P.1 

OAR Box 1131 

Prepped by Ollie Stewart 

Document Number: 

122)11-1-400 

Docket Number: 

A-83-22 

Printed 4/21/2008 2:34:12 PM Sheet 122 of 162 
P.2 

•12^33* 

flj B » mm n\ 

Assessing the Risks to Young Children 

of Three Effects Associated with 

Elevated Blood-Lead Levels 

(. 

\ 

v.^ 

T. S. Wallsten and R. G. Whitfield 

Operated by 

THE UNIVERSITY OF CHICAGO lor U. S. DEPARTMENT OF ENERGY 

under Contract W-31-10»-€ng-38 
P.3 

Argonne National LaMmimy. vnnh fasiiEJes in the states of Illinois and Idaho, is 

owned by the United States gevemmm, md operated by The Univenity of Chicago, 

under the provisions @f a esatraet mih the Department of Energy. 

= DISCLAIMER 

This report was prepared as sa aee@uat of work sponsored by an 

agency of Ehe Uasted Ssaigs Government. Neither the United 

States Governmeua nm amy agency thereof, nor any of their 

employees, makes any warranty0 express or implied, or assumes 

any legal liability 9? mponsibility for the accuracy, com* 

pktenesSo or usefulness @f aay Information, apparatus, produa, 

or process disclosed, or represents that its use would not infringe 

privately owned rights. -Reference herein to any specific com* 

mercial produce process, <as service by trade name, trademark, 

manufacturer, or atherwist, does not necessarily constitute or 

imply its endorsement recommendation, or favoring by the 

United States Govemmeaa @? any agency thereof. The views and 

opinions of authors expressed herein do not necessarily state or 

reflect shose @f isg United States Government or any agency 

thereof. 

JMasedl ta Efee MJMiisi StoEes of America 

Available from 

Nata@is&3 TeetocsaJ Information Service 

U. §. BeparaaeM @(f Commerce 

S28S P@R loyal load 

Springfield, 

usedl es 

Migs-^ftghe §opy: A01 
TTrvwipvaaaai^rw afpa • ~~^TM9.wy*ffi:Wl[\'Z '• V 

ARGONNE NATIONAL LABORATORY 

9700 South Cass Avenue, Argonne, Illinois 60439 

ANL/AA-32 

ASSESSING THE RISKS TO YOUNG CHILDREN 

OF THREE EFFECTS ASSOCIATED WITH 

ELEVATED BLOOD-LEAD LEVELS 

by 

Thomas S. Wallsten* and Ronald G. Whitfield 

Energy and Environmental Systems Division 

Decision Analysis and Systems Evaluation Section 

December 1986 

work sponsored by 

U.S. ENVIRONMENTAL PROTECTION AGENCY 

Office of Air Quality Planning and Standards 

P.4 

• -Vf ""•-•-WTfaT' 

*L.L. Thurstone Psychometric Laboratory, University of North Carolina, Chapel Hill 
P.5 

CONTENTS 

ACRONYMS ix 

SYMBOLS x 

ACKNOWLEDGMENTS ."* xi 

ABSTRACT 1 

1 INTRODUCTION 1 

1.1 Report Organization 2 

1.2 Motivation 2 

1.3 Judgmental Probability Encoding 5 

1.4 Dose-Response Uncertainty 6 

1.5 Risk Assessment Strategy 6 

2 PROBABILISTIC DOSE-RESPONSE FUNCTIONS FOR LEAD-INDUCED 

ELEVATED EP LEVELS 7 

3 PROBABILISTIC DOSE-RESPONSE FUNCTIONS FOR LEAD-INDUCED 

Hb DECREMENTS 11 

3.1 Protocol Development 11 

3.2 Protocol Outline 12 

3.3 Conduct of the Sessions 13 

3.4 Encoding the Judgments 13 

3.5 Representing the Judgments 15 

3.6 The Experts 17 

3.7 Results 17 

3.7.1 Hb Level < 11 g/dL, Ages 0-3 . 18 

3.7.2 Hb Level < 11 g/dL, Ages 4-6 20 

3.7.3 Hb Level < 9.5 g/dL, Ages 0-3 21 

3.7.4 Hb Level < 9.5 g/dL, Ages 4-6 22 

3.8 Discussion 23 

4 PROBABILISTIC DOSE-EFFECT AND DOSE-RESPONSE FUNCTIONS FOR 

LEAD-INDUCED IQ DECREMENTS 27 

4.1 Protocol Development 28 

4.2 Protocol Outline 30 

4.3 Conduct of the Sessions 30 

4.4 Encoding the Judgments 31 

4.5 Representing the Judgments 32 

4.6 The Experts 32 

4.7 Results 33 

4.7.1 Control-Group Mean IQ 34 

4.7.2 Within-Group IQ Standard Deviation 35 

4.7.3 Mean IQ Decrements for the Low SES Group 36 

4.7.4 Mean IQ Decrements for the High SES Group 36 

m 
P.6 

CONTENTS (Cont'd) 

4.7.5 Change in Percentage of Low SES Group with IQ < 85 37' 

4.7.6 Change in Percentage of High SES Group with IQ < 85 40 

4.8 Discussion 41 

5 "ESTIMATED RISKS OF ADVERSE HEALTH EFFECTS VERSUS GEOMETRIC 

MEAN PbB LEVEL 43 

5.1 Estimated PbB Distributions 43 

5.2 Overview of the Risk Results for EP 44 

5.3 Overview of the Risk Results for Hb 45 

5.4 Overview of the Risk Results for IQ 45 

5.4.1 Risk Distributions over Mean IQ Decrement 47 

5.4.2 Increased Probability of Lead-Induced IQ Levels Being 

< IQ* 48 

5.5 Sensitivity Analysis 49 

6 CONCLUDING REMARKS 51 

REFERENCES 52 

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

Levels 55 

APPENDIX B: Fitting Functions to Encoded Judgments Relating to 

Lead-Induced Hb Decrement 61 

APPENDIX C: Fitting Functions to Encoded Judgments Relating to 

Lead-Induced IQ Effects 101 

APPENDIX D: Risk Distributions 141 

TABLES 

1 Probability of Suffering a Specified Health Effect under Alternative 

NAAQS, Given Complete Information 4 

2 Probabilities of Suffering a Specified Health Effect under Alternative 

NAAQS, Given Incomplete Information 5 

3 Sample Sizes for the EP Data 9 

4 Consultants for the Hb Protocol 12 

5 Experts Participating in the Hb Encodings 17 

6 Consultants for the IQ Protocol 29 

7 Experts Participating in the IQ Encodings 33 

i v 
P.7 

TABLES (Cont'd) 

A.l Probability Distributions and Parameters for EP Levels among New York 

City Children 58 

B.l..Variables Pertaining to the NOLO Function .„ 75 

B.2 Encoded Judgments about Population Response Rates for Lead-Induced 

Hb Decrements 78 

B.3 Functions Fit to Judgments about Population Response Rates for 

Lead-Induced Hb Decrements 83 

B.4 Comparison of Judgments and Fitted Functions Concerning Population 

Response Rates for Lead-Induced Hb Decrements 86 

C.l Encoded Judgments about the Mean IQ of Children Unexposed to Lead 116 

C.2 Encoded Judgments about Population Standard Deviation 117 

C.3 Encoded Judgments about Mean IQ Decrements of Children Exposed to 

Lead 118 

C.4 Functions Fit to Judgments about Mean IQ Levels among Children 

Unexposed to Lead 120 

C.5 Functions Fit to Judgments about Population Standard Deviation for IQ 

Levels 121 

C.6 Functions Fit to Judgments about Mean IQ Decrements among Children 

Exposed to Lead 122 

C.7 Comparison of Judgments and Fitted Functions Concerning Lead-Induced 

IQ Effects 125 

C.8 Functions for Response Rate for IQ Levels below 85 and 70 .. . 131 

D.l Risk Estimates for Lead-Induced Elevated EP Levels, U.S. Children 

Aged 0-6 145 

D.2 Risk Estimates for Hb Levels < 9.5 and sl l g/dL, U.S. Children 

Aged 0-3 and 4-6 147 

D.3 Risk Estimates for IQ Decrement, U.S. Children Aged 7 151 

D.4 Risk Estimates for IQ Levels < 70 and < 85, U.S. Children Aged 7 154 

FIGURES 

1 Mean Response Rate vs. Dose for EP > 33 yg/dL and > 53 yg/dL 8 
P.8 

FIGURES (Cont'd) 

2 Median Response Rate and 90% CI vs. Dose for EP > 33 yg/dL ... . 9 

3 Median Response Rate and 90>% CI vs. Dose for EP > 53 yg/dL 10 

4 Dose-Response Functions, Hb < 11 g/dL, Ages 0-3, Expert A .'....... . 18 

5 Dose-Response Functions, Hjb < 11 g/dL, Ages 0-3, Experts A, C, D, 

and E 19 

6 Comparison of Judgments, Hb < 11 g/dL, Ages 0-3, Experts A, C, D, 

and E 20 

7 Dose-Response Functions, Hb < 11 g/dL, Ages 4-6, Experts A, C, D, 

and E 21 

8 Comparison of Judgments, Hb < 11 g/dL, Ages 4-6, Experts A, C, D, 

and E 22 

9 Dose-Response Functions, Hb < 9.5 g/dL, Ages 0-3, Experts C, D, 

and E 23 

10 Comparison of Judgments, Hb < 9.5 g/dL, Ages 0-3, Experts A, C, D, 

and E 24 

11 Dose-Response Functions, Hb < 9.5 g/dL, Ages 4-6, Experts C, D, 

and E 25 

12 Comparison of Judgments, Hb < 9.5 g/dL, Ages 4-6, Experts A, C, D, 

and E 26 

13 Median Values and 90% CIs fior Functions Fit to Judgments about the Mean 

IQ of the Control Group, Experts F, G, H, J, and K 34 

14 Median Values and 90%-Cl Judgments about a,Q, Experts F, G, H, J, 

and K 35 

15 Judgments about Lead-Induced IQ Decrements, Low SES Population, 

Experts F, G, H, I, J, and K 37 

16 Comparison of Judgments about Lead-Induced IQ Decrements, Low SES 

Population, Experts F, G, H, J, J, and K 38 

17 Judgments about Lead-Induced IQ Decrements, High SES Population, 

Experts F, G, H, I, J, and K .... 39 

18 Comparison of Judgments about Lead-Induced IQ Decrements, High SES 

Population, Experts F, G, H, I, J, and K 40 

19 Increased Probability of Having IQ < 85, Low SES Population, Experts 

F, G, H, J, and K 41 

v i 
P.9 

"TT''" ' T^IT* 

FIGURES (Cont'd) 

20 Comparison of Increased Probability of Having IQ < 85, Low SES 

Population, Experts F, G, H, J, and K '.. 42 

21 Risk Results for the Occurrence of EP Level > 53 yg/dL .j. 44 

22 Risk Results for the Occurrence of Hb Level < 9.5 g/dL among 

Children Aged 0-3 46 

23 Risk Results for Mean IQ Decrement in Low SES Children 47 

24 Response Rates for IQ Level < 70 among Low SES Children 48 

v i i 
P.10 

ACKNOWLEDGMENTS 

This enterprise had its origins in work for the U.S. Environmental Protection 

Agency by private consultants Thomas Feagans and William Biller, and their support and 

ideas were very helpful. John Haines and Jeff Cohen of the U.S. Environmental 

Protection Agency provided guidance throughout the project. Their support, as well as 

that of Thomas McCurdy, Harvey Richmond, Bruce Jordan, and others in the Office of 

Air Quality Planning and Standards, was a constant source of encouragement. The 

assistance of two other groups of people, whose names appear in the report, was essential 

for completion of this work: reviewers of the protocols and the 11 health experts who 

provided judgments on lead-induced health effects. 

