglobin Levels < 11 g/dL, Ages 4-6 Years 

Figures 3.3 and 3.4 display the judgments regarding dose- response functions for 

hemoglobin levels less than or equal to 11 g/dL for children age 4-6 years. They are read 

in exactly the same way as are Figures 3.1 and 3.2. 

As before, the judgments of experts C, D, and E overlap considerably, and differ 

from those of A. According to C, D, and E, there is no threshold; the most likely 

response rates are between 2% and 7% at PbB = 5 yg/dL, rising to between 14% and 26% 

at PbB = 55 yg/dL. 

In this case, expert D expresses the least uncertainty, while expert E continues 

to express the greatest uncertainty. With probability 0.05, response rate exceeds a value 

between 6% and 19% at PbB = 5 yg/dL, and with the same probability it exceeds a value 

between 19% and 46% at PbB = 55 yg/dL. 
P.40 

33 

t Expert A 

.-•0.95 

•*•*• ~ 

f Expert C 

Expert D 

o> 

V! 

3 0-

20-

JD 10 

Expert E 

i i i i i 

5 15 25 35 45 55 

-*L 

FIGURE 3.3 Dose-Response Functions, Hemoglobin Level < 11 g/dL, Ages 4-6 Years 
4 0 -

CT 30-

D> 

VI 

JD 

X 

JD 

d 

JD 

O 

2 0 -

10-

* i 

VI 

mt -**•*•-

T 

1 

II 

i 

i 

i 

il 

?Ii 

x

 I 

il 

ii 

il 

I! 

il 

I 

l 

u> 

I i i r—i III I 1 i i 1 1 1 r— i III I 1 1 1 1 r- -i 1 1 i i 1 I— I rACO E ACD E ACD E ACD E ACD E ACD E ACD E ACD E 

5 tig/dL 15 /xg/dL 25 /xg/dL 35 /xg/dl 45 /xg/dL 55 /xg/dL 65 xxg/dL 75 xtg/dL 

Blood-Lead Level 

FIGURE 3.4 Comparison of Judgments, Hb < 11 g/dL, Ages 4-6 Years 

TJ 

J*. 
P.42 

35 

As before, expert A's view is that there are extremely low probabilities of leadinduced hemoglobin effects at the exposure levels considered. In his judgment, bloodlead levels less than about 55 yg/dL do not cause hemoglobin levels to go below 11 g/dL 

in this age group. The most likely response rate at 55 yg/dL is 2%, while at 75 yg/dL it is 

11%. With probability 0.05, response rate exceeds 9% at 55 yg/dL, and with the same 

probability it exceeds 34% at 75 yg/dL. 

3.7.3 Hemoglobin Levels < 9.5 g/dL, Ages 0-3 Years 

Figures 3.5 and 3.6 display the judgments regarding dose-response functions for 

hemoglobin levels less than or equal to 9.5 g/dL for children age 0-3 years. They are 

read in the same manner as are the previous pairs of figures. 

In expert A's judgment, no amount of lead within the range of interest (below 

55 yg/dL) will cause hemoglobin levels to drop as low as 9.5 g/dL, and therefore no 

results are shown for him. Also, although the judgments for C, D, and E tend to overlap, 

they do not display the same degree of similarity that they do at the higher hemoglobin 

level. 

In particular, looking at the median judgments, C and E agree in estimating the 

most likely response rate at 2%, while D is certain that the response rate is 0%, at PbB = 

5 yg/dL. Then, expert Cs median response rate judgment increases relatively slowly 

with blood lead, while that of expert D increases relatively quickly. As a result, at PbB = 

55 yg/dL D and E agree that the most likely response rate is 20%, while C considers it to 

be 7%. 

Note further that expert E expresses considerable uncertainty in his judgments, 

while C and D express much less. Thus, depending on the expert, at PbB = 5 yg/dL 

response rate exceeds 3% or 18% with probability 0.05 (recall that according to expert D 

it is definitely 0%). At PbB = 55 yg/dL, it exceeds a value from 13% to 70% with 

probability 0.05. 
P.43 

36 

/•*""•. 

- J 

^ 

O) 

• 

o> 

VI 

JD 

*w 

a. 

t ExDert C 

10-

8-

6-

4-

2-

0-

• 0.95 * * 

* * ...0.75 

..••• ^0. 5 

, ' ...••'^^^...0.25 

' y'^y^.-" „-0.05 

1 1 1 1 1 * 

5 15 25 35 45 55 

t Expert D 

30-| 

| Expert E 

50-I 

cr 

^ 40 

u. 

*\ 30 

cn 

VI 20* 

JD 

X 10 

L. 

-i 1 1 1 r -

15 25 35 45 55 

•>L 

FIGURE 3.5 Dose-Response Functions, Hemoglobin Level < 9.5 g/dL, Ages 0-3 Years 
50 

40-\ 

m 

oi 30 

VI 

JD 

^ 20 

JD 

O 

JD 

O 

i_ 

OL 10 

T 

-i r 

T I 

i T i 

A l i 1 

T r 1 r -i 1 1 - r -i 1 1 r -i r 

u 

1 

' • : 

i i 1 

i r 

C D E 

5 ixg/dL 

C D E 

15 /ug/dL 

C D E 

25 /xg/dL 

C D E 

35 /Lxg/dL 

C D E 

45 /xg/dL 

C D E 

55 Axg/dL 

Blood-Lead Level 

OJ 

^1 

FIGURE 3.6 Comparison of Judgments, lib < 9.5, Ages 0-3 Years 
38 

3.7.4 Hemoglobin Levels < 9.5 g/dL, Ages 4-6 Years 

Figures 3.7 and 3.8 display the judgments regarding dose/response functions for 

hemoglobin levels less than or equal to 9.5 g/dL for children age 4-6 years. They are 

read in the same manner as are the previous pairs of figures. The pattern of judgments is 

very similar to that seen for the younger age group, but the response rate values are 

lower. 

Expert A judged that blood lead at the levels under consideration would not 

reduce hemoglobin to 9.5 g/dL, and expert D judged that it would take at least 25 yg/dL 

of blood lead to do so. The median judgments of experts C and E are consistently 

similar, while those of expert D join them at PbB = 35 yg/dL and higher. For experts C, 

D, and E, the median judgments at PbB = 5 yg/dL are 0% and 2%; at PbB = 55 yg/dL, they 

range from 7% to 13%. 

Again, expert E expresses the greatest degree of uncertainty. For C and E, at 

PbB = 5 yg/dL, response rate exceeds 3% and 9%, respectively, with probability 0.05. 

For C, D, and E, at PbB = 55 yg/dL, with probability 0.05, response rate exceeds 8% to 

50%. 

3.8 DISCUSSION 

It must be borne in mind that these judgments are with respect to lead-induced 

response rate over and above any base response rate due to iron deficiency and other 

factors. Thus, levels of uncertainty, as well as differences or similarities of opinion 

reflected here, are limited solely to the effects of lead on hemoglohin level. 

Although they differ in detail, it is notable that the judgments of experts C, D, 

and E have overriding similarities. Of particular interest, Cs judgments for the 0-6 

years age group tend to be just below those of D and E for ages 0-3 years, and just above 

their judgments for ages 4-6 years. Collectively, the judgments of C, D, and E differ 

from those of A, who considers that blood-lead levels considered have little or no effect 

on hemoglobin levels. 
39 

P.46 

t Expert C 

t Expert D Expert E 

FIGURE 3.7 Dose-Response Functions, Hemoglobin Level < 9.5 g/dL Ages 4-6 Years 
40 

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P.48 

A l 

In all cases, uncertainty (indicated by variance) increases with blood lead, as one 

would expect on rational grounds. This increase is rational because statistical 

uncertainty about a binomial parameter (response rate, in this case) increases as the 

estimated value moves toward the center of the range for that parameter. 

There is also less information available at the lower hemoglobin level than at the 

higher one, if for no other reason than that it occurs less frequently. As a result, 

judgments depend on a greater extrapolation from available data, and greater 

disagreement among experts is to be expected. This is precisely what happened. It is 

interesting, however, that experts A, C, and D exhibit more certainty at 9.5 g/dL than at 

11.0 g/dL, despite the greater extrapolation. Indeed, expert A is positive that there is no 

effect here. Apparently, A, C, and D's understanding of the effects of lead on 

hemoglobin level are such that each feels more confident about response rates at the 

lower hemoglobin level. The reverse is true for expert E. 

Finally, it should be recalled that the experts were selected to represent the 

range of respected opinion. The fact that nevertheless, there is considerable similarity 

in the pattern of judgments illustrates some of the benefits of the probability encoding 

procedure. The differences of opinion that have appeared in the literature and in debate 

have been due to a mix of disagreements about definitions, about interpretations of and 

extrapolations from data, and about what constitutes proper public health policy. 

However, it is clear that the experts exhibit much less disagreement when they are 

required to focus on the scientific issues and to consider carefully their uncertainty 

about these matters. 

The judgments represented here are of interest in their own right. However, in 

Chapter 5 they will be combined with estimated blood lead distributions under 

alternative NAAQS to obtain derived risk distributions. 
P.49 

42 

4 PROBABILISTIC DOSE-EFFECT AND DOSE-RESPONSE RELATIONSHIPS 

FOR LEAD-INDUCED IQ DECREMENTS 

As with hemoglobin, there are incomplete data regarding IQ effects of lead in 

the population of U.S. children prior to their seventh birthdays. Indeed, it is fair to say 

that the available data are themselves very controversial, making it doubly necessary to 

encode experts' subjective probabilities. 

An exact parallel to the hemoglobin situation would have entailed defining doseresponse functions in terms of percentage of the population with lead-induced IQ 

decrements exceeding a given amount, and then encoding subjective probabilities about 

such functions. This proved to be infeasible, however, because it did not frame the issue 

in the way that researchers in the area think about it, nor in terms of events that were in 

principle observable. Inferences about the effects of lead on IQ require complex 

statistics on group data, because IQ depends on multiple, correlated factors acting over 

long periods of time. Thus, it is impossible to observe an IQ decrement in an individual 

and to attribute that decrement to a particular cause. 

In order to pose questions about outcomes that the experts commonly think about 

and to elicit probabilistic judgments that are suitable for use in the risk assessment, a 

hypothetical experiment was created. In this hypothetical study, very large numbers of 

children are randomly assigned at conception either to a control group or to one of 

several lead exposure groups. Exposure levels remain approximately fixed at the 

specified level until the children's seventh birthdays, at which time the WISC IQ test is 

administered. Blood lead is measured at the third birthday. The very large numbers of 

subjects per group eliminate the need to think about sampling error, and the random 

assignment of subjects to conditions eliminates the need to think about complex analyses 

of covariance; groups differ only in terms of exposure to lead. The experts were asked to 

consider this experiment and to provide subjective probabilities about expected mean IQ 

differences between the control group and each of the exposure groups. 
P.50 

43 

Of course, such a study cannot and should not be done, but it is in principle 

doable. Furthermore, the hypothetical data are identical in form to data actually 

collected, but without the troublesome features. Indeed, the point of the necessary 

complex statistics on the real data is to attempt to draw inferences about what the IQ 

difference would be between a lead-exposed and a nonexposed group if the confounding 

variables were not present. Thus, researchers think about this issue, and it is precisely 

about it that the experts were asked to make probabilistic judgments. 

In order to calculate subjective probabilities about IQ dose-response functions 

from judgments about mean IQ differences, it was necessary to obtain judgments about 

other matters as well. Thus, probabilistic judgments were encoded about the mean IQ of 

the unexposed control group, as well as about the IQ standard deviation within exposure 

groups. The IQ measure is constructed so that it is approximately normally distributed 

within the population. The experts were asked whether they felt that the normal 

distribution was reasonably applied to IQ scores within each of the exposure groups. 

Subsequently, subjective probabilities about dose-response functions of interest could be 

calculated using normal distribution theory in conjunction with the probabilistic 

judgments about mean IQ decrement, mean IQ of the control group, and within-group 

standard deviation. 

Section 4.1 describes the protocol development, in which it is made clear how 

this hypothetical experiment was arrived at; the protocol is outlined in Sec. 4.2. Sections 

4.3-4.5 discuss the conduct of the encoding sessions, the methods of probability encoding, 

and the mathematical representation of the judgments, respectively. Section 4.6 

indicates whose judgments were encoded, Sec. 4.7 summarizes the results, and Sec 4.8 

provides some discussion. 
P.51 

44 

TABLE 4.1 Consultants for the IQ Protocol 

Consultants Affiliation 

Dr. Vernon Benignus 

Dr. Robert Bornshein 

Mr. Jeff Cohen 

Dr. Anita Curran 

Dr. Gerri Dawson 

Dr. Kim Dietrich 

Dr. Claire Ernhart 

Dr. Lester Grant 

Dr. Lloyd Humphreys 

Dr. Lyle Jones 

Dr. Herbert Needleman 

Dr. David Otto 

Dr. Steven Schroeder 

Dr. Bernard Weiss 

HERL, U.S. EPA 

University of Cincinnati 

OAQPS, U.S. EPA 

Westchester County 

Department of Health 

University of North Carolina 

University of Cincinnati 

Cleveland Metropolitan 

General Hospital 

ECAO, U.S. EPA 

University of Illinois 

University of North Carolina 

University of Pittsburgh 

HERL, U.S. EPA 

University of North Carolina 

University of Rochester 
P.52 

45 

TABLE 4.2 Experts Who Participated in the IQ 

Encodings 

Expert Affiliation 

Dr. Kim Dietrich 

Dr. Claire Ernhart 

Dr. Herbert Needleman 

Dr. Michael Rutter 

Dr. Gerhard Winneke 

Dr. William Yule 

University of Cincinnati 

Cleveland Metropolitan 

General Hospital 

University of Pittsburgh 

Institute of Psychiatry 

London, U.K. 

University of Dusseldorf 

Dusseldorf, F.R.G. 

Institute of Psychiatry 

London, U.K. 
P.53 

46 

4.1 PROTOCOL DEVELOPMENT 

A large number of people, listed in Table 4.1, served as consultants in the 

development of this protocol. As already indicated, our original intention was to develop 

a protocol analogous to the one for hemoglobin decrement, according to which we would 

encode experts' probabilistic judgments about dose-response functions for lead-induced 

IQ decrements. In preparation, we read relevant portions of the CD and consulted with 

Drs. Vernon Benignus, Robert Bornshein, Kim Dietrich, David Otto, and Stephen 

Schroeder. 

A first draft of a protocol was developed, designed to elicit probabilistic 

judgments about dose-response curves for adverse effects defined in terms of IQ 

decrements. This draft was discussed with most of the people mentioned above as well 

as with Drs. Claire Ernhart, Lester Grant, Lloyd Humphries, Lyle Jones, Herbert 

Needleman, and Bernard Weiss. Two factors became clear in the discussions. 

First, although the concept of a dose-response curve is well defined in this 

context, it is not commonly used, for reasons already introduced in Section 4.1. The 

second factor was that in attempting to respond to the questions, the experts were 

envisioning hypothetical experiments, considering what the outcomes might be, and then 

extrapolating from that to the dose-response functions of interest. 

Thus, it appeared that it would be far more consistent with the experts usual way 

of thinking and be easier for them to respond if their probabilistic judgments about 

outcomes of suitable hypothetical experiments were encoded directly. In addition, by 

properly designing these hypothetical experiments, it would be possible to eliminate the 

need to worry about some of the complexities that arise in actual research. The 

extrapolations that they were trying to do mentally could then be done mathematically. 

Accordingly, a new version of the protocol was developed to elicit probabilistic 

judgments about the outcomes of ideal hypothetical experiments. This protocol also 

indicated how the judgments would be used and the assumptions that would be 
P.54 

47 

incorporated in working with them. The new draft was discussed with Drs. Vernon 

Benignus, Anita Curran, Claire Ernhart, Lloyd Humphries, Lyle Jones, Herbert 

Needleman, David Otto, and Stephen Schroeder. They found it much easier and more 

natural to respond to this version than to the previous one. However, various comments 

lead to a third draft of the protocol incorporating an improved ideal hypothetical 

experimental design. This draft was discussed with most of the people who had seen the 

previous one, and some very minor changes were made. 

The protocol was then used with two pilot subjects, one an EPA environmental 

health scientist and the other a psychology graduate student doing a related 

dissertation. The judgmental probability encodings went very well. However, in 

analyzing the judgments and discussing these analyses with Dr. Lyle Jones, it became 

apparent that minor changes were still necessary. 

Thus, a final version of the protocol was created. It was discussed with a number 

of the people who had seen the previous drafts, and was considered suitable for 

subsequent use. 

4.2 PROTOCOL OUTLINE 

The full protocol is provided in App. C. Only an outline is given here. 

Section 1 is an introduction, describing the risk assessment project and the 

purpose of the probability encoding. Section 2 describes the ideal hypothetical 

experiment, in which large numbers of children are randomly assigned at conception to 

one of six exposure groups or to a control group sheltered from lead. Environmental lead 

exposure is roughly constant at the appropriate level for each child, such that when his or 

her blood lead is measured on the third birthday, it is at the designated level. The same 

environmental exposure continues until the seventh birthday, when the WISC-R IQ test is 

administered. Thus, each expert was to consider the time course of lead in the children's 
P.55 

48 

systems according to his or her own theoretical understanding, subject to the constraint 

that blood lead was at the designated level on the third birthday. 

It was explained in this section that probabilistic judgments would be encoded 

regarding the mean IQ decrement for each exposure group relative to the control group, 

the mean IQ of the control group, and within the group IQ standard deviation. Further, 

there was discussion regarding the shape of the within group IQ distribution. However, if 

an expert considered the IQ effects of lead to be different for lower socioeconomic 

status (SES) than for middle and upper SES subpopulations, then judgments would be 

encoded separately for the two groups. For this purpose, low SES children were defined 

as those coming from households with incomes below the fifteenth percentile. 

Section 3 defined the population at risk as children up to their seventh birthday, 

thereby indicating why the IQ measure is taken at that time. Sections 4 and 5 specified 

exposure, physiological, and environmental conditions to assume for the hypothetical 

experiment. 

As with the hemoglobin protocol, Section 6 focused on issues in the literature to 

elicit discussion prior to the probability encoding. The purposes were to insure that the 

problem was structured properly for the expert, to cause him or her to consciously 

review his or her knowledge prior to providing probabilistic judgments, and to provide a 

possible basis for understanding discrepant judgments, should they occur. Section 7 

discussed factors to be aware of when encoding probabilities, and Section 8 documented 

the encoding procedure. 

4.3 CONDUCT OF THE SESSIONS 

The sessions were conducted in the Spring of 1985, and with one exception were 

carried out in an analogous fashion to those for hemoglobin. In lieu of providing the 

details again, the reader is referred to Sec. 3.3. 
P.56 

49 

The single exception was that information was brought along to aid the expert, 

should the person have wanted it, in encoding probabilities about control group mean IQ 

and within group IQ standard deviation. The information concerned WISC-R IQ means 

and standard deviations for subpopulations stratified by various demographic variables, as 

compiled by Kaufman and Doppelt (1976) and subsequently summarized by Sattler 

(1982).* 

4.4 ENCODING THE JUDGMENTS 

Probability encoding began in the first session after the relevant literature and 

the factors affecting lead effects on IQ had been thoroughly discussed with the expert. 

The intention was to encode probability judgments for possible mean IQ decrements in six 

lead exposure groups relative to the control group. The exposures were such that at their 

third birthdays, members of respective groups had blood-lead levels of 5, 15, 25, 35, 45, 

and 55 yg/dL. However, higher levels were specified for a few of the experts. 

To determine useful points in the space of mean IQ decrements for encoding 

probabilities, each expert was first asked to supply broad "99% confidence interval" 

ranges for possible mean IQ differences between the control and each of the exposure 

groups. We helped the expert determine these ranges by posing suitable questions (e.g., 

after a range was specified, we asked whether the expert could construct a plausible 

explanation if someday it were found that the true mean difference was outside that 

range). In a similar manner, "99% confidence intervals" were obtained for the mean IQ 

of the control group and the within group standard deviation. At this point, all of the 

experts agreed that within SES level the same standard deviation judgments applied to all 

*It should be pointed out that these normative data could not be used in place of The 

experts' judgments regarding control group mean IQ and within group IQ standard 

deviation, because they were based on children with varying amounts of lead in their 

systems. Thus, each expert had to adjust these values as he or she thought appropriate 

given his or view on The IQ effects of lead. Each person had the option, of course, of 

taking the tabulated values as point estimates. 
P.57 

50 

exposure groups, and that it was reasonable to assume normal IQ distributions within 

subgroups. 

Functions were fit to the judgments following the first session. Summaries of 

the fits plus descriptive information were sent to those experts in the U. S. for their 

review prior to the second visit with them. Due to time and financial constraints, this 

was not possible to provide the European experts with an opportunity to review the same 

materials prior to the second meeting. Instead, they were brought to the second session 

and explained there. During the second visit with both the European and the U.S. 

experts, the materials were reviewed, additional probability encoding was done as 

necessary, and each person indicated whether the fitted distribution correctly 

represented his or her judgments. In a few instances, subsequent function fitting was 

carried out, and further discussion was continued by mail and telephone. Fortuitously, 

two of the Europeans were in the United States shortly after the second session, and it 

was possible to have a short third session with each one. 

As will be seen in App. D, the fitted functions were in fact very close to the 

encoded probabilities. When we reached the point that an expert felt that the 

probabilities correctly represented his or her judgments, that person felt that the fitted 

function did as well. 

4.5 REPRESENTING THE JUDGMENTS 

As with hemoglobin, it was necessary to fit distributions to the assessed points to 

calculate risk. The nature of the variables being judged were different than with 

hemoglobin, but as before, the judgments were generally S-shaped. Judged mean IQ 

difference was bounded from below by 0 (theoretically, this need not have been the case, 

but none of the experts gave any credence to the possibility of lead enhancing IQ). 

Judgments about mean control group IQ and within-group IQ standard deviation were so 

far from any limits that for practical purposes they could be treated as unbounded. Thus, 

different distributions were required here than with hemoglobin. 
P.58 

51 

For all the experts, judgments about mean control group IQ and within-group IQ 

standard deviation were fit well by normal or lognormal distributions. The goodness of 

fit measure here, as before and in what follows, was the r-square statistic comparing 

actual judgments to those predicted by the fitted function. 

With regard to mean IQ differences, some experts gave judgments for each lead 

level that were roughly symmetric around a particular value, and others gave judgments 

that were positively skewed, i.e., attributed small probabilities to very large 

differences. Generally, the former judgments were better fit with normal distributions 

and the latter with lognormal distributions, i.e., distributions over log IQ difference. 

Specifically, four families of distributions were fit to each expert's judgments 

about mean IQ differences. One was the normal distribution allowing a separate mean 

and variance for each lead level, another was the lognormal allowing a separate mean 

and variance for each lead level, and the remaining two were equal variance normal and 

lognormal distributions. In the latter two cases, normal and lognormal distributions were 

fit respectively using a single pooled variance estimate for each, but allowing separate 

mean values at each lead level. 

Generally, the normal function fit better than the equal-variance normal 

function, and the lognormal function fit better than the equal-variance lognormal 

function. However, each set of judgments were distinctly better fit by either the normal 

or the lognormal distributions, and only the better of the two types of distributions was 

considered further for that set. 

As argued in Sec. 3.5, the equal-variance distributions have the virtue of never 

crossing and therefore never leading to inconsistencies. However, the equal variance fits 

were so poor for all experts but one, that there was no point in pursuing them in those 

cases. In order for the equal-variance fits to be acceptable, the slopes of the 

transformed judgments must be about the same. That generally was not the situation for 

the case of IQ decrements, making it undesirable to utilize equal-variance fits. Although 
P.59 

52 

this causes the curves to cross at some point, the distributions are spaced sufficiently far 

apart, that the crossings occur in the very extreme tails. This is a small cost for 

representing the judgments accurately within the ranges of interest. 

4.6 THE EXPERTS 

In March of 1985 the individuals listed in Table 4.2 were selected by EPA/OAQPS 

staff for participation in the study. All agreed, again with the understanding that their 

judgments would be anonymous. The judgments presented here are attributed to Experts 

F through K, with these letter designations having been randomly assigned. We are 

grateful to these people for their hard work and the many hours they spent with us. 

4.7 RESULTS 

This section utilizes the functions fit to each individual's probabilistic judgments 

to present a summary of the quantitative results. The functions provide an accurate 

representation of the underlying encoded values, both because goodness of fit was 

excellent and because each expert endorsed the output of the respective functions as 

representing his or her judgments. 

Summaries of the qualitative discussions about the IQ and behavioral effects of 

lead are in Sec. C.4 of App. C. Detailed quantitative results, including the encoded 

judgments, parameter values for the fitted functions, goodness of fit measures, and 

derived subjective probabilities about dose-response functions, are listed in Appendix C. 

Recall that the experts were given the option of making separate judgments for 

lower and higher SES children. The lower SES group was defined as those children whose 

family incomes do not exceed the fifteenth percentile; the remaining children were to be 

considered in the higher SES group. All the experts except F believe that at the doses 

under consideration, lead interacts with variables that contribute to SES level. 

Therefore, all except F elected to provide separate judgments for the two SES levels. 
P.60 

53 

It is convenient to present simultaneously the judgments about the lower and 

higher SES control group mean IQ values, and to do the same with the judgments about 

the within-group standard deviations. However, the judgments about the mean IQ 

decrements are most easily comprehended if they are shown separately for the two SES 

levels. F's judgments will be repeated in the cases for purposes of comparison. 

4.7.1 Control Group Mean IQ 

Expert I felt unable to provide judgments about the mean IQ of a group of 

children sheltered from lead exposure. The other experts' judgments are shown in Figure 

4.1, categorized by SES level. The top four bars represent the low SES judgments of G, 

H, J, and K; the central bar represents the single overall judgment of F; and the lower 

four bars represent the high SES judgments of G, H, J, and K. 

The symbol within each bar is the median judged mean IQ value. In other words, 

for a given bar, according to that expert, there is a 0.50 probability that the control 

group mean IQ would be above the value indicated by the symbol and a 0.50 probability 

that it would be below the indicated value. The brackets immediately to the left and 

right of the symbol denote each expert's central 50% credible interval, i.e., the interval 

such that there is a 0.25 probability of the mean IQ falling below it, a 0.50 probability of 

the mean IQ falling within it, and a 0.25 probability of the mean IQ falling above it. The 

other pair of brackets denotes the central 90% credible interval. 

Experts G, H, and J show considerable agreement in their judgments regarding 

the low SES group. Their median judgments about the mean IQ range from 95 to 97 

points, and (from their 90% credible intervals), with probability 0.05, the mean IQ 

exceeds a value that is between 98 and 103 points. Expert K's median judgment is 85 

points, and according to him or her, the mean IQ exceeds 92 points with probability 0.05. 

The judgments of all four experts overlap considerably regarding the high SES 

group. Their median judgments range only from 104 to about 106 points. The upper 

limits of the 90% credible intervals range from 108 to 112 points. 
54 

P.61 

1 \o 

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Lower SES 

F G H J K 

Higher SES 

FIGURE 4.1 Judgments about Control Group Mean IQ 
P.62 

55 

Expert F displays the least uncertainty. His or her judgments about the entire 

population fall between those of the other experts for the low and high SES levels, as 

they should. The median judgment is 101 points; with probability 0.05, the mean IQ 

exceeds 102 points. 

4.7.2 Within-Group IQ Standard Deviation 

Expert I felt unable to provide judgments about this variable, as well. The 

judgments of the remaining experts are shown in Fig. 4.2, arranged according to the same 

format as Fig. 4.1. 

Expert F was certain that the within-group IQ standard deviation would be 

identical to thatnormed for the population as a whole, 15 points. Expert G, considering 

each of the two SES groups to be somewhat more homogeneous than the overall 

population, was certain that the within-group IQ standard deviation would be 14 points in 

each case. 

The judgments of experts H, J, and K were relatively similar. They thought that 

the IQs of the low SES group would be more homogeneous than those of the high SES 

group, and therefore estimated lower standard deviations. The median judged standard 

deviation for the lower SES level range from 12.4 to 13 points; upper limits of the 90% 

credible intervals range from 14 to 15 points. Expert J was certain that the standard 

deviation would be 14 points for the upper SES level, while H and K have median 

estimates of 13.5 and 14.3 points, respectively. The upper limits of their 90% credible 

intervals are 15.6 and 15.1 points, respectively. 

4.7.3 Mean IQ Decrements for the Low SES Group 

Figure 4.3 summarizes the judgments of all six experts regarding mean IQ 

decrements for the low SES group. Each person's judgments are shown in a separate 

panel. Blood lead is on the abscissa and mean IQ decrement (mean control group IQ 

minus mean exposed group IQ) is on the ordinate. 
56 

P.63 

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ID 

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Lower SES 

F G H J K 

Higher SES 

FIGURE 4.2 Judgments about o IQ 
P.64 

57 

25 35 45 55 65 5 15 25 35 45 55 

A

'Q | Expert H 

15H 

10H 

• * L 

5 15 25 35 45 55 

A,-** A 

•Q i Expert J 

15 25 35 45 55 65 

FIGURE 4.3 Judgments about A— for a Lower SES Population 
P.65 

58 

The dark, central curve in each panel shows the median judged IQ decrement for 

each lead level. In other words, for a given panel, according to that expert there is a 

0.50 probability that the actual mean IQ decrement would be greater than the indicated 

value, and a 0.50 probability that it would be less. The successively lighter pairs of 

curves that bracket the median curve represent central 50%, and 90% credible intervals. 

Figure 4.4 allows a comparison of judgments across the experts. The axes are 

the same as in Figure 4.3. The vertical bars at each lead level represent each expert's 

central 90% credible interval, and the symbols are his or her median judgments. 

Expert F consistently judges the IQ effects of lead to be less than do the other 

experts, and evidences considerably less uncertainty about the magnitude of these 

effects than do the others. Expert F is certain that there is no IQ effect of lead up to at 

least 15 yg/dL. At 25 yg/dL, the median judged IQ decrement is about 0.5 point, and this 

increases to a median judged IQ decrement of just under 2 points at 65 yg/dL. According 

to F, at 25 yg/dL, the IQ decrement exceeds approximately 1 point with probability 0.05, 

while at 65 yg/dL, it exceeds 5 points with the same probability. 

There are overriding similarities in the judgments of the other experts, although 

there are also small, consistent differences among them. Thus, only G, H, and J give any 

credibility to there being IQ effects as low as 5 yg/dL, while I does so at 15 yg/dL, and K 

does at 25 yg/dL. The judgments of H and J are consistently very close, as are those of 

G, I, and K, which as a group are somewhat lower than those of H and J. Considering the 

five sets of judgments, the median judged IQ decrement at 5 yg/dL ranges from 0 to 2.5 

points. The median judged IQ decrement at 55 yg/dL is from about 7 to 11 points. 

According to the judgments of G, H, and J, with probability 0.05, the IQ decrement 

exceeds 3 to 5.5 points at 5 yg/dL, while according to all 5 experts, it exceeds 11 to 17 

points at 55 yg/dL with the same probability. 
15-

12-

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—i—i—i—i—i—i— i 1—i— i 1 1 rr G H I J K F6HIJ K 

—i—-I ?—( 1—rr C H I J K 

—I—1—I—I—•—I—I—I—•—I—I—(—•—I—I—I—I—I—I—I—I—I—I—I—I— I I 

(fCHlJ K (GHIJ K rCNIJ K FGHIJ K 

5 Mg/dL 15 fig/dL 25 A*g/dL 35 fzig/dl 45 fig/dl 55 /ug/dL 

Blood-Lead Level 

65 fxg/dL 

FIGURE 4.4 Comparison of Judgments about Ay^ for a Lower SES Population 
P.67 

60 

4.7.4 Mean IQ Decrements for the High SES Group 

Figures 4.5 and 4.6 display the judgments about mean IQ decrement for the high 

SES group, and are read in the same fashion as are Figs. 4.3 and 4.4, respectively. As 

with the low SES population, F consistently judges the IQ effect to be less than do the 

other experts. From 25 yg/dL on, the judgments of the others overlap, with, as before, 

those of H and J being very similar and somewhat greater than those of G, K, and I, 

which themselves are similar. Only H gives any credibility to the existence of an IQ 

effect at 5 yg/dL, G, I, and J do so at 15 yg/dL, and F and K concur at 25 yg/dL. 

Considering all the experts simultaneously, the median judged IQ decrement at 

15 yg/dL ranges from 0 to 2.5 points; at 55 yg/dL, it ranges from 1.5 to 7.5 points. 

According to G, H, I, and J, with probability 0.05 it exceeds 1 to 7 points at 15 yg/dL, 

while according to all the experts it exceeds 4 to 11.5 points at 55 yg/dL with probability 

0.05. 

4.7.5 Change in Percentage of Low SES Group with IQs < 85 

The judgments about control group mean IQ, mean IQ decrement at each 

exposure level, and within-group IQ standard deviation can be used along with the 

assumption of within group normal IQ distributions to calculate subjective probabilities 

about the lead induced change in percentage of the population with IQ's below any 

critical level. These would correspond to judgments about IQ dose-response functions, 

and are the results necessary ultimately for the risk calculations. The mathematical 

details are in Appendix D. Here, we illustrate the results for a critical IQ of 85 points. 

We point out, however, that greater uncertainty is evidenced in these dose-response 

functions than in the separate judgments shown above, because uncertainty about three 

parameters is being combined. Note that calculations are not possible for expert I, 

because he or she declined to judge control group mean IQ and within-group IQ standard 

deviation. 
61 

Expert F 

25 35 45 55 65 

A

IQ t Expert G 

10-

8-

6-

4 -

2 -

n 

* 

- ' " .•*• / 

U T I I i I 

15 25 35 45 55 

Af7 A _ 

l u

 i txpert J 

FIGURE 4.5 Judgments about A— for a Higher SES Population 
10-

A

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5 /ug/dL 15 fig/dl 25 /xg/dL 35 /xg/dL 45 fig/dL 55 fig/dL 65 /ug/dL 

Blood-Lead Level 

FIGURE 4.6 Comparisons of Judgments about Ay^ for a Higher SES Population 
P.70 

63 

Figures 4.7 and 4.8 show the calculated subjective probabilities about the doseresponse function for increase in percentage of IQ's less than or equal to 85 points in the 

low SES population. The abscissa in both cases is blood lead, the ordinate is population 

response rate (i.e., lead induced increase in percentage below 85 points), and the curves 

are analogous to those in the preceding figures. 

As would be expected, F's judgments suggest much lower dose-response functions 

than do those of the others. The results from G, H, J, and K overlap considerably, with 

those from H and J being very similar and slightly greater than those from G and K, 

which themselves are similar. 

According to F, the median judged response rate is less than 1% at 25 yg/dL, 

rising to 4% at 65 yg/dL. With probability 0.05, it exceeds 1% at 25 yg/dL, and with the 

same probability, it exceeds 7% at 65 yg/dL. For G, H, and J, the median response rate 

is from 2.5% to 6% at 5 yg/dL, while including K, it is between 21% and 32% at 

55 yg/dL. For the same experts, the response rate exceeds about 4% to 11% at 5 yg/dL, 

14% to 26% at 25 yg/dL, and 29% to 45% at 55 yg/dL, each with probability 0.05. 

4.7.6 Change in Percentage of High SES Group with IQs < 85 

The pattern of similarities and differences across experts is the same here as it 

was above, so corresponding figures are not shown. Generally, higher SES children are 

less at risk than lower SES children. The results for F are the same as those shown 

previously, because they are based on the same judgments. According to G, H, and J, the 

median judged response rate is from about 0.5% to 3% at 15 yg/dL, while according to G, 

H, J, and K, it is from about 5% to 12% at 55 yg/dL. According to the same experts, the 

median response rate exceeds 2% to 7.5% at 15 yg/dL, 4% to 11% at 25 yg/dL, and 9.5% 

to 18% at 55 yg/dL, all with probability equal to 0.05. 
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Blood-Lead Level 

FIGURE 4.8 Blood-Lead Level Comparison of Increased Probabilities of Having IQ < 85 

for a Lower SES Population 
P.73 

66 

4.8 DISCUSSION 

Considering the extensive debate concerning the IQ effects of lead, the degree of 

consensus reflected in the present results is notable. This is particularly so, since the 

experts were selected so as to span the full range of opinion. As occurred with the 

hemoglobin results, asking the experts to encode their subjective probabilities about 

specific, well-defined scientific outcomes eliminated disagreements about definitions, 

policy, and other matters. The remaining disagreements, evidenced in the preceding 

results, are due to differing interpretations of, and extrapolations from, evidence. 

Generally, Experts H and J provided similar judgments, as did Experts G, I, and 

K. Furthermore, these two sets of judgments overlapped to a great extent. Expert F 

consistently estimated smaller effects than did anyone else, and indicated less 

uncertainty about them. 

Uncertainty (as indicated by variance) generally increased with blood lead within 

the range of interest, as would be expected. In addition, individual subjective 

probabilities cover broader ranges for the low SES than for the high SES group. This 

result may reflect more data at the high SES level, or more uncertainty about the 

influence of the covariates at the low SES level. 

The judgments regarding both mean IQ decrements and dose-response functions 

are of interest in their own right. However, in Sec. 5 they will be combined with 

exposure estimates to yield risk distributions. 
P.74 

67 

5 ESTIMATED RISKS OF ADVERSE HEALTH EFFECTS 

UNDER ALTERNATIVE AIR-LEAD SCENARIOS 

Risks of adverse health effects under alternative air-lead standards can be 

estimated by combining dose-response functions with blood-lead distributions appropriate 

to the alternative standards. The estimates must incorporate the uncertainty associated 

with dose-response functions as well as that associated with blood-lead distributions. 

The former has been discussed in Sees. 2-4 for EP, hemoglobin, and IQ, respectively; the 

latter will be covered in this section. 

The main focus of this section is to estimate the risks of adverse health effects 

under alternative air-lead scenarios for young children in the vicinity of several point 

sources of lead located in the U.S. Results were obtained by mathematically combining 

the PbB and dose-response information into a risk model. The exposure information (i.e., 

PbB levels for alternative air-lead scenarios) was developed by PEI Associates, Inc., 

under contract to EPA, using the integrated lead-uptake/ biokinetic model presented in 

the EPA staff paper. Since methodological development is not complete, these results 

are preliminary. 

This section is organized into five main subsections. The first covers alternative 

air-lead scenarios and estimated resultant PbB distributions among children residing in 

the vicinity of selected point sources of lead. The next three subsections present 

estimates of the risks of adverse health effects involving EP, hemoglobin, and IQ, 

respectively. 

5.1 EXPOSURE ESTIMATES 

EPA's OAQPS used an integrated lead-uptake/biokinetic model to estimate the 

relationships between air quality and blood-lead levels among U.S. children residing in 

the vicinity of point sources of lead emissions. The model incorporates a biokineticmetabolic model developed at New York University, which takes into account the 
P.75 

68 

absorption of lead into the bloodstream through inhalation and ingestion, and its 

subsequent movement among body compartments (i.e., blood, bone, and soft tissue). 

Blood lead is the index of lead exposure generated by the model for present purposes. 

Estimates of exposure take into account changes in activity patterns, physiology, and 

metabolism of children through various stages in their development. For example, 

children six months and six years of age differ in terms of numerous physiological 

indicators, as well as concentration of lead in the immediate environment, degree of 

hand-to-mouth activity, time spent outdoors vs. indoors, differences in lead absorption in 

the gastro-intestinal tract at different ages, etc. For this analysis, only children that 

live in housing that is free of lead-based paint hazard, and who are not exposed indirectly 

to occupational sources of lead from household members, were modeled. 

Blood-lead levels for children living in the vicinity of five U.S. point sources of 

lead emissions were included in our analysis. For the area surrounding these point 

sources, which will remain nameless at this time, the total number of children (0-6 

years), the number of children in the 84-month cohort, and the percentage of those 

children living in households having incomes below poverty level are listed in Table 5.1. 

This level approximately corresponds to the lower SES level (the lowest 15%, based on 

family income) used in the IQ encodings. 

Seven alternative air-lead scenarios were considered for each of the point 

sources. These are grouped in three categories: baseline, precontrol, and postcontrol. 

For illustrative purposes, air-quality estimates based on dispersion modeling used in the 

exposure analysis are presented in Table 5.2 for areas surrounding the five point sources 

under different air-lead scenarios. It is important to note that these air-lead values 

represent estimates at the geographic centers of the census tracts surrounding the 

9 

different point sources. Air-lead concentrations at other receptor sites closer to the 

point sources are generally higher than the ranges shown. The baseline scenario 

represents modeled air quality as it existed around the particular point source for the 
P.76 

69 

TABL E 5.1 1980 Population Dataa for Selected U.S. Point Sources of Lead 

Emissions 

Point 

Source 

1 

2 

3 

4 

5 

Type 

Secondary Smelter 

Secondary Smelter 

Battery Plant 

Battery Plant 

Primary Smelter 

Total Number 

of Children 

Aged 0-6 Years " 

15,835 

4,614 

23,422 

12,956 

12,576 

Number of 

Children in 

84-Month 

Cohort5 

2,273 

671 

3,305 

1,994 

1,718 

Percent below 

Poverty Level0 

14 

24 

19 

11 

6 

aNumbers calculated based on 1980 U.S. Bureau of Census data and aggregated 

across census tracts around each point source. Population data represent 

the number of children living in housing free of lead-based paint hazards 

and exposure to occupational sources of lead. 

In this case, the 84-month cohort is a group of children born in January 

1974 and already 7 years old at the end of the exposure period. 

cData are from Ferdo (1986). 
P.77 

70 

TABLE 5.2 Comparative Air Quality at Census Tract Centroids 

Surrounding Modeled Point Sources 

Range of Monthly Air-Lead Concentrations3 

Point 1990-1996 1990-1996 

Sources 1974-1980 1983-1989 (0.25 pg/m3)

b

 (1.5 yg/m3)

b 

1 0.53-1.83 0.01-0.92 0.01-0.03 0.01-0.13 

2 0.54-1.83 0.02-0.92 0.01-0.03 0.01-0.13 

3 0.53-1.83 0.01-0.92 0.01-0.03 0.01-0.13 

4 0.53-1.83 0.01-0.92 0.01-0.03 0.01-0.13 

5 0.01-1.27 0-0.64 0-0.04 0-0.23 

aMonthly air-lead concentrations expressed in micrograms per 

cubic meter and rounded to two significant digits were estimated by another contractor for EPA using ISC dispersionmodel and gasoline-lead-consumption data (based on previous, 

current, or future emission rates) at geographic centroids 

of census tracts surrounding each point source under 

different scenarios (Johnson and Paul, 1986). Ranges reflect 

spatial variability around point sources (decreasing air-lead 

levels with increased distances) and temporal trends (reduction in gasoline lead emissions since the 1970s). 

The 1990-1996 scenarios assume that the modeled point source 

is in compliance with whatever lead NAAQS is being analyzed. 

For example, the highest air-lead concentration projected at 

an air quality receptor under the 0.25 yg/m lead NAAQS is no 

higher than 0.25 pg/m , with all other receptor points just 

at or below that level. Air quality values at geographic 

centroids are considerably below other receptor values because 

of distance from the point source and an assumption that airlead levels in an area decline linearly with reductions in 

emission rates. 
P.78 

71 

1974-1980 time period. Similarly, the precontrol period covers the years 1983-89. 

Blood-lead levels are estimated to be lower in the precontrol vs. baseline periods 

primarily because of the beginning of the gasoline lead phasedown, the implementation of 

the ambient air quality standard for lead, and reductions of lead levels in canned foods. 

Lead exposure in the U.S. also declined in this era due to additional factors such as 

increased awareness of lead-based paint hazards and the gradual reduction in the old, 

lead-based painted housing stock. The postcontrol period spans 1990-96, and includes 

five alternative air-lead-level scenarios (lead NAAQS of 0.25, 0.5, 0.75, 1, and 

1.5 yg/m3). 

For each alternative air-lead scenario considered in the postcontrol period, it is 

assumed that the point source is in attainment with whatever standard is analyzed. In 

other words, the highest air-quality receptor site would be at or below whatever standard 

level is considered. If the dispersion modeling indicated that a standard level would be 

exceeded in the postcontrol scenario, the highest receptor site was adjusted down to the 

standard level, with all other receptor sites reduced proportionately. The reader is 

referred to a lead exposure report (Johnson and Paul, 1986) that details the method used 

to model air quality for each scenario. Blood-lead levels in the postcontrol period are 

estimated to be further reduced primarily because of the continued reductions in lead 

levels in canned foods and drinking water. 

For each air-lead scenario, upper and lower bound estimates of the geometric 

mean blood leads were calculated by the exposure model. These bounds were obtained by 

considering a range of "high" and "low" settings of parameter values that significantly 

affect final PbB estimates. Many of the alternative postcontrol scenarios resulted in 

mean PbB levels that were essentially equivalent and relatively low (< 5 yg/dL). This 

suggests that the small incremental changes in ambient air quality levels under the 

alternative NAAQS analyzed may not be sufficient to significantly influence PbB 

distributions among populations of children in the future. The result may be misleading, 
P.79 

72 

however, because major air-quality impacts are confined principally to the immediate 

vicinity (< 1 km) of the point sources, while the modeled blood leads were obtained by 

averaging over relatively large areas around the point sources (resulting in air-lead levels 

down to urban or rural background concentrations at the boundaries of the point source 

impact areas). A complete tabulation of the scenarios used in the risk calculations is 

provided in App. D. 

Each scenario contains upper- and lower-bound estimates of the geometric means 

of modeled blood leads for the 84-month cohort for four age periods: 0-3 years, 4-6 

years, 0-6 years, and the 36th month of life. Estimates for the first two periods are 

needed in order to combine expert judgments about hemoglobin decrements, which were 

obtained for subpopulations of children of those ages. The third is needed to estimate 

the risks of elevated EP levels, and the last is needed to estimate the risk of IQ effects. 

All risk estimates presented are for the 84-month cohorts modeled in each airlead scenario. The 84-month cohort is the cohort of children born in the beginning of 

each exposure period, and who reach their seventh birthdays at the end of the exposure 

period. The 84-month cohorts constitute only a small fraction of the total number or 

children aged 0-6 years surrounding each point source modeled. In addition, risk 

estimates for lead-induced IQ effects are presented solely for children from families of 

children from lower SES status. This group of children constitutes 6-24% of the total 

poulation of children around each of the five point sources (Table 5.1). As a result, any 

headcount risk numbers that would be calculated based on these risk estimates would 

underestimate the total risk in the population of young children modeled. At this time, 

headcount risk estimates are not presented. 

It is assumed that blood leads are described by lognormal distributions with the 

geometric mean (GM) values tabulated, and a single geometric standard deviation (GSD) 

of 1.42. Properties of the lognormal distribution are described in App. B. The geometric 

mean (GM) blood leads for all 84-month cohorts for the three scenarios that are 
P.80 

73 

significantly different from one another (for Sources 2 and 5) are listed in Table 5.3. All 

of the postcontrol scenarios result in PbB levels that are nearly identical, so only one 

postcontrol scenario (having upper and lower GM PbB values) is listed. Geometric mean 

blood-lead values are lowest around Source 5, which is located in a rural area, and 

highest around Source 2, an urban area. The others (also urban areas) are slightly less 

than those for Source 2. To illustrate, the upper-bound estimate of GM = 27 yg/dL for 

the baseline exposure scenario for Source 2 means that 55% of the population would have 

had PbB levels above the current Centers for Disease Control definition of an elevated 

PbB level of 25 yg/dL. The corresponding lower bound of GM = 19.4 yg/dL means that 

33% of the population would have exceeded that level. 

As a point of reference, over the years 1976-80, the second National Health and 

Nutrition Survey (NHANES II) (Annest et al., 1982) was conducted. It included representative examinees from urban and rural populations aged six months to five years. 

Urban examinees had a GM PbB level of approximately 17 yg/dL. This value is about 0.2 

yg/dL lower than the lower bound GM PbB estimate for children aged 0-6 years at Source 

2. Rural children had an average PbB level of 13.9 yg/dL, which is about 0.5 yg/dL 

higher than the upper bound for Source 5 for the baseline scenario. 

5.2 RISK RESULTS FOR EP 

A complete listing of results and descriptions of the models used to estimate the 

risk are provided in App. D. An overview is presented here. As discussed in Sec. 2 and 

App. A, EP dose-response uncertainty was calculated from the data published by Piomelli 

et al. (1982). Recall that two levels of EP were considered to be adverse health effects, 

33 yg/dL and 53 yg/dL, which are one and two standard deviations above the "reference" 

EP level (21.7 yg/dL) determined for the group of children having the lowest PbB levels. 

The probabilistic dose-response functions were combined with the PbB 

distributions (for children aged 0-6 years) described in Sec. 5.1 to produce the overall risk 
P.81 

74 

TABLE 5.3 Geometric Mean Blood-Lead 

Levels (yg/dL) for 84-Month Cohorts* 

Source 5 Source 2b 

Age Group Lower Upper Lower Upper 

Baseline Scenario (1974-80) 

0-3 Years 

4-6 Years 

0-6 Years 

36th Month 

8.6 

6.4 

7.7 

7.7 

13.9 

11.5 

13.4 

12.9 

19.4 

14.3 

17.2 

19.2 

27.0 

21.2 

24.5 

27.1 

Precontrol Scenario (1983-89) 

0-3 Years 

4-6 Years 

0-6 Years 

36th Month 

3.3 

2,0 

2.7 

2.9 

6.7 

5.5 

6.2 

6.5 

5.2 

2.4 

4.0 

4.4 

9.9 

5.9 

8.2 

9.7 

Postcontrol Scenarios (1990-96) 

0-3 Years 1.4 3.7 1.4 3.6 

4-6 Years 1.1 3.6 1.1 3.4 

0-6 Years 1.3 3.7 1.3 3.7 

36th Month 1.3 3.7 1.3 3.7 

aEstimated PbB levels are averages based 

on air-quality estimates for geographic 

centers of all census tracts within the 

impact area surrounding a given point 

source. 

Values for other sources are about 5-10% 

lower than those for Source 2. 
P.82 

75 

results for EP. These results are summarized in Figs. 5.1 and 5.2 for the 33-yg/dL and 

53-yg/dL EP levels, respectively. Each figure shows results for six air-lead scenarios 

(lower- and upper-bound GM values for baseline, precontrol, and postcontrol time 

periods) for Sources 2, ^ and 5. The full risk estimate for each scenario is a probability 

distribution over a number or fraction of the population, but only the median and 90% 

credible intervals are shown. The median is indicated by an X, and the 90% credible 

interval is indicated by bars extending both above and below the median value. 

For the precontrol and postcontrol scenarios for areas surrounding all sources but 

Source 5, EP risk estimates are approximately at background levels. Specifically, the 

median values are about 10.7% for the 33-yg/dL EP level, and 2.1% for the 53-yg/dL EP 

level. The 90% credible intervals around these median values are about 6-15% (for 

33 yg/dL) and 0.1-5% (for 53 yg/dL). 

For the baseline scenarios and Sources 1-4, the median response rates are about 

21% (for 33 yg/dL) and 8% (for 53 yg/dL) for the lower-bound GM PbB values and are 

about twice those rates for the upper-bound GM PbB values. The uncertainty about these 

values is quite small, indicated by 90% credible intervals that are about equal to the 

median values plus or minus 1-2%. The narrow 90% credible intervals are due to the 

large numbers of children in the higher PbB groups examined by Piomelli et al. (1982), 

which dominate the risk calculations for the baseline scenarios for Sources 1-4. 
P.83 

76 

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77 

P.84 

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P.85 

78 

5.3 RISE RESULTS FOR HEMOGLOBIN 

Recall from Sec. 3 that the probabilistic judgments of four experts regarding 

dose-response functions for lead-induced hemoglobin decrements were obtained for two 

hemoglobin levels considered to be below normal (9.5 g/dL and 11 g/dL). In a fashion 

exactly the same as that for calculating the risks of adverse EP effects, functions that 

the experts agreed represented their judgments (cf. Sec. 3) were combined with the 

various PbB distributions described in Sec. 5.1, to produce estimates of overall risk. 

The results of the calculations (App. D) are summarized in Figs. 5.3-5.6. Results 

are shown only for children aged 0-3 years, who are more sensitive to lead exposure than 

children aged 4-6 years. Median risk estimates for children aged 4-6 years and for 

children aged 0-6 years are just slightly lower than those for ages 0-3 years. The upper 

ends of the credible intervals for ages 0-3 years are about 25% higher than those for ages 

0-6 years. 

Figures 5.3 and 5.4 are for Source 5, for the 11-g/dL and 9.5-g/dL hemoglobin 

levels, respectively. Figures 5.5 and 5.6 are analogous and for Source 2. In these figures, 

median values of the risk distributions and 90% credible intervals around those values are 

indicated for each air-lead scenario, based on the functions fit to the judgments of 

Experts A, C, D, and E. The median is indicated by an X, and the 90% credible interval 

is indicated by bars extending both above and below the median value. The bars are of 

various textures to help one to visually discriminate results for the individual experts. 
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FIGURE 5.6 Point Source 2, with Hb < 9.5 yg/dL 
P.90 

83 

Figure 5.3 (for the 11-g/dL hemoglobin level) indicates that the Expert A risk 

estimates* are essentially zero for all cases and that the 90% credible intervals for 

Experts D and E risk estimates overlap to some degree. The differences between the risk 

estimates based on the lower and the upper GM PbB values are response rates of about 

2% for Experts C-E in the baseline scenarios and 1% for Experts C and E and 2% for 

Expert D for in the precontrol scenarios. Upper and lower GM PbB values are equal in all 

postcontrol scenarios. 

In the precontrol scenario, the median response rates for Expert C risk estimates 

are about twice those for Expert D and about 15% less than those for Expert E. The 

Expert D and E risk estimates demonstrate the largest amounts of uncertainty, having 

upper 90% credible interval (CI) values about twice the median values, and lower 90% CI 

values about half the median values. For Expert C, these differences are about 25-75% 

and 50-75%, respectively. This difference is evident from the wider 90% credible 

intervals indicated in Fig. 5.3 for the Expert D and E risk estimates. 

The highest risk estimates are obtained for.the baseline, upper-bound scenario, 

for which the age 0-3 GM blood lead is 13.9 yg/dL; the lowest risk estimates are obtained 

for the precontrol and postcontrol (lower GM scenarios) for which the age 0-3 GM blood 

lead is 1.4 yg/dL. The .ratios of the highest and lowest median risk estimates are about 

1.3, 1.9, and 1.5 for Experts C, D, and E, respectively. Thus, an order of magnitude 

reduction in blood lead results in at most a 50% reduction in the median value of 

estimated risk. Similarly, the largest upper bounds and the smallest lower bounds of the 

90% credible intervals on risk do not change much in going from the highest PbB scenario 

to the lowest PbB scenario. Thus, the range of estimated risks that are plausible is not 

very sensitive to the mean PbB levels associated with the scenarios considered in this 

study. 

•When we use the phrase "expert A risk estimates," we mean a longer statement, 

namely, "risk estimates based on the judgments of Expert A." 
P.91 

84 

In nearly all of the scenarios for Source 5, there is virtually no chance that any 

children will have hemoglobin levels less than or equal to 9.5 g/dL, based on the 

judgments of both Experts A and D. The Expert C and E risk estimates are about half 

those for the 11 g/dL hemoglobin level. The Expert C risk estimates again show the 

smallest degree of uncertainty. As for the 11 g/dL hemoglobin level, estimated risk 

varies little as GM blood lead is changed. The conclusion for Source 5 is that the 

probability of adverse hemoglobin levels occurring decreases as air lead (and hence blood 

lead) decreases, but the percent reduction in risk is considerably less than the percent 

reduction in exposure. 

For Source 2, modeled mean PbB levels are about double those for Source 5 for 

the baseline and precontrol scenarios, and about the same for the postcontrol scenarios. 

Subsequently, the risks (response rates) are higher -- about 10-25% higher for the 11 g/dL 

level and about 10-100% higher for the 9.5 g/dL level. In addition, nonzero risk 

estimates result for Expert D for all scenarios except the postcontrol 9.5-g/dL 

hemoglobin level scenario. All of these results are consistent with the observation for 

Source 5 that a plot of risk vs. GM blood lead would be relatively flat, especially at the 

11 g/dL hemoglobin level. 

The conclusions for Source 2 are that: estimated risks are higher than those for 

Source 5 in the baseline and precontrol scenarios (because of higher estimated exposure 

to lead), and the same for the postcontrol scenarios. For Source 5, the probability of 

adverse hemoglobin levels occurring decreases as air lead decreases, but the percent 

reduction in risk is considerably less than the percent reduction in exposure. For the 

other point sources, the GM PbB values are about 5-10% less than those for Source 2. 

5.4 RISK RESULTS FOR IQ 

Judgments regarding IQ effects were obtained in a manner that allowed 

consideration from two perspectives that roughly correspond to dose-effect and dose-
P.92 

85 

response functions of two types of health endpoints. The first of these is expected IQ 

decrement. The second is more complicated, involving the lead-induced increase in 

fraction of children having IQs below a specified critical level denoted by IQ*. We show 

results in this section for IQ* values of 85 and 70, which correspond to one and two 

standard deviations below 100, although other values of IQ* could have been used. 

Further details on calculating these quantities are provided in App. C. We discuss the 

risk results for these two health endpoints in the next two sections. 

Both health effects require combining the judgments about the dose-response 

functions with the exposure estimates from Sec. 5.1 to produce probabilistic risk 

estimates. Results are illustrated here for Sources 2 and 5, for the lower SES group (the 

most sensitive population)." Risk estimates calculated for Source 5 are smaller than those 

for any other point source because the modeled blood-lead levels are lower for this point 

source, and because the percentage of households having incomes below poverty level is 

the smallest. Modeled blood-lead levels and the percentage of households having incomes 

below the poverty level are highest around Source 2. For the remaining sources, modeled 

PbB levels are about 5-10% lower than those for Source 2. 

For the IQ health effects, the blood lead of interest is that at the 36th month. 

IQ, as described in Sec. 4, is measured on the seventh birthday. 

5.4.1 Expected IQ Decrement 

Expected IQ decrement is calculated by combining the judgments about IQ 

decrements (relative to a control group of children sheltered from lead) at each bloodlead level with a blood-lead distribution. Results are shown in Figs. 5.7 (for Source 5) 

and 5.8 (for Source 2). Results for the other sources are slightly less than those for 

Source 2. In these figures, median values of the expected IQ distributions and 90% 

credible intervals around those values are indicated for baseline, precontrol, and 
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P.95 

88 

postcontrol scenarios (upper- and lower-bound estimates; postcontrol scenario results are 

essentially equivalent for all NAAQS levels analyzed), based on the functions fit to the 

judgments of Experts F through K. The median is indicated by a unique symbol for each 

expert, and the 90% credible interval is indicated by bars extending both above and below 

the median value. The bars are of various textures to help to visually discriminate 

results for the individual experts. 

For Source 5, the risk estimates exhibit the following patterns. Expert G, H, and 

J risk estimates are quite similar to one another, as are Expert F, I, and K risk 

estimates. The 90% credible intervals for Experts G, H, and J overlap. The distributions 

for H and J are nearly identical, and their median estimates are about double that for 

G. The upper ends of the 90% credible intervals for H and J are around four IQ points. 

The upper GM, baseline scenario risk estimates (for all but Expert F) are about one IQ 

point higher than the other estimates. (These median estimates of IQ decrement are 

about 2.7 for H and J, 1 for G, and about 0-0.3 for F, I, and K.) Estimates of IQ 

decrement for I and K are essentially zero for all other scenarios. 

For Source 2, the estimates of IQ decrement are about two points higher in the 

baseline scenarios for all experts except F. (Estimates of IQ decrement for F are always 

equal to zero.) This is attributable to the higher blood-lead levels estimated around 

Source 2. Estimates for the precontrol and postcontrol periods are about equal to those 

for Source 5. As for EP and hemoglobin, the general pattern for estimates of IQ 

decrement is that they do not differ substantially (within an expert) in the precontrol and 

postcontrol scenarios. 

5.4.2 Increased Probability of Lead-Induced IQ Levels being < IQ* 

To obtain functions analogous to dose-response functions, uncertainty in mean IQ 

of children sheltered from lead, within-group IQ standard deviation, and mean IQ 

decrement given different blood-lead levels were combined to calculate the increased 
P.96 

89 

probability of having IQs less than or equal to IQ*, as a function of PbB for IQ* values of 

70 and 85. These results were then combined with the geometric mean blood leads 

summarized in Table 5.3 to calculate overall risk estimates. 

Results are shown in Figs. 5.9-5.12. The first two figures are for Source 5, and 

the next two are for Source 2. Figure 5.9 (for IQ* = 70) shows that the increased 

probability of having IQ levels less than or equal to IQ* for these modeled point sources 

are very small (median probability values around 0.01 to 0.02 for Experts G, H, and J) or 

essentially zero (for Experts F and K). There are no estimates for Expert I because that 

individual did not provide the needed judgments about mean IQ levels for children 

sheltered from lead exposure or about IQ standard deviations. 

The largest risk estimates are calculated in the upper GM, baseline scenario 

(median estimates range from 0.014-0.024 for the increased probability of having IQs _< 

70, as one would expect. For this scenario, the risk estimates based on the judgments of 

all experts but F are comparable. Estimates for K of this magnitude result because 

Expert K judges that mean IQ levels for lower SES children sheltered from lead will be 

quite low (around 85). For the scenarios with lower blood-lead levels, Expert K risk 

estimates become much smaller relative to the others because Expert K judges that 

there is a threshold for lead-induced IQ effects around 5-15 yg/dL. 

For IQ* = 85, the results in Fig. 5.10 indicate a five-fold higher degree of risk 

than just discussed. In the precontrol and postcontrol scenarios, credible intervals for 

Expert G, H, and J risk estimates overlap (median values of 0.014-0.061, while median 

estimates for F and K are zero and 0.004, respectively. Again, the distributions for H 

and J are quite similar, having upper 90% credible interval values around 0.1. Precontrol 

and postcontrol risk estimates for increased probability are about equal, and about 0.01 

lower in probability than those for the lower GM, baseline scenario. In the baseline 

scenario, a 60% decrease in GM (from the upper bound to the lower bound) is 
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P.2 

94 

accompanied by a 25-50% decrease in the risk estimates for Experts G, H, and J, and an 

80% decrease for Expert K. Further decreases in blood-lead levels do not substantially 

lower the risk estimates for any of the experts. Thus, the relative decrease in the risk 

measure vs. a decrease in exposure depends on the level of exposure. 

Results for Source 2 are shown in Figs. 5.11 (for IQ* = 70) and 5.12 (for 

IQ* = 85). For IQ* = 70, risk estimates based on the judgments of Experts G, H, J, and K 

are similar for the baseline scenarios. The 90% credible intervals overlap in the lower 

and upper GM cases. In fact, they are nearly overlapping across GM values. Median 

values of increased probability range from 0.024 to 0.04 for the lower GM values, and 

from 0.037 to 0.068 for the upper GM values. For the upper GM, precontrol scenario, 

median risk estimates range from 0.01 to 0.022 among these experts. Expert K risk 

estimates are zero for the remaining scenarios. The median values for the other experts 

are about 0.004-0.01, and upper 90% confidence limit values are 0.015-0.034. Probability 

distributions determined for Experts H and J in each scenario are quite similar. 

The risk estimates calculated for IQ* = 85 are generally about three to four 

times larger than those for IQ* = 70 for Experts G, H, and J, and about 50% higher for 

K. As for Source 5, there is agreement among the experts, as indicated by the 

overlapping 90% credible intervals. For a specific expert, the credible intervals for the 

lower and upper GM values overlap for the baseline scenario. Expert F risk estimates 

again are small (median values of 0.003 and 0.007 for the lower and upper GM cases). In 

the postcontrol scenarios, the Expert G, H, and J risk estimates have median values 

around 0.014-0.062 and upper 90% credible interval values around 0.04-0.1. The 

probability distributions for Expert H and J risk estimates again are quite similar, and 

Expert G risk estimates are about one-third those for H and J. As for the other health 

end points, the general pattern for estimates of the increased probability of having 

children with IQs less than or equal to IQ* is that those for the precontrol and 

postcontrol periods are about one-third to one-fourth those for the baseline period, and 

that the 90% credible intervals for the lower and upper GM blood-lead cases overlap. 
P.3 

95 

REFERENCES 
P.4 

96 

APPENDIX A 

FITTING FUNCTIONS TO DATA ON LEAD-INDUCED ELEVATED 

ERYTHROCYTE PROTOPORPHYRIN LEVELS 

Section 2 discusses published data (Piomelli et al., 1982) about dose-response 

relationships between PbB level and EP level. Because the data are complete and 

reliable, probability encoding of the judgments of experts was not necessary. The 

available data, when combined with sample-size data, are sufficient to develop 

probabilistic dose-response functions. Those functions are specified in this appendix. 

Figure 2.1 presents published dose-response data about lead-induced elevated EP 

levels, and Table 2.1 presents sample-size data. For the two EP levels (33 yg/dL and 53 

yg/dL) addressed, expressions can be determined for the mean dose-response curves 

shown. 

(

0.107, 

*"1(0.1( 

• w...w,, for L < 16.6 yg/dL 

EP 1 -1 ~ 

i . i,~ io348-(L-16.6)-1.22, for L > 16.6 yg/dL 

for EP levels greater than or equal to 33 yg/dL, and 

(

0.024, 

*

_ 1 ( 0 . 

for L < 16.6 yg/dL 

10348-(L-16.6)-2), for L > 16.6 yg/dL 

for EP levels greater than or equal to 53 yg/dL, 

where: 

R = population response rate (fraction of children having EP 

levels greater than or equal to a specific EP level), 

L = PbB level (yg/dL), and 

<J (•) = inverse of the cumulative distribution function of a 

standardized normal random variable. 

Piomelli et al.'s (1982) data indicate a threshold for EP effects at a PbB level about 16.6 
97 

yg/dL. Further, response rates of 0.024 and 0.107 were found to be "natural frequencies" 

for the occurrence of EP levels above 53 yg/dL and 33 yg/dL, respectively. 

Probability distributions over the population response rate determined for 10 

(PbB, EP) level combinations are summarized in Table A.l. These distributions are either 

beta 

8(R ) = CN-Di x-i (1 _ R ) N-X- I 

B U ;

 (X-l)I(N-X-D!

 R U R ; 

or normal at each PbB level, where N is the number of children at a specific PbB level, 

and X is the number of children having EP levels greater than or equal to either 33 yg/dL 

or 53 yg/dL. The cumulative probability function for the beta distribution is 

B(R) = 1 - V I IR1 (l-R) 1 1 "

1

"

1 

X-1 /N- A . 