The authors also extend their appreciation to those at Argonne National 

Laboratory who were instrumental in preparing this report. Mary Warren greatly 

improved the report as a result of her thorough editing. Christine Wegerer wrote many 

of the computer programs. Barbara Salbego prepared the manuscript for publication; 

Marie Reed and Louise Kickels prepared earlier drafts. The computer-generated 

graphics were the work of Linda Haley. 

This project was funded through Interagency Agreement DW89930551-01-02 

between the U.S. Department of Energy and the U.S. Environmental Protection Agency. 
P.11 

ACRONYMS 

' ALAD 6-aminolevulinic acid dehydrase 

ALAS 6-aminolevulinic acid synthase 

CD criteria document 

CDF cumulative distribution function 

CI credible interval 

CNS central nervous system 

ECAO Environmental Criteria Assessment Office 

EDTA ethylenediaminetetraacetate 

EEG electroencephalogram 

EP erythrocyte protoporphyrin 

EPA U.S. Environmental Protection Agency 

FEP free erythrocyte protoporphyrin 

GM geometric mean 

GSD geometric standard deviation 

Hb hemoglobin 

HERL Health and Environmental Research Laboratory 

IQ intelligence quotient 

NAAQS National Ambient Air Quality Standard(s) 

NHANES II second National Health and Nutrition Survey 

NOLO normal-on-log-odds 

OAQPS Office of Air Quality Planning and Standards 

PbB blood lead 

PDF probability density function 

PMF probability mass function 

SES socioeconomic status 

ZPP zinc protoporphyrin 

IX 
P.12 

SYMBOLS 

E[R] expected value of R 

F: encoded cumulative probability value 

F. cumulative probability value that results from fitting a regression -line to 

1

 a set of data 

f(R) probability distribution over R 

F(R) cumulative probability distribution over R 

IQ mean IQ of children sheltered from lead exposure 

IQ* specified critical level of IQ 

L blood-lead level 

In natural logarithm 

R response rate, or percentage of a population experiencing a specified 

health effect 

2 . . . 

r regression r-square statistic 

SD[R] standard deviation of R 

X odds variable, X = R/(100 - R); if X is lognormally distributed, R is 

normal-on-log-odds distributed 

Y log-odds variable, Y = ln(X); if Y is normally distributed, X is lognormally 

distributed 

A-=Q mean IQ decremen t 

y mean of Y 

OJQ within-group IQ standard deviation 

o' estimate of ov obtained by pooling data across several blood-lead levels 

o standard deviation of Y 

o variance of Y 

y 

•(X) cumulative distribution function for the standardized normal random 

variable 
ASSESSING THE RISKS TO YOUNG CHILDREN 

OF THREE EFFECTS ASSOCIATED WITH 

ELEVATED BLOOD-LEAD LEVELS 

by 

Thomas S. Wallsten and Ronald G. Whitfield 

ABSTRACT 

Formal risk assessments were conducted as part of the U.S. 

Environmental Protection Agency's current review of the primary 

National Ambient Air Quality Standard for lead. The assessments 

focused on three potentially adverse effects of exposure to lead in 

children from birth through the seventh birthday: erythrocyte 

protoporphyrin (EP) elevation, hemoglobin (Hb) decrement, and 

intelligence quotient (IQ) effect. The same general strategy was 

followed in all three cases: for two levels of each effect, probability 

distributions over population response rate were estimated at a series 

of blood-lead (PbB) levels. These distributions were estimated from 

data in the case of EP elevation and from expert judgments in the 

cases of Hb decrement and IQ effect. Although of interest in their 

own right, these estimates were combined with PbB distributions to 

yield probability distributions over the estimated percentages of 

children experiencing the particular health effects. 

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 Atr Quality Criteria for Lead (EPA, 1986a), 

hereafter referred to as the criteria document (CD). It summarizes and analyzes 

available scientific evidence about the adverse health effects of lead. After evaluating 

and interpreting the information in the CD, a draft EPA staff paper (EPA, 1986b) 

identifies the critical elements that EPA staff believe should be considered in the review 

and possible revision of the lead NAAQS. Particular attention is paid to those subject 

•All acronyms used in this report are listed alphabetically on pp. ix and x. 
P.14 

areas requiring judgments 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. The information and recommendations in'the 

staff paper guide the EPA Administrator on alternative regulatory approaches for 

controlling atmospheric lead emissions. 

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

primary NAAQS for lead was set. Instead of quantifying uncertainty, deterministic 

assumptions were made that were considered conservative given qualitative assessment 

of the uncertainty associated with available evidence. Calculations based on these 

assumptions resulted in a primary NAAQS for lead of 1.5 yg/m of air. Soon thereafter 

EPA's Office of Air Quality Planning and Standards (OAQPS) began exploring risk 

assessment methods that incorporate uncertainty into the standard-setting process in a 

formal, defensible, and open manner. 

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

OAQPS selected three for inclusion in this risk assessment: hemoglobin (Hb) decrement, 

elevated erythrocyte protoporphyrin (EP) levels, and intelligence quotient (IQ) effect. 

The population at risk for this risk assessment was limited to all U.S. children from birth 

through their seventh birthdays. Constituting a formal risk assessment regarding these 

three adverse health effects of lead, this report should aid in the current review of the 

primary NAAQS for lead. 

1.1 REPORT ORGANIZATION 

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

assessments are presented in the appendixes. Nevertheless, readers will gain a good 

understanding of the risk assessments from the main text. Section 1.2 presents the 

reasons for choosing the particular form of the risk assessments; Sec. 1.3 discusses the 

role of judgmental probability encoding in the risk assessments; Sec. 1.4 discusses doserevwnse uncertainty; and Sec. 1.5 summarizes the overall risk assessment strategy. 

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

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

was unnecessary. Sections 3 and 4 focus on the dose-response uncertainty for leadinduced Hb decrements and IQ effects, respectively. Judgmental probability encoding 

was required in these cases. Section 5 presents the results of combining dose-response 

uncertainty with blood-lead (PbB) distributions in the specified population. The results 

are probability distributions over response rate as a function of geometric mean PbB 

level. Section 6 summarizes the main findings. The report concludes with four 

appendixes. 

1.2 MOTIVATION 

Assessing the health risks associated with exposing young children to lead 

requires estimating the probabilities of certain fractions of the population at risk 

suffering well-defined health effects under alternative primary NAAQS for lead. The 
P.15 

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 reduced through experimental manipulation, 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 specified population on the basis of epidemiological 

or clinical data on different populations under varying or different exposure conditions, 

or on the basis of laboratory data on other species or on in vitro preparations. Statistical 

techniques cannot quantify this type of uncertainty because it is judgmental. 

Uncertainty 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 underlying their 

extrapolations from the data to the effect in question and on their perception of the 

distance over which the extrapolation must be made. Therefore, the procedures must 

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 available knowledge. 

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

accommodated responds to the following challenge issued by William Ruckleshaus in a 

speech at Princeton University when he headed EPA (Ruckleshaus, 1984, p. 158). 

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

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

placed in the estimates of risk that prompted those controls. 

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

risk (p. 161): 

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. 

Second, we must expose to public scrutiny the assumptions that 

underlie] our analysis in management of risk. 

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

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

distribution for each alternative NAAQS under consideration. Table 1 illustrates a risk 

assessment output of this type. For NAAQS alternative 1, the probability is 0.01 that 

fewer than 0.5% of the population will suffer the health effect, the probability is 0.05 
P.16 

that fewer than 1% of the population will TABLE 1 Probability of Suffering a 

suffer it, and so forth. (Equivadently, the Specified Health Effect under Alternative 

probability is 0.99 that more than 99.5% of NAAQS, Given Complete Information 

the population will not suffer the health 

effect, 0.95 that more than 99% will not _ _ 

suffer it, and so forth.) NAAQS alternative „..., : 

. _ .. ... . . , » . ' . Probability under 

4 provides the greatest degree of protection _ UAA^P »I -• . • 

. ._

 B e

 . \ Response NAAQS Alternatives 

in that a greater chance exists that fewer Rat e < R

 3 

people will suffer the health effect. (Z) ° 1 2 3 4 Output of the sort illustrated in 

Table 1 would presumably be helpful to EPA 0.5 0.01 0.06 0.19 0.38 

in selecting a standard that in its judgment 1.0 0.05 0.11 0.23 0.60 

would protect public health with an 1.5 0.41 0.53 0.64 0.75 

adequate margin of safety. For example, if ... . 

EPA determined that the intent of the 

Clean Air Act would be met by protecting 

99.5% of the population at risk with

 : 

probability 0.99, then NAAQS alternative 1 » 

would be selected. If the intent would be 

met by protecting 99.5% of the population with probability 0.95, then NAAQS alternative 

2 would be appropriate. Of course, this example is highly simplified because multiple 

health effects will generally be at issue, and populations can be defined in various ways. 

However, it illustrates the role that formal risk analysis can play in setting standards. 

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

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

respect to the associated judgmental uncertainty. The degree of agreement among the 

experts will be a measure of how firm the probability estimates are and will provide 

useful information in setting the standard. 

One way of representing'the degree of agreement is to propagate the encoded 

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

probability distributions under etch alternative NAAQS. Table 2 illustrates this case. 

Under NAAQS alternative 1, for example, there is a 0.01 to 0.02 probability range based 

on the judgments of several experts that fewer than 0.5% of the population will suffer 

the health effect. The closer together are the distributions for a particular NAAQS, the 

more firm are the corresponding probability estimates. 

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

account in a number of ways. One possibility is to place requirements on the 

probabilities based on the judgments of experts (e.g., that at least 99.5% of the 

population be protected). For this level of protection, it may be decided that the 

smallest probability should be at least 0.01, or that the probability be greater than or 

equal to 0.02 in at least 75% of the risk distributions. The second approach helps to 

ensure that individual experts do -not exert undue influence. 

The probability encoding sessions with each expert can include informal 

discussions of the relevant data. Summaries of these discussions can supplement the 
P.17 

TABLE 2 Probabilities of Suffering a Specified Health Effect 

under Alternative NAAQS, Given Incomplete Information 

Response 

Rate < R0 

(Z) 

0.5 

1.0 

1.5 

Probabil 

1 

0.01-0.02 

0.01-0.05 

0.29-0.41 

.ty Ranges fot 

2 

0.02-0.06 

0.04-0.11 

0.40-0.53 

• NAAQS Alternatives 

3 4 

0.11-0.19 0.26-0.38 

0.15-0.23 0.49-0.60 

0.53-0.64 0.68-0.75 

probability distributions and can provide guidance on their use. The three risk 

assessments presented in this report include outputs similar to those in Tables 1 and 2 

and summaries of the associated discussions. While endeavoring to make the risk 

assessments 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 judgmental probability encoding is unnecessary 

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

are unavailable, and the only alternatives to encoding judgmental probabilities are 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 satisfy two 

important criteria. The first criterion is that judgments must be obtained from experts 

who span the range of respected opinion. The problem of establishing the range of 

opinion and selecting appropriate experts appears to be difficult and judgmental in 

nature; however, the relevant issues tend to be debated frequently and publicly enough 

that such decisions are possible. For the Hb and IQ risk assessments, EPA's OAQPS 

selected the experts whose judgments were to be encoded. Although their names are 

given in the report, their individual judgments and discussion summaries are identified by 

code letter only. In this way, 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 those who may disagree. 