-I (JRl 

The mean E(R) and variance V(R) of the beta distribution and, where appropriate, its 

normal approximation are 

E(R) = £ and V(R) = *( N~

X ) 

N

 NZ(N+1) 

For most PbB and EP combinations, the quantity NR(l-R) was large enough to allow use 

of the normal approximation. 
TABLE A.1 Probability Distributions and Parameters for Piomelli's Data on Erythrocyte 

Protoporphyrin (EP) Levels among New York City Chil-dren 

PbB 

(yg/dL) 

5 

15 

25 

35 

50 

Functional 

Form 

Normal 

Normal 

Normal 

Normal 

Beta 

EP > 33 yg/dL 

Parameter Values 

E(R)a=0.107 

E(R)=0.107 

E(R)=0.337 

E(R)=0.728 

X=42 

V(R)b=0.0292 

V(R)=0.0092 

V(R)=0.0202 

V(R)=0.0432 

N=43 

Functional 

Form 

Beta 

Normal 

Normal 

Normal 

Beta 

EP > 53 yg/dL 

Parameter Values 

X=3 

E(R)=0.024 

E(R)=0.124 

E(R)=0.449 

X=40 

N=128 

V(R)=0.0042 

V(R)=0.0142 

V(R)=0.0472 

N=43 

a

E(R) denotes the expected value of R. 

^/(R) denotes the varianc e of R. 

Source: Data ar e from Piomelli et al. (1982). 

VO 

oo 
P.7 

99 

APPENDIX B 

HEMOGLOBIN 

Appendix B is organized as follows. Section B.l reproduces the protocol used 

during the hemoglobin encoding sessions. Section B.2 details the mathematical 

formulations for the dose-response models. Section B.3 tabulates encoded judgments, 

specifications for functions fit to those judgments, and credible intervals for encoded 

judgments and fitted functions. Section B.4 summarizes the discussions held with each of 

the interviewed experts. 

B.1 HEMOGLOBIN PROTOCOL 

B.1.1 Introduction 

The Environmental Protection Agency (EPA) is charged by the Clean Air Act 

with setting and revising National Ambient Air Quality Standards (NAAQS) for selected 

pollutants, at levels sufficient to protect the public health with an adequate margin of 

safety. As you know, the scientific bases for NAAQS are presented and reviewed in 

criteria documents. In support of the forthcoming review of the lead NAAQS, EPA has 

just prepared a new Air Quality Criteria for Lead. It presents scientific evidence from 

which the most susceptible populations can be determined and from which various 

adverse health effects can be identified. The criteria document summarizes and 

evaluates the available clinical, epidemiological, and animal or toxicological laboratory 

evidence with regard to the physiological and adverse health effects of lead, and 

therefore represents our most up to date knowledge on lead effects. 

As one aspect of the review process, EPA assesses health risks by identifying the 

most sensitive populations for each pollutant, and estimating probabilistically the 

numbers of people in the populations who may suffer each of various well-defined 

adverse health effects attributable to the pollutant. It is believed that information about 
P.8 

100 

the health risks associated with various potential standards will aid the EPA 

administrator in selecting that standard which, in his judgment, protects the public 

health with an adequate margin of safety. 

Because the risk estimates that EPA seeks are often based in part on doseresponse relationships and lead exposure estimates which are uncertain, it is necessary to 

make probability judgments about relevant dose-response functions based on the 

available evidence, and to probabilistically estimate lead exposure under alternative 

NAAQS. Obtaining the health risk estimates then involves combining dose-response and 

exposure probability estimates. 

The problem of estimating dose-response relationships is similar to that which 

exists in clinical medicine when there do not exist data that bear precisely on the 

patient's problem. In that case it is necessary to use scientific judgment to extrapolate 

from the data to make a best decision for the patient. Here, too, it is necessary to use 

scientific judgment to extrapolate from the available data. The extrapolation is not 

certain and, therefore, we will aid you to represent your opinion probabilistically. 

Furthermore, since the extrapolation depends on one's interpretation of the literature, 

different people will have different judgments. For each health effect we intend to 

obtain the probabilistic judgments of about five experts to sample the range of respected 

opinions. The model for estimating risks will not merge these judgments into a single 

average judgment, but rather will estimate the range of risks based on the range of 

judgments. If we as risk analysts do our job properly, then not only will we be able to 

show the EPA administrator the range of estimates based on the range of judgments, but 

we will also be able to show some of the sources of the disagreements. Indeed, a side 

benefit of this exercise in which we probe your knowledge in a structured manner may be 

to help identify sources of greatest disagreement. 

Based on the evidence in the lead criteria document, two populations have been 

identified as being most susceptible to the effects of lead intoxication. One is children 
P.9 

101 

from birth through the seventh birthday, and the other is pregnant women, or more 

precisely, the fetuses being carried by the pregnant women. A number of adverse health 

effects have been identified for which we would like to estimate dose-response functions 

including the one discussed below. 

B.l.2 Lead-Induced Hemoglobin Decrements 

We would like to represent in probabilistic form your opinion about the location 

and shape of dose-response functions for certain well defined levels of lead-induced 

hemoglobin reduction in the population of U.S. children from conception through the 

seventh birthday. We realize that available data do not fully define these functions; if 

they did, then it would be unnecessary to obtain your and other experts' opinions about 

them. Nevertheless, if the population, the exposure conditions, and the health effects 

are all precisely defined; then such functions in fact exist and we would like your best 

judgment about what they would look like if the data could be collected. 

B.l.2.1 Definition of Hemoglobin Decrement as an Adverse Health Effect 

There are differences of opinion, of course, as to what degree of reduction in 

hemoglobin level constitutes a health risk. The Clean Air Act makes it clear that EPA 

should set its standards to protect against adverse health effects. However, the 

reduction in hemoglobin level considered to be adverse may be different for regulatory 

purposes than for clinical action. Since it is generally agreed for children that a 

hemoglobin level of about 12 grams per deciliter is normal and about 9 grams per 

deciliter is anemic, we will specify two hemoglobin levels in that interval, namely 9.5 

and 11 gm/dl, and treat each as the physiological effect for purposes of specifying a 

dose-response function. We will elicit from you probability judgments about the shape 

and location of the dose-response curve for each of the two levels of effects in the 

sensitive population. 
P.10 

102 

B.1.3 Population at Risk 

We are defining the most susceptible group as all United States children from 

conception through their seventh birthday. However, you may believe on various grounds 

that younger and older children in this group have different dose-response functions for 

lead-induced hemoglobin reduction. If so, then we will elicit your judgments separately 

for the age groups 0-3 and 4-6. 

B.1.4 Exposure Conditions 

We will be asking your judgment about population response rates at various 

blood-lead levels. Assume that the blood-lead level under consideration for a given 

judgment is in equilibrium as a result of a sufficiently long-term constant lead exposure 

without gross excursions above or below the stated level. 

B.l.5 Physiological Conditions 

Because the effect of lead on hemoglobin level depends on many parameters of a 

person's system, it is necessary to specify assumptions about those parameters in the 

population. The effect of lead in the system depends on the person's nutritional and 

metabolic status. The incidence of iron deficiency is greater in children than in adults, 

and greater yet in children age 0-3 than age 4-6, with a wide range of iron levels in 

children up to their seventh birthday. Assume that the distribution of iron levels is that 

which you believe it actually to be in the age groups 0-3 and 4-6. The effect of lead also 

depends on the levels of zinc, copper, vitamins A, C, D, and E, calcium, phosphorous and 

magnesium. Assume in all cases that these nutrients are distributed in the two age 

groups as you believe they in fact are, taking into account the wide range of diets and 

nutritional levels of U.S. children. 

It is well established, of course, that erythrocyte protoporphyrin (EP) level is 

positively correlated with blood-lead level. However, the correlation is not perfect, and 
P.11 

103 

there is a range of EP values at any given blood lead. You may believe that the effect of 

lead varies with EP level. If so, assume that EP is distributed at each blood-lead level as 

you believe it in fact is. 

B.1.6 Factors to Consider 

In order to help you bring to mind the relevant evidence so that you may consider 

it systematically, and also in order to help us to interpret your judgments, we would like 

to ask you to discuss briefly your interpretations of various aspects of the literature. 

First of all, could you tell us something about how, in your judgment, lead and iron 

interact to reduce hemoglobin levels and something about the relation between iron and 

lead levels in the body? Similarly, we would be interested in your opinions about the 

same questions with regard to zinc and lead and to calcium and lead. It appears that lead 

affects hemoglobin levels through three somewhat separate routes: interference with 

heme synthesis, interference with globin synthesis, and decreased life expectancy of 

erythrocytes. Briefly, what is your interpretation of the literature on these various 

effects of lead? EP level increases with iron deficiency, but it also increases with blood 

lead and is considered to be a proxy measure for the amount of lead recently cumulated 

in body tissue. Considering only that portion of EP elevation due to lead, in your 

judgment, is the relationship between blood lead and hemoglobin different at different 

EP levels? 

Finally, we know that some groups of children are at greater risk of exposure to 

lead due to their living in deteriorating pre-1950 housing or in urban areas with large 

amounts of vehicular traffic. These children would tend to have high lead levels, but do 

you believe that there are also independent reasons to think that their dose-effect curves 

will be different from children who live in other circumstances? For example, these may 

be the same children who tend to have poorer diets and less access to medical care. 

What is your opinion regarding the possibility of a correlation between increased 
P.12 

104 

exposure and increased susceptibility? Are there other factors to consider in thinking 

about the dose-response functions for lead-induced hemoglobin decrements that we 

should discuss now? 

B.1.7 Factors to Keep in Mind When Making Probability Judgments 

There is usually uncertainty associated with conclusions that we draw from 

research, and more generally in our everyday thinking. However, not everyone is aware 

of all the sources that should contribute to their uncertainty, nor are most people 

familiar with the process of actually expressing their uncertainty in probabilistic terms. 

When an expert is asked to make probability judgments on socially important matters, it 

is particularly important that he or she consider the relevant evidence in a systematic 

and effective manner and provide judgments that represent his or her opinions well. 

Experimental psychologists and decision analysts have amassed a considerable 

amount of data concerning the way people form and express probabilistic judgments. The 

evidence suggests that when considering large amounts of complex information, most 

people employ simplifying heuristics and demonstrate certain systematic distortions of 

thought, i.e., cognitive biases, which adversely affect their judgments. The purpose of 

this section is to make you aware of these biases and heuristics so that, as much as 

possible, you can avoid them in making probability judgments. We will first review the 

most widespread biases and heuristics, and then offer some suggestions to help you 

mitigate their effects. 

B.l.7.1 Sequential Consideration of Information 

Generally, the order in which evidence is considered influences the final 

judgment, although logically that should not be the case. Of necessity, pieces of 

information are considered one by one in a sequential fashion. However, those 

considered first and last tend to dominate judgment. In part, initial information has its 
P.13 

105 

undue influence because it provides the framework which subsequent information is then 

tailored to fit. For example, people usually search for evidence to confirm their initial 

hypotheses; they rarely look for evidence that weighs against them. The later evidence 

has its undue effect simply because it is fresher in memory. 

Related to these sequential effects is the phenomenon of anchoring and 

adjustment. Based on early partial information, one forms an initial probability estimate 

regarding the event in question. This anchor judgment is then adjusted as subsequent 

information is considered. Unfortunately, such adjustments tend to be too 

conservative. In other words, too little weight is attached to information considered 

subsequent to the formation of the initial judgment. 

B.l.7.2 Effects of Memory on Judgment 

It is difficult for most people to conceptualize and make judgments about large, 

abstract universes or populations. A natural tendency is to recall specific members and 

then to consider them representative of the population as a whole. However, the specific 

instances often are recalled precisely because they stand out in some way, such as being 

familiar, unusual, especially concrete, or of personal significance. Unfortunately, the 

specific characteristics of these singular examples are then attributed, often incorrectly, 

to all the members of the population of interest. Moreover, these memory effects are 

often combined with the sequential phenomena discussed earlier. For example, in 

considering the evidence regarding the dose-response curve of a particular pollutant, you 

might naturally first think of a study you or a personal friend recently completed. Or 

you might think of a study you recently read, or one that was unusual and therefore 

stands out. The tendency might then be to treat the recalled studies as typical of the 

population of relevant research, ignoring important differences among studies. 

Subsequent attempts to recall information could result in thinking primarily of evidence 

consistent with the initial items you thought of. 
P.M 

106 

B.l.7.3 Estimating Reliability of Information 

People tend to overestimate the reliability of information, ignoring factors such 

as sampling error and imprecision of measurement. Rather they summarize evidence in 

terms of simple and definite conclusions, causing them to be overconfident in their 

judgments. This tendency is stronger when one has a considerable amount of intellectual 

and/or personal involvement in a particular field. In such cases, information is often 

interpreted in a way which is consistent with one's beliefs and expectations, results are 

overgeneralized, and contradictory evidence is ignored or underestimated. 

B.l.7.4 Relation Between Event Importance and Probability 

Sometimes the importance of events, or their possible costs or benefits, 

influence judgments about the certainty of the events when, rationally, importance 

should not affect probability. In other words, one's attitudes towards risk tend to affect 

one's ability to make accurate probability judgments. For example, many physicians tend 

to overestimate the probability of very severe diseases, because they feel it is important 

to detect and treat them; and similarly, many smokers underestimate the probability of 

adverse consequences of smoking, because they feel that the odds do not apply to 

themselves personally. 

B.l.7.5 Estimation of Probabilities 

Another limitation is related to one's ability to discriminate between levels of 

uncertainty, and to use appropriate criteria of discrimination for different ranges of 

probability. One result of this fact is that people tend to estimate both extreme and 

mid-range probabilities in the same fashion, usually doing a poor job in the extremes. It 

helps here to think in terms of odds as well as probabilities. Thus, for example, changing 

a probability estimate from 0.510 to 0.501 is equivalent to a change in odds from 1.041:1 

to 1.004:1, but a change from an estimate of 0.999 to 0.990 changes the odds by a factor 
P.15 

107 

of about 10? from 999:1 to 99:1 The closer to the extremes (either 0 or 1) that one is 

estimating probabilities, the greater the impact of small changes. 

B.l.7.6 Recommendations 

Although extensive and careful training would be necessary to eliminate all the 

problems mentioned above, some relatively simple suggestions can help minimize them. 

Most important is to be aware of one's natural cognitive biases, and to try consciously to 

avoid them. 

To avoid sequential effects keep in mind that the order in which you think of 

information should not influence your final judgment. It may be helpful to actually note 

on paper the important facts you are considering and then to reconsider them in two or 

more sequences, checking the consistency of your judgments. Try to keep an open mind 

until you have gone through all the evidence, and don't let the early information you 

consider sway you more than is appropriate. 

To avoid adverse memory effects, define various classes of information that you 

deem relevant, and then search your memory for examples of each. Don't restrict your 

thinking only to items that stand out for specific reasons. Make a special attempt to 

consider conflicting evidence, and to think of data that may be inconsistent with a 

particular theory. Also, be careful to concentrate on the given probability judgment and 

do not let your own values (how you would make the decision yourself) affect those 

judgments. 

To accurately estimate the reliability of information, pay attention to such 

matters as sample size and power of the statistical tests. Keep in mind that data are 

probabilistic in nature, subject to elements of random error, imprecise measurements, 

and subjective evaluation and interpretation. In addition, the further one must 

extrapolate, or generalize, from a particular study to a situation of interest, the less 

reliable is the conclusion and the less certainty should be attributed to it. Rely more 
P.16 

108 

heavily on information which you consider more reliable, but do not treat it as "absolute 

truth." 

Keep in mind that the importance of an event or an outcome should not influence 

its judged probability. It is rational to let the costliness or severity of an outcome 

influence the point at which action is taken with respect to it, but not the judgment that 

is made about the outcome's likelihood. 

Finally, in making probability judgments, think primarily in terms of the measure 

(probability or odds) with which you feel more comfortable, but sometimes translate to 

the alternative scale, or even to measures of other events (e.g,, the probability of the 

event not happening). When estimating very small or very large likelihoods, it is usually 

best to think in terms of odds, which are unbounded, instead of probabilities, which are 

bounded. For example, one can more easily conceptualize odds of 1:200 than a 

probability of .005. 

B.1.8 Possible Adverse Health Effects of Elevated Erythrocyte 

Protoporphyrin (EP) 

It seems well established that there is a positive dose-response relationship 

between blood lead arid EP. Although this elevated EP can be traced to heme synthesis 

interference, there is disagreement as to what, if any adverse health effects are 

associated with lead induced elevated EP. We would like to discuss your views on this 

issue in our second visit after we have completed encoding your probabilistic judgments 

concerning the hemoglobin blood-lead dose-response function. 

In your judgment, is lead-induced elevated EP associated with alterations in any 

of the following, and if so, at what level or range of levels of EP would you consider the 

effects to become adverse? These are alterations in: 

1. Neurochemistry or other CNS functions, 

2. Liver detoxification capabilities, or 
P.17 

109 

3. Renal or endocrine function (in particular, reduced biosynthesis of 1,25-

dihydroxyvitamin D). 

Is there a relation between lead induced elevated EP and anemia of any sort 

beyond that which can be indexed by blood-lead level alone? Does elevated EP suggest 

that the individual is more susceptible to lead toxicity due to subsequent exposures? Are 

there other adverse health effects that you believe may be associated with elevated EP? 

B.1.9 Final Preparation for Elicitation of Probability Judgments 

The shape and location of the dose-response curve as we defined it above is 

uncertain, because the existing data do not determine the dose-response relationship 

exactly. Yet, if we have defined the dose-response curve precisely, in a mathematical 

sense such a relationship does exist. Our goal is to have you represent probabilistically 

your own uncertainty about the location and shape of this mathematically existent 

function, based on your expertise and the available knowledge. In responding to the 

questions we will ask you, please think carefully about the relevant information reviewed 

in the criteria document, and consult it, the literature, or your files as you deem 

appropriate. 

The previous section suggests ways to think about the relevant data. The purpose 

of that section is to help minimize the biasing effects that frequently accompany the 

information overload naturally resulting from rapid consideration of large amounts of 

complex evidence. You may find it helpful to review the section or raise questions about 

the points made in it before we begin. 

Uncertainty about a dose response relationship can be represented 

probabilistically in two different ways. 

1. Uncertainty about the percentage of the defined population that 

would be affected by given blood-lead concentrations can be 

represented probabilistically. 
P.18 

110 

2. Uncertainty about the blood-lead concentrations that would be 

required to affect a given percentage of the defined population can 

be represented probabilistically. 

We will concentrate on one way at a time, focusing primarily on the first one. 

For these purposes it is helpful to imagine that everyone in the population has a 

specified blood-lead level that has become stabilized in the manner described above 

under Exposure Conditions. Then, as a result, some percentage of the population will 

suffer the hemoglobin response. 

Now, in order for us to determine your uncertainty about the percentages of the 

population that would be affected by given blood lead levels we must introduce a 

definition. Let C be the given blood-lead concentration in question. 

Definition: R(C) is the percentage of the population for which a blood-lead level 

of C would cause the defined hemoglobin health effect. 

Thus, R(C) is precisely the percent of the population that would show a response if the 

entire population had blood-lead levels of C under the conditions defined above. R(C) is 

usually called the population response rate. 

The value of R(C) for a given C is uncertain, and we would like to obtain 

probability judgments from you about its possible values. We will elicit your judgments 

about the possible values of R(C) by specifying a particular percentage and having you 

consider how likely it is that R(C) is less than that value. To help you make your 

probability judgments, we will make use of a device called a probability wheel, which has 

adjustable sectors of blue and orange. We can read on the back of the wheel the 

percentage of the wheel that is each color. In making your judgments you are to imagine 

that the wheel is a perfectly fair random device, and that therefore the probability of its 

stopping with the pointer on blue is exactly represented by the relative area that is blue. 

We will then proceed as follows. For each blood lead concentration C, we will 

specify a particular percent r, and also set the probability wheel to have a specific 

relative area of blue. Then you are to consider carefully the question: 
P.19 

111 

Do you consider it more probable that the true population response rate R(C) is 

less than r or that the wheel would stop with the pointer on blue (on a random 

spin)? 

You can give one of three responses: 

1. You judge it to be more probable that R(C) is less than r; 

2. You judge it to be more probable that the wheel would stop with 

the pointer in blue; 

3. You cannot judge either event as more probable than the other. 

For a particular concentration C and percent r, some wheel settings will have a 

small enough relative area of blue that you will feel confident making response (1). 

Other wheel settings will have a large enough relative area of blue that you will feel 

confident making response (2). The intermediate settings will be more difficult to 

judge. However, we will manipulate the wheel settings to find the one for which you feel 

most comfortable making response (3). 

Once we have determined the point at which you are most comfortable with 

response (3), and still focusing on the given blood lead C, we will specify a new percent 

r', and repeat the procedure. This will continue for the given C until we have specified 

various percents. Then we will have elicited one of the probabilistic representations of 

your uncertainty about the dose-response relationship we need. We will obtain the next 

probabilistic representation by specifying a new C and continuing as before. We will do 

this for a number of values of C. 

It frequently happens that an expert's judgments alter somewhat over the course 

of a session such as this, as he or she considers the evidence from various perspectives 

and thinks about the various responses called for. Hence, we will graph your responses 

and, at appropriate times, show them to you for your consideration and comparison. At 

these times you may wish to change some of the judgments you gave earlier. 
P.20 

112 

We should emphasize that the judgments we are asking you to make are not 

simple ones, nor of course are there known correct answers. Rather, we want your best 

and most considered judgment in light of the available relevant scientific data, 

Therefore, please reflect on the available data carefully, feeling free to consult the lead 

criteria document or other sources as you wish as you formulate your judgments. 

(Encode judgments for at least two concentrations of one dose-response function, 

then continue with instructions.) 

Recall that uncertainty about the dose-response function can also be expressed in 

terms of the blood-lead concentration necessary to produce the effect in a given 

percentage of the population r, if the entire population had the same blood-lead 

concentration, stabilized as the result of exposure in the manner discussed earlier. More 

specifically, proceeding as before, let us introduce a definition: 

Definition: C(R) is the blood-lead level that would cause the defined hemoglobin 

health effect in R percent of the population. 

The value of C(R) is uncertain for a given R, and we want to obtain your 

judgments about its possible values. Analogously to what we have already done, for a 

given R we will specify concentrations c and ask you to consider how likely it is that the 

true C(R) is less than the specified c. More specifically, utilizing the wheel as before, 

we will ask you the question: 

Do you consider it more likely that the true concentration C(R) is less than c, or 

that the wheel would stop with the pointer on blue (on a random spin)? 

You can give one of three responses: 

1. You judge it more probable that C(R) is less than c; 

2. You judge it more probable that the wheel would stop with the 

pointer in blue; 

3. You cannot judge either event as more probable than the other. 
P.21 

113 

After determining the wheel setting at which you feel most comfortable with 

response (3), we will specify a new c and repeat the process. As before, for each R we 

will elicit your comparative judgments for various values of c. 

B.2 DETAILED MATHEMATICAL FORMULATIONS 

This section discusses in detail the mathematical techniques used to represent 

probability judgments about dose-response relationships. First, basic definitions and the 

notation are introduced. Then the normal-on-log-odds function is discussed as a 

distribution that can be fitted to probability judgments and that meets certain criteria. 

Methods are presented for obtaining least-squares estimates of the parameters of a 

normal-on-log-odds distribution and for assessing the goodness of fit. A family of equalvariance normal-on-log-odds distributions may sacrifice some goodness of fit to the 

judgments, but it meets all the criteria specified. This family is presented next, along 

with methods for obtaining least-squares estimates of its parameters and assessing its 

goodness of fit. 

B.2.1 Definitions and Notation 

This section presents definitions and notation. The reader is assumed to be 

familiar with the basic concepts of probability theory (e.g., definitions of random 

variables, probability density functions, and expectation and higher moments). 

For uncertain quantity X, let 

f jr(x) = judgmental probability density function (PDF) for X and 

Fx(x ) = cumulative judgmental density function (CDF) for X 

= / ° fY(x)dx. 
P.22 

114 

Thus Fx^o-1 1S th e i u dS

m

ental probability* that X is less than or equal to xQ. 

Furthermore, let 

y = E(X) = expected value of X 

x 

= JJ x fv(x )dx 

 o X o o 

2 

o = V (X) variance of X 

= J [* - E(X)]ZfY(x^)dxrt 

O X 0 0 

The uncertain quantities of interest in this report are population response rates, 

denoted R, at each of several blood-lead levels, denoted L. During encoding sessions 

with recognized experts, judgments representing a cumulative density function (CDF) for 

a response rate R given a population blood-lead level L [i.e., judgments representing 

FJWJJR)] will be elicited for a number of blood-lead levels. Taken together, these 

judgments will provide a family of probabilistic relationships that represents the 

judgmental probability that the population response rate (a fraction between 0 and 1) will 

be less than or equal to a particular value R, given a blood-lead level of L, for a specific 

adverse health effect, population, and exposure conditions. 

As already discussed, the calculation of risk generally requires an interpolation 

between specifically assessed points. Such interpolation is best accomplished by fitting a 

function to the judged probabilities. Section B.2.2 describes a method for doing this. 

•Hereafter, all probabilities referred to are judgmental probabilities, even if not 

explicitly stated. 
P.23 

115 

B.2.2 Normal-on-Log-Odds Function 

Because probabilistic judgments about dose-response relationships are generally 

"s-shaped" over the closed [0,1] interval, they can be difficult to represent with closedform mathematical functions. One particularly useful function that is relatively easy to 

work with is the normal-on-log-odds distribution. The normal-on-log-odds distribution is 

obtained by fitting a normal distribution to the natural log of the odds implied by the 

population response rates R. Thus, the following relationships are defined: 

X = -j-l-jj, 0<X < 

Y = ln(X) , - » < Y <_ » 

where X is the odds variable and Y is the log of the odds variable. The variable Y is 

2 

assumed to be normally distributed with mean y and variance o . The degree to which 

the assumption is appropriate can be tested with each set of judgments. If Y is normally 

distributed, X is log-normally distributed. Although no closed-form expression is readily 

available for the distribution on R, all probabilistic and statistical results of interest on 

R can be obtained through the distribution on Y since 

pr(R < r) = pr X < T—-— = pr Y < In r-^— — — 1- r

 r

 — 1- r 

and 

y

o " y y o " V 

pr(Y < y ) = pr Z < — = * — — o — a a 

where pr(-) denotes probability and Z is the unit normal random deviate for which <i>(Z) is 

extensively tabulated and available in computer libraries. Thus 
P.24 

116 

V

r>

 -

 Fx(rb> 

- <-Y i-(rrr) 

. t

 ln(r^» -

Z o 

= * i H (B.l) 

Table B.l summarizes quantities of interest for these variables. 

The parameters y and o can be estimated in a least-squares sense from an 

assessed distribution. Let the n assessed points for a CDF be denoted (Rj, Fj) for i = 1, 

..., n, where Rj is the population response rate and Fj is the associated cumulative 

judgmental probability. 

Least squares estimates y and 3 for y and o can be obtained by linearly regressing the Zj on the yj. The reciprocal of the slope of the regression equation is Sand y 

is the y-intercept, i.e., the value of y corresponding to z = 0 in the regression equation. 

Since m judgmental distributions are assessed, one for each blood-lead level j for j = 1, 

..., m, there are m means (y^, ... , ym) and standard deviations (oj_, ... , om), one 

pair for each of the judged distributions. 

The goodness of fit of each distribution fit to the judgments for each blood-lead 

level is given by the standard regression r statistic obtained by regressing the F^ on the 

F., where 

r

2

 = l -
P.25 

117 

TABLE B.l Summary of Variables Pertaining to the Normal-On-Log-Odds Function 

Quantity 

of Interest 

Defining 

Equations 

Distribution3 

Meanb 

Variance 

Y 

Y = ln(X) 

N(y,o2) 

y 

a

2 

Variable 

X 

X = eY = R/(l -

A(y,a ) 

_ y+a2/2 

y = eK 

X 

2 2 

2 2y+a r a 

a = e le -

R) 

1) 

R = 

y 

X 

" \ 

,

2

 r 

R 

X 

1 + X 

-

2 

a 

X 

(1 + y ) 3 

X 

, . . 1* 

Median y e y 

Mode y e 

2 

1 

e

y 

1 • eM 

2 

2 

y-o 

+ e 

aN(y,a2) denotes the normal PDF; A(y,o2) denotes the lognormal PDF; 

the PDF for R cannot be expressed in closed form. 

Mean and variance expressions for R are approximate; they were derived with 

the method of moments; other estimates can be obtained with numerical 

methods on Fy = N(y,o ). 
P.26 

118 

and F£ denotes the estimated F values {i.e. , F^ = «(y£ - ]i)la, from Eq. B.l}, and 

o 2 

obtaining the r value of this regression. If the r value is sufficiently high, the normalon-log-odds distribution with parameters y j and o; describes the judgments well for lead 

level j . This distribution can then be used for interpolation. 

To summarize, formulas were presented to calculate the parameters of a normalon-log-odds distribution, which can be used to represent a judged probability distribution 

over population response rate for a given blood-lead level. Goodness of fit is given by a 

regression r statistic. The normal-on-log-odds distribution variable and its PDF can be 

used to estimate judgmental probabilities for the response rate variable R, which is then 

used to estimate risk. 

B.2.3 Representing a Probabilistic Dose-Response Surface with a Family 

of Equal-Variance Normal-on-Log-Odds Distributions 

If the o; are approximately equal, it is desirable to set them equal to a single 

pooled value before proceeding further (i.e., set o: = a' = a = o for all j). This step 

assures that the fitted distributions for two different lead levels never cross one 

another. (Crossed distributions would imply that exceeding a specified response rate is 

more probable at blood-lead level L, than at L«, where L« is greater than L..) Because 

of the manner in which judgments were obtained from the pilot subjects, crossings did 

not occur. Furthermore, judgments will be obtained from the health experts over a wider 

probability range so that crossings would only be possible at cumulative probabilities very 

near to 0 and 1. However, even crossings like these represent an inconsistency the 

experts ought to avoid and therefore should not be allowed. 

A pooled estimate of o, denoted ol, can be obtained by first subtracting the 

mean y- for each set of assessed points, 

y. . = y. . - y'. for i = 1, ... , n. and i = 1, ... , m J ,i J»i J J 
P.27 

119 

where n^ is the number of assessed points for F D n . and y- -. is an assessed point on 

FR/L-' Th e y ' ' ca n the n

 ^ e usec**

 t o caiculat e a mean (which should be very close to 

zero) and a variance (which will be the pooled, least-squares estimate o ' ) by regressing 

P 

the Z-. on the y. • . The individual, least-squares estimates of the means can be 

J*1 JJ 1 

recalculated at each lead level by finding the best-fitting line (in the least squares sense) 

with a slope of Ilo'. Under these conditions, the result is simply 

n . 

J 

y . = — ) y . . . 

J

 n j i-1 J' 1 

Denote the results of these last steps as y' , ... , y' . Goodness of fit again can be 

1 m 

obtained by regressing the recalculated estimates (which may be denoted as the F' .) on 

J » 1 

the original Fj j . 

If a functional relationship can be established between blood-lead levels and the 

y ' , a judgmental probability density function over R can be calculated for any blood-lead 

level, should that be necessary for interpolating between blood-lead levels. This 

continuum of density functions in essence is a probability surface over the dose-response 

plane. 

Any blood-lead distribution can be combined with the dose-response curve 

corresponding to judgmental cumulative probability F, Dp(L), to yield an estimate of the 

overall fraction of the population R suffering the adverse health effect with cumulative 

probability F. Such calculations result in the risk estimates summarized in Sec. 5 and 

described in detail in App. D. 

B.3 RESULTS 

Results are presented in three tables: Table B.2 covers encoded judgments, 

Table B.3 summarizes the functions fit to the judgments, and Table B.4 compares the 
P.28 

120 

TABLE B.2 Encoded Probability Judgments of Experts Regarding Lead-Induced 

Hemoglobin Decrements 

Expert A, Hemoglobin < 11 g/dL, Ages 0-3 Years 

Blood-Lead Levels 

45 y 

Rf 

0.01 

0.02 

0.04 

0.05 

0.07 

0.09 

0.1 

8/dL 

ll 

0.1 

0.25 

0.4 

0.5 

0.8 

0.95 

0.99 

0.19 

55 y 

R 

0.01 

0.03 

0.06 

0.09 

0.12 

0.15 

0.16 

0.999 

g/dL 

F 

0.05 

0.18 

0.4 

0.5 

0.6 

0.95 

0.99 

65 yg 

R 

0.04 

0.07 

0.1 

0.13 

0.16 

0.19 

0.22 

/dL 

F 

0.05 

0.15 

0.35 

0.45 

0.6 

0.9 

0.98 

0.4 

75 yg/dL 

R F 

0.05 0.05 

0.1 0.2 

0.15 0.4 

0.2 0.5 

0.25 0.6 

0.3 0.7 

0.35 0.95 

0.99 

Expert A, Hemoglobin < 11 g/dL, Ages 4-6 Years 

25 yg/dL 35 yg/dL 45 yg/dL 

R 

0.01 

0.02 

0.03 

0.05 

0.06 

F 

0.05 

0.4 

0.5 

0.9 

0.95 

R 

0.03 

0.05 

0.09 

0.12 

0.15 

F 

0.02 

0.2 

0.45 

0.55 

0.6 

R 

0.04 

0.05 

0.1 

0.15 

0.2 

F 

0.05 

0.1 

0.4 

0.5 

0.8 

0.08 0.99 0.18 0.98 0.25 0.98 

aR denotes population response rate (fraction having hemoglobin levels < 9.5 

or 11 g/dL). 

F denotes cumulative probability. 
P.29 

121 

TABLE B.2 (Cont'd) 

5 yg/dL 

R 

0.005 

0.01 

0.0175 

0.03 

0.035 

0.045 

0.03 

0.06 

0.08 

0.09 

0.12 

0.15 

F 

0.01 

0.05 

0.5 

0.8 

0.95 

0.99 

0.01 

0.28 

0.5 

0.5 

0.96 

0.99 

Expert C, 

15 yg/dL 

R F 

0.015 0.001 

0.02 0.02 

0.03 0.5 

0.04 0.75 

0.05 0.99 

0.06 0.999 

Expert C, 

0.05 0.03 

0.08 0.2 

0.09 0.5 

0.11 0.6 

0.14 0.91 

0.17 0.99 

0.2 0.999 

Expert D, 

0.01 0.5 

0.03 0.999 

Hemoglobin < 9.5 g/dL, Ages 

Blood-Lead Levels 

25 yg/dL 35 yg/dL 

R 

0.025 

0.03 

0.035 

0.04 

0.05 

0.06 

0.0675 

Hemoglob 

0.05 

0.09 

0.12 

0.13 

0.17 

0.21 

F R F 

0.01 0.035 0.01 

0.02 0.04 0.04 

0.25 0.05 0.5 

0.5 0.06 0.75 

0.75 0.07 0.97 

0.97 0.075 0.99 

0.99 

in < 11 g/dL, Ages 

0.001 0.1 0.01 

0.11 0.14 0.2 

0.5 0.16 0.5 

0.7 0.18 0.7 

0.98 0.22 0.98 

0.99 0.25 0.99 

Hemoglobin < 9.5 g/dL, Ages 

0.005 

0.03 

0.07 

0.01 0.03 0.001 

0.5 0.06 0.25 

0.999 0.08 0.5 

0.11 0.75 

0.15 0.999 

0-6 Years 

45 yg/dL 

R F 

0.045 0.01 

0.05 0.05 

0.06 0.5 

0.07 0.8 

0.08 0.97 

0.085 0.99 

0-6 Years 

0.15 0.01 

0.2 0.5 

0.25 0.7 

0.3 0.98 

0.35 0.999 

0.3 Years 

0.07 0.001 

0.11 0.25 

0.16 0.5 

0.19 0.75 

0.25 0.999 

55 yg 

R 

0.05 

0.06 

0.07 

0.08 

0.09 

0.1 

0.15 

0.2 

0.25 

0.27 

0.3 

0.35 

0.4 

0.1 

0.16 

0.2 

0.25 

0.33 

/dL 

F 

0.01 

0.05 

0.5 

0.8 

0.95 

0.99 

0.001 

0.08 

0.3 

0.5 

0.8 

0.98 

0.999 

0.001 

0.25 

0.5 

0.75 

0.999 
TABLE B.2 (Cont'd) 

5 yg 

R 

0.01 

0.02 

0.04 

0.1 

0.118 

0.01 

0.01 

0.02 

0.06 

0.001 

0.01 

0.03 

0.1 

0.15 

/dL 

F 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.99 

0.01 

0.1 

0.5 

0.9 

0.99 

Expert D, 

15 yg/dL 

R F 

Expert D, 

0.02 0.01 

0.04 0.25 

0.06 0.5 

0.12 0.75 

0.15 0.99 

Expert D 

0.01 0.01 

0.02 0.25 

0.03 0.5 

0.09 0.99 

Expert E, 

0.002 0.01 

0.03 0.05 

0.07 0.5 

0.11 0.61 

0.15 0.83 

0.19 0.9 

0.23 0.99 

— --•*--- " *W *' •" ' * 

122 

Hemoglobin < 9. 

Blood-Lead 

25 yg/dL 

R F 

0.00005 0.001 

0.005 0.5 

0.015 0.999 

5 g/dL, 

Levels 

Ages 

35 yg/dL 

R 

0.02 

0.05 

0.06 

0.08 

Hemoglobin < 11 g/dL, 

0.11 0.01 

0.115 0.25 

0.15 0.5 

0.178 0.75 

0.21 0.99 

, Hemoglobin < 

0.05 0.01 

0.07 0.5 

0.085 0.75 

0.12 0.99 

Hemoglobin < 9. 

0.003 0.01 

0.035 0.05 

0.04 0.1 

0.07 0.25 

0.09 0.5 

0.15 0.75 

0.21 0.9 

0.25 0.99 

0.15 

0.16 

0.18 

0.22 

0.24 

F 

0.001 

0.5 

0.75 

0.999 

Ages 

0.01 

0.25 

0.5 

0.75 

0.99 

g/dL, Ages 4-

0.07 

0.09 

0.105 

0.14 

5 g/dL, 

0.025 

0.05 

0.1 

0.15 

0.2 

0.26 

0.01 

0.5 

0.75 

0.99 

Ages 

0.01 

0.08 

0.27 

0.56 

0.81 

0.98 

4-6 Years 

45 yg/dL 

R F 

0.04 0.001 

0.06 0.25 

0.08 0.5 

0.1 0.75 

0.12 0.999 

0.3 Years 

0.17 0.05 

0.19 0.25 

0.22 0.5 

0.26 0.75 

0.29 0.95 

-6 Years 

0.08 0.01 

0.1 0.5 

0.16 0.99 

0.3 Years 

0.03 0.01 

0.06 0.06 

0.1 0.2 

0.19 0.5 

0.31 0.75 

0.41 0.99 

• 

55 yg/dL 

R 

0.06 

0.08 

0.1 

0.11 

0.15 

0.23 

0.26 

0.3 

0.4 

0.47 

0.1 

0.12 

0.14 

0.155 

0.17 

0.05 

0.08 

0.22 

0.36 

0.4 

0.47 

F 

0.001 

0.25 

0.5 

0.75 

0.999 

0.125 

0.25 

0.5 

0.75 

0.875 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.1 

0.5 

0.75 

0.9 

0.99 

P.30 

• 
P.31 

123 

TABLE B.2 (Cont'd) 

5 y 

IPO 

0.004 

0.01 

0.06 

0.09 

0.02 

0.04 

0.08 

0.12 

0.16 

0.2 

0.24 

0.02 

0.05 

0.08 

0.11 

0.14 

g/dL 

F 

0.15 

0.5 

0.78 

0.98 

0.01 

0.15 

0.5 

0.61 

0.83 

0.9 

0.98 

0.15 

0.47 

0.55 

0.78 

0.98 

Expert E, 

15 yg/dL 

R F 

0.01 0.15 

0.02 0.5 

0.07 0.78 

0.1 0.98 

Expert E, 

0.03 0.01 

0.06 0.15 

0.1 0.5 

0.14 0.61 

0.18 0.83 

0.22 0.9 

0.26 0.98 

Expert E, 

0.01 0.01 

0.04 0.15 

0.07 0.47 

0.1 0.55 

0.13 0.78 

0.16 0.98 

Hemoglobin < 9 .5 g/dL, Ages 

Blood-Lead Levels 

25 yg/dL 

R 

0.02 

0.04 

0.1 

0.13 

Hemoglob 

0.035 

0.06 

0.095 

0.15 

0.195 

0.25 

0.28 

Hemoglob 

0.05 

0.08 

0.11 

0.17 

0.2 

F 

0.17 

0.5 

0.9 

0.99 

35 yg/dL 

R F 

0.015 0.1 

0.03 0.22 

0.06 0.54 

0.1 0.85 

0.13 0.95 

in < 11 g/dL, Ages 

0.01 

0.1 

0.25 

0.5 

0.75 

0.9 

0.99 

0.04 0.01 

0.08 0.08 

0.15 0.27 

0.2 0.56 

0.25 0.81 

0.3 0.98 

in < 11 g/dL, Ages 

0.06 

0.16 

0.5 

0.9 

0.99 

0.05 0.07 

0.08 0.1 

0.11 0.27 

0.14 0.54 

0.17 0.85 

0.2 0.95 

4-6 Years 

45 yg/dL 

R F 

0.02 0.03 

0.065 0.1 

0.105 0.42 

0.165 0.6 

0.215 0.8 

0.265 0.99 

0-3 Years 

0.06 0.01 

0.1 0.07 

0.16 0.25 

0.22 0.5 

0.35 0.75 

0.45 0.99 

4-6 Years 

0.05 0.03 

0.1 0.1 

0.15 0.43 

0.2 0.6 

0.25 0.8 

0.3 0.99 

55 yg 

R 

0.06 

0.11 

0.15 

0.22 

0.26 

0.3 

0.1 

0.2 

0.3 

0.4 

0.5 

0.55 

0.05 

0.1 

0.15 

0.2 

0.25 

0.3 

0.35 

/dL 

F 

0.05 

0.4 

0.5 

0.75 

0.9 

0.98 

0.01 

0.35 

0.5 

0.62 

0.94 

0.99 

0.01 

0.05 

0.4 

0.5 

0.75 

0.9 

0.98 
P.32 

124 

TABLE B.3 Summary of Functions Fit to the Probabilistic Judgments of Experts 

Regarding Lead-Induced Hemoglobin Decrements 

Expert A, Hemoglobin < 11 g/dL, Ages 0-3 Years 

Blood-Lead 

Level 

(yg/dL 

45 

55 

65 

75 

Parameters of 

Normal-on-Ln (R/U-R)) 

Distribution 

Mean 

-3.3546 

-2.9338 

-2.0724 

-1.5754 

SDa 

0.6820 

0.6820 

0.6820 

0.6820 

Moment s of 

NOLO Distribution 

E[R]b 

0.0412 

0.0607 

0.1275 

0.1869 

Over R 

SD[R]C 

0.0311 

0.0454 

0.0910 

0.1263 

r

2 for 

Regression of 

F on F 

0.8914 

0.8388 

0.9305 

0.9407 

Expert A, Hemoglobin < 11 g/dL, Ages 4-6 Years 

55 

65 

75 

-3.6826 

-2.2713 

-2.0617 

0.5945 

0.5945 

0.5945 

0.0288 

0.1051 

0.1254 

0.0184 

0.0635 

0.0745 

0.9734 

0.8968 

0.9464 

aSD denotes standard deviation. 

E[R] denotes the mean of the distribution for R. 

SD[R] denotes the standard deviation of the distribution for R. 
I— 

1 

P.33 

125 

TABLE B.3 (Cont'd) 

Blood-Lead 

Level 

(yg/dL 

5 

15 

25 

35 

45 

55 

Expert C, Hemoglobin < 9.5 g/dL, Ages 0-6 Years 

Parameters 

Normal-onof 

-Ln (R/U-R)) 

Distribut 

Mean 

-3.9995 

-3.4481 

-3.1298 

-2.9187 

-2.7424 

-2.5781 

ion 

SDa 

0.2764 

0.2764 

0.2764 

0.2764 

0.2764 

0.2764 

Moments of 

NOLO Distribution 

E[R]b 

0.0187 

0.0319 

0.0433 

0.0529 

0.0624 

0.0727 

Over R 

SD[R]C 

0.0052 

0.0087 

0.0117 

0.0142 

0.0166 

0.0191 

r

2 for 

Regression of 

0.9806 

0.9899 

0.9906 

0.9917 

0.9900 

0.9713 

Expert C, Hemoglobin < 11 g/dL, Ages 0-6 Years 

5 

15 

25 

35 

45 

55 

-3.6826 

-2.2713 

-2.0617 

-1.6965 

-1.3190 

-1.0498 

0.5945 

0.5945 

0.5945 

0.2720 

0.2720 

0.2720 

0.0288 

0.1051 

0.1254 

0.1582 

0.2144 

0.2624 

0.0184 

0.0635 

0.0745 

0.0372 

0.0471 

0.0542 

0.9734 

0.8968 

0.9464 

0.9857 

0.9683 

0.9816 
P.34 

126 

TABLE B.3 (Cont'd) 

Expert D, Hemoglobin < 9.5 g/dL, Ages 0-3 Years 

Blood-Lead 

Level 

(yg/dL 

15 

25 

35 

45 

55 

Parameters of 

Normal-on-Ln (R/(l-R)) 

Distribution 

-4.5852 

-3.8759 

-2.4991 

-1.7769 

-1.4097 

SDa 

0.3557 

0.3557 

0.3557 

0.3557 

0.3557 

Moments of 

NOLO Distribution 

E[R]b 

0.0107 

0.0215 

0.0797 

0.1500 

0.2019 

Over R 

SD[R]C 

0.0039 

0.0078 

0.0272 

' 0.0475 

0.0602 

r

2 for 

Regression of 

F on F 

1.0000 

0.8421 

0.9805 

0.9654 

0.9935 

Expert D, Hemoglobin < 9.5 g/dL, Ages 4-6 Years 

25 

35 

45 

55 

-6.4604 

-3.0443 

-2.5123 

-2.2433 

1.0409 

0.2177 

0.2177 

0.2177 

0.0027 

0.0464 

0.0764 

0.0976 

0.0037 

0.0098 

0.0156 

0.0195 

0.8374 

0.9536 

0.9437 

0.9820 

Expert D, Hemoglobin < 11 g/dL, Ages 0-3 Years 

Blood-Lead 

Level 

(yg/dL 

5 

15 

25 

35 

45 

55 

Parameters 

Normal-onof 

-Ln (R/(l-R)) 

Distribut 

Mean 

-3.1747 

-2.7097 

-1.7442 

-1.4655 

-1.2485 

-0.7254 

Lon 

SDa 

0.4919 

0.4919 

0.4919 

0.4919 

0.4919 

0.4919 

Moment s of 

NOLO Distribution 

E[R]b 

0.0445 

0.0686 

0.1586 

0.1975 

0.2322 

0.3312 

Over R 

SD[R]C 

0.0225 

0.0340 

0.0720 

0.0858 

0.0967 

0.1196 

r

l

 for 

Regression of 

0.9285 

0.9565 

0.9693 

0.9674 

0.9966 

0.9729 
P.35 

127 

TABLE B.3 (Cont'd) 

Expert D, Hemoglobin < 11 g/dL, Ages 4-6 Years 

Blood-Lead 

Level 

(yg/dL 

5 

15 

25 

35 

45 

55 

Parameters of 

Normal-on-Ln (R/(l-R)) 

Distribution 

Mean 

-3.8759 

-3.4866 

-2.5049 

-2.2446 

-2.0993 

-1.8573 

SDa 

0.4894 

0.4894 

0.1777 

0.1777 

0.1777 

0.1777 

Moments of 

NOLO Distribution 

E[R]b 

0.0227 

0.0331 

0.0764 

0.0969 

0.1104 

0.1364 

Over R 

SD[R]C 

0.0116 

0.0168 

0.0127 

0.0157 

0.0176 

0.0212 

r

2 for 

Regression of 

F on F 

0.9448 

0.9968 

0.9579 

0.9674 

0.9358 

0.9749 

Expert E, Hemoglobin < 9.5 g/dL, Ages 0-3 Years 

Blood-Lead 

Level 

(yg/dL 

5 

15 

25 

35 

45 

55 

Parameters 

Normal-onDist 

Mean 

-3.7820 

-2.7992 

-2.4725 

-1.9602 

-1.5643 

-1.4002 

of 

-Ln (R/U-R)) 

ribut ion 

SDa 

0.9600 

0.9600 

0.9600 

0.9600 

0.9600 

0.9600 

Moment s of 

NOLO Distribution 

E[R]b 

0.0331 

0.0773 

0.0994 

0.1413 

0.1786 

0.1951 

Over R 

SD[R]C 

0.0414 

0.0987 

0.1280 

0.1836 

0.2301 

0.2486 

r

2 for 

Regression of 

F on F 

0.9817 

0.9553 

0.9586 

0.9646 

0.9854 

0.9866 

Expert E, Hemoglobin < 9.5 g/dL, Ages 4-6 Years 

5 

15 

25 

35 

45 

55 

-4.1623 

-3.6856 

-3.3376 

-3.0218 

-2.1141 

-1.9121 

0.8224 

0.8224 

0.8224 

0.8224 

0.8224 

0.8224 

0.0209 

0.0329 

0.0454 

0.0602 

0.1275 

0.1481 

0.0206 

0.0323 

0.0444 

0.0588 

0.1217 

0.1398 

0.9802 

0.9884 

0.9804 

0.9503 

0.9848 

0.9327 
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TABLE B.4 Summary and Comparison of Judgments and Fitted Functions Concerning Lead-Induced Hemoglobin 

Decrements 

Expert A, Hemoglobin < 11 g/dL, Ages 0-3 Years 

Blood-Lead Level 

Index 45 yg/dL 55 yg/dL 65 yg/dL 75 yg/dL 

Encoded Judgments 

Median 0.05 0.09 0.14 0.20 

50% C.I. a (0.02 , 0.07) (0.04 , 0.13) (0.09 , 0.18) (0.11 , 0.31) 

90% C.I. (0.01 , 0.09) (0.01 , 0.15) (0.04, 0.21) (0.05 , 0.35) 

Pitted Functions 

Median 0.03 0.05 0.11 0.17 

50% C.I. (0.02 , 0.05) (0.03 , 0.08) (0.07 , 0.17) (0.12 , 0.25) 

90% C.I. (0.01 , 0.10) (0.02 , 0.14) (0.04 , 0.28) (0.06 , 0.39) 

98% C.I. (0.01 , 0.15) (0.01 , 0.21) (0.03 , 0.38) (0.04 , 0.50) 

Expert A, Hemoglobin < 11 g/dL, Ages 4-6 Years 

ro 

vo 

Encoded Judgments 

Median 0.03 0.11 0.15 

50% C.I. (0.02, 0.04) (0.06, 0.16) (0.08, 0.19) 

90% C.I. (0.01, 0.06) (.03, 0.18) (0.04, 0.24) 

Fitted Functions 

Median 0.02 0.09 0.11 

50% C.I. (0.02, 0.04) (0.06, 0.13) (0.08, 0.16) 

90% C.I. (0.01, 0.06) (0.04, 0.22) (0.05, 0.25) 

98% C.I. (0.01, 0.09) (0.03, 0.29) (0.03, 0.34) 

"CI. denotes Credible Interval. 
TABLE B.4 (Cont'd) 

(a 

Expert C, Hemoglobin < 9.5 g/dL, Ages 0-^ Years 

Index 

Median 

50% C.I. 

90% C.I. 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

5 yg/dL 

0.02 

(0.01 , 0.03) 

(0.01 , 0.04) 

0.02 

(0.01 , 0.02) 

(0.01 , 0.03) 

(0.01 , 0.04) 

Blood-Lead Level 

15 yg/dL 25 yg/dL 35 yg/dL 

Encoded Judgments 

0.03 

(0.02, 0.04) 

(0.02, 0.05) 

0.03 

(0.03, 0.04) 

(0.02, 0.05) 

(0.02, 0.06) 

0.04 

(0.04, 0.05) 

(0.03, 0.06) 

Fitted Functions 

0.04 

(0.04, 0.05) 

(0.03, 0.06) 

(0.02, 0.08) 

0.05 

(0.04, 0.06) 

(0.04, 0.07) 

0.05 

(0.04, 0.06) 

(0.03, 0.08) 

(0.03, 0.09) 

45 yg/dL 

0.06 

(0.05, 0.07) 

(0.05, 0.08) 

0.06 

(0.05, 0.07) 

(0.04, 0.09) 

(0.03, 0.11) 

55 yg/dL) 

0.07 

(0.06, 0.08) 

(0.06, 0.09) 

0.07 

(0.06, 0.08) 

(0.05, 0.11) 

(0.04, 0.13) 

CO 

o 

Expert C, Hemoglobin < 11 g/dL, Ages 0-6 Years 

Median 

50% C.I, 

90% C.I, 

0.08 

(0.06, 0.10) 

(0.03, 0.10) 

0.09 

(0.08, 0.12) 

(0.05, 0.13) 

Encoded Judgments 

0.12 

(0.10, 0.14) 

(0.07, 0.15) 

Fitted Functions 

0.16 

(0.14, 0.19) 

(0.11, 0.20) 

0.20 

(0.17, 0.26) 

(0.15, 0.27) 

0.27 

(0.24, 0.29) 

(0.18, 0.31) 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

0.07 

(0.06, 0.09) 

(0.05, 0.11) 

(0.04, 0.13) 

0.10 • 

(0.08, 0.11) 

(0.06, 0.14) 

(0.05, 0.17) 

0.12 

(0.10, 0.14) 

(0.08, 0.17) 

(0.06, 0.20) 

0.15 

(0.13, 0.18) 

(0.10, 0.22) 

(0.09, 0.26) 

0.21 

(0.18, 0.24) 

(0.15, 0.29) 

(0.12, 0.33) 

0.26 

(0.23, 0.30) 

(0.18, 0.35) 

(0.16, 0.40) 
TABLE B.4 (Cont'd) 

Expert D, Hemoglobin < 9.5 g/dL, Ages 0-3 Years 

Blood-Lead Level 

/f 3% 35T <+< 5T 

Index /5 yg/dL Xb yg/dL >5 yg/dL tf> yg/dL 4-$ yg/dL -55 yg/UL) 

Encoded Judgments 

Median 0.01 0.03 0.08 0.16 0.20 

50% C.I. (—, 0.02) (0.02, 0.05) (0.06, 0.11) (0.11, 0.19) (0.16, 0.25) 

90% C.I. (—, 0.03) (0.01, 0.07) (0.04, 0.14) (0.08, 0.24) (0.11, 0.31) 

Fitted Functions 

Median 0.01 0.02 0.08 0.14 0.20 

50% C.I. (0.01, 0.01) (0.02, 0.03) (0.06, 0.09) (0.12, 0.18) (0.16, 0.24) 

90% C.I. (0.01, 0.02) (0.01, 0.04) (0.04, 0.13) (0.09, 0.23) (0.12, 0.30) 

98% C.I. (0.00, 0.02) (0.01, 0.04) (0.03, 0.16) (0.07, 0.28) (0.12, 0.36) 

Expert D, Hemoglobin < 9.5, Ages 4-6 Years 

Encoded Judgments 

Median 0.005 0.05 0.08 0.10 

50% C.I. (0.00, 0.01) (0.03, 0.06) (0.06, 0.10) (0.08, 0.11) 

90% C.I. (0.00, 0.01) (0.02, 0.08) (0.04, 0.12) (0.06, 0.14) 

Fitted Functions 

Median 0.002 0.05 0.07 0.10 

50% C.I. (0.00, 0.00) (0.04, 0.05) (0.07, 0.09) (0.08, 0.11) 

90% C.I. (0.00, 0.01) (0.03, 0.06) (0.05, 0.10) (0.07, 0.13) 

98% C.I. (0.00, 0.02) (0.03, 0.07) (0.05 0.12) (0.06, 0.15) 

CO 
TABLE B.4 (Cont'd) 

Expert D, Hemoglobin < 11 g/dL, Ages 0-3 Years 

Index 

Median 

50% C.I. 

90% C.I. 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

5 yg/dL 

0.04 

(0.02, 0.10) 

(0.01, 0.03) 

0.04 

(0.03, 0.06) 

(0.02, 0.09) 

(0.01, 0.12) 

15 yg/dL 

0.06 

(0.04, 0.12) 

(0.02, 0.15) 

0.06 

(0.05, 0.08) 

(0.03, 0.13) 

(0.02, 0.17) 

Blood-Lead Level 

25 yg/dL 35 yg/dL 

Encoded Judgments 

0.15 

(0.11, 0.18) 

(0.11, 0.21) 

Fitted Functions 

0.15 

(0.11, 0.20) 

(0.07, 0.28) 

(0.05, 0.35) 

0.18 

(0.16, 0.22) 

(0.14, 0.26) 

0.19 

(0.14, 0.24) 

(0.09, 0.34) 

(0.07, 0.42) 

45 

0.22 

(0.19, 0.26) 

(0.17, 0.29) 

0.22 

(0.17, 0.29) 

(0.11, 0.39) 

(0.08, 0.47) 

55 

0.30 

(0.26, 0.40) 

(0.21, 0.52) 

0.33 

(0.26, 0.40) 

(0.18, 0.52) 

(0.13, 0.60) 

CO 

INJ 

Expert D, Hemoglobin < 11 g/dL, Ages 4-6 Years 

Median 

50% C.I. 

90% C.I. 

0.02 

(0.01, 0.04) 

(0.01, 0.06) 

0.03 

(0.02, 0.06) 

(0.01, 0.09) 

Encoded Judgments 

0.07 

(0.06, 0.09) 

(0.05, 0.11) 

Fitted Functions 

0.09 

(0.08, 0.11) 

(0.07, 0.13) 

0.10 

(0.09, 0.13) 

(0.08, 0.16) 

0.14 

(0.12, 0.16) 

(0.10, 0.17) 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

0.02 

(0.01, 0.03) 

(0.01, 0.04) 

(0.01, 0.06) 

0.03 

(0.02, 0.04) 

(0.01, 0.06) 

(0.01, 0.09) 

0.08 

(0.07, 0.08) 

(0.06, 0.10) 

(0.05, 0.11) 

0.10 

(0.09, 0.11) 

(0.07, 0.12) 

(0.07, 0.14) 

0.11 

(0.10, 0.12) 

(0.08, 0.14) 

(0.07, 0.16) 

0.14 

(0.12, 0.15) 

(0.10, 0.17) 

(0.09, 0.19) 
TABLE B.4 (Cont'd) 

Expert E, Hemoglobin < 9.5 g/dL, Ages 0-3 Years 

Index 

Median 

50% C.I. 

90% C.I. 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

5 yg/dL 

0.03 

(0.02, 0.07) 

(0.01, 0.12) 

0.02 

(0.01, 0.04) 

(0.00, 0.10) 

(0.00, 0.18) 

15 yg/dL 

0.07 

(0.05, 0.13) 

(0.03, 0.21) 

0.06 

(0.03, 0.10) 

(0.01, 0.23) 

(0.01, 0.36) 

Blood-Lead Level 

25 yg/dL 35 yg/dL 

0.09 

(0.06, 0.15) 

(0.03, 0.23) 

Fitted Functions 

0.08 

(0.04, 0.14) 

(0.02, 0.29) 

(0.01, 0.44) 

0.14 

(0.09, 0.19) 

(0.04, 0.24) 

0.12 

(0.07, 0.21) 

(0.03, 0.41) 

(0.01, 0.57) 

45 yg/dL 

0.19 

(0.11, 0.31) 

(0.05, 0.39) 

0.17 

(0.10, 0.29) 

(0.04, 0.50) 

(0.02, 0.66) 

55 yg/dL) 

0.22 

(0.13, 0.36) 

(0.06, 0.44) 

0.20 

(0.11, 0.32) 

(0.05, 0.54) 

(0.03, 0.70) 

u> 

CO 

Expert E, Hemoglobin < 9.5 g/dL, Ages 4-6 Years 

Encoded Judgments 

Median 

50% C.I. 

90% C.I. 

0.01 

(0.01, 0.05) 

(0.00, 0.09) 

0.02 

(0.01, 0.06) 

(0.00, 0.10) 

0.04 

(0.01, 0.07) 

(0.00, 0.11) 

0.06 

(0.03, 0.09) 

(0.01, 0.13) 

0.13 

(0.08, 0.20) 

(0.03, 0.25) 

0.15 

(0.09, 0.22) 

(0.06, 0.29) 

Fitted Functions 

Median 

50% C.I, 

90% C.I, 

98% C.I, 

0.02 

(0.01, 0.06) 

(0.00, 0.06) 

(0.00, 0.10) 

0.02 

(0.01, 0.09) 

(0.02, 0.09) 

(0.00, 0.15) 

0.03 

(0.02, 0.12) 

(0.01, 0.12) 

(0.01, 0.19) 

0.05 

(0.03, 0.16) 

(0.01, 0.16) 

(0.01, 0.25) 

0.11 

(0.06, 0.32) 

(0.03, 0.32) 

(0.02, 0.45) 

0.13 

(0.08, 0.36) 

(0.04, 0.36) 

(0.02, 0.50) 

•p. 
TABLE B.4 (Cont'd) 

II 

Expert E, Hemoglobin <-9T5 g/dL, Ages 0-3 Years 

Index 

Median 

50% C.I. 

90% C.I. 

5 yg/dL 

0.08 

(0.05, 0.14) 

(0.03, 0.22) 

Blood-Lead Level 

15 yg/dL 25 yg/dL 35 yg/dL 

Encoded Judgments 

0.10 

(0.07, 0.16) 

(0.04, 0.24) 

0.15 

(0.09, 0.19) 

(0.05, 0.26) 

Fitted Functions 

0.19 

(0.14, 0.24) 

(0.06, 0.28) 

45 yg/dL 

0.22 

(0.16, 0.35) 

(0.09, 0.43) 

55 yg/dL) 

0.30 

(0.17, 0.44) 

(0.11, 0.51) 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

Median 

50% C.I. 

90% C.I. 

0.09 

(0.06, 0.13) 

(0.03, 0.20) 

(0.02, 0.28) 

0.06 

(0.03, 0.10) 

(0.01, 0.14) 

0.11 

(0.07, 0.15) 

(0.04, 0.24) 

(0.03, 0.33) 

0.13 0.16 

(0.09, 0.18) (0.11, 0.22) 

(0.05, 0.28) (0.07, 0.34) 

(0.03, 0.37) (0.05, 0.44) 

Expert E, Hemoglobin < 11 g/dL, Ages 4-6 Year 

0.08 

(0.05, 0.12) 

(0.02, 0.16) 

Encoded Judgments 

0.11 0.13 

(0.09, 0.15) (0.10, 0.16) 

(0.04, 0.19) (0.04, 0.20) 

0.21 

(0.15, 0.29) 

(0.09, 0.42) 

(0.06, 0.52) 

s 

0.16 

(0.12, 0.24) 

(0.06, 0.29) 

0.28 

(0.21, 0.37) 

(0.13, 0.52) 

(0.09, 0.62) 

0.20 

(0.13, 0.25) 

(0.10, 0.33) 

i — * 

UJ 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

0.05 

(0.04, 0.08) 

(0.02, 0.13) 

(0.01, 0.09) 

0.07 

(0.05, 0.10) 

(0.03, 0.16) 

(0.02, 0.22) 

Fitted Functions 

0.10 

(0.07, 0.14) 

(0.04, 0.22) 

(0.03, 0.30) 

0.12 

(0.08, 0.17) 

(0.05, 0.27) 

(0.03, 0.35) 

0.15 

(0.11, 0.21) 

(0.06, 0.32) 

(0.04, 0.42) 

0.18 

(0.13, 0.24) 

(0.08, 0.36) 

(0.05, 0.46) 
P.43 

135 

encoded judgments and the fitted functions. Each table is organized so that each 

expert/hemoglobin-level/age-category combination is listed in the table, beginning with 

Expert A, continuing in alphabetical order, and ending with Expert E. 

B.3.1 EXPERT A 

Expert A chose to separate the population of U.S. children aged 0-6 years into 

two subpopulations, ages 0-3 and 4-6 years. This individual provided judgments only at 

the 11 g/dL hemoglobin level. Since his judgments indicated that there is a very small 

lead-induced hemoglobin effect at blood-lead levels below 45 yg/dL, it was not necessary 

to obtain probabilistic judgments at the 9.5 g/dL level. 

The probabilistic judgments of Expert A regarding the effects of lead exposure 

on hemoglobin levels among U.S. children aged 0-3 years are listed in Table B.2 for the 

11.0 g/dL hemoglobin level. The probability judgments are cumulative distribution 

functions (CDFs) of judgmental probability. That is, for each blood-lead level L, the 

entries in column F in Table B.2 represent the judged probability that the true response 

rate Rj is less than or equal to the rate R shown in column R of the table. There are 

four CDFs, one each for blood-lead levels of 45, 55, 65, and 75 yg/dL. Expert A did not 

feel that there was a measurable, lead-induced hemoglobin effect at blood-lead levels 

below 45 yg/dL. The curves display a wider range of plausible population response rates 

at successively higher blood-lead levels. This may be interpreted to mean the Expert A 

is less certain about what actual response rates may be at the higher blood-lead levels. 

There is no indication of a threshold for a hemoglobin effect in the range of 45-75 yg/dL. 

For the reasons presented in Sec. 1, mathematical functions were fit to the 

judgments of Expert A (and the judgments of the other experts). For Expert A, the 

mathematical representations for the various blood-lead levels are guaranteed never to 

cross. They were obtained by fitting regression lines to transformations of the 

judgments. The transformation used was the normal-on-log-odds transformation. It 
P.44 

136 

happens that this transformation leads to distributions that are normal distributions, with 

a high degree of accuracy. These distributions are also convenient for use in subsequent 

analysis. We call these fitted representations "normal-on-log-odds" (NOLO) functions. 

They are uniquely defined by the mean and variance of the underlying normal 

distributions, and the transformation functions; these are summarized in Sec. B.2. Table 

B.3 summarizes relevant parameters for each of the conditional CDFs fit to the 

judgments of Expert A. Included in the table for each lead level at which a CDF was 

assessed are the mean and standard deviation of the underlying normal distribution, the 

mean and standard deviation of the NOLO distribution, and the R-squares of regressions 

of the fitted representations on encoded judgments. In general, the regression R-square 

values are reassuringly high. Finally, Table B.4 summarizes and compares the judgments 

and the fitted representations. Included in the table are medians and several credible 

intervals. The median is that value that is exceeded with probability 0.5. The 90% 

credible interval is a set of response rate values such that there is a 0.9 probability of 

the true value falling within it. For example for children aged 0-3 having blood-lead 

levels of 55 yg/dL, the median encoded response rate is 9%, and the 90% credible interval 

is 1% to 15%; that is, with probability 0.05 the true response rate is less than or equal to 

1%, and with probability 0.05 it is greater than 15%. Similar statements apply to the 

fitted representation. Note the the encoded median values are fairly close to the 

medians of the fitted representations, differing by two to four percentage points. 