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

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

represent his or her uncertainty. Research relating to these issues has been reviewed by 
P.18 

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 DOSE-RESPONSE UNCERTAINTY 

Two types of uncertainty were discussed in Sec. 1.2. Ambiguity also exists 

regarding the level of an effect that should be considered adverse and for which a doseresponse function would be of interest. We dealt with this issue by specifying two levels 

of the relevant variable for each health effect and estimating a dose-response function 

for each. 

A dose-response function exists for a particular population and effect under 

specified conditions. Relatively complete data were available regarding the doseresponse functions for EP effects, although the data were somewhat uncertain because of 

sampling and mesurement errors. In the Hb and IQ assessments, the data regarding the 

dose-response functions were incomplete or indirect, and the need to extrapolate 

resulted in judgmental uncertainty (see Sec. 1.3). Because unique factors were 

associated with each of these latter assessments, the procedures and models used for 

quantifying uncertainty were different. 

1.5 RISK ASSESSMENT STRATEGY 

Our risk assessment strategy is most easily understood by first assuming that no 

uncertainty is involved. In this case, dose-response functions are determined for each 

selected lead-induced health effect. The dose-response curves plot the percentage of the 

specified population exhibiting the particular physiological or behavioral effect as a 

function of PbB level. The actual distribution of PbB levels in the population will be 

affected by the particular NAAQS scenario. The dose-response function for a specified 

health effect is then combined with the estimated PbB (dose) distribution under each 

alternative scenario to yield the percentage of the population that would suffer the 

effect under that scenario. In reality, however, uncertainty is present at each step and 

must be incorporated into the analysis in a manner providing final outputs of the forms 

shown in Tables 1 and 2. 

For this assessment, we produced risk results that are a function of geometric 

mean PbB level. When an exposure model linking alternative NAAQS to PbB levels in the 

population is available, it will be possible and straightforward to achieve the ultimate 

goal of relating alternative NAAQS to overall risk measures. 
P.19 

2 PROBABILISTIC DOSE-RESPONSE FUNCTIONS FOR 

LEAD-INDUCED ELEVATED EP LEVELS 

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

children aged 2-12, 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. We used the data directly because 

our consultants believed that the population from which the sample was drawn was 

sufficiently close to the population of interest (children up to their seventh birthdays) to 

make extrapolation unnecessary. 

Because of the very careful procedures used by Piomelli et al. (1982), sampling 

but not measurement error needed to be considered. Each of the points on a doseresponse function is based on a number of observations (N), in which X exhibit the health 

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

proportion P of the population suffering the health effect at the PbB level in question. 

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 

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 in App. A. 

*Blood-lead level is generally used as the index of lead exposure in health studies and is 

so used in this report. 

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 caused by their 

longitudinal nature made them unsuitable for the present purpose. Neither of these 

studies directly controlled for interactions between iron status and lead in determining 

EP levels. Recent reanalyses of data from the second National Health and Nutrition 

Survey (NHANES II) (Annest et al., 1982) indicate somewhat different dose-response 

relationships between PbB and EP when adjustments are made for iron status (Schwartz, 

1986). 
P.20 

Figure 1 presents the dose-response data for two EP levels (Piomelli et al., 1982), 

and Table 3 presents the sample-size data. Each of the two EP levels (> 33 yg/dL and 

> 53 yg/dL) was considered adverse. Expressions can be determined for the mean doseresponse curves shown (see App. A). These expressions are functions of PbB level, and 

what Piomelli et al. call "natural frequencies" for the occurrence of EP levels > 33 yg/dL 

and > 53 yg/dL and involve the normal probability distribution function. A natural 

frequency is the frequency of occurrence of elevated EP levels among children having 

PbB levels below the threshold level at which lead-induced EP effects begin to occur. In 

Fig. 1, a threshold of about 16.5 yg/dL for lead-induced EP effects is indicated by the 

"hockey-stick"-shaped functions. 

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 below 41 yg/dL, sample sizes are large enough that the 

normal distribution can be used to closely approximate beta distributions for both EP 

levels. In those cases, the mean is at least 2.5 standard deviations greater than zero. 

Table A.1 in App. A summarizes the probabilistic dose-response functions that were 

derived. 

Figures 2 and 3 show median dose-response relationships and 90% credible 

intervals (CIs) for EP levels > 33 yg/dL and > 53 yg/dL, respectively. For cases in which 

99-

fl) 

O 

Q£ 

V 

CO 

C 

o Q. 

ff] 

« OC 

c 

o 0) 

2 

95 

90 

75 

50 

25 

10 

5-

1-

—r10 20 3300 40 

PbB Level (jug/dL) 

50 

FIGURE 1 Mean Response Rate vs. Dose for EP 2 33 yg/dL 

and > 53 yg/dL (Source: Adapted from Piomelli et aL, 1982) 
P.21 

a normal approximation is adequate, the 

median and mean response rates are 

identical, and the CIs 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 CI 

range and a probability of 0.05 that it is 

above it. 

The 90% CIs are fairly small at PbB 

= 15 yg/dL (9-12% and 2-3% for EP 

> 33 ug/dL and > 53 yg/dL, respectively) 

because of the large number of children 

with PbB levels in the 10- to 20-yg/dL 

range. The 90% CIs are larger, as 

expected, at PbB = 35 ug/dL (66-80% and 

37-52% for EP > 33 ug/dL and > 53 yg/dL, 

respectively) because there were fewer 

children. 

TABLE 3 Sample 

Sizes for the EP Data 

PbB 

Level 

(yg/dL) 

2-17 

17-21 

21-31 

31-41 

41-98 

Number- of 

Children 

829 

479 

544 

109 

43 

Source: Based on 

data from Piomelli 

et al., 1982 

(Seaman, 1985). 

99-

95-

& 904 

o 

cc 

0) 

ff) 

c o Q. 

ff) 

O 

OC 

75 

50 

2b 

10 

5 

1-

90% Cl 

Median 

10 

— I — 

20 30 40 50 

PbB Level (/J.g/dl) 

FIGURE 2 Median Response Rate and 90% CI vs. Dose for EP 

> 33 yg/dL 
P.22 

99T 

, - s

 95

~ 

^ 90-

0) I 

1

 7H 

S 50-1 

a ! 

a> 25-! 

a ! 

i 

10-T 

10 

10 

I 

20 30 40 

PbB Level (yug/dL) 

90% Cl 

Median 

50 

FIGURE 3 Median Response Rate and 90% CI vs. Dose for EP 

> 53 yg/dL 
P.23 

11 

PROBABILISTIC DOSE-RESPONSE FUNCTIONS 

FOR LEAD-INDUCED Hb DECREMENTS 

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

decrements in the full population of U.S. children prior to their seventh birthdays. 

Therefore, it was necessary to encode expert judgmental probabilities about the 

population response rates at a series of PbB levels. Encoded probabilities must satisfy 

two requirements. They must be internally consistent as determined by criteria to be 

specified shortly, and they must be .satisfactory to the experts in the sense that the 

experts agree that the encodings properly represent their judgments. 

Only a finite number of PbB levels can be presented to the experts for encoding; 

in this study the number was about six. To use the judgments in the risk assessments, 

interpolation between encoded values was necessary. Such interpolations were 

accomplished by fitting a suitable probability distribution to the encoded values. The 

distribution must fit the judgments by a reasonable mathematical criterion, but it is 

equally important that the expert agree that the function is accurate. 

To meet these requirements and to follow the recommendations in Wallsten et al. 

(1983), we developed a protocol for the probability encodings and then met with each 

expert on two occasions about a month apart. Judgments were encoded during the first 

session, and functions were fit to them before the next visit. The judgments and functions were reviewed during the second session, and any changes deemed necessary by the 

expert were made. Additional follow-up by mail and telephone was sometimes required. 

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

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

encoding methods, and the procedures for fitting functions to the encoded judgments are 

presented in Sees. 3.3, 3.4, and 3.5, respectively. Section 3.6 indicates whose judgments 

were encoded, Sec. 3.7 summarizes the results for the various PbB levels and ages, and 

Sec. 3.8 provides some summary discussion. 

3.1 PROTOCOL DEVELOPMENT 

The consultants listed in Table 4 aided us in developing the protocol for Hb 

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

literature with us, guiding us in reading key studies, and 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 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. The protocol was then revised accordingly. 
P.24 

12 

TABLE 4 Consultants for the Hb Protocol 

Consultant 

Julian Chisolm 

Jeff Cohen 

Anita Curran 

Thomas Feagans 

Lester Grant 

John Haines 

Paul Hammond 

Robert Kellam 

Paul Mushak 

Affiliation 

Johns Hopkins University 

EPA, OAQPS* 

Westchester County Department 

of Health 

EPA, OAQPS 

EPA, ECAOb 

EPA, OAQPS 

University of Cincinnati 

EPA, OAQPS 

University of North Carolina, 

Chapel Hill 

aOffice of Air Quality Planning and Standards. 

Environmental Criteria Assessment Office. 

In this fashion, the protocol went through several drafts. If all the respondents 

viewed the problem in the same way, that way was specified in the protocol. When the 

consultants differed, or indicated that others might differ, we modified the protocol to 

allow the experts to individualize the scenario, subject only to the constraints that the 

obtained judgments could be mapped into the rest of the model and that they could be 

compared 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 probability 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 complete protocol is presented in Sec. B.1 of App. B; only an outline is 

provided here: Section 1 introduces what we were attempting to do and why; Sees. 2-5 
13 

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

defined; Sec. 6 raises various points in the literature for discussion; Sees. 7 and 9 discuss 

ttie process of probability encoding; and Sec. 8 deals peripherally with Hb decrement and 

raises issues concerning possible adverse health effects associated with elevated EP 

levels. 

More specifically, Sec. 2 defines adverse Hb 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 birth through their seventh birthdays. However, the experts 

were given the option of considering two age groups (0-3 and 4-6) if they thought for any 

reason that the two groups would have different dose-response functions. Therefore, 

experts who chose this option had their probabilistic judgments encoded for four doseresponse relationships. 

Section 6 is intended to stimulate discussion with the experts on relevant 

theories and data. This step helped ensure that the problem was structured properly, 

that the experts consciously reviewed their knowledge before providing probability 

judgments, and that a possible basis was provided for understanding any discrepant 

judgments. 

Sections 7 and 9, which cover the probability encoding, are based on 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 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 encoding session. Section 9 was provided 

and explained during the first encoding session. The protocol was then used to guide 

discussion and interaction during the sessions. 

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

discussing the material in Sees. 2-6. The concepts in Sec. 7 were then discussed and 

illustrated, after which the probability encoding began. (Discussion of Sec. 9 was delayed 

until the second encoding session.) The actual encoding took four to six hours. 

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

lasted from two to four hours. It included 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. 

3.4 ENCODING THE JUDGMENTS 

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

the factors determining the dose-response function had been thoroughly discussed with 
P.26 

„ ., rz» 

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 encoded 

with one expert. 