However, the fitted representations exhibit more uncertainty than do the judgments. 

These features and differences were carefully pointed out to Expert A. He finally 

concluded that the fitted representations better captured his best judgments about the 

effects of lead on hemoglobin levels among U.S. children. 
P.45 

137 

B.3.2 Expert B 

Expert B did not feel comfortable with the process of giving probabilistic 

judgments about the effects of lead on hemoglobin levels among children. However, he 

was able to discuss qualitatively the effects of lead exposure on hemoglobin and EP 

levels. A summary of that discussion is presented in Sec. B.4. 

B.3.3 Expert C 

Expert C chose to provide judgments for the population of children aged 0-6 

years. He acknowledged that there certainly were differences in metabolism between 

children aged 0-3 and 4-6, but he felt that these differences were difficult to quantify 

considering other uncertainties. Thus, he provided two sets of judgment's, one set at each 

of the hemoglobin levels of interest. 

Following the format introduced for discussing the judgments of Expert A, it can 

be seen that the fitted functions closely match the encoded judgments. The median 

response rate values are no more than 1% apart. The fitted functions do display larger 

uncertainty at the higher blood-lead levels. Expert C concluded, after study and 

reflection, that the mathematical representations did capture his best judgments. 

B.3.4 Expert D 

Expert D chose to divide the population into two subgroups, children aged 0-3 and 

4-6 years, and provided judgments at both the 9.5 and 11.0 g/dL hemoglobin levels. This 

resulted in four sets of judgments for Expert D. 

At the 9.5 g/dL hemoglobin level, there is evidence of a slight threshold between 

blood-lead levels 25 and 35 yg/dL, indicated by the wider spacing between these levels 

compared to the other levels. At the 11 g/dL hemoglobin level, a threshold is indicated 

between the 15 and 25 yg/dL blood-lead levels. This was recognized and agreed to by 

Expert D. 
P.46 

138 

In general, there is again good agreement between the mathematical 

representations and the judgments for Expert D. R-square values for regressions of F on 

F are generally around 0.95. 

B.3.5 EXPERT E 

Like Expert D, Expert E provided four sets of judgments, one for each of the age 

and hemoglobin level combinations that result from dividing the age range into subgroups 

aged 0-3 and 4-6 years. The judgments and fitted mathematical representations are 

listed and compared in the tables already mentioned. 

Only one case for Expert E showed evidence of a threshold effect. That was at 

the 9.5 g/dL hemoglobin level for children aged 4-6 years. The threshold appears 

between the blood-lead levels of 35 and 45 yg/dL. In this case, as well as the others for 

Expert E, the fitted mathematical representations matched the judgments quite well, 

the R-square values of the regressions of F on F were generally around 0.95. 

B.4 SUMMARY DISCUSSIONS 

B.4.1 Summary of Discussion with Expert A 

1. There is absolutely no evidence that ZPP is toxic per se. 

2. The biosynthenis of heme is regulated by a negative feedback 

process (Stanbury, "Metabolic Basis of Inherited Disease"). The 

rate limiting factors are heme, heme oxygenase, and ALA 

synthase. The enzymes in the pathway from ALAD dehydratase 

to ferrochelatase are present in substantial excess. There is 

normally a substantial excess capacity of these intermediary 

enzymes. For example, there is sixteen times as much ALADdehydratase as is necessary to metabolize the amount of ALA 
P.47 

139 

produced by ALA synthase. Overall, for every 10,000 molecules 

of heme produced, the equivalent of one molecule is lost as ALA, 

copper porphyrin, and protoporphyrin. 

3. Lead causes partial inhibition of ALA dehydratase and ferrochelatase. EP is a marker of the partial inhibition that occurs at the 

ferrochelatase step. In the presence of lead, it has been observed 

that increased FEP levels correlate with decreased ALAD 

levels. Some genetic studies suggest that high FEP levels are 

associated with decreased ALAD activities, even in the absence 

of lead. 

4. ZPP is bound to the red cell and therefore remains throughout the 

life of the red cell, which is about 120 days. Insofar as is known, 

all cells synthesize the heme necessary for the cell's function, and 

lead inhibits heme synthesis in most other cells of the body, 

including liver, kidney, and brain. The heme enzymes in these 

other cells may have very short half lives. These are probably 

quite important in considering lead effects. One of these is the 

P-450 family of enzymes. Also of concern is the activation rate 

of an enzyme in the kidney, which may be inhibited to a harmful 

level. In the liver, the P-450 enzymes are essential in the 

metabolism of drugs. 

5. There is a dose-dependent decrease in the level of 1,25 dihydroxyvitamin D in serum. This relationship is nonlinear, and the level 

decreases at a much higher rate as lead rises above 35-40 yg/dL. 

Although the mechanism for the reduction of 1,25 dihydroxyvitamin D in serum is not fully understood, it is possible that this 

may be realted to an effect of lead on production of P-450 in the 
P.48 

140 

kidney. P-450 is one of the factors necessary for the 

hydroxylization of 1,25 dihydroxyvitamin D at the 1 position, 

which occurs in the kidney. Further research will be required to 

evaluate the biological significance of reduced serum levels of 

1,25 dihydroxyvitamin D. 

6. A new disease related to the virtual absence of ALAD has been 

described. This is a genetic disorder transmitted as a recessive 

trait. People so affected have symptoms similar to those having 

acute intermittent prophyria, another genetic disorder of 

porphyrin metabolism. It is extremely doubtful that this has 

anything to do with low-level lead exposure, although at high PbB 

levels (70-80 yg/dL or higher), it is possible that lead inhibits 

ALAD to the same extent as that found in this new disease. In 

this new disease, ALAD activities are about 1% of normal. 

Furthermore, people have been identified with ALAD levels at 

about 20% of normal, and these people are healthy and without 

any symptoms whatsoever. 

7. Clinically speaking, children with blood leads around 40 yg/dL, 

elevated EP, and other evidence of iron deficiency can be treated 

with iron and this anemia and/or iron deficiency can be corrected, 

even though no specific treatment for lead is given. The 

symptoms associated with anemia would be the same irrespective 

of whether the cause was lead exposure or iron deficiency. 

However, the presence of iron deficiency increases the absorption 

of lead from the gut. 

8. Another possible effect involves tryptophane pyrrolase. This is a 

heme-dependent enzyme in the liver. It has been postulated that 
P.49 

141 

the reduced level of heme in porphyria may be responsible for 

some of the symptoms seen in acute intermittent porphyria. A 

Science article by Corriea about a year ago addresses this issue. 

9. Regarding the possible effects of ALA itself, effects are not 

likely because ALA does not readily cross the blood-brain barrier. 

10. Dick Bull and McCauley (EPA, Cincinnati) have found delay of 

myelinization of the nerve sheaths in the brain in conjunction 

with lead in the 30-40 yg/dL range in neonatal rats. It is known 

that lead interferes with oxidative phosphorylation and hence 

energy production. This lead-related disruption of energy 

production may be responsible for this delay in mylenization. 

11. Patients with sickle-cell anemia appear to be more susceptible to 

the toxic effects of lead, although the mechanisms responsible for 

these are not understood. 

12. In general, there seems to be good evidence that elevated EP 

levels indicate increased risk of adverse health effects. It seems 

to be a good indicator of both FeD and Pb exposure. This places a 

child in double jeopardy since both lead to the same result. EP 

level is useful for monitoring long-term exposure. 

13. Epidemiological studies should be based on data acquired through 

extraction techniques rather than through the 

hematofluorometer. Extraction techniques are used to calibrate 

hemotofluoremeters. There are data showing that hemotofluoremeters give readings taht are systematically low. It would appear 

that hematofluoremeters should be recalibrated at the factory 

every three months or so. At this time, the technical difficulties 

with the hematofluoremeter have not been resolved. 
P.50 

142 

B.4.2 Summary of Discussion with Expert B 

The discussion with Expert B covered two main topics: hemoglobin and EP. 

1. A child can have a high PbB (say, 500 mcg/dL), no reduction in 

hemoglobin level, and die. Thus, hemoglobin level is not a very 

useful index for adverse health effects of lead, at least from a 

clinical point of view. 

2. Neurological and behavioral (aggression, hyperactivity) effects 

occur much more quickly in children than hematological effects, 

and at much lower levels (about 40 mcg/dL). 

3. The body can also compensate for reduced hemoglobin; other 

processes will begin to transport oxygen, offsetting, to some 

degree, the possible adverse effects of reduced hemoglobin. 

4. Anemia only becomes a problem when the body's ability to 

compensate is lost. 

5. Damage to the heme synthetic pathway is crucial; but this is not 

attributable to reduced hemoglobin. 

6. A rough dose/effect relationship between PbB and Hb was 

expressed, one for Fe deficient kids, and one for non-Fe deficient 

kids. Expert B estimated that, on the average, non-Fe deficient 

kids with PbB=10 mcg/dL would have hemoglobin levels of about 

12 g/dL; at PbB=50, Hb=10.5. For Fe deficient kids, Expert B 

estimated Hb=10 at PbB=10, and Hb=6.5-7.0 at PbB=50. However, 

Expert B felt that it was quite possible that it could be even 

lower for the later kids at PbB=50, but just couldn't be sure, and 

could not express these feelings quantitatively, despite efforts to 

assist Expert B using judgmental probability encoding techniques. 
P.51 

143 

B.4.3 Summary of Discussion with Expert C 

1. Very high EP levels can cause porphyria due to errors in 

metabolism with clinically recognizable skin and CNS effects. 

However, there is no evidence of a lead worker ever developing 

porphyria as a result of lead exposure. Thus, it is reasonable to 

conclude that lead exposure does not cause porphyria. 

2. There is no evidence in the literature that lead-induced elevated 

EP itself causes health problems; it simply is a mrker, or 

indicator, of adverse health effects due, possible, to lead 

exposure. EP levels > 1 sigma above the mean should be followed 

by a look at blood lead. 

3. Since EP levels tend to lag changes in PbB levels, it is important 

to be looking at both over time to get a good idea of what is going 

on. The rate of rise of EP vs. an increase in PbB is greater than 

linear, but lagged in time. A plot of log (EP) versus PbB would be 

roughly linear under chronic relatively constant lead exposure 

conditions. 

4. Lead-induced elevated EP is an indicator of interference with 

heme synthesis which may or may not be compensated by 

derepression of ALA synthetase, the rate-limiting enzyme 

involved in heme systhesis, depending on the degree of lead 

exposure. 

5. It is possible that elevated EP is an indicator of an interference 

by lead of the body's ability to produce 1,25 dihydroxyvitamin D. 

The cytochrome P-450 enzymes, of which there are over 50 

differenct isozymes, are related to the synthesis of 1,25 

dihydroxyvitamin D. There are strong indications that lead 
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reduces synthesis of the P-450 enzymes. This in turn may reduce 

the metabolism of 25-(OH)D, a necessary ingredient in the 

biosynthesis of 1,25 dihydroxyvitamin D. Reference was made to 

an important review paper concerning 1,25 dihydroxyvitamin D 

metabolism [D.R. Fraser, Physiological Reviews, 60:551 (1983)]. 

6. There is also suggestive evidence, but not proof, that elevated EP 

indicated reduced ability of the liver to detoxify, this effect has 

been shown in a number of studies involving high lead exposure in 

workers and children. 

7. Furthermore, elevated EP levels may indicate sufficient exposure 

to lead (and/or other metals) to accelerate the destruction (i.e., 

reduce their half-lives) of the hemoproteins [M.D. Maines, Annals 

of Clinical Research, 8:39 (1976)]. 

8. Regarding the CNS, it is not clear whether elvated EP ger se 

causes any effects. There are some animal studies concerning 

CNS effects when very large doses of the EP precursor ALA are 

administered. Some report CNS effects and others not [M. Moore 

<Sc P.A. Meredith, Trace Substances in Environmental Hlth. 10:363 

(a977); S. Edwards, Neurosci. Lett. 50:169 (1984)]. 

9. In a lead worker study [Hammond, et al, J. Occ. Med., 2:475-484 

(July, 1980)], ALA in plasma and in urine was found to be as good 

a marker of the degree of toxicity of Pb as was PbB; ALA was as 

good a marker as EP for hematopoietic system damage; for other 

effects (neurological, renal, etc.), ALA and PbB were better 

indicators of damage than EP. Another study by Ruth Lillis et 

al. at Mt. Sinai showed that EP was a better indicator of 

hematopoietic effects than ALA and PbB. The differences 
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between the two studies may be due to differential measurement 

reliabilities in the two labs. 

10. There is no evidence of an EP vs. hemoglobin relationship in 

children at PbB's <50. There are factors other than lead that 

affect EP level. 

11. The possibility of Pb exposure causing hypertension is a new issue. 

12. To summarize, there is no evidence that elevated EP pjr se due 

to lead causes adverse health effects. 

B.4.4 Summary of Discussions with Expert D 

The discussion with Expert D included FEP, liver, calcium, and 1,25 dihydroxyvitamin D (l,25(OH)2D) effects. 

FEP: 

1. Elevated EP due to lead exposure indicates direct toxic effects of 

lead on heme, which is a basic physiological system that is 

common to many organs and cell types. 

2. Piomelli has postulated, and Silbergeld have published some data, 

and both suggest that some of the CNS effects of lead may be 

attributable to altered metabolism of porphyrin compounds. 

Others have suggested that there may be perturbations in CNS 

intracellular calcium metabolism. 

Liver: 

3. There is evidence at 30-40 ygPb/dL that liver metabolism of 

model compounds (e.g., Cortisol is altered. This implies a reduced 

ability to detoxify the blood stream. Since many drugs have 
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metabolic pathway that are similar to that of Cortisol, their 

metabolism may also be affected by lead. 

Calcium: 

4. There is evidence that calcium-mediated basic enzymatic systems 

in all mamallian cells are affected at lead levels above about 5 

micromolar. Any disruption of these systems may have pervasive 

effects. Calcium from calmodulin can be displaced by lead. 

Calmodulin is a central component of the normal chemistry of 

cells. Lead can purturb this process. 

1,25 Dihydroxy-vitamin D: 

5. A complex enzyme system is responsible for the production of 

this vitamin D hormone. Lead is known to impair several 

ingredients of this enzyme system. Some of these ingredients 

include electron transport, mitochondrial function, and the 

cytochrome P-450 family of enzymes. Observations of 

impairment in the production of the vitamin D hormone in leadtoxic children have been confirmed in experimental studies in 

vivo and in vitro. 

6. At 33-55 ygPb/dL, there is evidence of about 66% decrease in the 

kidney's ability to produce the vitamin D hormone. 

7. At levels above 62 ygPb/dL, there is evidence of a decrease in 

l,25(OH)2D levels to a degree that have been reported in children 

with inborn errors in metabolism. 

8. Between 12 to 120 ygPb/dL, there is a statistically significant 

negative correlation between vitamin D level and lead level. 
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9. At blood-lead levels above 55 ygPb/dL, chelation therapy is 

immediately used. At 25-55 ygPb/dL, the results of the EDTA 

provocative test is used to determine which children would 

benefit from chelation therapy. 

10. l,25(OH)2D affects the maturation of cells and enhances the 

differentiation of cells. 

• Rats and mice having leukemia were treated with picomolar 

concentrations of l,25(OH)2D. Results indicated that the 

lifespans of the animals were extended. 

• In vitro experiments on a variety of human cells (e.g. 

lymphoma, myeloid leukemia cells, monocytes) have 

replicated such findings. 

11. There is recent research showing that l,25(OH)9D evidences some 

immuno-regulatory functions like other steroid hormones. 

12. There is early, evolving evidence that l,25(OH)9D has a role in 

controlling insulin secretion from the pancreas. 

13. The actions of the vitamin D hormone involve not only mineral 

absorption, bone remodeling, and calcium homeostasis in virtually 

alll mammalian cells, but recently reported information indicates 

that the vitamin D hormone has even more pervasive effects in 

humans. Some of these effects, which are now recognized, 

include enhancement of cell differentiation (maturation), and 

immuno-regulatory capacity. This, in consideration also of points 

608, reasonably suggests that a decrease of vitamin D hormone is 

likely to have pervasive effects on the function of other organs. 
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B.4.5 Summary of Discussions with Expert E 

Discussions with Expert E focused primarily on FEP effects of lead. 

1. There does not seem to be any evidence that elevated EP is itself 

an adverse health effect. However, it is possible because anytime 

the balance of an essential metabolite is upset, there is a risk of 

damage to other organs or functions. For example: 

• Phenylalanine is an essential amino acid, but is toxic at high 

levels. This is seen in the disease phenylketonuria, in which 

there is an inability to metabolize excess phenylalanine. Thus, 

(in the absence of a special diet) the phenylalanine builds up 

and affects the developing central nervous system, causing 

mental retardation. 

• Excess levels of fluoride cause teeth to become brittle, 

although proper levels increase hardness of teeth. 

Thus, there is the chance that future research might show that elevated 

FEP is an adverse health effect. 

2. Elevated EP is a valuable index of adverse lead effects in other 

organs, e.g., the central nervous system, the liver, the kidney, 

etc. 

3. The body has the ability to compensate for lead insult up to a 

point. For example, at low lead levels the inhibition of EP is 

compensated for, but not at slightly higher levels. Piomellis's 

analysis indicates a threshold around 16-17 yg/dL. ALAD shows 

no threshold. 

4. Regarding measurement of EP, care must be taken if the 

hematoflorometer is used because the amount of EP that is zinc 

protoporphyrin (ZPP) decreases proportionately as total EP rises; 
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since the hematoflorometer measures ZPP, it may be 

underestimating total EP. Below 35 yg/dL there is good 

agreement between FEP (extraction) and ZPP 

(hemotofluorometer). Above 35 yg/dL there appears to be a 30% 

difference between ZPP (lower) and FEP (higher). 

5. In assessing the need for treatment, both EP and PbB levels 

should be considered (as the Centers for Disease Control does). 

6. Critical blood-lead levels for regulatory purposes may need to be 

less than those considered for clinical purposes in order to provide 

an adequate margin of safety for the population at large. 
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APPENDIX C 

INTELLIGENCE QUOTIENT 

This appendix is organized in a fashion similar to App. B for hemoglobin. Section 

C l is the IQ protocol, and Sec. C.2 summarizes the mathematical formulations. Section 

C.3 tabulates the encoded judgments, specifications for functions fit to those judgments, 

various credible intervals, and comparisons of encoded judgments vs. fitted functions. 

Section C.4 summarizes of the discussions with each of the IQ experts. 

C l IQ PROTOCOL 

Cl. l Introduction 

The Environmental Protection Agency (EPA) is charged by the Clean Air Act 

with setting and revising National Ambient Air Quality Standards (NAAQS) for selected 

pollutants, at levels sufficient to protect the public health with an adequate margin of 

safety. As you know, the scientific bases for NAAQS are presented and reviewed in 

criteria documents. In support of the forthcoming review of the lead NAAQS, EPA has 

just prepared a new Air Quality Criteria for Lead. It presents scientific evidence from 

which the most susceptible populations can be determined and from which various 

adverse health effects can be identified. The criteria document summarizes and 

evaluates the available clinical, epidemiological, and animal or toxicological laboratory 

evidence with regard to the physiological and adverse health effects of lead, and 

therefore represents our most up to date knowledge on lead effects. 

As one aspect of the review process, EPA assesses health risks by identifying the 

most sensitive populations for each pollutant, and estimating probabilistically the 

numbers' of people in the populations who may suffer each of various well-defined 

adverse health effects attributable to the pollutant. It is believed that information about 
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the health risks associated with various potential standards will aid the EPA 

administrator in selecting that standard which, in his judgment, protects the public 

health with an adequate margin of safety. 

Because the risk estimates that EPA seeks are often based in part on doseresponse relationships and lead exposure estimates which are uncertain, it is necessary to 

make probability judgments about relevant dose-response functions based on the 

available evidence, and to probabilistically estimate lead exposure under alternative 

NAAQS. Obtaining the health risk estimates then involves combining dose-response and 

exposure probability estimates. 

The problem of estimating dose-response relationships is similar to that which 

exists in clinical medicine when there do not exist data that bear precisely on the 

patient's problem. In that case it is necessary to use scientific judgment to extrapolate 

from the data to make a best decision for the patient. Here, too, it is necessary to use 

scientific judgment to extrapolate from the available data. The extrapolation is not 

certain and, therefore, we will aid you to represent your opinion probabilistically. 

Furthermore, since the extrapolation depends on one's interpretation of the literature, 

different people will have different judgments. For each health effect we intend to 

obtain the probabilistic judgments of about five experts to sample the range of respected 

opinions. The model for estimating risks will not merge these judgments into a single 

average judgment, but rather will estimate the range of risks based on the range of 

judgments. If we as risk analysts do our job properly, then not only will we be able to 

show the EPA administrator the range of estimates based on the range of judgments, but 

we will also be able to show some of the sources of the disagreements. Indeed, a side 

benefit of this exercise in which we probe your knowledge in a structured manner may be 

to help identify sources of greatest disagreement. 

Based on the evidence in the lead criteria document, two populations have been 

identified as being most susceptible to the effects of lead intoxication. One is children 
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from birth through the seventh birthday, and the other is pregnant women, or more 

precisely, the fetuses being carried by the pregnant women. A number of adverse health 

effects have been identified for which we would like to estimate dose-response functions 

including the one discussed below. 

C.1.2 Lead-Induced IQ Decrements 

C.l.2.1 Central Nervous System and Behavioral Effects of Lead 

A large number of studies reviewed in the Criteria Document suggest that there 

are numerous central nervous system (CNS) and behavioral effects of lead exposure. 

Considerable uncertainty surrounds all of these effects, however, because of the 

enormous difficulty in defining and measuring them, and in isolating them from the 

effects of covariates. Since our goal is to obtain probabilistic estimates about the shape 

of a dose-response curve for a particular well-defined effect if a sufficient amount of 

pertinent data could be collected, our first task is to select one CNS or behavioral effect 

that is of acknowledged importance and that can be well specified. 

The search for lead-induced effects has included studies of: EEG effects; 

sensory motor, perceptual, and attentional deficits; cognitive decrements of various 

sorts; hyperactivity; negative classroom behaviors; and other effects that so far have 

been studied only in animal models. From this large assortment of effects, we have 

selected IQ decrement as the adverse effect upon which to focus. We are not considering 

IQ to be the only nor necessarily the best measure of cognitive abilities. Nor is it being 

considered as a surrogate for the other systems in which effects have been explored. 

(Because of its multifaceted nature it probably involves many of them.) Rather, we have 

selected IQ decrement because there are more data on this effect than on any other, and 

because its functional or "clinical" significance is clear. It is quite conceivable that as 

research continues in future years, other more "pure" CNS or behavioral effects will 
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emerge that are obviously adverse and for which a substantial body of data has 

developed. Until such an event occurs, it appears that lead-induced IQ decrement is the 

most appropriate effect to consider. 

C.l.2.2 Definition of IQ Decrement 

Because it is generally thought that CNS effects of lead may be cumulative, it is 

necessary to specify the children's ages at which the IQ decrements are estimated. In all 

cases, assume that IQ tests are given on the children's seventh birthdays. Assume further 

that the WISC-R is the test employed. 

A lead-induced IQ change cannot be measured directly for a given child, and 

therefore the change would have to be estimated statistically from suitable data. Thus, 

rather than ask you directly about dose-response functions, we will encode your 

judgments about the outcomes of hypothetical ideal experiments. If you agree with the 

assumptions on which the hypothetical experiments are based, then your judgments about 

the potential outcomes will lead naturally to probabilistic estimates about dose-response 

functions for IQ decrements. 

There are differences of opinion, of course, as to what IQ decrements should be 

considered adverse. The Clean Air Act makes it clear that EPA should set standards to 

protect against adverse health effects, but the level defined as adverse may be different 

for regulatory than for clinical or remedial purposes. We will not focus on particular 

magnitudes of IQ decrements, but rather will encode your probabilistic judgments about 

IQ distributions given various blood-lead levels. Then we will use your judgments to 

derive probabilistic statements about the percent of children at each lead level whose IQ 

scores are below any value of interest, such as, for example, below IQs of 70, 80, 90, 

or 100. 
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C.1.2.3 Hypothetical Ideal Experiments 

Assume that at conception, subjects are randomly assigned to groups 

differentiated by blood lead level targeted for the third birthday. Members of each 

treatment group are exposed to lead from conception until their seventh birthdays, while 

members of a control group are sheltered from lead from conception until their seventh 

birthdays. The level of environmental lead assigned to a child is roughly constant for the 

seven years, however, each child's lead uptake is not constant, due to the changes with 

age of his or her physiology and behavior. Nevertheless, the experimental conditions are 

such that at their third birthdays, all the children in each group have essentially the same 

measured blood lead. Thus, groups differ in terms of mean blood lead on the third 

birthday. Environmental lead levels necessary to yield a given blood-lead level at age 

three in a particular child remain constant through the seventh birthday. 

The experimental manipulation affects only lead exposure, and no other aspect of 

the children's lives. Then the WISC-R IQ test is administered to all children on their 

seventh birthdays. The children in each group have a distribution of IQ scores with some 

mean and standard deviation. We are interested in your probabilistic judgments about 

the IQ distributions for groups of children on their seventh birthdays, all of whom had 

specific blood-lead levels on their third birthdays. 

Note three features about this hypothetical experiment. First, it is similar to a 

longitudinal study; children are in a group from conception until their seventh birthdays. 

Second, it involves random assignment of children to groups, making it unnecessary to 

worry about covariates. Third, blood lead is measured at age three, and IQ at age seven. 

If you believe IQ effects of lead to be different for lower SES than for middle 

and upper SES subpopulations of children under these experimental conditions, then we 

will consider separate hypothetical experiments for the two subpopulations. Otherwise, 

we will consider only a single such experiment. 
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SES is a complex variable. For simplicity, if we divide the population into low 

SES and middle or upper SES categories, let us define low SES as those children coming 

from households with incomes in the lowest 15 percent. 

Unless you disagree, we will also assume that the distribution of IQ scores is 

normal within each group. (The WISC-R was developed to yield normally distributed IQ 

scores for the general population, with mean IQ equal to 100 and a standard deviation of 

15.) 

Furthermore, if we consider only a single hypothetical experiment, sampling 

from the full population of children, then, unless you disagree, we will assume that the IQ 

standard deviation is 15 at each blood-lead level and we will only have to encode your 

probabilistic judgment about the mean IQ at age seven for each of several blood-lead 

levels at age three. 

If we consider two hypothetical experiments, each sampling from a different SES 

subpopulation, then the IQ standard deviation will possibly be less than 15. Assuming 

that IQ standard deviation is the same at all blood-lead levels within SES subpopulations, 

we will have to encode your probabilistic judgment about the standard deviation for each 

SES group. 

Then, separately for each SES group or for the population as a whole, as 

appropriate, we will encode your probabilistic judgment about the mean IQ at age seven 

of the control group. Finally, we will encode your probabilistic judgments about the 

differences in mean IQ at age seven between children with negligible blood lead (the 

control group) and children at each of several elevated blood leads at age three (the 

treatment groups). 

The following sections specify further the conditions to be assumed in this 

hypothetical experiment. 
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C.1.3 Population at Risk 

Based on the Criteria Document, we can specify the most susceptible population 

as all United States children from conception through their seventh birthdays. We have 

already defined the effect as being measured on the seventh birthday, but on the assumption that younger children will reach their seventh birthdays, the effect is well-defined 

for the whole population. 

However, as already discussed, you may consider IQ effects of lead to be different for lower SES than for middle and upper SES subpopulations of children, resulting 

in different experimental outcomes for the two groups. If so, then we will elicit your 

judgments separately for lower SES children and for middle and upper SES children. 

C.1.4 Exposure Conditions 

We will be asking your judgment about mean IQ values on the seventh birthdays 

at various blood-lead levels. Assume that the blood-lead levels under consideration for a 

given judgment have been measured on the children's third birthdays. Assume further 

that external environmental conditions supporting those levels have been more or less 

constant since birth, and that in interacting with the environment, the children exhibited 

the usual range of behaviors at each age. Thus, blood-lead levels were not necessarily 

constant from birth to age seven, but exposure and behavioral factors were such that at 

age three, blood lead was at a specific level. Finally, assume that the changes in blood 

lead levels from birth until the seventh birthday are distributed as you believe they 

actually are. 

C.1.5 Physiological and Environmental Conditions 

Because the effects of lead depend on many parameters, it is necessary to 

specify assumptions about those parameters in the population(s). 
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C.l.5.1 Physiological Conditions 

The effect of lead in the system depends on the person's nutritional and metabolic status. Assume that the levels of iron, zinc, copper, vitamins A, C, D, and E, 

calcium, phosphorus, and magnesium are distributed within the population or within each 

of the two SES groups as you believe they in fact are, taking into account the wide range 

of diets and nutritional levels of children within the population or within each of the two 

SES groups. 

C.1.5.2 Environmental Conditions 

The effect of lead on IQ also may depend on numerous environmental and caregiving factors that vary within SES level, such as those assessed in the HOME scale 

(Home Observation for. Measurement of the Environment), parental IQ, and so forth. 

Assume that these factors are distributed within the population or within each of the two 

SES groups as you believe they in fact are. 

C.1.6 Factors to Consider 

In order to help you bring to mind the relevant evidence so that you may consider 

it systematically, and also in order to help us to interpret your judgments, we would like 

to ask you to discuss briefly your interpretations of various aspects of the literature. 

How do you evaluate the research concerning the effects of low level lead exposure on 

cognitive and behavioral development? Is it your feeling that lead has a deleterious 

effect on this development over and above that which can be explained by other factors 

frequently associated with lead exposure? If so, do you believe that the effects of lead 

simply add to the effects of other factors, or that the effects of lead depend on the 

levels of other factors? In the latter case, what are the variables that lead exposure 

interacts with? A related question concerns your opinion about the relationship between 

exposure and susceptibility. That is, do you think that those children who are at greatest 
158 

risk of exposure due to their living in deteriorating pre-1950 housing or in urban areas 

with large amounts of vehicular traffic or due to other reasons, are also most susceptible 

to the effects of lead? For example, these may be the same children who also have 

poorer diets, less access to medical care, poorer care-giving environments, and less 

intellectual resources to fall back on. 

What is your opinion about the time course of lead exposure and of lead effects 

on CNS, cognitive and behavioral development? What are the relative effects of cumulative versus current exposure. Are the effects reversible? Is there a threshold for the 

effects? What are the implications of the animal model research, both the behavioral 

and the morphological, for human CNS, cognitive, and behavioral effects of lead? Are 

there other factors to consider in thinking about the dose-response functions for leadinduced IQ effects that we should discuss now? 

C.1.7 Factors to Keep in Mind When Making Probability Judgments 

There is usually uncertainty associated with conclusions that we draw from 

research, and more generally in our everyday thinking. However, not everyone is aware 

of all the sources that should contribute to their uncertainty, nor are most people 

familiar with the process of actually expressing their uncertainty in probabilistic terms. 

When an expert is asked to make probability judgments on socially important matters, it 

is particularly important that he or she consider the relevant evidence in a systematic 

and effective manner and provide judgments that represent his or her opinions well. 

Experimental psychologists and decision analysts have amassed a considerable 

amount of data concerning the way people form and express probabilistic judgments. The 

evidence suggests that when considering large amounts of complex information, most 

people employ simplifying heuristics and demonstrate certain systematic distortions of 

thought, i.e., cognitive biases, which adversely affect their judgments. The purpose of 

this section is to make you aware of these biases and heuristics so that, as much as 
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possible, you can avoid them in making probability judgments. We will first review the 

most widespread biases and heuristics, and then offer some suggestions to help you 

mitigate their effects. 

C.1.7.1 Sequential Consideration of Information 

Generally, the order in which evidence is considered influences the final 

judgment, although logically that should not be the case. Of necessity, pieces of 

information are considered one by one in a sequential fashion. However, those 

considered first and last tend to dominate judgment. In part, initial information has its 

undue influence because it provides the framework that subsequent information is then 

tailored to fit. For example, people usually search for evidence to confirm their initial 

hypotheses; they rarely look for evidence that weighs against them. The later evidence 

has its undue effect simply because it is fresher in memory. 

Related to these sequential effects is the phenomenon of anchoring and 

adjustment. Based on early partial information, one forms an initial probability estimate 

regarding the event in question. This anchor judgment is then adjusted as subsequent 

information is considered. Unfortunately, such adjustments tend to be too 

conservative. In other words, too little weight is attached to information considered 

subsequent to the formation of the initial judgment. 

C.l.7.2 Effects of Memory on Judgment 

It is difficult for most people to conceptualize and make judgments about large, 

abstract universes or populations. A natural tendency is to recall specific members and 

then to consider them representative of the population as a whole. However, the specific 

instances often are recalled precisely because they stand out in some way, such as being 

familiar, unusual, especially concrete, or of personal significance. Unfortunately, the 

specific characteristics of these singular examples are then attributed, often incorrectly, 
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to all the members of the population of interest. Moreover, these memory effects are 

often combined with the sequential phenomena discussed earlier. For example, in 

considering the evidence regarding the dose-response curve of a particular pollutant, you 

might naturally first think of a study you or a personal friend recently completed. Or 

you might think of a study you recently read, or one that was unusual and therefore 

stands out. The tendency might then be to treat the recalled studies as typical of the 

population of relevant research, ignoring important differences among studies. 