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

each expert was first asked to supply broad 98%-CI 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 20-70%, encodings were recorded at 20%, 30%, 40%, 

50%, 60%, and 70%. 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 random order; for a particular 

PbB level, response rates were also presented in 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 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 L is less than R, or 

that a random spin of the wheel will 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 had been encoded for a particular 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 L 

under consideration such that if a bet were made in which the payoff depended on 

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 initially specified a 

response rate such that in his judgment it was equally likely that the true rate would be 
15 

above or below it. After discussion, it frequently turned out that the expert was not 

indifferent between the two sides of the bet. Adjustments were made until a response 

rate was found at which he was indifferent. 

Having determined the response rate corresponding to a cumulative subjective 

probability of 0.50, the expert was then asked to imagine that 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 about half of the occasions at this point, he was to 

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

true rate was greater than that indicated earlier, 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 response rate being above or below it. The resultant value 

corresponded to a cumulative subjective probability of F(R|L) = 0.75. In this manner, 

response rates corresponding to probabilities of 0.25, 0.50, and 0.75 were encoded. 

Finally, response rates corresponding to subjective probabilities of 0.01 and 0.99 were 

determined by imagining bets with 1:99 and 99:1 odds. 

After the cumulative probability distribution over response rate was encoded for 

the first PbB level, regardless of the encoding method used, the distribution was graphed 

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

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

monotonically as the response rate increases (Wallsten et al., 1983). 

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

squally 

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. 

for R- > Rj, F(RjlL) = 0.25 and F(R-|L) = 0.75 imply that the true response rate is equal! 

likely to fall either inside the (Rj, R.-) interval or outside it. If the expert disagreed wil 

After the probability distributions had been encoded for all selected PbB levels, 

they were plotted on one graph and discussed with the expert. If two distributions 

crossed at any point, this inconsistency was resolved (Wallsten et al., 1983). When the 

expert was satisfied that the entire set of distributions represented his probabilistic 

judgments, the encoding was finished. 

Following the first session, the encoded probabilities (distributions) were fit to 

functions in the manner described in Sec. 3.5. Summaries of the encoded judgments and 

the respective fits, along with explanatory text, were sent to each expert before the 

second visit. During the second visit, these materials were reviewed, the expert was 

asked to indicate whether the fitted distributions correctly represented his judgments, 

and additional probability encoding was carried out if necessary. In a few instances, 

further function fitting was necessary, and subsequent discussion was conducted by letter 

and telephone. 

3.5 REPRESENTING THE JUDGMENTS 

Calculating risk required finding mathematical functions that fit the assessed 

points. Because probabilistic judgments about dose-response relationships generally form 
P.28 

16 

S-shaped curves over the closed [0%, 100%] interval (Wallsten et al, 1983; Whitfield and 

Wallsten, 1984), it is difficult to represent them with simple mathematical functions. 

One particularly useful function that is relatively easy to work with is the normal-on-logodds (NOLO) 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

 " lOCrhi' ^ r 0 , X < -

and 

Y = ln(X), for -» < Y < » 

where X is the odds variable and Y is the log of the odds variable. If Y is normally 

distributed (with mean y and variance o ), then X is lognormally distributed, and 

the distribution induced on R is called a7 NOLO distribution. Although the NOLO 

distribution cannot be expressed in a closed form, all probabilities of interest can easily 

be derived from the normal distribution over Y (see App. B). 

A separate NOLO distribution function was fit to the elicited cumulative 

distribution functions (CDFs) for the probability Judgments over response rate R, at each 

PbB level Lj, where j = 1, ..., m (m = 6). This fitting was accomplished by deriving leastsquares estimates of the parameters v: and o-, denoted by y; and o;, 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 a-, are 

referred to as the best-fitting NOLO 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 shown in App. B, the NOLO distribution described the 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 compromised to a small degree by fitting an 

expert's probability judgments with a family of equal-variance NOLO distributions. This 

procedure ensures that the derived distributions at different PbB levels never cross one 

another, not even at the extremes. Crossing would imply that exceeding a specified 

response rate is judged more probable at PbB level Lj than at L2, where L2 is greater 

than Lj. 

Equal-variance NOLO distributions were derived by (1) obtaining a least-squares 

estimate of the standard deviation pooled over PbB levels, o', (2) setting all the 

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

App. B). The result is a set of NOLO distributions, one for each PbB level Lj, tha tr1 has a 

common variance and that differs only in the mean. Goodness of fit can be assessed by 

calculating r between observed and fitted judgments. 

Because probability judgments were elicited for each PbB level Lj over virtually 

the entire closed [0%, 100%] interval, and because these judgments exhibited no 

inconsistencies (i.e., crossings), the fit of the equal-variance NOLO distributions was 
P.29 

17 

generally close to that of the best-fitting NOLO distributions. Because the equalvariance distributions cannot give rise to inconsistencies, these representations of expert 

judgments are preferred for estimating risk. Indeed, each expert accepted them, with a 

slight adjustment required for Expert D. 

3.6 THE EXPERTS 

The individuals listed in Table 5 were selected in the fall of 1984 by OAQPS for 

participation as experts in the Hb risk assessment. All of them agreed to participate, 

with the understanding that their judgments would remain anonymous. The results 

presented are for Experts A through E, but the letter designations are randomly assigned. 

3.7 RESULTS 

In Sec. 3.7, the functions fit to each expert's probabilistic judgments are used to 

summarize the quantitative results. These functions accurately represent the underlying 

encoded values, both because the goodness of fit was excellent and because each expert 

endorsed the output of the respective functions as representing his judgments. Appendix 

B presents the detailed quantitative results, including encoded judgments, parameter 

values for fitted functions, and goodness-of-fit measures. Section B.4 summarizes the 

qualitative discussions held with each expert about the effects of lead exposure. 

Recall that probabilistic judgments were encoded about dose-response functions 

for lead-induced Hb decrements among U.S. children aged 0-6. Hemoglobin levels of 

< 9.5 g/dL and < 11 g/dL were considered, and most experts divided the population of 

children into two age groups (0-3 and 4-6). Results are presented separately for the four 

combinations of Hb level and age group. 

TABLE 5 Experts Participating in the Hb Encodings 

Expert Affiliation 

Julian Chisolm Johns Hopkins University 

Bernard Davidow New York City Board of Health 

Paul Hammond University of Cincinnati 

Sergio Piomelli Columbia University, New York City 

Lead Poisoning Prevention Program 

John Rosen Montefiore Hospital and Medical 

Center 
P.30 

18 

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

two age groups. Expert C believes that a single dose-response function applies to 

children aged 0-6 and therefore provided a single set of probabilistic judgments for each 

Hb level. Expert B was uncomfortable with the notion of judgmental probability 

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

presented in Sec. B.4.2 of App. B. 

3.7.1 Hb Level < 11 g/dL, Ages 0-3 

The format of the figures used to display the judgments of the experts is 

explained using the judgments of Expert A regarding the dose-response function for Hb 

level < 11 g/dL in U.S. children aged 0-3 (see Fig. 4). The curves shown are analogous to 

dose-response functions found in the literature, except that they are based on 

probabilistic judgments rather than on actual data. The solid curve shows the median 

dose-response curve — at each PbB 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 dotted lines on either side of the median curve bound the central 

50% CI. Thus, at each PbB level there is a 0.25 probability that the true response rate is 

below the lower dotted curve, a 0.50 probability that it is between the two dotted curves, 

and a 0.25 probability that it is above the upper one. In a similar manner, the dashed pair 

of curves bounds the 90% CI. 

^ 7 . o".05/r<Lei

,

I45 

n r 

55 

i 

65 75 

PbB Level (/zg/dQ 

FIGURE 4 Dose-Response Functions, Hb < 11 g/dL, Ages 0-3, 

Expert A 
P.31 

19 

Figure 5 represents the probabilistic judgments of Experts A, C, D, and E rather 

cpmpletely regarding the dose-response function for Hb level < 11 g/dL in U.S. children 

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

reproduced in the figures for each age group.) Each expert's judgments are shown in a 

separate panel. Different scales are used to maximize the amount of detail shown for 

each expert. 

Although Fig. 6 is less complete, it provides a convenient means of comparing 

judgments across experts. The axes are the same as those in Fig. 5: the vertical bars at 

each PbB level represent each expert's central 90% CI for response rate, and the symbol 

within each bar indicates the median judgment at that PbB level. Substantial overlap is 

evident in the judgments of Experts C, D, and E, even though Expert Cs judgments are 

for children aged 0-6, whereas those of the other experts are for children aged 0-3. The 

judgments of Expert A tend to differ from those of Experts C, D, and E. None of the 

overlapping judgments of Experts C, D, and E suggest a PbB-level threshold below which 

there is no discernable lead-induced Hb decrement. However, the implications of the 

change in slope between 15 yg/dL and 25 ug/dL for Expert D's judgments may prove 

important. The median judgments of Experts C, D, and E indicate that the best estimate 

of the true response rate falls between 4% and 9% at PbB = 5 yg/dL, and that it rises to 

between 26% and 33% at PbB = 55 yg/dL. 

/"•v 

^ 

o 

o 

OC 9 

V) 

C 

O 

CL 

V) 

© 

oc 

2 

o 

o 

ac 

Q> 

tn 

r o Q. 

© 

OC 

40-i 

3 0 -

2 0 -

10-

0 -

i 

6 0 -

50 -| 

4 0 -

3 0 -

2 0 -

1 0 -

i 

Expert A 

/ 

/ 

/ / 

••yy.. 

> 45 55 

Expert D 

* 

* 

./ 

/ .•• / ..• • ^^* • ~ 

' s's* .•••' 

/0.9 5 / 

/ / 

/ ' .. 0.75 

.• 

.••' ^0. 5 

y^\ - ••• °- 2 5 

•••*' ,--0.0 5 

"* "" 

65 75 

/ c 

/ 

/ 

,' 

.*' / 

y , 

^^y m»* 

,** "•' +' 

___,* ••/. ~-*' 

•Hjinf>"-

iii i 

i 15 25 35 

I - i 

45 55 

* u -

3 0 -

2 0 -

10-

Expert C 

x 

• 

• 

• 

• ." 

y y y 

y .* y^ 

y *m . ^ . ' 

* * y •" 

* •*• ••" y y * ** 

- * ~ .-'Jyy'* *' 

" * _ ' **"*'*" "^ 

;-•'-"—" ' 

° 1 I 1 1 T 1 

5 15 25 35 45 55 

6O-1 

50-

40-

30-

20-' 

10-

Expert E 

PbB Level (_ug/dL) 

—i 1 1 1 1— 

15 25 35 45 55 

PbB Level (Atg/dL) 

FIGURE 5 Dose-Response Functions, Hb < 11 g/dL, Ages 0-3, 

Experts A, C, D, and E (response-rate and PbB scales were 

selected to show the details of each expert's judgments) 
P.32 

60- , 

5 0 -

&? 40 -

£ "5 

oc 

0> 3 0 

OT 

c 

o 

a 

w 

© 20 

a: 

1 0 -

T T 

T 

T 

: • 

hi *|i

 ;ii 

0 

1

 i ' 

'^1 

(t 

I 1 

II 

i 

l ! 