Subsequent attempts to recall information could result in thinking primarily of evidence 

consistent with the initial items you thought of. 

C.l.7.3 Estimating Reliability of Information 

People tend to overestimate the reliability of information, ignoring factors such 

as sampling error and imprecision of measurement. Rather they summarize evidence in 

terms of simple and definite conclusions, causing them to be overconfident in their 

judgments. This tendency is stronger when one has a considerable amount of intellectual 

and/or personal involvement in a particular field. In such cases, information is often 

interpreted in a way which is consistent with one's beliefs and expectations, results are 

over-generalized, and contradictory evidence is ignored or underestimated. 

C 1.7.4 Relation Between Event Importance and Probability 

Sometimes the importance of events, or their possible costs or benefits, 

influence judgments about the certainty of the events when, rationally, importance 

should not affect probability. In other words, one's attitudes towards risk tend to affect 

one's ability to make accurate probability judgments. For example, many physicians tend 

to overestimate the probability of very severe diseases, because they feel it is important 

to detect and treat them; and similarly, many smokers underestimate the probability of 

adverse consequences of smoking, because they feel that the odds do not apply to 

themselves personally. 
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C.l.7.5 Estimation of Probabilities 

Another limitation is related to one's ability to discriminate between levels of 

uncertainty, and to use appropriate criteria of discrimination for different ranges of 

probability. One result of this fact is that people tend to estimate both extreme and 

mid-range probabilities in the same fashion, usually doing a poor job in the extremes. It 

helps here to think in terms of odds as well as probabilities. Thus, for example, changing 

a probability estimate from 0.510 to 0.501 is equivalent to a change in odds from 1.041:1 

to 1.004:1, but a change from an estimate of 0.999 to 0.990 changes the odds by a factor 

of about 10 from 999:1 to 99:1 The closer to the extremes (either 0 or 1) that one is 

estimating probabilities, the greater the impact of small changes. 

C.1.7.6 Recommendations 

Although extensive and careful training would be necessary to eliminate all the 

problems mentioned above, some relatively simple suggestions can help minimize them. 

Most important is to be aware of one's natural cognitive biases, and to try consciously to 

avoid them. 

To avoid sequential effects keep in mind that the order in which you think of 

information should not influence your final judgment. It may be helpful to actually note 

on paper the important facts you are considering and then to reconsider them in two or 

more sequences, checking the consistency of your judgments. Try to keep an open mind 

until you have gone through all the evidence, and don't let the early information you 

consider sway you more than is appropriate. 

To avoid adverse memory effects, define various classes of information that you 

deem relevant, and then search your memory for examples of each. Don't restrict your 

thinking only to items that stand out for specific reasons. Make a special attempt to 

consider conflicting evidence, and to think of data that may be inconsistent with a 

particular theory. Also, be careful to concentrate on the given probability judgment and 
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do not let your own values (how you would make the decision yourself) affect those 

judgments. 

To accurately estimate the reliability of information, pay attention to such 

matters as sample size and power of the statistical tests. Keep in mind that data are 

probabilistic in nature, subject to elements of random error, imprecise measurements, 

and subjective evaluation and interpretation. In addition, the further one must 

extrapolate, or generalize, from a particular study to a situation of interest, the less 

reliable is the conclusion and the less certainty should be attributed to it. Rely more 

heavily on information which you consider more reliable, but do not treat it as "absolute 

truth." 

Keep in mind that the importance of an event or an outcome should not influence 

its judged probability. It is rational to let the costliness or severity of an outcome 

influence the point at which action is taken with respect to it, but not the judgment that 

is made about the outcome's likelihood. 

Finally, in making probability judgments, think primarily in terms of the measure 

(probability or odds) with which you feel more comfortable, but sometimes translate to 

the alternative scale, or even to measures of other events (e.g., the probability of the 

event not happening). When estimating very small or very large likelihoods, it is usually 

best to think in terms of odds, which are unbounded, instead of probabilities, which are 

bounded. For example, one can more easily conceptualize odds of 1:200 than a 

probability of .005. 

C.1.8 Final Preparation for Elicitation of Probability Judgments 

The outcomes of the ideal experiments described above are uncertain. Existing 

data are relevant, but do not allow exact predictions. Our goal is to have you represent 

probabilistically your own uncertainty about the experimental outcomes based on your 

expertise and the available knowledge. In responding to the questions we will ask you, 
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please think carefully about the relevant information reviewed in the criteria document, 

and consult it as well as the literature or your files as you deem appropriate. 

The previous section suggests ways to think about the relevant data. The purpose 

of that section is to help minimize the biasing effects that frequently accompany the 

information overload naturally resulting from rapid consideration of large amounts of 

complex evidence. You may find it helpful to review the section or raise questions about 

the points made in it before we begin. 

Uncertainty about the effects of lead exposure on mean decrement in IQ 

(relative to mean IQ at zero blood lead) can be represented probabilistically in two 

different ways. 

1. Uncertainty about the mean IQ decrement that would result when 

the exposed group has a given blood-lead concentration. 

2. Uncertainty about the blood-lead concentration that would be 

required to cause a given mean IQ decrement. 

We will concentrate on one way at a time, focusing primarily on the first one. 

For these purposes recall that everyone in the exposed population has a specified 

blood-lead level while everyone in the zero blood-lead population has negligible blood 

lead, as described above under Exposure Conditions. Then, in order for us to determine 

your uncertainty about the mean IQ decrement of the exposed group with a given bloodlead level relative to the negligible blood-lead group, we must introduce a definition. 

Let L be the given blood-lead concentration in question. 

Definition: D(L) is the mean IQ decrement of the exposed group with 

blood-lead level L relative to the negligible group. 

The value of D(L) for a given L is uncertain, and we would like to obtain 

probability judgments from you about its possible values. We will elicit your judgments 

about the possible values of D(L) by specifying a particular mean IQ decrement d and 

having you consider how likely it is that D(L) is less than that value. To help you make 
P.72 

164 

your probability judgments, we will make use of a device called a probability wheel, 

which has adjustable sectors of blue and orange. We can read on the back of the wheel 

the percentage of the wheel that is each color. In making your judgments you are to 

imagine that the wheel is a perfectly fair random device, and that therefore the 

probability of its stopping with the pointer on blue is exactly represented by the relative 

area that is blue. 

We will then proceed as follows. For each blood lead concentration L, we will 

specify a particular mean IQ decrement d, and also set the probability wheel to have a 

specific relative area of blue. Then you are to consider carefully the question: 

Do you consider it more probable that D(L) is less than d or that the 

wheel would stop with the pointer on blue (on a random spin)? 

You can give one of three responses: 

1. You judge it to be more probable that D(L) is less than d; 

2. You judge it to be more probable that the wheel would stop with 

the pointer on blue; 

3. You cannot judge either event as more probable than the other. 

For a particular concentration L and mean IQ decrement d, some wheel settings 

will have a small enough relative area of blue that you will feel confident making 

response (1). Other wheel settings will have a large enough relative area of blue that you 

will feel confident making response (2). The intermediate settings will be more difficult 

to judge. However, for a fixed blood lead L, and mean IQ decrement d, we will 

manipulate the wheel settings to find the one for which you feel most comfortable 

making response (3). 

Once we have determined the point at which you are most comfortable with 

response (3), and still focusing on the given blood lead L, we will specify a new mean IQ 

decrement d', reset the wheel to a new relative area of blue, and proceed to obtain your 

judgments regarding the probabilistic relation between d' and D(L). This will continue for 
P.73 

165 

the given L until we have obtained comparisons of various mean values to D(L). Then we 

will have elicited the probabilistic representation of your uncertainty about the mean IQ 

decrement for one blood-lead level. We will obtain the probabilistic representation of 

your uncertainty fpr the outcome of another experiment by specifying a new L and 

continuing as before. We will do this for a number of values of L. 

It frequently happens that an expert's judgments alter somewhat over the course 

of a session such as this, as he or she considers the evidence from various perspectives 

and thinks about the various responses called for. Hence, we will graph your responses 

and, at appropriate times, show them to you for your consideration and comparison. At 

these times you may wish to change some of the judgments you give earlier. 

Also, although the probability judgments are entirely your own, we must 

introduce one logical constraint: namely, that your final judgments are coherent in a 

sense that we can explain as we go along. It is quite common for initial judgments to 

exhibit some incoherencies. That is another reason we will consider together the graphs 

of your judgments. Our objective is to obtain a coherent set of judgments that represent 

your opinions well by the end of this elicitation process. You are not expected to give us 

such a set immediately. All of this will become clearer as we go along. 

We should emphasize that the judgments we are asking you to make are not 

simple ones, nor of course are there known correct answers. Rather, we want your best 

and most considered judgment in light of the available relevant scientific data. 

Therefore, please reflect on the available data carefully, feeling free to consult the lead 

criteria document or other sources as you wish as you formulate your judgments. 

(Encode judgments for two blood-lead concentrations, then continue with 

instructions.) 

Recall that uncertainty about the experimental outcomes can also be expressed 

in terms of the blood-lead concentration necessary to produce a given mean IQ 

decrement D, if the entire exposed population had the same blood-lead concentration, 
P.74 

166 

established in the manner discussed earlier. More specifically, proceeding as before, let 

us introduce a definition: 

Definition: L(D) is the blood-lead level that would cause a mean IQ 

decrement D in an exposed group relative to the negligible group. 

The value of L(D) is uncertain for a given D, and we want to obtain your 

judgments about its possible values. Analogously to what we have already done in 

obtaining the D(L) judgments, for a given D we will specify concentrations 2, and ask you 

to consider how likely it is that the L(D) is less than the specified £. More specifically, 

utilizing the wheel as before, we will ask you the question: 

Do you consider it more likely that L(D) is less than I or that the wheel 

would stop with the pointer on blue (on a random spin)? 

You can give one of three responses: 

1. You judge it more probable that L(D) is less than 8,; 

2. You judge it more probable that the wheel would stop with the 

pointer on blue; 

3. You cannot judge either event as more probable than the other. 

After determining the wheel setting at which you feel most comfortable with 

response (3), we will specify a new a and repeat the process. As before, for each D we 

will elicit your comparative judgments for various values of 2,. 

We must encode your probabilistic judgment about the mean IQ of children in the 

population, or in the two SES groups, who have negligible blood-level under the exposure 

conditions described previously. We start with a definition: 

Definition: Let y be the true population mean IQ for children with negligible 

blood lead. (Or, let y : be the true population mean IQ for children with negligible blood 

lead in SES group i.) 

The value of y or y • is uncertain, and we will obtain your judgment about its 

possible values. Analogously to what we have already done, we will specify a mean y and 
P.75 

167 

* * 

ask you to consider how likely it is that y or y • is less than y. We will elicit your 

judgments about various values of y with the aid of the probability wheel, in the same 

manner as was done previously. 

If you felt it necessary to consider separate experiments for two SES groups, 

then you may believe that the within-group IQ standard deviation is different from 15. 

If so, we must encode your probabilistic judgment about that value. If you agree, we will 

assume that the standard deviation is unaffected by lead-level. However, you may feel 

that the standard deviation is different for the two SES groups. If so, we must encode 

your opinion separately about each case. 

As before, we start with a definition: 

Definition: Let oj* be the true IQ standard deviation for SES group i. 

The value of ar* is uncertain, and we will obtain your judgment about its possible 

values. Analogously to what we have already done, we will specify a standard deviation o 

and ask you to consider how likely it is that o-* is less than o. We will elicit your 

judgments about various values of o with the aid of the probability wheel, in the same 

manner as was done previously. 

C.2 SUMMARY OF FUNCTIONS FIT TO IQ JUDGMENTS 

Normal-on-log-odds (NOLO) probability functions were fit to all of the judgments 

of the hemoglobin experts. Because of the diverse nature of the judgments obtained 

from the IQ experts, it was necessary to choose among normal, lognormal, and NOLO 

probability functions to adequately represent those judgments. Fitting normal and 

lognormal distributions to judgments are intermediate steps in the process of fitting a 

NOLO distribution, so it is unnecessary to repeat those details here. The reader can 

refer to Sec. B.2 for all of the necessary information. 

In fitting lognormal distributions to judgments, the variable of interest is that 

designated X in Sec. B.2.2; for fitting normal distributions, the variable of interest is 
P.76 

168 

that designated Y. Lognormal distributions were found to be particularly useful in fitting 

functions to judgments about mean IQ levels of children sheltered from lead exposure, 

and normal distributions were particularly useful in fitting functions to judgments about 

population standard deviation. 

C.3 RESULTS 

Results are presented in seven tables which cover: 

• Encoded judgments for the mean IQ, E[IQ ] of the distribution over 

IQ of children sheltered from lead (Table Cl), 

• Encoded judgments for within-group standard deviation, o (Table 

C2), 

• Encoded judgments for mean IQ decrements, A—, for exposed 

children relative to unexposed children (Table C.3), 

• Specifications (form, parameters, moments) for functions fit to the 

judgments for A— (Table C4), 

^o 

• Specifications for functions fit to judgments for o (Table C5), 

• Specifications for functions fit to judgments for A— (Table C.6), 

and 

• Comparisons of medians and credible intervals for encoded 

judgments vs. fitted functions (Table C.7). 

C.3.1 Expert F 

Expert F did not feel that SES level was a significant factor influencing the 

effects of lead on IQ. Thus, only one set of judgments was obtained from Expert F. In 

addition, Expert F did not feel that it was necessary to use a probability distribution to 

characterize population standard deviation and simply gave a point estimate for that 

quantity. 
P.77 

169 

TABLE C l Encoded Judgments about the Mean IQ of Children 

Sheltered from Lead Exposure 

Expert F 

Both SES 

Levels 

^ 

100 

100 

101 

101 

102 

• 

F 

0.01 

0.01 

0.42 

0.80 

0.99 

Expert G 

*% 

90 

93 

94 

96 

98 

100 

WQ 

100 

104 

106 

108 

110 

F 

0.01 

0.25 

0.50 

0.76 

0.92 

0.99 

F 

0.01 

0.15 

0.50 

0.85 

0.99 

Expert H 

Lower SES 

W0 F 

92 0.01 

94 0.20 

98 0.50 

99 0.65 

102 0.99 

Expert J 

Levels 

*% 

90.0 

93.5 

95.0 

96.0 

98.0 

F 

0.01 

0.25 

0.50 

0.75 

0.90 

Higher SES Levels 

WQ F 

100 0.02 

102 0.11 

104 0.30 

106 0.49 

108 0.75 

110 0.96 

^ 0 

100 

102 

104 

106 

108 

110 

F 

0.001 

0.1 

0.77 

0.90 

0.99 

0.999 

Expe 

*% 

78 

83 

85 

88 

91 

**~o 

100 

102 

104 

106 

108 

110 

rt K 

F 

0.01 

0.25 

0.50 

0.75 

0.99 

F 

0.01 

0.17 

0.42 

0.60 

0.85 

0.99 
P.78 

170 

TABLE C.2 Encoded Judgments about Population Standard 

Deviation 

Expert F 

Both SES 

Levels 

°IQ

 F 

15 1 

Expert G 

^Q 

14 

14 

F 

1 

1 

Expe 

^Q 

10 

11 

12 

13 

14 

15 

13 

13.5 

14 

14.3 

15 

15.5 

rt H 

Lower 

F 

0.04 

0.1 

0.35 

0.5 

0.85 

0.999 

Expert J 

SES Levels 

°^Q 

11 

12 

13 

14 

15 

Higher SES 

0.04 

0.07 

0.275 

0.5 

0.9 

0.99 

11 

12 

13 

14 

15 

F 

0.001 

0.125 

0.5 

0.875 

0.999 

Levels 

0.001 

0.125 

0.5 

0.875 

0.999 

Exp 

°?Q 

10 

11 

12 

13 

14 

15 

12 

13 

13.5 

14 

15 

art K 

F 

0.01 

0.05 

0.14 

0.53 

0.93 

0.999 

0.2 

0.25 

0.5 

0.75 

0.99 
P.79 

171 

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moesocooo o 

O—IrHCSCSCOtfv O 
TABLE C.3 (Cont'd) 

Blood-Lead Level 

-IQ A

IQ

 F k

iQ 'IQ 1

IQ *IQ 

Expert K, Higher SES Levels 

15 yg/dL 25 yg/dL 

0.5 

1.0 

1.5 

2.0 

0.01 

0.35 

0.5 

0.99 

35 yg/dL 45 yg/dL 55 yg/dL 65 yg/dL 

1.0 

1.5 

2.0 

2.5 

3.0 

0.01 

0.11 

0.5 

0.9 

0.99 

2.0 

3.0 

3.5 

4.0 

5.0 

0.01 

0.2 

0.5 

0.75 

0.99 

3.0 

4.0 

4.5 

5.0 

6.0 

0.02 

0.25 

0.5 

0.78 

0.98 

4.0 0.010 

5.0 0.170 

6.0 0.500 

7.0 0.820 

8.0 0.990 

sl 

ON 

*Aj0 denotes the mean IQ decrement among children with the specified blood-lead levels, 

rererenced to unexposed children. 

F denotes cumulative probability. 
TABLE C.4 Parameters of Functions Fit to the Probabilistic Judgments of Experts 

Regarding Mean IQ Levels among Children Sheltered from Lead Exposure 

Expert SES Case 

Functional 

Form 

Parameters of 

Normal-on-Ln (IQQ) 

Distribution 

Mean SDd 

Moments of 

Distribution 

Over IQQ 

E[IQ J b SD[IQ 1( 

r

2 of 

F on F 

Combined Lognormal 4.6140 0.0046 100.9 0.47 0.931 

G 

H 

J 

K 

G 

H 

J 

K 

Lower 

Lower 

Lower 

Lower 

Higher 

Higher 

Higher 

Higher 

Lognormal 

Lognormal 

Normal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

4.5495 

4.5763 

-

-

4.6591 

4.6596 

4.6454 

-

0.0232 

0.0249 

-

-

0.0206 

0.0265 

0.0158 

-

94.6 

97.2 

94.8 

85.0 

105.6 

105.6 

104.1 

104.9 

2.20 

2.42 

1.93 

2.92 

2.17 

2.80 

1.65 

2.36 

0.994 

0.966 

0.996 

0.993 

0.987 

0.992 

0.960 

0.988 

aSD denotes standard deviation. 

E[IQ ] denotes the mean of the distribution for IQ_. 

sl 

sl 

'SD[IQ ] denotes the standard deviation of the distribution for IQQ. 
TABLE C.5 Summary of Functions Fit to the Probabilistic Judgments of Experts Regarding 

Population Standard Deviation for IQ Levels 

Expert 

Functional 

SES Case Form 

Parameters of 

Normal-on-Ln (°TQ) 

Distribution 

Mean SDe 

Moments of 

Distribution 

Over OJQ 

E[oIQ] SD[oIQ]

c 

r

2 of 

F on F 

Combined Point 15.0 

G 

H 

J 

K 

G 

H 

J 

K 

Lower 

Lower 

Lower 

Lower 

Higher 

Higher 

Higher 

Higher 

Point 

Lognormal 

Normal 

Normal 

Point 

Lognormal 

Lognormal 

Normal 

— 

2.5056 

-

-

-

2.6541 

2.5590 

-

— 

0.0915 

-

-

-

0.0416 

0.0531 

-

14.0 

12.3 

13.0 

12.6 

14.0 

14.2 

12.9 

13.5 

— 

1.13 

0.68 

0.93 

-

0.59 

0.69 

0.69 

— 

0.999 

0.999 

0.999 

-

0.999 

0.999 

0.999 

sl 

oo 

a S D denotes standard deviation. 

E[OJQ ] denotes the mean of the distribution of OJQ . 

C SD[OJQ ] denotes the standard deviation of the distribution for OTA -
P.87 

179 

TABLE C.6 Summary of Function Fit to the Probabilistic Judgments of Experts 

Regarding Mean IQ Decrements among Children Exposed to Lead 

Blood-Lead 

Level (yg/dL) 

Functional 

Form 

Parameters of 

Normal on 

LN (ATM) 

Distribution 

Mean SDe 

Moments of 

Distribution 

Over A ^ 

E[^iQ]b SD[AJQ]C 

r

2 of 

F on F 

Expert F, Both SES Levels 

25 

35 

45 

55 

65 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

-1.4059 

-0.7127 

-0.0329 

0.3350 

0.5574 

0.4628 

0.4628 

0.4628 

0.4628 

0.4628 

0.2729 

0.5457 

1.0770 

1.5559 

1.9434 

0.1334 

0.2667 

0.5264 

0.7604 

0.9498 

0.9990 

0.9990 

0.9986 

0.9984 

0.9885 

Expert G, Lower SES Levels 

5 

15 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

-0.4816 

0.3316 

0.9775 

1.3548 

1.7359 

1.9905 

0.6422 

0.5429 

0.5229 

0.3807 

0.3011 

0.3174 

0.7593 

1.6145 

3.0471 

4.1675 

5.9369 

7.6970 

0.5425 

0.9452 

1.7089 

1.6459 

1.8287 

2.5060 

0.9789 

0.9789 

0.9689 

0.9825 

0.9701 

0.9782 

Expert H, Lower SES Levels 

5 

15 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

0.8268 

1.2481 

1.5860 

2.0323 

2.2422 

2.4045 

0.4087 

0.3989 

0.3749 

0.3087 

0.2366 

0.1887 

2.4851 

3.7724 

5.2397 

8.0040 

9.6807 

11.2714 

1.0596 

1.5669 

2.0356 

2.5307 

2.3224 

2.1458 

0.9715 

0.9765 

0.877 

0.9879 

0.9898 

0.9888 

Expert I, Lower SES Levels 

15 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

-0.3276 

0.8495 

1.3361 

1.7009 

1.9041 

0.5351 

0.4110 

0.3282 

0.3088 

0.2845 

0.8316 

2.5445 

4.0148 

5.7465 

6.9908 

0.4789 

1.0915 

1.3540 

1.8178 

2.0298 

0.9984 

0.9945 

0.9926 

0.9980 

0.9949 
TABLE C.6 (Cont'd) 

180 

P.88 

Blood-Lead 

Level (yg/dL) 

Functional 

Form 

Parameters of 

Normal on 

LN (ATM) 

Distribution 

Mean SDa 

Moments of 

Distribution 

Over A ^ 

— ib E[AJQ] SD[AJQ]C 

r

2 of 

F on F 

Expert J, Lower SES Levels 

5 

15 

25 

35 

45 

55 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

2.3874 

3.4704 

4.7747 

6.8264 

8.8357 

10.7412 

0.8956 

1.1878 

1.4872 

1.5025 

1.5642 

1.6007 

0.9608 

0.9907 

0.9927 

0.9949 

0.9889 

0.9791 

Expert K, Lower SES Levels 

15 

25 

35 

45 

55 

65 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

1.2764 

2.8910 

3.7668 

6.4349 

7.7608 

10.3694 

0.4426 

1.1027 

1.0816 

1.2201 

1.3071 

1.5855 

0.9540 

0.9913 

0.9900 

0.9800 

0.9889 

0.9920 

Expert G, Higher SES Levels 

15 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

-0.3430 

0.2059 

0.9575 

1.3548 

1.7497 

0.5671 

0.5045 

0.4847 

0.3807 

0.3068 

0.8335 

1.3954 

2.9299 

4.1675 

6.0298 

0.5133 

0.7512 

1.5079 

1.6459 

1.8942 

0.9546 

0.9668 

0.9854 

0.9825 

0.9613 

Expert H, Higher SES Levels 

5 

15 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

-0.5767 

0.8960 

1.4785 

1.6873 

1.8859 

2.0688 

0.5207 

0.4498 

0.2607 

0.1955 

0.1297 

0.1103 

0.6433 

2.7106 

4.5382 

5.5090 

6.648a 

7.9635 

0.3590 

1.2837 

1.2035 

1.0873 

0.8661 

0.8809 

0.9961 

0.9833 

0.9899 

0.9968 

0.9842 

0.9967 
TABLE C.6 (Cont'd) 

181 

P.89 

Blood-Lead 

Level (yg/dL) 

Functional 

Form 

Parameters of 

Normal on 

LN (L-) 

Distribution 

Mean SDe 

Moments of 

Distribution 

Over ATQ" 

E[Ajp]b SD[AJQ]C 

r

2 of 

F on F 

Expert I, Higher SES Levels 

15 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

-1.18001 

0.0637 

0.8495 

1.3198 

1.4719 

0.6191 

0.6022 

0.4110 

0.3193 

0.3839 

0.3722 

1.2776 

2.5445 

3.9383 

4.6909 

0.2544 

0.8448 

1.0915 

1.2902 

1.8692 

0.9987 

0.9903 

0.9945 

0.9970 

0.9974 

Expert J, Higher SES Levels 

15 • 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

0.4542 

1.0069 

1.2982 

1.6180 

1.9489 

0.4502 

0.3640 

0.2762 

0.1991 

0.1466 

1.7429 

2.9246 

3.8053 

5.1442 

7.0970 

0.8262 

1.1007 

1.0713 

1.0344 

1.0463 

0.9620 

0.9410 

0.9590 

0.9979 

0.9923 

Expert K, Higher SES Levels 

25 

35 

45 

5.5 

65 

Normal 

Normal 

Normal 

Normal 

Normal 

1.2836 

1.9953 

3.5216 

4.4858 

6.0070 

0.3485 

0.4232 

0.6461 

0.7262 

0.8948 

0.9322 

0.9993 

0.9989 

0.9992 

0.9976 
TABLE C.7 Summary and Comparison of Judgments and Fitted Functions Concerning Lead-Induced IQ Effects 

Expert F, Both SES Groups 

AIQ 

Blood-Lead Level 

.9 

( - , 1.5) 

( - , 2) 

1.5 

(1.1 , 1.9) 

( - , 3) 

2 

(1.3 , 2.6) 

(--, 4) 

Index IQQ o 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 65 yg/dL 

Encoded Judgments 

Median 100.5 15 .25 .5 

50% C.I.a (100.2, 101.3) — ( — , .62) (--, 1.2) 

90% C.I. (100.1, 101.9) — ( — , .92) (—, 1.9) 

Fitted Representations °> 

Median 100.9 15 .25 .49 .97 1.4 1.7 

50% C.I. (100.6, 101.2) — (.12, .34) (.36, .67) (.71, 1.32) (1.02, 1.91) (1.28, 2.39) 

90% C.I. (100.1, 101.7) — (.11, .52) (.23, 1.05) (.45, 2.07) (.65, 2.99) (.81, 3.74) 

98% C.I. (99.8, 102) — (.08, .72) (.17, 1.4) (.33, 2.84) (.48, 4.10) (.59, 5.12) 

aC.I. denotes credible interval. 

Tl 

CO 
TABLE C.7 (Cont'd) 

Expert G, Lower SES Group 

AIQ 

Blood-Lead Level 

Index IQQ o 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Encoded Judgments 

14 0.5 1.5 3.0 3.5 5.0 7.0 

(5, 10) 

Median 

50% C.I. 

90% C.I. 

94 

(93, 96) 

(91, 99) 

0.5 

(.3 , 1) 

(.2 , 3) 

1.5 

(.7 , 2) 

(.5 , 5) 

3.0 

(1.3 , 4) 

( 1 , 8.5) 

3.5 

(2.5 , 5) 

( 2 , 10) 

5.0 

( 4 , 7) 

(3.5 , 12) (4, 15) 

Fitted Representations oo 

CO 

Median 94.6 14 0.6 1.4 2.7 3.9 5.7 7.3 

50% C.I (93, 96) — (.4, .9) (1, 2) (1.9, 3.8) (3, 5) (4.6, 7) (5.9, 9.1) 

90% C.I (91, 98) — (.2, 1.8) (.6, 3.5) (1.1, 6.3) (2.1, 7.3) (3.5, 9.3) (4.3, 12.3) 

98% C.I. (90, 100) — (.1, 2.8) (.4, 4.9) (.8, 9) (1.6, 9.4) (2.8, 11.4) (3.5, 15.3) 

TJ 

CO 
TABLE C.7 (Cont'd) 

Expert G, Higher SES Groups 

AIQ 

Blood-Lead Level 

Index IQQ o 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Encoded Judgments 

Median 106 14 — 0.5 

50% C.I. (105, 107) — — (.4, 1) 

90% C.I. (103, 109) — — (.3, 3) 

Fitted Representations oo 

Median 105.6 14 ~ 0.7 1.2 2.6 3.9 5.8 

50% C.I. (104, 107) — — (.5, 1) (.9, 1.7) (1.9, 3.6) (3, 5) (4.7, 7.1) 

90% C.I. (102, 109) — — (.3, 1.8) (.5, 2.8) (1.2, 5.8) (2.1, 7.3) (3.5, 9.5) 

98% C.I. (101, 111) — — (.2, 2.7) (.4, 4) (.8, 8) (1.6, 9.4) (2.8, 11.7) 

1.0 

(.7 , 2) 

(.5 , 4) 

2.5 

(1.5 , 4) 

( 1 , 8) 

3.5 

(2.5 , 5) 

( 2 , 10) 

5.0 

( 4 , 7.5) 

(3.5 , 12) 
TABLE C.7 (Cont'd) 

Expert H, Lower SES Group 

AIQ 

Blood-Lead Leve l 

Index IQQ o 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL . 45 yg/dL 55 yg/dL 

Encoded Judgments 

Median 

50% C.I. 

90% C.I. 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

98 

(95, 100) 

(92, 102) 

97.2 

(96, 99) 

(93, 100) 

(92, 103) 

13 

(12,14) 

(10, 15) 

12.4 

(12, 13) 

(11, 14) 

(10, 15) 

2.6 3.0 5.2 

(1.6, 3.4) (2.6, 5) (3.4, 7.2) 

(1.1, 4.5) (1.9, 6.1) (2.4, 9.2) 

Fitted Representations 

2.3 3.5 4.9 

(1.7, 3) (2.7, 4.6) (3.8, 6.3) 

(1.2, 4.5) (1.8, 6.7) (2.6, 9) 

(.9, 5.9) (1.4, 8.8) (2, 11.7) 

8.2 

(6, 9.7) 

(4.2, 12) 

7.6 

(6.2, 9.4) 

(4.6, 12.7) 

(3.7, 15.7) 

9.5 

(7.4, 11.3) 

(6.2, 14) 

9.4 

(8,11) 

(6.4, 13.9) 

(5.4, 16.3) 

10.5 

(9.7, 11.8) 

(8.2, 16) 

11.1 

(9.7, 12.6) 

(8.1, 15.1) 

(7.1, 17.2) 

185 
TABLE C.7 (Cont'd) 

Expert H, Higher SES Group 

AIQ 

Blood-Lead Level 

Index IQQ o 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Encoded Judgments 

Median 106 14.3 0.6 2.5 4.5 5.5 6.5 8.0 

50% C.I. (104, 108) (13.8, 14.7) (--, .9) (1.8, 3.5) (3.8, 5.6) (4.4, 6.4) (6.1, 7.1) (7.4, 8.7) 

90% C.I. (101, 110) (13.2, 15.2) ( — , 1.3) (1.2, 4.1) (2.7, 6.7) (3.9, 7.8) (5.3, 8.4) (6.4, 9.6) 

Fitted Representations 

Median 105.6 14.3 0.6 2.4 4.4 5.4 6.6 7.9 

50% C.I. (104, 108) (13.8, 14.6) (.4, .8) (1.8, 3.3) (3.7, 5.2) (4.7, 6.2) (6, 7.2) (7.3, 8.5) 

90% C.I. (101, 110) (13.3, 15.2) (.2, 1.3) (1.2, 5.1) (2.9, 6.7) (3.9, 7.5) (5.3, 8.2) (6.6, 9.5) 

98% C.I. (99, 112) (12.9, 15.6) (.2, 1.9) (.9, 7) (2.4, 8) (3.4, 8.5) (4.9, 8.9) (6.1, 10.2) 

oo 

ON 
TABL E C.7 (Cont'd) 

Median 

5 0% C.I. 

9 0% C.I. 

Expert I, Lower SES Groups 

AIQ 

Blood-Lead Level 

Index IQQ a 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Encoded Judgments 

0.7 

(0.5 , 1.1) 

( 0 , 2) 

2.3 

(1.9 , 3.2) 

( 1 , 5) 

3.6 

(3.1 , 5.1) 

( 2 , 7) 

5.3 

(4.5 , 6.9) 

( 3 , 10) 

6.3 

(5.5 , 8.2) 

( 4 , 12) 

Fitted Representations oo 

Median — — — .7 2.3 3.8 5.5 6.7 

5 0% C.I. — -- -- (.5, 1.0) (1.7, 3.1) (3.0, 4.7) (4.4, 6.7) (5.5, 8.1) 

90% C.I. -- — -- (.3, 1.7) (1.2, 4.6) (2.2, 6.5) (3.3, 9.1) (4.2, 10.7) 

98% C.I. — -- — (.2, 2.5) (.9, 6.1) (1.8, 8.2) (2.7, 11.3) (3.5, 13.1) 

sj 
TABLE C.7 (Cont'd) 

Median 

50% C.I. 

90% C.I. 

Expert I, Higher SES Group 

AIQ 

Blood-Lead Level 

Index IQQ o 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Encoded Judgments 

0.3 

(.2 , .5) 

( 0, 1) 

1.0 

(.7 , 2) 

( 0, 3) 

2.3 

(1.9 , 3.2) 

( 1 , 5) 

3.6 

(3.1 , 4.7 ) 

( 2 , 7) 

4.3 

(3.5 , 5.8) 

( 2 , 9) 

Fitted Representations 55 

Median — — ~ 0.4 1.1 2.4 3.8 4.5 

50% C.I. ~ — — (.2, .5) (.6, 1.7) (1.8, 3.2) (3.1, 4.7) (3.4, 5.7) 

90% C.I. — — — (.0, .9) (.1, 2.8) (1.2, 4.5) (2.2, 6.3) (2.3, 8.0) 

98% C.I. -- — -- (0.7, 1.3) (.3, 4.3) (.9, 6.1) (1.8, 7.9) (1.8, 10.6) 
TABLE C.7 (Cont'd) 

Expert J, Lower SES Group 

AIQ 

Blood-Lead Level 

Index IQQ o 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Encoded Judgments 

Median 

50% C.I. 

90% C.I. 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

95 

(94, 96) 

(91, 99) 

94.8 

(94, 96) 

(92, 98 

(90, 99) 

13 

(12, 14) 

(11, 15) 

13 

(13, 14) 

(12, 14) 

(12, 14) 

2 

(1, 3) 

(.2, 5) 

2.4 

(1.8, 3.0) 

(0.9, 3.9) 

(0.3, 4.5) 

3.5 5 

(2.3, 4.5) (4, 5.8) 

(.4, 6.4) (1, 8) 

Fitted Representations 

3.5 4.8 

(2.7, 4.3) (3.8, 5.8) 

(1.5, 5.4) (2.3, 7.2) 

(0.7, 6.2) (1.3, 8.2) 

7 

(6, 8) 

(3, 9.6) 

6.8 

(5.8, 7.8) 

(4.4, 9.3) 

(3.3, 10.3) 

9 

(7.5, 10.5) 

(5, 11.7) 

8.8 

(7.8, 9.9) 

(6.3, 11.4) 

(5.2, 12.5) 

11 

(9, 12.5) 

(6.6, 13.7) 

10.7 

(9.7, 11.8) 

(8.1, 13.4) 

(7.0, 14.5) 

oo 
TABLE C.7 (Cont'd) 

Expert J, Higher SES Group 

Index IQ, 

AIQ 

Blood-Lead Level 

o 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Encoded Judgments 

Median 

50% C.I 

90% C.I. 

94 

(93, 96) 

(91, 99) 

14 

(1.3, 2.3) 

(.7, 3) 

(2.8, 3.5) 

(1.4, 6.4) 

Fitted Representations 

(3.5, 5) 

(2, 6.7) 

(4.5, 5.8) 

(3.3, 7.6) 

(6.5, 7.5) 

(5.3, 9.7) 

VO 

o 

Median 

50% C.I. 

90% C.I. 

98% C.I. 

94.6 

(93, 96) 

(91, 98) 

(90, 100) 

14 1.6 

(1.2, 2.2) 

(.7, 3.4) 

(.5, 4.6) 

2.9 

(2.2, 3.8) 

(1.5, 5.7) 

(1.1, 7.6) 

3.8 

(3.1, 4.7) 

(2.2, 6.4) 

(1.8, 8.0) 

5.0 

(4.4, 5.8) 

(3.6, 7.0) 

(3.2, 8.0) 

7.0 

(6.4, 7.8) 

(5.5, 8.9) 

(5.0, 9.9) 

CO 
TABLE C.7 (Cont'd) 

Expert K, Lower SES Group 

AIQ 

Blood-Lead Level 

Index IQQ o 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 65 yg/dL 

Encoded Judgments 

Median 

50% C.I. 

90% C.I. 

85 

(83 , 88) 

(79, 90.4) 

13 

(12.2 , 13.5) 

(11 , 14) 

1.5 

(0.8 , 1.7) 

(0.3 , 2) 

3.1 

( 2 , 3.8) 

( 1 , 4.8) 

4 

(3.2 , 4.7) 

( 2 , 5.8) 

6 

(5.4 , 7.5) 

(4.5 , 8.8) 

8.1 

(6.8 , 8.6) 

(5.5 , 9.8) 

10 

(8.8 , 11.8) 

(7.5 , 13.7) 

Fitted Representations 

Median 85 12.6 1.3 2.9 3.8 6.4 7.8 10.4 

50% C.I. (83, 87) (11.9, 13.2) (0.7, 1.6) (2.1, 3.6) (3, 4.5) (5.6, 7.3) (6.9, 8.6) (9.3, 11.4) 

90% C.I. (80, 90) (11, 14.1) (0.5, 1.8) (1.1, 4.7) (2, 5.5) (4.4, 8.4) (5.6, 9.9) (7.8, 13) 

98% C.I. (78, 92) (10.4, 14.7) (0.2, 2.3) (0.3, 5.5) (1.3, 6.3) (3.6, 9.3) (4.7, 10.8) (6.7, 14) 
TABLE C.7 (Cont'd) 

Expert K, Higher SES Group 

AIQ 

Blood-Lead Level 

Index IQQ o 25 yg/dL 35 yg/dL 45 yg/dL 55 yig/dL 65 yg/dL 

Encoded Judgments 

Median 104.9 13.5 1.5 2 3.5 4.5 6 

50% C.I. (102.6, 107.2) (13, 14) (.8, 1.7) (1.6, 2.3) (3.1, 4) (4, 4.8) (5.2, 6.8) 

90% C.I. (100.6, 109.4) (12.2, 14.8) (.6, 1.9) (1.2, 2.9) (2.2, 4.8) (3.1, 5.9) (4.3, 7.8) 

Fitted Representations N> 

Median 104.9 13.5 1.3 2 3.5 4.5 6 

50% C.I. (103.3, 106.5) (13, 14) (1, 1.5) (1.7, 2.3) (3.1, 4) (4, 5) (5.4, 6.6) 

90% C.I. (101, 108.8) (12.3, 14.6) (.7, 1.9) (1.3, 2.7) (2.5, 4.6) (3.3, 5.7) (4.5, 7.5) 

98% C.I. (99.A, 110.4) (11.9, 15.1) (.5, 2.1) (1, 3) (2, 5) (2.8, 6.2) (3.9, 8.1) 
_E2_ 

193 

Thus, Expert F judged a probability of 0.5 that the mean IQ of the unexposed 

group would be < 100.5, 0.8 probability that it would be <_ 101.5, and so on. These and 

other judgments about mean IQ of an unexposed group of children are listed in Table 

C.l. Expert F provided a point value of 15.25 for o, which appears in Table C.2. 

Expert F provided judgments on IQ differences at five PbB levels: 25, 35 ,45, 55, 

and 65 yg/dL. These judgments are listed in Table C.3. For example, at a PbB level of 65 

yg/dL, Expert F judged a probability of 0.9 that IQ difference would be _< 3. Figure 4.3 

shows that Expert F is increasingly uncertain about the magnitude of IQ differences as 

PbB level increases. Table C.l indicates that judgments on IQ differences having 

cumulative probabilities less than 0.5 were not provided at the lower three PbB levels. 

Expert F cited difficulty in providing judgments on what would be very small IQ 

differences. 

For the reasons presented in Sec. 1, mathematical functions were fit to the 

judgments of Expert F. For Expert F, the mathematical representations of the CDFs for 

IQ differences conditional on PbB level are guaranteed never to cross. They were 

obtained by fitting regression lines to transformations of the judgments. The 

transformation used was the log (ln) transformation. Similar to the hemoglobin case, this 

transformation leads to distributions that are normal distributions, with a high degree of 

accuracy. 

Thus, the fitted distributions are lognormal distributions. They are uniquely 

defined by the mean and variance of the underlying normal distributions, and the 

transformation function. Properties of the lognormal distribution are summarized in 

Table B.l. A variety of distributions were fit to the judgments, and the ones reported 

here were determined (with input from the experts) to be best. 

Tables C.4-C.6 summarize relevant information about the distributions fit to the 

judgments of the experts. In Table C.4, columns identify the functional form, mean and 

standard deviation of an underlying normal distribution (if a transformation is used), 
P.3 

194 

mean (E[IQ ]) and standard deviation (SD[OJQ]) of the IQ distribution, and r of the 

regression of fitted cumulative probability values F versus encoded values (F). 

Similar column headings appear in Tables C.5 and C.6. In Table C.5, E[OTQ] 

denotes the mean, and SD[CJJQ] denotes the standard deviation of the distribution for 

population standard deviation. L denotes PbB level, and E[A—] and SD[A—] denote the 

means and standard deviations of probability distributions for IQ decrements in Table 

C.6. 

For Expert F, the fitted distribution of the uncertain mean IQ of the unexposed 

group has a mean value of. 100.9; it is a lognormal distribution and the r value of the 

regression of the F values vs. the F values is 0.93. The standard deviation of the 

distribution is 0.47. The mean and standard deviation of the underlying normal 

distribution (which results after taking the natural log of the encoded mean IQ values) 

are 4.6 and 0.0046. These values are needed to calculate points on a cumulative 

probability function for the mean IQ variable. For population standard deviation, a point 

estimate of 15 was given. 

Lognormal distributions provided the best fits of Expert F's judgments about IQ 

differences. Thus, all of the columns have entries. The mean values of the distributions 

over IQ decrement vary from about 0.3 at a PbB level of 25 yg/dL to about 1.9 at 65 

yg/dL. In general, the fitted functions represent these judgments quite well, having r 

values around 0.99 or higher. 

C.3.2 Expert G 

Expert G provided probabilistic judgments about mean IQ for an unexposed group 

and IQ decrements for populations exposed to varying levels of lead for both SES 

categories. A point estimate for population standard deviation (OJQ=14) was made for 

both SES catetories. Lognormal distributions provided the best fits for the rest of the 

judgments. The mean values of the IQ distributions were 94.6 and 105.6 for the lower 
P.4 

195 

and higher SES cases, respectively. Averaging across SES level results in an average 

value of about 104 for the mean IQ for unexposed children. Mean values of the 

distributions for IQ decrements range from 0.8 (at 5 yg/dL) to 7.7 (at 55 yg/dL) for the 

lower SES category, and from 0.5 (at 15 yg/dL) to 6.0 (at 55 yg/dL) for the higher SES 

category. The r values of the regressions of the fitted distributions versus the encoded 

distributions were quite good. The lowest value was 0.95. 

C.3.3 Expert H 

This expert provided probabilistic judgments about all of the variables for both 

SES categories. Lognormal distributions again provided excellent fits to all of the 

encoded judgments. The mean values of the fitted IQ distributions were 97.2 and 105.6, 

and the mean values of the fitted standard deviation distributions were 12.3 and 14.2. 

The standard deviations of the fitted IQ distributions were 2.4 and 2.8. Mean values of 

the fitted distributions for IQ decrements ranged from 2.5 (at 5 yg/dL) to 11.3 (at 55 

9 

yg/dL), and from 0.6 (at 5 yg/dL) to 8 (at 55 yg/dL). Again, the r values of the 

regressions are quite good (0.98 or higher). (In all cases, the values for the lower SES 

cases are first, and the values for the higher SES cases are second.) 

C.3.4 Expert I 

Expert I only provided probabilistic judgments for IQ decrement. This individual 

was not comfortable about providing judgments, reasonding that it should be possible to 

solve for the other variables, given what is currently known and published about 

population IQ distributions. However, we found that it was not possible to do this 

without making strong assumptions about Expert l's probability judgments. In particular, 

we would either have to assume that judgments of IQ effects at each lead level are 

independent of each other, or assume a particular pattern of dependencies. Since we 

were certain that an assumption of independence would be wrong, and had no basis for 

any other specific assumptions, we simply accepted the judgments as provided. 
P.5 

196 

Lognormal distributions provided the best fits to these judgments. Judgments 

were provided at five PbB levels (15-55 yg/dL). Mean values of the fitted distributions on 

IQ decrement ranged from 0.8 to 7 for the lower SES group, and from 0.4 to 4.7 for the 

higher SES group. The r values for the regressions of the fitted distributions (F values) 

vs. the encoded distributions (F values) were all greater than 0.99. 

C.3.5 Expert J 

Expert J provided probabilistic judgments on all three IQ variables. Lognormal 

distributions were used to represent these judgments. The mean values of the fitted IQ 

distributions were 94.7 and 104.1, and the mean values of the fitted standard deviation 

distributions were 13 and 12.9. Mean values of the distributions fitted to the judgments 

on IQ decrements ranged from 2.4 to 10.7 for the lower SES case, and from 1.7 to 7.1 for 

9 the higher SES case. The r values for regressions of fitted values versus encoded values 

were generally around 0.99 for the lower SES case, and slightly less than 0.99 for the 

higher SES case. 

C.3.6 Expert K 

Expert K provided probabilistic judgments on all three IQ variables. Normal 

distributions provided the best fits to all of the judgments. The mean values of the fitted 

IQ distributions were 85.0 and 104.9, and the mean values of the fit standard deviation 

distributions were 12.6 and 13.5. Mean values of the distributions fit to the judgments on 

IQ decrements ranged from 1.3 to 10.4 for the lower SES case, and from 1.3 to 6 for the 

higher SES case. The r values for regressions of fitted values versus encoded values 

were generally around 0.99 for both of the SES cases. 
P.6 

197 

C.3.7 Comparison of Judgments and Fitted Functions 

Table C.7 summarizes and compares encoded judgments and corresponding points 

on the functions fit to the judgments of each of the experts. The table can be further 

used to compare and contrast the judgments of the different experts. Many tables like 

this one (one per case per expert) were used to help the experts understand the 

implications of their judgments and choose mathematical functions that best represented 

those judgments. 

The main point of the table is that the fitted functions match the judgments 

quite well. The fitted median values generally are quite close to the assessed median 

values. This is also the case for the 50% and 90% credible intervals. For example, 

consider the judgments of Expert G. The median judgment for the mean TQ level for 

unexposed children in the lower SES category is 94, and the median of the fitted 

distribution is 94.6. The encoded medians for IQ decrement are 0.5, 1.5, 3.0, 3.5, 5.0, and 

7.0 for PbB levels of 5, 15, 25, 35, 45, and 55 yg/dL, respectively. The respective 

medians of the fitted distributions are 0.6, 1.4, 2.7, 3.9, 5.7, and 7.3. The lower ends of 

the 50% credible intervals (the 0.25 points on the cumulative probability curves) are 0.3, 

0.7, 1.3, 2.5, 4, and 5 for the encoded judgments, and 0.4, 1, 1.9, 3, 4.6, and 5.9 for the 

fitted functions. The upper ends of the 50% credible intervals (the 0.75 points on the 

cumulative probability curves) are 1, 2, 4, 5, 7, and 10 for the judgments, and 0.9, 2, 3, 8, 

5, 7, and 9.1 for the fitted functions. 

Expert F judged that the mean IQ of children sheltered from lead should be 

around 101 with a high degree of certainty (indicated by a standard deviation of about 

0.5). The other experts judged that the mean IQ would be one to three points higher, on 

the average, but with much less certainty as indicated by standard deviations for the 

mean IQ distribution that ranged from 1.5 to 3.0. Similarly, Expert F judged much 

smaller IQ decrements attributable to lead exposure than did the other experts. First 

judgments were at PbB levels of 25 yg/dL for Expert F, 15 yg/dL for Expert K, and 5 

yg/dL for the other experts. 
P.7 

198 

While these judgments are interesting in and of themselves, they take on added 

meaning when included in a health risk assessment. Thus, the results of Sec. 5 provide 

further insight into the significance of the differences in judgments among the experts. 

C.4 SUMMARY DISCUSSIONS 

C.4.1 Summary of Discussions with Expert F 

1. Low lead levels (below 30 yg/dL or 40 yg/dL) do not have a 

discernable, deleterious effect on IQ. Studies that purport to 

show such an effect have methodological and bias problems. 

2. Although low lead levels do not have independent effects on IQ, 

one cannot currently rule out the possibility that lead at higher 

levels interacts with other variables to affect IQ. Nor can we 

rule out completely the possibility that IQ influences lead level. 

These variables could relate to general health status, mental 

health status, or other environmental factors. 

3. Numerous covariates are associated with lead exposure, many of 

which are known to be negatively related to IQ. It is difficult to 

use regression techniques to determine which of the variables are 

"causative." 

4. Behavioral, social, and cognitive measures have some degrees of 

unreliability that add uncertainty to any conclusions. 

5. Cord blood lead may be related to a few negative birth outcomes, 

but one cannot infer direction of causality from such data. 

Perhaps a distressed fetus accumulates lead. 

6. There is a fairly strong correlation (around 0.8) between maternal 

blood lead and cord blood lead. 
P.8 

199 

7. Children are robust and can recover from minor disruptions in 

their cognitive development. It is not clear to what degree they 

can recover from larger disruptions. Middle-class children, in 

particular, might be able to compensate. 

8. The available evidence does not indicate what is the threshold 

level for IQ effects of lead. 

9. The assumption of normal IQ distributions within exposure groups 

in our hypothetical experiment is reasonable, except that at high 

lead levels, the IQ distribution may be skewed negatively, so that 

the percentage of children below a specified IQ level would be 

underestimated. 

C.4.2 Summary of Discussions with Expert G 

1. IQ effects of lead on lower SES children may be less in European 

countries than in the U.S., because the educational and health 

disparities between the SES levels are probably less in these 

countries than in the U.S. 

2. There are no data to suggest that physiological response to lead 

varies as a function of SES level. 

3. The effects of lead on the developing central nervous system are 

probably long lasting and not reversible. 

4. If there is a threshold for IQ effects of lead, it is very low. 

5. Animal models for risk assessment are limited in usefulness, 

because of the difficulty in extrapolating to humans in a 

quantitative manner. Their importance is in studying mechanisms 

of lead effects and other important topics (e.g., reversibility of 

effects and vulnerable periods of development), not in 
P.9 

200 

establishing dose-response relationships directly applicable to 

humans. 

6. Specific neurobehavioral effects of lead, such as attentional 

deficits, should not be overlooked. 

7. The assumption of normally distributed IQ scores within exposure 

groups in our hypothetical experiment is reasonable. 

C.4.3 Summary of Discussions with Expert H 

1. Lead interacts with other factors in its effect on IQ. These 

factors include SES, maternal stimulation, and nutrition. 

2. The concept of critical developmental periods is crucial in 

understanding the effects of lead. When opportunities for 

intellectual development are lost, it is very hard to compensate 

later. This is especially true in lower SES children. Furthermore, 

the effect can snowball, in that skills generally build on each 

other. 

3. Children who are exposed to lead also tend to get more cadmium, 

pesticides, etc. This is especially true among lower SES children. 

4. There are no data on the minimum exposure time necessary to 

produce an effect. 

5. At a given dose level, the cumulative are worse than the 

immediate effects. Exposures earlier in life have more impact 

than do exposures later in life. 

6. Some lead effects are reversible and others are not. 

7. The half-life of lead in the brain is very long, based on rat studies 

by Gary Goldstein at UCLA. 
P.10 

201 

8. Some recent research suggests that lead may be involved in 

senility. Specifically, the amount of bone lead goes down with 

aging. The question is, where does the lead go? Is it eliminated, 

or is Lt recirculated (in which case it may have neurobehavioral 

effects)? 

9. It is reasonable to assume that IQ scores are normally distributed 

within exposure groups in our hypothetical experiment. 

10. There is important and relevant work by Bernard Weiss and by 

Ketz that involves behavioral toxicology. 

C.4.4 Summary of Discussions with Expert I 

1. The meta-analyses occasionally done with the studies on IQ 

effects of lead are inappropriate because the studies differ in so 

many ways, including different ages of the subjects, different 

sorts of control groups, different methods, and different exposure 

conditions. 

2. It is reasonably certain that there is an IQ effect of lead above 30 

yg/dL, but less clear about whether there is an effect at lower 

levels. 

3. There is an exposure-sensitivity interaction, in that children who 

suffer the greatest exposures tend to be those who are most 

susceptible to the effects of lead. 

4. Except for high acute exposures, neurobehavioral effects are 

more likely to result from chronic than from acute exposures. 

5. One should distinguish between biological and functional effects 

of lead, but in either case there are no data suggesting that the 

effects are necessarily irreversible. 
P.11 

202 

6. The data are not clear either way with regard to the question of 

whether there is a threshold for the IQ effects of lead. 

C.4.5 Summary of Discussions with Expert J 

1. Lead does have a deleterious effect on neurobehavioral 

development. In this regard, lead interacts with diet and SES 

factors. 

2. Middle-class children are somewhat buffered against the negative 

effects of lead by virtue of their better diet, general health 

status, and richer intellectual resources. 

3. Lead crosses the blood-brain barrier, and once in the cells stays 

there. This lead cannot be chelated out and affects the 

neurotransmitters. The effects are irreversible. 

4. Research with animals suggests that lead causes demyelination. 

It is not clear whether this effect would occur in children. 

5. The implications of the EEG data are not clear because there is 

uncertainty as to what the measures refer and because findings 

are somewhat inconsistent. 

6. Although some functional effects of lead may be reversible, 

morphological effects are not. 

7. There is probably no threshold for lead effects; if there is one, it 

is very low. The German studies on primates suggest the absence 

of a threshold. 

8. There may be racial differences in terms of the effects of lead. 

However, this is a very complicated issue that remains to be 

untangled. 

9. The assumption that IQ scores are normally distributed within 
P.12 

203 

exposure groups in our hypothetical experiment is reasonable with 

the possible exception of the 55-yg/dL group. 

C.4.6 Summary of Discussions with Expert K 

1. Children of all genotypes are vulnerable to the effects of lead. 

2. Some neurobehavioral effects of lead, such as the effect on 

attention span, are reversible. These are generally associated 

with low levels of exposure. Even some perinatal effects can be 

reversed given proper treatment. 

3. Other neurobehavioral effects are irreversible. These include 

morphological changes, as well as effects on some behaviors that 

depend on critical developmental periods. (Is there evidence or 

theory that allows specificity as to which behaviors might be 

irreversibly affected, or is this to be taken as a generalized 

statement that some behaviors might be irreversibly altered?) 

4. Lead in the range of 5-55 yg/dL has a deleterious effect in the 

presence of other factors. In that sense, lead interacts with other 

factors. However, the interaction is only in one direction, so that 

a usual MANOVA (multivariate analysis of variance) would show 

both an interaction and a main effect. 

5. Some of the factors that lead interacts with are physical and 

psychological hygiene, physiological status, parental IQ, 

nutritional and health status, organophosphates, and pesticides. 

6. Early, long-term exposure to lead can lead to long-term effects, 

while eposodic exposure is more likely to lead to reversible 

effects, if the exposure is not too great. 

7. There is a threshold for IQ effects of lead. 
P.13 

204 

8. The assumption that IQ scores are normally distributed within 

exposure groups in the hypothetical experiment is reasonable. 
P.M 

205 

APPENDIX D 

RISK ESTIMATES 

This appendix consists mainly of tables that list the functions and the parameters 

that describe the risk estimates for lead-induced EP, hemoglobin, and IQ health effects. 

Some discussion is also provided to explain the formats of the tables. The tabular 

material can be used to generate data for the figures presented and discussed in Sec. 5, 

and to perform additional analyses. 

PbB distributions are assumed to be lognormal with geometric standard deviation 

(GSD) 1.42 and the geometric mean (GM) values listed in Table D.l. GM values are 

tabulated for six air-lead scenarios at each of 5 point sources of lead emissions. The six 

air-lead scenarios result from 3 time periods (baseline, precontrol, and postcontrol 

periods), each of which have upper- and lower-bound estimates for the GM. 

D.l ESTIMATES FOR THE RISKS OF LEAD-INDUCED ERYTHROCYTE 

PROTOPORPHYRIN EFFECTS AMONG U.S. CHILDREN AGED 0-6 

YEARS 

Probabilistic dose-response functions for 2 EP levels considered to be adverse (33 

yxA<H av4> 5 3 yg/dL) were considered in Sec. 2 and App. A. We calculated the overall 

response rates for populations of children by combining the dose-response functions 

(which are specified at particular PbB levels) with PbB distributions. In the simplest of 

cases, the probabilistic dose-response functions were normal probability distributions and 

the overall risk result was also normal with mean 

v = I P^i 

and standard deviation 

2 2-.1/2 

a - (I P^) 
TABLE D.l Upper- and Lower-Bound Estimates of the Geometric Mean Blood-Lead 

Levels Children Living around Selected U.S. Sources of Lead Emissions8 

Source 1 Source 2 Source 3 Source 4 Source 5 

Age Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper 

0-3 yr 

4-6 yr 

0-6 yr 

36th month 

0-3 yr 

4-6 yr 

0-6 yr 

36th month 

4.8 

2.2 

3.7 

3.8 

9.5 

5.4 

7.7 

9.1 

Baseline Period 

19.1 

14.0 

16.9 

18.8 

26.6 

20.8 

24.1 

26.7 

19.9 

14.3 

17.2 

19.2 

27.0 

21.2 

24.5 

27.1 

18.7 

13.7 

16.6 

18.4 

26.2 

20.4 

23.7 

26.2 

18.7 

13.7 

16.6 

18.5 

26.2 

20.4 

23.7 

26.3 

8.6 

6.4 

7.7 

7.7 

13.9 

11.5 

12.9 

13.4 

5.2 

2.4 

4.0 

4.4 

Precontrol Period 

9.9 

5.9 

8.2 

9.7 

4.7 

2.1 

3.6 

3.6 

9.1 

5.0 

7.3 

8.6 

4.6 

2.1 

3.5 

3.8 

8.6 

4.8 

7.0 

8.2 

3.3 

2.0 

2.7 

2.9 

6.7 

5.5 

6.2 

6.5 

to 

o 

Postcontrol Period 

0-3 yr 

4-6 yr 

0-6 yr 

36th month 

1.4 

1.0 

1.2 

1.3 

3.4 

3.2 

3.3 

3.4 

1.4 

1.1 

1.3 

1.3 

3.6 

3.4 

3.7 

3.7 

1.4 

1.0. 

1.3 

1.3 

3.4 

3.1 

3.4 

3.3 

1.4 

1.0 

1.2 

1.2 

3.1 

2.8 

3.0 

3.1 

1.4 

1.1 

1.3 

1.3 

3.7 

3.6 

3.7 

3.7 

aThe PbB distribution is assumed to be lognormal with GSD = 1.42 and the tabulated 

GM values. 
P.16 

207 

where i denotes a PbB level, Pj is the probability of PbB level i, and y- and a- are the 

mean and variance of the EP distribution at PbB level i. 

These calculations implicitly assume statistical independence, a necessary 

assumption that we were unable to verify. In some cases, it was necessary to use beta 

distributions in the calculations. Fortunately, in those cases the final result was nearly 

identical to the dose-response function at a PbB of 5 yg/dL. This occurred in all of the 

postcontrol scenarios and most of the precontrol scenarios because modeled PbB levels 

were quite low, (<10 yg/dL). 

Risk results for EP are tabulated in Table D.2. In the table, the form (either 

normal or beta), the expected value, and the standard deviation of each risk distribution 

are listed for the two critical EP levels specified above. When the form of the 

distribution is beta, the values of the parameters are always a = 3 and b = 128, which 

result in a mean of 2.3% and a standard deviation of 1.3%. 

D.3 ESTIMATES OF THE RISKS OF LEAD-INDUCED HEMOGLOBIN EFFECTS 

AMONG U.S. CHILDREN AGED 0-3 YEARS 

Calculation of risk estimates for lead-induced hemoglobin effects is in principle 

identical to that for EP risks. The only difference is that normal-on-log-odds (NOLO) 

distributions were found to best represent the judgments of the experts we consulted, so 

a computation analogous to a convolution integral had to be employed. Numerical 

methods were used to perform the calculations, and it was necessary to assume 

statistical independence. 

Results are listed in Table D.3. Included are the form (normal or NOLO), 

parameters, mean, and standard deviation of the risk distributions. All of these items 

are provided for NOLO distributions for the reasons discussed in App. B. The parameters 

of the normal distribution are the mean and standard deviation, so only the latter are 

listed for normal distributions. The functions were determined applying linear regression 
P.17 

208 

TABLE D.2 Specification of Distributions for the Risks of 

Elevated EP Levels among Children Ages 0-6 Years 

Seen, 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

Lower 

Upper 

irio 

Base 

Base 

Pre 

Pre 

Post 

Post 

Base 

Base 

Pre 

Pre 

Post 

Post 

Base 

Base 

Pre 

Pre 

Post 

Post 

Base 

Base 

Pre 

Pre 

Post 

Post 

EP* 

Form 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

= 33 yg/dL 

Mean S.D.a 

Source 1 

20.10 

38.69 

10.70 

10.78 

10.70 

10.70 

0.82 

1.24 

2.69 

2.09 

2.70 

2.70 

Source 2 

20.75 

39.78 

10.70 

10.83 

10.70 

10.70 

0.83 

1.26 

2.69 

1.95 

2.70 

2.69 

Source 3 

19.46 

37.60 

10.70 

10.75 

10.70 

10.70 

0.81 

1.22 

2.70 

2.21 

2.70 

2.70 

Source 4 

19.46 

37.60 

10.70 

10.73 

10.70 

10.70 

0.81 

1.22 

2.70 

2.29 

2.70 

2.70 

EP* 

Form 

Normal 

Normal 

Betab 

Normal 

Beta 

Beta 

Normal 

Normal 

Beta 

Normal 

Beta 

Beta 

Normal 

Normal 

Beta 

Beta 

Beta 

Beta 

Normal 

Normal 

Beta 

Beta 

Beta 

Beta 

= 53 yg 

Mean 

7.52 

21.14 

2.34 

2.43 

2.34 

2.34 

7.92 

22.07 

2.34 

2.46 

2.34 

2.34 

7.13 

20.22 

2.34 

2.34 

2.34 

2.34 

7.13 

20.22 

2.34 

2.34 

2.34 

2.34 

/dL 

S.D. 

0.52 

1.15 

1.30 

1.04 

1.30 

1.30 

0.54 

1.19 

1.30 

0.96 

1.30 

1.30 

0.50 

1.11 

1.30 

1.30 

1.30 

1.30 

0.50 

1.11 

1.30 

1.30 

1.30 

1.30 
P.18 

209 

TABLE D.2 (Cont'd) 

Scenario 

Lower Base 

Upper Base 

Lower Pre 

Upper Pre 

Lower Post 

Upper Post 

EP* 

Form 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

= 33 yg/dL 

Mean S.D.a 

Source 5 

10.78 

13.45 

10.70 

10.71 

10.70 

10.70 

2.09 

0.89 

2.70 

2.47 

2.70 

2.69 

EP* 

Form 

Normal 

Normal 

Beta 

Beta 

Beta 

Beta 

= 53 yg/dL 

Mean 

2.43 

3.74 

2.34 

2.34 

2.34 

2.34 

S.D. 

1.04 

0.45 

1.30 

1.30 

1.30 

1.30 

aStandard Deviation. 