1 

o-»-«-

A 

i i i 

C 0 E 

» r - i ~ •—T -

A C 0 £ 

—15 — 

A C D E 

25 — 

-I— • I I 

A C 0 E 

35 — 

1 

T"" i • r • f 

1 

T-I—r-r—r-r-i— r 

ACO E ACO E ACO E 

— 45 55— — 65 — 

A C D E 

— 75 — 

PbB Level (ug/dL) 

FIGURE 6 Comparison of Judgments, Hb < 11 g/dL, Ages 0-3, Experts A, C, D, and E 

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

relationships, and Expert E expresses the most. In all cases, the variance in the 

judgments increases with PbB level within the range considered, as indicated by the 

increasing size of the 90% CIs represented by the vertical bars in Fig. 6. For Experts C, 

D, and E, the low ends of the 9>0% CIs for response rate range between 9% and 20% at 

PbB - 5 yg/dL, and between 35% and 62% at PbB = 55 yg/dL. 

According to Expert A's judgments, PbB levels less than about 45 yg/dL do not 

cause Hb levels below 11 g/dL in this age group. At PbB = 45 yg/dL, the most likely 

response rate is 3%; at PbB = 75 yg/dL, it rises to 17%. Furthermore, with probability 

0.05, the actual response rate at PbB = 45 yg/dL is judged to be greater than 10%; with 

the same probability, it is judged to be greater than 39% at PbB = 75 yg/dL. Although 

our primary interest is in PbB levels < 55 yg/dL, we inquired about higher levels here to 

provide a fuller picture of Expert A's judgments. 

3.7.2 Hb Level < 11 g/dL, Ages 4-6 

Figures 7 and 8 display the experts' judgments regarding dose-response functions 

for Hb level sl l g/dL for children aged 4-6. They present the data in exactly the same 

way as Figs. 5 and 6. As before, the judgments of Experts C, D, and E overlap 
21 

© 

30 

20-

© 

OT 

§ 10-

a 

OT 

© 

oc 

Expert A 

,-0.9 5 

0.75 

-//—i -

55 

—J— 

65 

—r75 

40-, 

30-

20-

Expert C 

10-. 

25-i 

Expert D 

PbB Level {.ug/dL) 

4 U -

30-

70-

10-

0 -

Expert E 

• 

x 

* . •* 

y -** 

• .-* ^ 

• ,•* ^^**^ 

• •* * j^ -""*" ^ •••* " 

"TTm-***** _»——"*"*— 

On i i i i i 

5 15 25 35 45 55 

PbB Level (^g/dL) 

FIGURE 7 Dose-Response Functions, Hb < 11 g/dL, Ages 4-6, 

Experts A, C, D, and E (response-rate and PbB scales were 

selected to show the details of each expert's judgments) 

considerably and are different from those of Expert A. According to Experts C, D, and 

E, there is no threshold PbB level. The most likely response rates are between 2% and 

7% at PbB = 5 yg/dL, with the rates rising to between 14% and 26% at PbB = 55 yg/dL. 

In this case, Expert D expresses the least uncertainty among the three, while Expert E 

continues to express the greatest uncertainty. The 0.05 fractiles for response rate for 

Experts C, D, and E range between 4% and 13% at PbB = 5 yg/dL, and between 17% and 

36% at PbB = 55 yg/dL. 

As before, Expert A's view is that the probabilities of lead-induced Hb effects at 

the exposure levels considered are extremely low in this age group. In his judgment, PbB 

levels less than about 55 yg/dL do not cause Hb levels below. 11 g/dL. The most likely 

response rate at 55 yg/dL and 75 yg/dL are 2% and 11%, respectively. With probability 

0.05, the actual response rate is judged to exceed 6% at 55 yg/dL; with the same 

probability, it is judged to exceed 25% at 75 yg/dL. 

3.7.3 Hb Level < 9.5 g/dL, Ages 0-3 

Figures 9 and 10 display the judgments regarding dose-rerponse functions for Hb 

level < 9.5 g/dL for children aged 0-3. In Expert A's judgment, PbB levels within the 
40-i 

22 

P.34 

30-

^ 

"o 

QC 

0) 20-

c 

o 

CL 

W 

» 

ac 

10-

T 

I 

I 

I 

6 

T 

MM 

• ! 

ii! 

il 

i • 

i 

A ^ ! 

i 

ii 

! 

• 

ii 

IT 

• i I j ii • 

T 

o-»-«-

A 

| | T |#T|»|^IITI» I I IT^I I T I lll l 

C D E ACO E ACO E ACO E ACO E ACO E ACO E ACO E 

5 15 -25 35— —45 55— —65 75 — 

PbB Level (/xg/dL) 

FIGURE 8 Comparison of Judgments, Hb < 11 g/dL, Ages 4-6, Experts A, C, D, and E 

range of interest (< 55 yg/dL) do not cause Hb levels to drop as low as 9.5 g/dL. Also, 

although the judgments for Experts C, D, and E tend to overlap, they do not display the 

same degree of similarity as at the higher Hb level. In particular, Experts C and E agree 

that at PbB = 5 yg/dL, the most likely response rate is 2%, while Expert D is certain that 

the response rate is 0%. Further, Expert Cs median-response-rate judgments increase 

relatively slowly with increasing PbB, while those of Expert D increase relatively 

quickly. As a result, at PbB = 55 yg/dL, Experts D and E agree that the most likely 

response rate is 20%, while Expert C judges it to be 7%. 

Expert E expresses considerable uncertainty in his judgments, while Experts C 

and D express much less. The 0.05 fractiles for response rate are 3% and 10% at PbB = 

5 yg/dL, and 11% and 54% at 55 yg/dL for Experts C and E, respectively. Expert D 

believes the response rate is definitely 0% at PbB = 5 yg/dL. 

3.7.4 Hb Level < 9.5 g/dL, Ages 4-6 

Figures 11 and 12 display the judgments regarding dose-response functions for Hb 

level < 9.5 g/dL for children aged 4-6. The pattern of judgments is very similar to that 

for the younger age group, but the response rates are lower. 
23 "«\ 

40-i 

a, 30-

"5 Oi 

O 20-

OT 

c 

o 

CL 10H 

OT 

© 

ce 

0 -

12-i 

£ 10-

© 

"5

 8" 

ac 

© 6-

OT 

§ 4-

Q. 

©

 Z H 

cr 

flE x P

6rt C

 .-0.95 

* 

..0.75 

• •• 

, ' " ..---"_ ^b-s 

y .-•''^•^..••0.25 

^ -•* ' a^^ ^ ••• ' 

•' .-yy- ,--0.05 

^ . • . •' ^y *' /^. • , * • * — «• •" m -• ** 

* c * * *•• ^ ^ 

U-li i | | | 

5 15 25 35 45 55 

60-, 

Expert D 

50-

s 

s 4 0 -

• 

/ 

' .-'V

 30_ 

' •** ,*y 

/.••/>•'.. 2 ° -

Expert E 

y 

s * 

y 

y 

y i * . -

/ 

J&'''' "-'''y^yz^---

&ut J

 n_ 

•* i- - ~ - - ~ u

 1 1 1 1 1 "» lll l 

5 15 25 35 45 55 5 15 25 35 45 

V 

" 

--

•**" 

.... 

1 

55 

PbB Level Ug/dL) PbB Level Ug/dL) 

FIGURE 9 Dose-Response Functions, Hb < 9.5 g/dL, Ages 0-3, 

Experts C, D, and E (response-rate and PbB scales were 

selected to show the details of each expert's judgments) 

Expert A judges that the PbB levels under consideration would not reduce Hb 

below 9.5 g/dL, and Expert D judges that the PbB level would have to be at least 

25 yg/dL to do so. The median judgments of Experts C and E are consistently similar, 

while those of Expert D are similar to those of Experts C and E at PbB = 35 yg/dL and 

higher. For Experts C, D, and E, the ranges of median judgments are 0% to 2% at PbB = 

5 yg/dL, and 7% to 13% at PbB = 55 yg/dL. 

Expert E again expresses the greatest degree of uncertainty. For Experts C and 

E, at PbB = 5 yg/dL, the 0.05 fractiles for response rate are 3% and 6%, respectively. 

For Experts C, D, and E, at PbB = 55 yg/dL, the 0.95 fractiles for response rate range 

from 11% to 36%. 

3.8 DISCUSSION 

The lead-induced response rates reported in Sec. 3.7 are over and above any 

baseline response rate related to iron deficiency or other factors. Thus, the levels of 

uncertainty, as well as any differences or similarities of opinion, are limited solely to the 

effects of lead on Hb level. 
P.36 

25 —3 5 

PbB Level (/xg/dL) 

FIGURE 10 Comparison of Judgments, Hb < 9.5 g/dL, Ages 0-3, Experts A, C, D, and E 

Although the judgments of Experts C, D, and E differ in detail, they are broadly 

similar. It is particularly interesting that Expert Cs judgments for children aged 0-6 

tend to be just below those of Experts D and E for children aged 0-3 and just above those 

for children aged 4-6. The judgments of Experts C, D, and E differ from those of Expert 

A, who believes that PbB levels in the range considered (< 55 yg/dL) have little or no 

effect on Hb levels. 

In all cases, uncertainty, as indicated by the length of the 90% CI, increases as 

the PbB level increases. This pattern is expected 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. In addition, less information is 

available at lower Hb levels than at higher ones, if for no other reason than the lower 

ones occur less frequently. Since judgments at lower levels require greater extrapolation 

from available data, more disagreement among experts is to be expected. However, 

Experts A, C, and D are more certain at < 9.5 g/dL than at < 11 g/dL, despite the greater 

extrapolation. Indeed, Expert A is positive that there is no effect at < 9.5 g/dL. 

Apparently, Experts A, C, and D understand the effects of lead on Hb level such that 

each is more confident about response rates at the lower Hb level. The reverse is true 

for Expert E. 
25 

© 

o oc 

9 

M c 

o 

Q. 

OT 

9 

ac 

iz9-

6-

Expert C 

«* * * 

+ 

+ # .* 

^ ••* 

* ' .-•''^-* '" '-""^y^ —•-•• " 

<'..-''yy-'" ---

' a.' aS^a ...- -

* ' .a'a^..' " - » " 

3-'..-><7> ,- -

0- 1 1 1 1 

-0.95 

0.75 

^0.5 

0.25 

-0.05 

i 

15 25 35 45 55 

30-i 

Expert D 4 U -

30-

20-

10-

0 -

Expert E 

/ / / / / / 

/ 

**•— i 1 ~ " i 1 V 

25 35 45 55 

PbB Level Ug/dL) 

5 15 25 35 45 55 

PbB Level Ug/dL) 

FIGURE 11 Dose-Response Functions, Hb < 9.5 g/dL, Ages 4-6, 

Experts C, D, and E (response-rate and PbB scales were 

selected to show the details of each expert's judgments) 

Although the experts were selected to represent the range of respected opinion, 

the patterns of their judgments are rather similar. This result illustrates the benefit of 

encoding judgmental probabilities. The differences of opinion evident in the literature 

and in debate can reasonably be attributed to problems with definitions, to differences in 

how to interpret and extrapolate data, and to disagreements about what constitutes 

proper public health policy. When the experts are required to focus on the scientific 

issues and to consider carefully their levels of uncertainty about these matters, they 

disagree much less. 