'For every beta distribution, the parameters values are 

a = 3 and b = 128, which results in the tabulated mean and 

S.D. values. 
210 

TABLE D.3 Summary of Hemoglobin Risk Distributions for Children 

Aged 0-3 Years 

P.19 

Source 1, Hb* =9.5 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C ' 

E 

C 

E 

g/dL 

MU Y 

-3.1800 

-3.6945 

-2.0239 

-2.9741 

-2.9266 

-1.7214 

-3.9254 

-8.7457 

-3.3975 

-3.6385 

-4.4620 

-2.7415 

-3.9995 

-3.7820 

-4.0004 

-3.7829 

SIG Y 

0.1567 

0.1671 

0.4752 

0.1433 

0.1879 

0.4283 

0.2237 

0.3518 

0.7363 

0.1770 

0.2845 

0.5559 

0.2764 

0.9600 

0.2764 

0.9600 

MU R 

0.0404 

0.0246 

0.1252 

0.0490 

0.0516 

0.1594 

0.0198 

0.0002 

0.0408 

0.0260 

0.0119 

0.0683 

0.0187 

0.0331 

0.0186 

0.0330 

SIG R 

0.0061 

0.0040 

0.0565 

0.0067 

0.0093 

0.0615 

0.0044 

0.0001 

0.0342 

0.0045 

0.0034 

0.0392 

0.0052 

0.0414 

0.0052 

0.0413 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

211 

P.20 

Source 2, Hb* = 9.5 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

E 

C 

E 

g/dL 

MU Y 

-3.1718 

-3.6630 

-2.0128 

-2.9671 

-2.8938 

-1.7078 

-3.9172 

-8.1926 

-3.3824 

-3.6118 

-4.4551 

-2.6880 

-3.9995 

-3.7820 

-4.0010 

-3.7836 

SIG Y 

0.1570 

0.1675 

0.4741 

0.1444 

0.1890 

0.4290 

0.2236 

0.3519 

0.7357 

0.1802 

0.2844 

0.5600 

0.2764 

0.9600 

0.2764 

0.9600 

MU R 

0.0407 

0.0253 

0.1264 

0.0494 

0.0533 

0.1612 

0.0200 

0.0003 

0.0414 

0.0267 

0.0119 

0.0718 

0.0187 

0.0331 

0.0186 

0.0330 

SIG R 

0.0062 

0.0042 

0.0568 

0.0068 

0.0096 

0.0622 

0.0044 

0.0001 

0.0346 

0.0047 

0.0034 

0.0414 

0.0052 

0.0414 

0.0052 

0.0413 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

212 

P.21 

Source 3, Hb* = 9.5 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

E 

C 

E 

g/dL 

MU Y 

-3.1912 

-3.7376 

-2.0373 

-2.9823 

-2.9596 

-1.7337 

-3.9270 

-8.8980 

-3.4004 

-3.6642 

-4.4677 

-2.7959 

-3.9995 

-3.7820 

-4.0004 

-3.7829 

SIG Y 

0.1568 

0.1669 

0.4761 

0.1430 

0.1868 

0.4276 

0.2237 

0.3518 

0.7365 

0.1743 

0.2845 

0.5528 

0.2764 

0.9600 

0.2764 

0.9600 

MU R 

0.0399 

0.0236 

0.1238 

0.0487 

0.0500 

0.1577 

0.0198 

0.0001 

0.0407 

0.0253 

0.0118 

0.0649 

0.0187 

0.0331 

0.0186 

0.0330 

SIG R 

0.0061 

0.0039 

0.0561 

0.0067 

0.0090 

0.0609 

0.0044 

0.0001 

0.0341 

0.0043 

0.0034 

0.0371 

0.0052 

0.0414 

0.0052 

0.0413 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

213 

P.22 

Source 4, Hb* = 9.5 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

E 

C 

E 

g/dL 

MU Y 

-3.1912 

-3.7376 

-2.0373 

-2.9823 

-2.9596 

-1.7337 

-3.9283 

-9.0534 

-3.4030 

-3.7472 

-5.7803 

-3.1071 

-3.9995 

-3.7820 

-3.9999 

-3.7824 

SIG Y 

0.1568 

0.1669 

0.4761 

0.1430 

0.1868 

0.4276 

0.2237 

0.3518 

0.7366 

0.2083 

0.3530 

0.7050 

0.2764 

0.9600 

0.2764 

0.9600 

MU R 

0.0399 

0.0236 

0.1238 

0.0487 

0.0500 

0.1577 

0.0198 

0.0001 

0.0406 

0.0235 

0.0033 

0.0525 

0.0187 

0.0331 

0.0186 

0.0331 

SIG R 

0.0061 

0.0039 

0.0561 

0.0067 

0.0090 

0.0609 

0.0044 

0.0000 

0.0340 

0.0048 

0.0012 

0.0412 

0.0052 

0.0414 

0.0052 

0.0414 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

214 

P.23 

Source 5, Hb* = 9.5 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

C 

D 

E 

C 

D 

E 

C 

E 

C 

D 

E 

C 

E 

C 

E 

g/dL 

MU Y 

-3.7472 

-5.7803 

-3.1071 

-3.3970 

-4.2326 

-2.3392 

-4.0002 

-3.7827 

-3.8628 

-6.7643 

-3.3026 

-3.9995 

-3.7820 

-4.0015 

-3.7840 

SIG Y 

0.2083 

0.3530 

0.7050 

0.1981 

0.2230 

0.5762 

0.2764 

0.9600 

0.2186 

0.3522 

0.7138 

0.2764 

0.9600 

0.2764 

0.9599 

MU R 

0.0235 

0.0033 

0.0525 

0.0330 

0.0147 

0.0985 

0.0186 

0.0331 

0.0210 

0.0012 

0.0440 

0.0187 

0.0331 

0.0186 

0.0330 

SIG R 

0.0048 

0.0012 

0.0412 

0.0064 

0.0033 

0.0576 

0.0052 

0.0414 

0.0046 

0.0004 

0.0353 

0.0052 

0.0414 

0.0052 

0.0413 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

215 

P.24 

Source 1, Hb* = 11.0 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

A 

C 

D 

E 

A 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

g/dL 

MU Y 

-7.7633 

-2.0191 

-1.9726 

-1.7216 

-3.0621 

-1.7932 

-1.5492 

-1.5361 

-2.4527 

-3.0274 

-2.1708 

-2.3090 

-2.7356 

-1.9982 

-2.5162 

-3.1747 

-2.3463 

-2.5171 

-3.1756 

-2.3473 

SIG Y 

0.6530 

0.1550 

0.2625 

0.3184 

0.5087 

0.1409 

0.2493 

0.2885 

0.2211 

0.3888 

0.4716 

0.1717 

0.2976 

0.3587 

0.2720 

0.4919 

0.5991 

0.2720 

0.4919 

0.5991 

MU R 

0.0005 

0.1182 

0.1249 

0.1561 

0.0498 

0.1435 

0.1780 

0.1809 

0.0807 

0.0493 

0.1103 

0.0914 

0.0631 

0.1244 

0.0769 

0.0445 

0.0987 

0.0768 

0.0445 

0.0986 

SIG R 

0.0004 

0.0163 

0.0294 

0.0435 

0.0261 

0.0174 

0.0373 

0.0441 

0.0167 

0.0191 

0.0501 

0.0144 

0.0181 

0.0409 

0.0198 

0.0225 

0.0606 

0.0198 

0.0225 

0.0605 

R SQR 

0.9997 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

216 

P.25 

Source 2, Hb* = 11.( 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

A 

C 

D 

E 

A 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

3 g/dL 

MU Y 

-7.6745 

-2.0123 

-1.9528 

-1.7153 

-3.0602 

-1.7829 

-1.5344 

-1.5276 

-2.4493 

-3.0210 

-2.1681 

-2.2977 

-2.7048 

-1.9864 

-2.5162 

-3.1747 

-2.3463 

-2.5178 

-3.1763 

-2.3480 

SIG Y 

0.6530 

0.1551 

0.2635 

0.3173 

0.5085 

0.1415 

0.2495 

0.2894 

0.2211 

0.3887 

0.4716 

0.1742 

0.2991 

0.3598 

0.2720 

0.4919 

0.5991 

0.2720 

0.4919 

0.5990 

MU R 

0.0006 

0.1189 

0.1270 

0.1568 

0.0499 

0.1448 

0.1802 

0.1821 

0.0810 

0.0496 

0.1105 

0.0923 

0.0650 

0.1257 

0.0769 

0.0445 

0.0987 

0.0768 

0.0445 

0.0985 

SIG R 

0.0004 

0.0164 

0.0299 

0.0435 

0.0261 

0.0177 

0.0377 

0.0445 

0.0167 

0.0192 

0.0502 

0.0147 

0.0187 

0.0414 

0.0198 

0.0225 

0.0606 

0.0197 

0.0225 

0.0605 

R SQR 

0.9997 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

217 

P.26 

Source 3, Hb* = 11.0 g/dL 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

A 

C 

D 

E 

A 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

MU Y 

-7.9091 

-2.0286 

-1.9969 

-1.7295 

-3.0660 

-1.8038 

-1.5649 

-1.5439 

-2.4533 

-3.0286 

-2.1713 

-2.3206 

-2.7637 

-2.0081 

-2.5162 

-3.1747 

-2.3463 

-2.5171 

-3.1756 

-2.3473 

SIG Y 

0.6529 

0.1550 

0.2610 

0.3194 

0.5091 

0.1405 

0.2489 

0.2874 

0.2211 

0.3888 

0.4716 

0.1701 

0.2964 

0.3583 

0.2720 

0.4919 

0.5991 

0.2720 

0.4919 

0.5991 

MU R 

0.0005 

0.1172 

0.1222 

0.1551 

0.0497 

0.1422 

0.1758 

0.1797 

0.0807 

0.0492 

0.1102 

0.0904 

0.0615 

0.1233 

0.0769 

0.0445 

0.0987 

0.0768 

0.0445 

0.0986 

SIG R 

0.0003 

0.0162 

0.0287 

0.0434 

0.0260 

0.0173 

0.0369 

0.0437 

0.0167 

0.0190 

0.0500 

0.0141 

0.0176 

0.0405 

0.0198 

0.0225 

0.0606 

0.0198 

0.0225 

0.0605 

R SQR 

0.9997 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

218 

Source 4, Hb* = 11.0 g/dL 

P.27 

SCENARIO EXPERT MU Y SIG Y MU R SIG R R SQR 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

A 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

7o9091 

2.0286 

1.9969 

1.7295 

1.8038 

1.5649 

1.5439 

2.4539 

3.0297 

2.1718 

2.3810 

2.9024 

2.1345 

2.5162 

3.1747 

2.3463 

2.5166 

3.1751 

2.3467 

0.6529 

0.1550 

0.2610 

0.3194 

0.1405 

0.2489 

0.2874 

0.2212 

0.3888 

0.4716 

0.2065 

0.3674 

0.4477 

0.2720 

0.4919 

0.5991 

0.2720 

0.4919 

0.5991 

0.0005 

0.1172 

0.1222 

0.1551 

0.1422 

0.1758 

0.1797 

0.0807 

0.0492 

0.1102 

0.0860 

0.0550 

0.1130 

0.0769 

0.0445 

0.0987 

0.0769 

0.0445 

0.0986 

0.0003 

0.0162 

0.0287 

0.0434 

0.0173 

0.0369 

0.0437 

0.0167 

0.0190 

0.0500 

0.0165 

0.0199 

0.0482 

0.0198 

0.0225 

0.0606 

0.0198 

0.0225 

0.0606 

0.9997 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.3 (Cont'd) 

219 

Source 5, Hb* = 11.0 g/dL 

P.28 

SCENARIO EXPERT MU Y SIG Y MU R SIG R R SQR 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

C 

D 

E 

2.3810 

2.9024 

2.1345 

2.1832 

2.4202 

1.9013 

2.5169 

3.1754 

2.3470 

2.4254 

2.9829 

2.1509 

2.5162 

3.1747 

2.3463 

2.5183 

3.1767 

2.3485 

0.2065 

0.3674 

0.4477 

0.1934 

0.3221 

0.4014 

0.2720 

0.4919 

0.5991 

0.2196 

0.3819 

0.4686 

0.2720 

0.4919 

0.5991 

0.2720 

0.4919 

0.5990 

0.0860 

0.0550 

0.1130 

0.1026 

0.0849 

0.1364 

0.0769 

0.0445 

0.0986 

0.0828 

0.0513 

0.1121 

0.0769 

0.0445 

0.0987 

0.0768 

0.0444 

0.0985 

0.0165 

0.0199 

0.0482 

0.0180 

0.0259 

0.0501 

0.0198 

0.0225 

0.0606 

0.0169 

0.0194 

0.0504 

0.0198 

0.0225 

0.0606 

0.0197 

0.0225 

0.0605 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
P.29 

220 

techniques to the results of the convolution step. The regression r-square values were 

about equal to 1 in most cases, so they are not listed in this table. Such high r-square 

values resulted for two reasons. First, in the case of a low PbB scenario, the doseresponse function for PbB = 5 yg/dL essentially became the overall result. In higher PbB 

scenarios, the distributions tend to become normal. 

D.4 ESTIMATES OF THE RISKS OF LEAD-INDUCED IQ EFFECTS AMONG 

U.S. CHILDREN AGED 7 YEARS 

Two IQ health effects were considered, IQ decrement and the increased 

probability of having IQ values less than specified critical levels. A critical level is 

denoted by IQ*. Calculations for the risk of IQ decrements are quite simple and similar 

to both the EP and hemoglobin risk calculations. They followed directly from the 

encoded judgments of the experts regarding IQ decrement. Calculation of risks of the 

second type is much more complicated and includes uncertainty in: the mean IQ of 

populations of children sheltered from lead exposure, within-group standard deviation, 

and IQ decrements among children exposed to lead. The probabilistic judgments of 

experts regarding these quantities were obtained for both lower and higher SES 

populations. The spirit of the calculation is as follows. 

Numerical methods were used to perform the calculations. The first step was to 

change each probability density function into a discrete probability mass function with a 

reasonable number of points. Consider just one expert for the moment. For every 

combination of mean IQ, standard deviation, and IQ decrement, a distribution for the 

increased probability of having IQ values < IQ* was calculated at each PbB level for 

which IQ decrement judgments were obtained. Distribution functions (either normal or 

NOLO) were fit to the results to facilitate further calculations. At this point, the 

calculations became quite similar to those for EP, hemoglobin, and expected IQ 

decrement. These distributions were combined with a PbB distribution, again using 
P.30 

221 

numerical methods analogous to a convolution integral, to produce an overall risk 

distribution for a particular SES group. If desired, these distributions can also be 

combined across SES to produce further risk distributions based on the judgments of each 

expert. Table D.4 lists relevant information about the IQ decrement risk distributions, 

and Tab. D.5 lists relevant informaton about the increased probability of children having 

IQ levels < IQ*. 
222 

TABLE D.4 Summary of Distributions for Expected IQ Decrement 

at Age 7 for Lower SES Populations of Children 

P.31 

Source 1, Expected IC, 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

J 

G 

H 

I 

J 

K 

Decrement 

MU R 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Lognormal 

Lognormal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

MU Y 

-0 

0 

-6 

-0 

0 

-0 

0 

-7 

.4816 

.8268 

.1658 

.4816 

.8268 

.4816 

.8268 

.2644 

SIG Y 

0 

0 

0 

0 

0 

0 

0 

0 

.6422 

.4087 

.5315 

.6422 

.4087 

.6422 

.4087 

.5315 

MU AIQ 

2.2875 

4.5786 

1.6460 

4.1610 

1.9940 

3.3145 

6.0238 

2.8566 

5.3974 

3.1143 

0.7593 

2.4851 

0.0021 

2.4045 

0.0032 

1.0974 

2.9885 

0.3307 

2.8175 

0.4953 

0.7593 

2.4851 

2.4018 

0.7593 

2.4851 

0.0007 

2.4027 

0.0011 

SD AIQ 

0.7794 

1.1163 

0.4579 

0.8254 

0.4443 

0.8823 

• 1.1424 

0.6046 

0.7917 

0.5629 

0.5425 

1.0596 

0.0012 

0.8865 

0.0011 

0.4876 

0.8825 

0.1764 

0.7049 

0.1623 

0.5425 

1.0596 

0.8887 

0.5425 

1.0596 

0.0004 

0.8879 

0.0004 
TABLE D.4 (Cont'd) 

223 

P.32 

Source 2, Expected 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

J 

G 

H 

I 

J 

K 

IQ Decrement 

MU R 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Lognormal 

Lognormal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

MU Y 

-0.4816 

0.8268 

-0.4816 

0.8268 

-0.4816 

0.8268 

-6.4378 

SIG Y 

0.6422 

0.4087 

0.6422 

0.4087 

0.6422 

0.4087 

0.5315 

MU AIQ 

2.3400 

4.6489 

1.7080 

4.2207 

2.0522 

3.3637 

6.0991 

2.9144 

5.4617 

3.1669 

0.7593 

2.4851 

0.0068 

2.4106 

0.0105 

1.1665 

3.0888 

0.4000 

2.9010 

0.5948 

0.7593 

2.4851 

2.4018 

0.7593 

2.4851 

0.0016 

2.4039 

0.0025 

SD AIQ 

0.7872 

1.1141 

0.4673 

0.8219 

0.4541 

0.8796 

1.1429 

0.6081 

0.7878 

0.5621 

0.5425 

1.0596 

0.0040 

0.8815 

0.0036 

0.5091 

0.9009 

0.2076 

0.7095 

0.1910 

0.5425 

1.0596 

0.8887 

0.5425 

1.0596 

0.0009 

0.8870 

0.0009 
224 

TABLE D.4 (Cont'd) 

Source 3, Expected IQ Decrement 

P.33 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

J 

G 

H 

I 

J 

K 

MU R 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal . 

Lognormal 

Lognormal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

MU Y 

-0 

0 

-6 

-0 

0 

-0 

0 

-7 

.4816 

.8268 

.7254 

.4816 

.8268 

.4816 

.8268 

.6009 

S3 

0 

0 

0 

0 

0 

0 

0 

0 

[G Y 

.6422 

.4087 

.5315 

.6422 

.4087 

.6422 

.4087 

.5315 

MU AIQ 

2.2356 

4.5095 

1.5849 

4.1023 

1.9358 

3.2589 

5.9439 

2.7919 

5.3278 

3.0537 

0.7593 

2.4851 

0.0012 

2.4034 

0.0019 

1.0384 

2.9020 

0.2721 

2.7454 

0.4095 

0.7593 

2.4851 

2.4018 

0.7593 

2.4851 

0.0005 

2.4025 

0.0008 

SD AIQ 

0.7713 

1.1177 

0.4486 

0.8282 

0.4344 

0.8820 

1.1408 

0.5996 

0.7941 

0.5616 

0.5425 

1.0596 

0.0007 

0.8874 

0.0007 

0.4760 

0.8796 

0.1478 

0.7113 

0.1360 

0.5425 

1.0596 

0.8887 

0.5425 

1.0596 

0.0003 

0.8881 

0.0003 
TABLE D.4 (Cont'd) 

225 

Source 4, Expected 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

G 

H 

I t-i 

K 

G 

H 

I t-i 

K 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H 

J 

G 

H 

I 

J 

K 

IQ Decrement 

MU R 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

Normal 

Normal 

Normal . 

Normal 

Normal 

Lognormal 

Lognormal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

MU Y 

-0.4816 

0.8268 

-6.1658 

-0.4816 

0.8268 

-0.4816 

0.8268 

-8.1117 

SIG Y 

0.6422 

0.4087 

0.5315 

0.6422 

0.4087 

0.6422 

0.4087 

0.5315 

MU AIQ 

2.2470 

4.5264 

1.5983 

4.1164 

1.9486 

3.2701 

5.9601 

2.8050 

5.3419 

3.0660 

0.7593 

2.4851 

0.0021 

2.4045 

0.0032 

0.9969 

2.8407 

0.2309 

2.6945 

0.3490 

0.7593 

2.4851 

2.4018 

0.7593 

2.4851 

0.0003 

2.4022 

0.0004 

SD AIQ 

0.7716 

1.1172 

0.4495 

0.8275 

0.4352 

0.8821 

1.1412 

0.6007 

0.7936 

0.5619 

0.5425 

1.0596 

0.0012 

0.8865 

0.0011 

0.4729 

0.8863 

0.1274 

0.7223 

0.1171 

0.5425 

1.0596 

0.8887 

0.5425 

1.0596 

0.0002 

0.8884 

0.0002 
TABLE D.4 (Cont'd) 

226 

P.35 

Source 5, Expected IC 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

G 

H 

I 

J 

K 

G 

H 

I 

J 

K 

G 

H t-i 

K 

G 

H 

I 

J 

K 

G 

H 

J 

G 

H 

I 

J 

K 

Decrement 

MU R 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Lognormal 

Lognormal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Lognormal 

Lognormal 

Normal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

MU Y 

-0.4816 

0.8268 

-0.4816 

0.8268 

-0.4816 

0.8268 

-6.4378 

SIG Y 

0.6422 

0.4087 

0.6422 

0.4087 

0.6422 

0.4087 

0.5315 

MU &IQ 

0.9464 

2.7657 

0.1811 

2.6323 

0.2747 

1.6103 

3.6991 

0.8664 

3.4139 

1.1977 

0.7593 

2.4851 

2.4020 

0.0002 

0.8477 

2.6182 

0.0845 

2.5099 

0.1288 

0.7593 

2.4851 

2.4018 

0.7593 

2.4851 

0.0016 

2.4039 

0.0025 

SD aIQ 

0.4753 

0.9047 

0.1012 

0.7434 

0.0931 

0.6746 

1.1076 

0.3447 

0.8357 

0.3206 

0.5425 

1.0596 

0.8885 

0.0001 

0.5017 

0.9740 

0.0483 

0.8084 

0.0444 

0.5425 

1.0596 

0.8887 

0.5425 

1.0596 

0.0009 

0.8870 

0.0009 
P.36 

227 

TABLE D.5 Summary of Distributions for Increased Probability of 

IQ<IQ* at Age 7 for Lower SES Populations of Children 

Source 1, IQ* = 70 

SCENARIO EXPERT 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

G 

H t_i 

K 

G 

H 

ti 

K 

G 

H t_i 

G 

H <-> 

K 

G 

H t_i 

G 

H 

J 

MU Y 

-3.7137 

-3.4238 

-3.3198 

-3.1979 

-3.2636 

-2.9822 

-2.9282 

-2.6357 

-5.4148 

-4.7670 

-4.4231 

-4.6162 

-4.1058 

-3.8932 

-3.7984 

-5.4123 

-4.7645 

-4.4206 

-5.4132 

-4.7654 

-4.4215 

SIG Y 

0.3469 

0.3823 

0.2950 

0.3685 

0.3000 

0.3366 

0.2442 

0.2747 

0.7608 

0.7706 

0.6651 

0.4346 

0.4560 

0.3769 

0.4650 

0.7608 

0.7706 

0.6652 

0.7608 

0.7706 

0.6651 

MU R 

0.0252 

0.0337 

0.0363 

0.0416 

0.0383 

0.0506 

0.0521 

0.0689 

0.0059 

0.0112 

0.0146 

0.0107 

0.0179 

0.0213 

0.0242 

0.0059 

0.0112 

0.0147 

0.0059 

0.0112 

0.0147 

SIG R 

0.0088 

0.0130 

0.0106 

0.0153 

0.0114 

0.0167 

0.0123 

0.0181 

0.0052 

0.0101 

0.0108 

0.0049 

0.0085 

0.0082 

0.0117 

0.0052 

0.0101 

0.0109 

0.0052 

0.0101 

0.0109 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.5 (Cont'd) 

228 

Source 2, IQ* = 70 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

G 

H 

J 

K 

G 

H 

J 

K 

G 

H 

J 

G 

H 

Lj 

K 

G 

H 

J 

G 

H 

J 

MU Y 

-3.6877 

-3.4020 

-3.2994 

-3.1709 

-3.2471 

-2.9628 

-2.9105 

-2.6157 

-5.4206 

-4.7728 

-4.4290 

-4.5434 

-4.0560 

-3.8558 

-3.7851 

-5.4123 

-4.7645 

-4.4206 

-5.4143 

-4.7664 

-4.4225 

SIG Y 

0.3451 

0.3812 

0.2928 

0.3674 

0.2995 

0.3365 

0.2434 

0.2729 

0.7607 

0.7706 

0.6651 

0.4370 

0.4600 

0.3770 

0.4664 

0.7608 

0.7706 

0.6652 

0.7608 

0.7706 

0.6651 

MU R 

0.0258 

0.0344 

0.0370 

0.0427 

0.0389 

0.0515 

0.0529 

0.0702 

0.0058 

0.0111 

0.0145 

0.0115 

0.0188 

0.0221 

0.0245 

0.0059 

0.0112 

0.0147 

0.0059 

0.0112 

0.0146 

SIG R 

0.0090 

0.0132 

0.0107 

0.0156 

0.0115 

0.0170 

0.0124 

0.0182 

0.0052 

0.0100 

0.0108 

0.0052 

0.0090 

0.0085 

0.0119 

0.0052 

0.0101 

0.0109 

0.0052 

0.0101 

0.0108 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.5 (Cont'd) 

229 

P.38 

Source 3, IQ* = 70 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

G 

H 

J 

K 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

MU Y 

-3.8755 

-3.5978 

-3.4468 

-3.2633 

-3.2819 

-3.0035 

-2.9467 

-2.6587 

-5.4138 

-4.7660 

-4.4221 

-4.8645 

-4.3354 

-4.0670 

-5.2291 

-5.4123 

-4.7645 

-4.4206 

-5.4130 

-4.7651 

-4.4212 

SIG Y 

0.4381 

0.4820 

0.3707 

0.3861 

0.2994 

0.3365 

0.2444 

0.2759 

0.7608 

0.7706 

0.6651 

0.5504 

0.5772 

0.4781 

0.5802 

0.7608 

0.7706 

0.6652 

0.7608 

0.7706 

0.6651 

MU R 

0.0222 

0.0296 

0.0328 

0.0393 

0.0377 

0.0496 

0.0512 

0.0675 

0.0059 

0.0112 

0.0146 

0.0089 

0.0151 

0.0188 

0.0063 

0.0059 

0.0112 

0.0147 

0.0059 

0.0112 

0.0147 

SIG R 

0.0100 

0.0148 

0.0122 

0.0152 

0.0111 

0.0164 

0.0121 

0.0178 

0.0052 

0.0101 

0.0108 

0.0052 

0.0094 

0.0094 

0.0040 

0.0052 

0.0101 

0.0109 

0.0052 

0.0101 

0.0109 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.5 (Cont'd) 

230 

Source 4, IQ* = 70 

P.39 

SCENARIO EXPERT MU Y SIG Y MU R SIG R R SQR 

LOWER 

UPPER 

LOWER 

UPPER 

LOWER 

UPPER 

BASE 

BASE 

PRE 

PRE 

POST 

POST 

G 

H 

J 

K 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

-3.7347 

-3.4401 

-3.3334 

-3.2196 

-3.2784 

-2.9995 

-2.9431 

-2.6539 

-5.4148 

-4.7670 

-4.4231 

-4.9027 

-4.3573 

-4.0867 

-5.3788 

-5.4123 

-4.7645 

-4.4206 

-5.4127 

-4.7648 

-4.4209 

0.3481 

0.3831 

0.2969 

0.3683 

0.2996 

0.3364 

0.2442 

0.2756 

0.7608 

0.7706 

0.6651 

0.5509 

0.5759 

0.4810 

0.5797 

0.7608 

0.7706 

0.6652 

0.7608 

0.7706 

0.6651 

0.0247 

0.0332 

0.0358 

0.0408 

0.0378 

0.0498 

0.0513 

0.0678 

0.0059 

0.0112 

0.0146 

0.0085 

0.0148 

0.0184 

0.0054 

0.0059 

0.0112 

0.0147 

0.0059 

0.0112 

0.0147 

0.0087 

0.0128 

0.0105 

0.0150 

0.0112 

0.0165 

0.0121 

0.0178 

0.0052 

0.0101 

0.0108 

0.0051 

0.0092 

0.0093 

0.0034 

0.0052 

0.0101 

0.0109 

0.0052 

0.0101 

0.0109 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.5 (Cont'd) 

231 

Source 5, IQ* = 70 

P.40 

SCENARIO EXPERT MU Y SIG Y MU R SIG R R SQR 

LOWER 

UPPER 

LOWER 

UPPER 

LOWER 

UPPER 

BASE 

BASE 

PRE 

PRE 

POST 

POST 

G 

H 

J 

K 

G 

H •-> 

K 

G 

H 

Cj 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

-4.9*81 

-4.3852 

-4.1138 

-5.6092 

-4.2739 

-3.8419 

-3.6962 

-3.6965 

-5.4125 

-4.7646 

-4.4207 

-5.0453 

-4.4330 

-4.1446 

-6.3526 

-5.4123 

-4.7645 

-4.4206 

-5.4143 

-4.7664 

-4.4225 

0.5534 

0.5760 

0.4855 

0.5791 

0.4805 

0.4893 

0.4115 

0.4609 

0.7608 

0.7706 

0.6652 

0.5672 

0.5853 

0.5057 

0.5777 

0.7608 

0.7706 

0.6652 

0.7608 

0.7706 

0.6651 

0.0082 

0.0144 

0.0180 

0.0043 

0.0153 

0.0235 

0.0262 

0.0267 

0.0059 

0.0112 

0.0147 

0.0075 

0.0138 

0.0176 

0.0021 

0.0059 

0.0112 

0.0147 

0.0059 

0.0112 

0.0146 

0.0049 

0.0090 

0.0091 

0.0027 

0.0077 

0.0120 

0.0110 

0.0127 

0.0052 

0.0101 

0.0109 

0.0046 

0.0088 

0.0094 

0.0013 

0.0052 

0.0101 

0.0109 

0.0052 

0.0101 

0.0108 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.5 (Cont'd) 

232 

P.41 

Source 1, IQ* = 85 

SCENARIO EXPERT 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

G 

H 

J 

K 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

MU Y 

-2.6805 

-1.8746 

-2.2625 

-1.5063 

-4.2354 

-2.8860 

-3.5192 

-2.4489 

-4.2328 

-2.8834 

-4.2337 

-2.8843 

SIG Y 

0.2977 

0.2786 

0.2581 

0.2471 

0.7058 

0.5182 

0.3840 

0.3155 

0.7058 

0.5182 

0.7058 

0.5182 

MU R 

0.0665 

0.1362 

0.1114 

0.0605 

0.0966 

0.1843 

0.1478 

0.0942 

0.0180 

0.0589 

0.0616 

0.0308 

0.0826 

0.0735 

0.0152 

0.0181 

0.0591 

0.0618 

0.0180 

0.0590 

0.0617 

SIG R 

0.0190 

0.0337 

0.0232 

0.0137 

0.0230 

0.0380 

0.0231 

0.0171 

0.0144 

0.0313 

0.0237 

0.0119 

0.0247 

0.0191 

0.0052 

0.0144 

0.0314 

0.0237 

0.0144 

0.0313 

0.0237 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.5 (Cont'd) 

233 

Source 2, IQ* = 85 

P.42 

SCENARIO EXPERT MU Y SIG Y MU R SIG R R SQR 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

G 

H 

J 

K 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

2.6554 

1.8563 

2.2450 

1.4893 

4.2413 

2.8922 

3.4542 

2.4067 

4.2328 

2.8834 

4.2348 

2.8854 

0.2955 

0.2772 

0.2568 

0.2467 

0.7057 

0.5180 

0.3833 

0.3180 

0.7058 

0.5182 

0.7058 

0.5182 

0.0680 

0.1383 

0.1130 

0.0622 

0.0981 

0.1868 

0.1498 

0.0957 

0.0179 

0.0586 

0.0613 

0.0327 

0.0858 

0.0758 

0.0182 

0.0181 

0.0591 

0.0618 

0.0180 

0.0590 

0.0616 

0.0192 

0.0340 

0.0231 

0.0139 

0.0232 

0.0383 

0.0231 

0.0171 

0.0143 

0.0311 

0.0235 

0.0127 

0.0258 

0.0193 

0.0061 

0.0144 

0.0314 

0.0237 

0.0144 

0.0313 

0.0237 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.5 (Cont'd) 

234 

Source 3, IQ* = 85 

P.43 

SCENARIO EXPERT MU Y SIG Y MU R SIG R R SQR 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

G 

H 

J 

K 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

2.8112 

1.9831 

2.2813 

1.5247 

4.2343 

2.8850 

3.7270 

2.5868 

4.2328 

2.8834 

4.2335 

2.8840 

0.3738 

0.3455 

0.2587 

0.2469 

0.7058 

0.5182 

0.4877 

0.3907 

0.7058 

0.5182 

0.7058 

0.5182 

0.0601 

0.1257 

0.1073 

0.0570 

0.0950 

0.1816 

0.1458 

0.0924 

0.0180 

0.0590 

0.0617 

0.0262 

0.0743 

0.0706 

0.0120 

0.0181 

0.0591 

0.0618 

0.0181 

0.0591 

0.0617 

0.0220 

0.0396 

0.0232 

0.0134 

0.0227 

0.0375 

0.0231 

0.0171 

0.0144 

0.0313 

0.0237 

0.0133 

0.0282 

0.0191 

0.0043 

0.0144 

0.0314 

0.0237 

0.0144 

0.0314 

0.0237 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
TABLE D.5 (Cont'd) 

235 

P.44 

Source 4, IQ* = 85 

SCENARIO 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

EXPERT 

G 

H 

J 

K 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

MU Y 

-2.6990 

-1.8901 

-2.2775 

-1.5210 

-4.2354 

-2.8860 

-3.7631 

-2.6094 

-4.2328 

-2.8834 

-4.2332 

-2.8837 

SIG Y 

0.2991 

0.2799 

0.2586 

0.2471 

0.7058 

0.5182 

0.4917 

0.3910 

0.7058 

0.5182 

0.7058 

0.5182 

MU R 

0.0653 

0.1345 

0.1101 

0.0592 

0.0953 

0.1821 

0.1462 

0.0928 

0.0180 

0.0589 

0.0616 

0.0254 

0.0728 

0.0694 

0.0103 

0.0181 

0.0591 

0.0618 

0.0181 

0.0591 

0.0617 

SIG R 

0.0188 

0.0335 

0.0232 

0.0134 

0.0228 

0.0376 

0.0231 

0.0171 

0.0144 

0.0313 

0.0237 

0.0130 

0.0277 

0.0194 

0.0037 

0.0144 

0.0314 

0.0237 

0.0144 

0.0314 

0.0237 

R SQR 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 
236 

TABLE D.5 (Cont'd) 

Source 5, IQ* = 85 

P.45 

SCENARIO EXPERT MU Y SIG Y MU R SIG R R SQR 

LOWER BASE 

UPPER BASE 

LOWER PRE 

UPPER PRE 

LOWER POST 

UPPER POST 

G 

H 

J 

K 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

K 

G 

H 

J 

G 

H 

J 

3.8108 

2.6388 

3.1956 

2.2355 

4.2330 

2.8835 

3.8960 

2.6816 

4.2328 

2.8834 

4.2348 

2.8854 

0.4985 

0.3925 

0.4214 

0.3727 

0.7058 

0.5182 

0.5234 

0.4057 

0.7058 

0.5182 

0.7058 

0.5182 

0.0243 

0.0708 

0.0679 

0.0082 

0.0425 

0.1014 

0.0886 

0.0356 

0.0181 

0.0591 

0.0618 

0.0226 

0.0684 

0.0648 

0.0039 

0.0181 

0.0591 

0.0618 

0.0180 

0.0590 

0.0616 

0.0127 

0.0271 

0.0199 

0.0030 

0.0181 

0.0356 

0.0230 

0.0101 

0.0144 

0.0314 

0.0237 

0.0125 

0.0272 

0.0216 

0.0014 

0.0144 

0.0314 . 

0.0237 

0.0144 

0.0313 

0.0237 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000