Although the judgments presented here are of interest in their own right, they 

are combined in Sec. 5 with a range of PbB-level distributions to obtain overall risk 

distributions. 
35-

26 

P.38 

3 0-

25-

^ 

Q> 

"5 2o^ 

QC 

Q> 

OT 

g «H 

Q. 

w 

V 

QC 

10 H 

T 

T 

0 -I—•—i—•— i 1—•—i—•—i 1—•—i 1 1 1—• -

T. 

i j . i ; 1 . . 

i i i.i i.i

 ! i i ! i i 

* T 1

 iii 

-i—i—i— r 

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

2.5 7.5 —12.5 — —17.5 — —22.5 -

Geometric Mean PbB Level (^xg/dL) 

•27.5-

FIGURE 12 Comparison of Judgments, Hb < 9.5 g/dL, Ages 4-6, Experts A, C, D, and E 
wrmwji'w ty ^T!* ' 

27 

4 PROBABILISTIC DOSE-EFFECT AMD BOSE-EESPOMSE 

FTOCTIQMS FOE LEAD-MDTCED IQ DECEEE3ES3T8 

As was true for the Hb assessment, the data regarding the effects of lead on IQ 

in the population of all U.S. children before their seventh birthdays are incomplete. 

Moreover, the data are very controversial, which makes it doubly necessary to encode 

expert judgmental probabilities. 

To parallel the Hb situation exactly would have entailed defining dose-response 

functions in terms of the percentage of the population with lead-induced IQ decrements 

exceeding two selected amounts and then encoding judgmental probabilities about such 

functions. This approach proved infeasible because it did not frame the issue in the way 

that researchers think about it or in terms of events that were in principle observable. 

Because IQ depends on multiple, correlated factors acting over long periods of time, 

inferences about the effects of lead on IQ require complex statistical operations using 

group data. Thus, it is impossible to attribute an IQ decrement in an individual to a 

particular cause. 

To pose questions about outcomes that experts commonly think about and to 

elicit probabilistic judgments suitable for a risk assessment, a hypothetical (ideal) 

experiment was created. Very large numbers of children were to be randomly assigned at 

birth either to a control group or to one of several lead-exposure groups. Exposure levels 

were to remain approximately fixed at the specified level until the children's seventh 

birthdays, at which time the WISC-R IQ test was to be administered. Blood-lead level 

was to be measured at the third birthday. The very large number of subjects per group 

eliminates 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. The 

groups differ only in their exposure to lead. The experts were asked to consider this 

experiment and to provide probability judgments about expected mean IQ differences 

between the control group and each of the exposure groups. 

The hypothetical 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 certain troublesome features. Indeed, the point of doing the 

complex statistics on the real data is to infer what the IQ difference would be between a 

lead-exposed and a lead-unexposed group in the absence of confounding variables. Thus, 

researchers have been thinking about this issue, which is precisely the one that the 

experts were asked to make probabilistic judgments about. 

To calculate subjective probabilities concerning IQ dose-response functions based 

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

other matters as well. Thus, probabilistic judgments were also encoded concerning the 

mean IQ of the unexposed control group and the standard deviation in IQ within the 

different exposure groups. The IQ measure was constructed so that it was approximately 

normally distributed within the population. The experts were asked whether they 

believed that a normal distribution could reasonably be applied to IQ scores within each 

of the exposure groups. Subsequently, judgmental probabilities about dose-response 

functions of interest were calculated using normal distribution theory in conjunction with 

tiitik^u^MiikJdluiwIIMBMnllAiiMkJi J I iiim i. i 
P.40 

28 

probabilistic judgments about mean IQ decrement, control-group mean IQ, and withingroup standard deviation. 

Section 4.1 describes the development of the protocol, and Sec. 4.2 outlines the 

protocol itself. 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 summary discussion. 

As will be discussed, the encoding sessions took place in the spring of 1985 before 

the availability of several important neurological studies on children. These recent 

studies are discussed in an addendum (EPA, 1986c) to the CD for lead (EPA, 1986a). 

4.1 PROTOCOL DEVELOPMENT 

Table 6 lists the people who served as consultants in developing the protocol. As 

already indicated, our original intention was to develop a protocol analogous to the one 

for Hb decrement. In other words, we planned to encode expert probabilistic judgments 

about dose-response functions for lead-induced IQ decrements. In preparation, we read 

relevant portions of the CD and talked with several of our consultants. 

The first draft of the protocol was designed to elicit probabilistic judgments 

about dose-response curves for IQ decrement. This draft was discussed with most of the 

people listed in Table 4. Two factors quickly became apparent. First, although the 

concept of a dose-response curve is well defined in this context, it is not commonly used, 

for reasons mentioned earlier. Second, in responding to the questions, the experts were 

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

extrapolating from those outcomes to the dose-response functions of interest. 

We concluded that it would be far more consistent with the way the experts 

usually thought, and thus easier for them to respond, if their probabilistic judgments 

about outcomes of a suitable hypothetical experiment were encoded directly. By 

properly designing the hypothetical experiment, we would not need to worry about some 

of the complexities that arise in actual research. Also, the extrapolations that the 

experts were trying to do mentally could be done mathematically. 

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

judgments about the outcomes of the hypothetical experiment. This protocol also 

indicated how the judgments would be used and how the assumptions made in working 

with them would be incorporated. The new draft was discussed with most of the 

consultants. They all found it much easier and more natural to respond to this version 

than to the previous one. However, their comments led to a third draft, which 

incorporated an improved design for the hypothetical experiment. This draft was 

discussed with most of the people who had seen the previous one, and only very minor 

changes were necessary. 
-X*t~-- "''TR""" 

29 

TABLE 6 Consultants for the IQ Protocol 

P.41 

Consultants Affiliation 

Vernon Benignus 

Robert Bornshein 

Jeff Cohen 

Anita Curran 

Cerri Dawson 

Kim Dietrich 

Claire Ernhart 

Lester Grant 

Lloyd Humphreys 

Lyle Jones 

Herbert Needleman 

David Otto 

Stephen Schroeder 

Bernard Weiss 

EPA, HERLa 

University of Cincinnati 

EPA, OAQPS 

Westchester County Department 

of Health 

University of North Carolina, 

Chapel Hill 

University of Cincinnati 

Cleveland Metropolitan General 

Hospital 

EPA, ECAOb 

University of Illinois, 

Champaign-Urbana 

University of North Carolina, 

Chapel Hill 

University of Pittsburgh 

EPA, HERL 

University of North Carolina, 

Chapel Hill 

University of Rochester 

aHealth and Environmental Research Laboratory. 

Environmental Criteria Assessment Office. 
. _ P.42 

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. Although the judgmental probability encodings went very well, minor changes to 

the protocol were made after analyzing the judgments and discussing these analyses with 

Lyle Jones. The final version of the protocol was discussed with several people who had 

seen the previous drafts. Everyone agreed that it was suitable for its intended use. 

4.2 PROTOCOL OUTLINE 

The complete protocol is presented in Sec. C.l of App. C; only an outline is 

provided here: Sec. 1 introduces the risk assessment project and the purpose of the 

probability encoding, and Sec. 2 describes the hypothetical experiment, in which large 

numbers of children are randomly assigned at birth to one of six exposure groups or to a 

control group completely sheltered from lead. Environmental lead exposure is assumed 

to be roughly constant at the appropriate level for each child. That is, when the PbB 

level is measured on his or her third birthday, it is at the designated level. The 

environmental exposure remains the same until the seventh birthday, when the WISC-R 

IQ test is administered. Thus, each expert was asked to consider the time course of lead 

in the children's systems according to his or her own theoretical understanding, subject to 

the constraint that PbB remained at the level designated for the third birthday. 

Section 2 also explains that probabilistic judgments would be encoded regarding 

(1) the mean IQ decrement for each exposure group relative to the unexposed control 

group, (2) the mean IQ of the unexposed control group, and (3) the standard deviation in 

IQ within the individual groups. Further, the shape of the IQ distribution within the 

individual groups is discussed. However, if an expert considered the effects of lead on IQ 

to be different for low socioeconomic status (SES) than for high SES subpopulations, then 

judgments would be encoded separately for the two groups. For this purpose, low SES 

children were defined as those living in households with incomes at or below the fifteenth 

percentile, whereas high SES children were defined as those living in households with 

incomes above the fifteenth percentile. 

Section 3 defines the population at risk as U.S. children up to their seventh 

birthday, which explains why IQ is measured at that time. Sections 4 and 5 specify the 

exposure, physiological, and environmental conditions assumed for the hypothetical 

experiment. 

As was true for the Hb protocol, Sec. 6 elicits discussion prior to the probability 

encoding by focusing on relevant issues in the literature. The purposes were to ensure 

that the problem was structured properly for the experts, to make sure that the experts 

consciously reviewed their knowledge before providing probability judgments, and to provide a basis for understanding any discrepant judgments. Section 7 discusses factors to 

be aware of when encoding probabilities, and Sec. 8 documents the encoding procedure. 

4.3 CONDUCT OF THE SESSIONS 

The sessions took place in the spring of 1985; with one exception, they were 

conducted in the same way as those for the Hb assessment (see Sec. 3.3). The sole 
31 

exception was that we brought information to aid the experts, should they have wanted 

it, in encoding probabilities about the mean IQ of the unexposed control group and about 

the standard deviation in IQ within individual groups. The information concerned WISC-R 

IQ means and standard deviations for subpopulations stratified by various demographic 

variables, as compiled in Kaufman and Doppelt (1976) and subsequently summarized in 

Sattler (1982).* 

4.4 ENCODING THE JUDGMENTS 

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

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

expert. We encoded probability judgments for possible mean IQ decrements in six leadexposure groups relative to the unexposed control group. The exposures were such that 

at their third birthdays, members of respective groups had PbB levels of 5, 15, 25, 35, 45, 

and 55 yg/dL. However, higher levels were encoded at the request of 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 (98%-CI) ranges for possible 

mean IQ differences between the control group and each of the exposure groups. 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 someday it were found that the true mean difference were outside that 

range. In a similar manner, 98% CIs 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 a particular SES level, the same standard deviation judgments applied to all 

exposure groups and that it was reasonable to assume normal (Gaussian) IQ distributions 

for an individual subgroup. 

Following the first session, functions were fit to the judgments. Summaries of 

the fitted functions and descriptive information were sent to the U.S. experts for their 

review before the second session. Because of time and financial constraints, it was 

impossible for the European experts to review these materials before the second 

meeting. During the second visit, all materials were reviewed, additional probability 

encoding was carried out as necessary, and each expert indicated whether the fitted 

distribution correctly represented his or her judgments. In several instances, subsequent 

function, fitting was necessary, and further discussion was conducted 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 of them. 

•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, the experts had to 

adjust these values as they thought appropriate given their views on the effects of lead 

on IQ. Each person could choose to take the tabulated values as point estimates. 
P.44 

32 

4.5 REPRESENTING THE JUDGMENTS 

As in the Hb risk assessment, calculating risk required that distributions be fit to' 

the assessed points. Although the nature of the variables being judged was different 

from that of the Hb variables, the judgment curves were again generally S shaped. The 

judged difference in mean IQ was bounded from below by zero. Theoretically, this need 

not.have been the case, but none of the experts gave any credence to the possibility of 

lead exposure enhancing IQ. Judgments about the mean IQ of the control group and the 

standard deviation in IQ for individual groups were so far from any limits that for all 

practical purposes they could be treated as unbounded. Thus, the required distributions 

were different from those used for the Hb assessment. 

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

IQ standard deviation were fit well by either normal or lognormal distributions. The 

goodness-of-fit measure was again the r statistic, which compares actual judgments 

with those predicted by the fitted function. With regard to differences in mean IQ, the 

judgments of some experts for each PbB level were roughly symmetric about a particular 

value, whereas other judgments were positively skewed (i.e., small probabilities were 

attributed to very large differences). In general, the former were better fit with normal 

distributions and the latter with lognormal distributions (i.e., distributions over the 

logarithms of IQ differences). 

More specifically, the following four families of distributions were fit to each 

expert's judgments about differences in mean IQ: (1) normal, allowing a separate mean 

and variance for each PbB level; (2) lognormal, allowing a separate mean and variance 

for each PbB level; (3) equal-variance normal; and (4) equal-variance lognormal. In the 

two latter cases, the distributions were fit using a single pooled variance for each, but 

allowing separate mean values at each PbB level. 

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

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

functions. However, each set of judgments was distinctly better fit by either the normal 

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

considered further for that set. 

As argued in Sec. 3.5, 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. For the 

equal-variance fits to be acceptable, the slopes of the transformed judgments must be 

about the same, which was not the case for the IQ decrement judgments. Although the 

fitted curves do cross, the distributions are spaced so far apart that the crossings occur 

only toward the extreme ends of the curves. It is far more important that the judgments 

are represented accurately within the ranges of interest. 

4.6 THE EXPERTS 

The individuals listed in Table 7 were selected in March of 1985 by OAQPS for 

participation in the risk assessment. All of them agreed to participate, with the 
33 

TABLE 7 Experts Participating in the IQ Encodings 

Expert Affiliation 

Kim Dietrich 

Claire Ernhart 

Herbert Needleman 

Michael Rutter 

Gerhard Winneke 

William Yule 

University of Cincinnati 

Cleveland Metropolitan 

General Hospital 

University of Pittsburgh 

Institute of Psychiatry, 

London, United Kingdom 

University of Dusseldorf, 

Dusseldorf, West Germany 

Institute of Psychiatry, 

London, United Kingdom 

understanding that their judgments would remain anonymous. The results presented are 

for Experts F through K, but the letter designations are randomly assigned. 

4.7 RESULTS 

in Sec. 4.7, the functions fit to each expert's probabilistic judgments are used to 

summarize the quantitative results. These functions accurately represent the underlying 

encoded values, both because the goodness of fit was excellent and because each expert 

endorsed the output of the respective functions as representing his or her judgments. 

Appendix C presents the detailed quantitative results, including encoded judgments, 

parameter values for fitted functions, goodness-of-fit measures, and derived probabilities 

about dose-response functions. Section C.4 summarizes the qualitative discussions held 

with the experts about the effects of lead on IQ and behavior. 

Recall that the experts were given the option of making separate judgments for 

low and high SES children. The low 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 high SES group. All of the experts, with the exception of Expert F, 

believe that at the doses under consideration, lead interacts with variables that 

contribute to SES level. Therefore, separate judgments were provided for the two SES 

levels by all experts except Expert F. 

Judgments about the mean IQ values of the low and high SES levels of the control 

group are presented simultaneously, as are the judgments about within-group standard 

deviations. However, judgments about mean IQ decrements are most easily understood if 
P.46 

34 

they are discussed separately for the two SES levels. Expert F's judgments will be 

repeated for comparison purposes. 

4.7.1 Control-Group Mean IQ 

Expert I was unable to provide judgments about the mean IQ of a group of 

children sheltered from lead exposure; the judgments .of the other experts are shown in 

Fig. 13. Expert F provided one set of judgments, reasoning that SES status was not a 

factor influencing these judgments. The symbol within each bar is the median judged 

value for mean IQ. In other words, there is a 0.50 probability that the control-group 

mean IQ would be above the indicated value and a 0.50 probability that it would be 

below. The horizontal brackets at the ends of the bars bound each expert's 90% CI, that 

is, the interval such that there is a 0.05 probability of the true mean IQ falling below it, 

a 0.90 probability of its falling within it, and a 0.05 probability of its falling above it. 

Experts G, H, and J show considerable agreement in their judgments regarding 

the mean IQ of the low SES group. Their median judgments range from about 95 to 97 

points. The upper ends of the 90%-CI bars range between 98 and 100 points. Expert K's 

median judgment is 85 points; the mean IQ is judged to exceed 90 points, with probability 

o 

IO 

115 n 

110-

105-

100-

95-

90-

85-

80 

T 

T 

I • I T 

t i t 

:

 l i 

—i 1 1 1 r 

F G H J K 

— Low SES — 

T 

I 

I T 

* A 1 I i 

—i 1 i 

F G H J K 

High SES — 

FIGURE 13 Median Values and 90% CIs for Functions Fit to Judgments about the Mean IQ of 

the Control Group, Experts F, G, H, J, and K 
35 

0.05. The judgments of these four experts regarding the high SES group overlap 

considerably. Their median judgments range from 103 to about 106 points. The upper 

ends of the 90% CIs range from 107 to 110 points. 

Expert F displays the least uncertainty, with judgments about the entire 

population falling as expected between those of the other experts for both low and high 

SES levels. Expert F's median judgment is 101 points; the true mean IQ is judged to 

exceed 102 points, with probability 0.05. 

4.7.2 Within-Group IQ Standard Deviation 

Expert I was. unable to provide judgments about this variable as well; the 

judgments of the remaining experts are shown in Fig. 14. Expert F was certain that the 

within-group IQ standard deviation would be 15 points. Considering each SES group to be 

somewhat more homogeneous than the overall population, Expert G was certain that the 

standard deviation would be 14 points in each case. 

The judgments of Experts H, J, and K are relatively similar. They estimated 

lower standard deviations for the low SES group because its IQs would be more 

homogeneous than those of the high SES group. The median standard deviation for the 

16-, 

15-

14-

i^ 

12-

11-

10 

T 

t 

I 

I 

1 

i i r 

F G H J K 

Low SES — 

i i i 

F G H 

—i r 

J K 

High SES — 

FIGURE 14 Median Values and 90%-CI Judgments about 0|Q, Experts F, G, H, J, and K 
P.48 

36 

low SES level was judged to be about 13 points in all cases; the largest upper limit of the 

90% CIs is about 14 points. Expert J gave the same judgments for both the low and high 

SES levels. Experts H and K estimated median values of approximately 14 points for the 

high SES level. The upper limits of their 90% CIs are about 15 points. 

4.7.3 Mean IQ Decrements for the Low SES Group 

Figure 15 summarizes the judgments of the experts regarding mean IQ 

decrements for the low SES group. The solid curves show the median judged IQ 

decrements for each PbB level. In other words, 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 dotted and dashed pairs of curves bound the 50% and 90% CIs, 

respectively. 

Figure 16 compares the judgments of the six experts. The vertical bars represent 

each expert's 90% CI; the symbols are his or her median judgments. The effects of lead 

on IQ are consistently judged to be less by Expert F than by the other experts. Expert F 

also evidences considerably less uncertainty about the magnitude of those effects 

compared with the other experts. Expert F is certain that there is no effect of lead on 

IQ up to at least 15 yg/dL. At 25 yg/dL, his or her median judged IQ decrement is about 

0.25 points; at 65 yg/dL, it increases to 1.7 points; According to Expert F, at 25 yg/dL, 

the IQ decrement exceeds approximately 0.5 points, with probability 0.05; at 65 yg/dL, i. 

exceeds 3.7 points, with the same probability. 

Similarities are evident in the judgments of the other experts, but small, 

consistent differences occur as well. Only Experts G, H, and J give any credence to IQ 

effects at PbB levels as low as 5 yg/dL; Experts I and K believe there are effects at 

levels as low as 15 yg/dL. The judgments of Experts H and J are consistently very close, 

as are those of Experts G, I, and K, which as a group are somewhat lower than those of 

Experts H and J. For the five sets of expert judgments (i.e., excluding Expert F), the 

median judged IQ decrement at 5 yg/dL ranges from 0 to 2.3 points; at 55 yg/dL, it 

ranges from about 6.7 to 11.1 points. According to the judgments of Experts G, H, and J, 

the 0.95 fractiles for IQ decrement range from 1.8 to 4.5 points at 5 yg/dL; according to 

the five experts, they range from 9.9 to 15.1 points at 55 yg/dL. 

4.7.4 Mean IQ Decrements for the High SES Group 

Figures 17 and 18 display the judgments about mean IQ decrement for the high 

SES group. As was true for the low SES population, the effect of lead on IQ is judged to 

be less by Expert F than by the other experts. At PbB levels of 25 yg/dL and above, the 

judgments of the others overlap, with those of Experts H and J again being very similar 

and somewhat greater than those of Experts G, K, and I, which are similar. Only Expert 

H gives any credence to the existence of an effect on IQ at 5 yg/dL; Experts G, I, and J 

do so at 15 yg/dL, and Experts F and K do so at 25 yg/dL. 

The median IQ decrement as judged by all the experts ranges from 0 to 2.4 points 

at 15 yg/dL and from 1.4 to 7.9 points at 55 yg/dL. According to Experts G, H, I, and J, 
37 

" "ffrTTT""' 

P.49 

4-i 

Expert F 

-•0.75 

Expert G 

16-, 

Expert H 

l -

9-

6-

3 1 

j 

Expert I 

• 

+ • 

• 

/ 

• / .• 

• .• 

** •*'* y^^ 

* ** ^y •*' f •* _^y . * * 

/ .* -/^ •* *» ^ / y'yy.y' ^<** 

* Sy\-- ** f ">* • ' ^ ^ 

TVC- ' *. "* 

>''"" 

1 1 1 1 1 

j 15 25 35 45 55 

15-i 

Expert J 

PbB Level Oug/dL) 

15-i 

12 

9-

6-

3-

Expert K 

—i 1 1 ; i r5 15 25 35 45 55 65 

PbB Level Oug/dL) 

FIGURE 15 Judgments about Lead-Induced IQ Decrements, Low SES 

Population, Experts F, G, H, I, J, and K (Ayx and PbB scales were 

selected to show the details of each expert's judgments) 

the 0.95 fractiles for IQ decrement range from 0.9 to 5.1 points at 15 yg/dL; according to 

all the experts, the 0.95 fractiles range from 3 to 9.5 points at 55 yg/dL, with probability 

0.05. 

4.7.5 Change in Percentage of Low SES Group with IQ < 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 
45-

4 0 -

3 5 -

&? 30 -

O 

QC 2 5 -

© 

V) 

C 20 

O 

Q. 

V) 

&

 1 5 

10-

IT 

111 i 

o 

u. 

•-i—I -

F 6 H 

T 

j t 

T it 

iiir 

i : 

r 6 M J K 

P4 

?

ii 

15-

e H J 

-25 -

T 

_ I 

u 

I 

T 

I 

I 

1* 

IT 

IT 

U 

IT 

I:-

ti i 

T 

. X 

T 

1 

T 

1 

S H 

- 3 5 

J K F C H 

45 

J K 6 H 

- 5 5 

J K F C H J K 

65 — 

PbB Level (.ug/dL) 

FIGURE 16 Comparison of Judgments about Lead-Induced IQ Decrements, Low SES 

Population, Experts F, G, H, I, J, and K 

assumption of within-group normal IQ distributions, to calculate probabilities about the 

lead-induced change in the percentage of the population with IQs below any critical 

level. These probabilities, which should correspond to judgments about IQ dose-response 

functions are response rates and are the results needed for further risk calculations. 

Here, we illustrate the results for a critical IQ of 85 points. Results for critical IQ 

values of 70 and 85 points are tabulated in App. C, Table C.8. Greater uncertainty is 

evident in these dose-response functions than in the separate judgments shown above, 

because the uncertainties surrounding three parameters are being combined. Calculations are not possible for Expert I, because that person declined to judge control-group 

mean IQ and within-group IQ standard deviation. 

Figures 19 and 20 show the calculated probabilities about the dose-response 

function for the percentage increase in IQs < 85 points in the low SES population. The 

curves are analogous to those in preceding figures. As expected, Expert F's judgments 

suggest much lower dose-response functions than those of the others. The results from 

Experts G, H, J, and K overlap considerably, with those from Experts H and J being very 

similar and slightly higher than those from Experts G and K, which are also similar. 

According to Expert F, the median 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; with the 
- 3 9 

P.51 

4 - i 

3-

J?>J 

1-

Expert F •0.95 

•0.75 

0 -I—//—i 1 1 1 r— 

5 25 35 45 55 65 

10 

8-

6-

4-

2-

Expert G 

— i 1 1 1 r~ 

5 15 25 35 45 55 

9-i 

6-

12 

< 

3-

Expert J 

—i 1 1 1 r— 

15 25 35 45 55 

PbB Level (/zg/dL) 

Expert K 

8-i 

6-

4 -

2 -

0-\-//—\ 1 1 1 r5 25 35 45 55 65 

PbB Level (/zg/dL) 

FIGURE 17 Judgments about Lead-Induced IQ Decrements, High 

SES Population, Experts F, G, H, I, J, and K (A— and PbB scales 

were selected to show the details of each expert's judgments) 
-FTI. »» » 

40 

P.52 

10-1 

8-

12 

< 

4 -

2-

0-+-

T 

• -O-r-O-A-VF • H I i t 

1 1 ! 

F • N I 

- 7 -

a J. 

I

-

I 1 

T 

l 

I 

I 

I 

I 

I 

I 

I 

I 

9 

I 

IT 

i 

ii 

IT 

II. 

* t H 

* T 

I i 

AT 

1 i "• 

I 

I 

IT 

T 

i 

1 

1 1 

F I N i I F • M I J K F S H I J I F • H I 

III I 

J « F t H I J K 

•15- 25 35 45 

PbB Level (/xg/dL) 

55 65 

FIGURE 18 Comparison of Judgments about Lead-Induced IQ Decrements, High SES 

Population, Experts F, G, H, I, J, and K 

same probability, it exceeds 7% at 65 yg/dL. For Experts G, H, and J, the median 

response rate is from 2.5% to 6% at 5 yg/dL; including K, it is between 21% and 32% at 

55 yg/dL. For Experts G, H, and J, the 0.95 fractiles (0.95 cumulative probability levels) 

for response rate range from about 5-11% at 5 yg/dL, 17-26% at 25 yg/dL, and 32-45% at 

55 yg/dL. 

4.7.6 Change in Percentage of High SES Group with IQ < 85 

The pattern of similarities and differences across experts is the same here as it 

was above, so corresponding figures are not shown. Generally, high SES children are less 

at risk than low SES children. The results for Expert F are the same as those shown 

previously, because they are based on the same judgments. According to Experts G, H, 

and J, the median response rate is from about 1% to 3% at 15 yg/dL, while according to 

Experts G, H, J, and K, it is from about 5% to 12% at 55 yg/dL. According to Experts G, 

H, and J, the 0.95 fractiles for response rate range from about 2% to 8% at 15 yg/dL, 4% 

to 11% at 25 yg/dL, and 16% to 18% at 55 yg/dL. 
41 

8-i 

9 H 

"5 

oc 

9 4-| 

V) 

c 

o 

S-

 2~l 

V) 

© 

Expert F 

• 0.95 Fractlle 

.-•0.75 Fractlle 

•0.50 Fraetil* 

...-0.25 Fraetil* 

0-\-//—p 

tjyy'l.- 0.05 Fraetil. 

T 1 1 1 -

5 25 35 45 55 65 

40-i Expert G Expert H 

© 

o 

ac 

9 

c 

o a 

tn 

9 

CC 

4 0 -

30-

20-

10-

I 

Expert J ,' * 

* • 

* • 

y y * 

y . ' / 

y •* y •* 

y.y.-'' 

y..<y.- * y..yy.- ,' yy- * 

"Z-" .-- ' „»•" 

i i i i i 

j 15 25 35 45 55 

40-i 

30-

20-

10-

Expert K 

PbB Level (/zg/dL) 

//- i 1 1 1 1 1— 

5 15 25 35 45 55 65 

PbB Level (jug/dL) 

FIGURE 19 Increased Probability of Having IQ < 85, Low SES 

Population, Experts F, G, H, J, and K (A-TQ and PbB scales 

were selected to show the details of each expert's judgments) 

4.8 DISCUSSION 

In view of the extensive debate concerning the effects of lead on IQ, the degree 

of consensus reflected in the study's results is notable, especially since the experts were 

selected so as to span the full range of opinion. As occurred with the Hb 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 differences are attributable to differing interpretations of, and extrapolations 

from, evidence. 
P.54 

15-

12-

12 

< 

9-

6-

3-

i 1 

T 

I * 

o-J-»-

M

1

; 

I T T T 

! • I : 

T i I* 

i l l 

42 

T 

• • 

i l l 

_ o 

• + . 

ill 

t 

ii 

ti 

T 

T 

i ii 

1 1 

F 8 H I j I F 8 H I J « f • H I J K 

i i . i i i i i i i i i i i 

FOMITI K F » H I J I F • M I J [ f 8 H I J K 

•15 25 35- 45- •55- •65-

PbB Level (/xg/dL) 

FIGURE 20 Comparison of Increased Probability of Having IQ < 85, Low SES Population, 

Experts F, G, H, J, and K 

Generally, Experts H and J provided similar judgments, as did Experts G, I, and 

K. 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 increasing PbB 

levels within the range of interest, as 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 being available at the high SES level or more uncertainty 

about the influence of covariates at the low SES level. 

The judgments regarding both mean IQ decrements and dose-response functions 

are of interest in their own rigiht. However, they will be combined in Sec. 5 with PbB 

distributions (which represent different levels of exposure) to yield risk distributions. 
43 

5 ESTIMATED RISKS OF ADVERSE HEALTH EFFECTS 

VERSUS GEOMETRIC MEAN PbB LEVEL 

Our strategy for assessing the risks of adverse health effects associated with any 

particular NAAQS scenario is to combine the dose-response function for a specified 

health effect with a PbB distribution estimated for the scenario (see Sec. 1.5). In the 

absence of any uncertainty, the calculation results in a number that represents the 

fraction of the population that would suffer the health effect under the particular 

scenario. In reality, however, the uncertainty present at each step must be incorporated 

into the analysis. Thus, the calculation produces a family of probability distributions 

from which values like those in Table 2 can be estimated. 

The estimated PbB distribution associated with a particular NAAQS will depend 

on numerous factors, including lead uptake from nonambient air sources, definition of the 

population at risk, and geographic distribution of the population with respect to point 

sources of lead. However, investigation of such factors is beyond the scope of the 

present work. To maximize the work's usefulness, risk estimates were derived for 

various specific PbB distributions. Given an exposure model that links alternative 

NAAQS to population PbB distributions, it will be straightforward to relate alternative 

NAAQS to overall risk measures. 

Appendix D presents the method and the necessary assumptions for deriving risk 

estimates given a particular PbB distribution and tabulates the results. Section 5.1 

explains and justifies the particular PbB distributions used. Sections 5.2-5.4, 

respectively, present estimates of the risks of adverse health effects involving EP, Hb, 

and IQ. Of particular interest are the most severe hea'th effect levels and the most 

sensitive populations. Thus, the main focus is on EP level > 53 yg/dL, Hb level < 9.5 g/dL 

among children aged 0-3, IQ decrement among low SES children, and response rate for IQ 

level < 70 among low SES children. Section 5.5 presents the results of the sensitivity 

analysis. 

5.1 ESTIMATED PbB DISTRIBUTIONS 

The 11 lognormal PbB distributions used assume the same geometric standard 

deviation (GSD) of 1.42 yg/dL, but differ in geometric mean (GM). The GM values 

increase in steps of 2.5 yg/dL from 2.5 yg/dL to 27.5 yg/dL. The lognormal form and the 

GSD value correspond fairly well to the actual PbB distributions among populations. The 

range of GM values used is broad enough to represent the effects of any air-lead scenario 

of interest to EPA. 

If other PbB distributions are assumed, then significantly different risk estimates 

may result. Complete listings of the dose-response uncertainties are provided in 

Apps. A-C; those who believe that a different PbB distribution is appropriate can use the 

method described in App. D to obtain additional risk estimates. 
P.56 

44 

5.2 OVERVIEW OF THE RISK RESULTS FOR EP 

As discussed in Sec. 2 and App. A, EP dose-response uncertainty was calculated 

from data published in Piomelli et al. (1982). Recall that two levels of EP were 

considered to be adverse to health: > 33 yg/dL and > 53 yg/dL. These levels are one and 

two standard deviations above tne "reference" EP level (21.7 yg/dL) measured in the 

group of children having the lowest PbB levels. The following discussion "focuses on the 

more severe of these two levels (> 53 yg/dL). 

To produce risk results for EP, the probabilistic dose-response functions were 

combined according to the method presented in App. D with the PbB distributions 

described in Sec. 5.1. Results for EP level > 53 yg/dL as a function of GM PbB values are 

summarized in Fig. 21. The risk estimate for each GM value is actually a probability 

distribution over a percentage of the population, but only the medians and the 90% CIs 

are shown. 

The EP response rate distributions are essentially the same for GM values 

< 10 yg/dL. At GM = 12.5 yg/dL, the median increases slightly. A larger increase in the 

35-i 

30-

25-

*? 

© 

"5 20-

OC 

© 

tn 

Q. 

tn 

© 

oc 

10 

5-

T 

1 

T 

i 

T 

i 

T 

i 

5 10 15 20 25 

Geometric Mean PbB Level (/zg/dL) 

- 1 

30 

FIGURE 21 Risk Results for the Occurrence of EP Level > 53 yg/dL 

(median values are indicated by circles and 90% CIs by bars 

extending above and below the median values) 
P.57 

45 ""• 

response rate occurs for GM values from 15 yg/dL to 17.5 yg/dL, a range that includes 

the threshold (PbB = 16.5 yg/dL) reported in Piomelli et al. (1982).* 

• As a point of reference, the median PbB is 15 for 2372 children aged six months 

to five years examined during the second NHANES II (Annest et al., 1982). At GM = 

15 yg/dL, the EP response rate distribution has a median value of 5.5% and a 90% CI of 

4.1-6.8%. 

5.3 OVERVIEW OF THE RISK RESULTS FOR Hb 

Recall from Sec. 3 that the probabilistic judgments of four experts regarding 

dose-response functions for lead-induced Hb decrements were obtained for two Hb levels 

(< 9.5 g/dL and < 11 g/dL). Functions that the experts agreed represented their 

judgments were combined with various PbB distributions to produce risk distributions. 

The method used was the same as that used for the EP risk distributions. 

Results of the calculations for Hb level < 9.5 g/dL for children aged 0-3 are 

summarized in Fig. 22. Median values of the risk distributions and the 90% CIs around 

those values are indicated for each GM PbB value, based on functions fit to the 

judgments of Experts A, C, D, and E. The 90%-CI bars are of various textures to help 

readers distinguish the results of individual experts. Results for six GM values that 

increase in steps of 5 yg/dL from 2.5 yg/dL to 27.5 yg/dL are shown for the four 

experts. Table D.2 gives the results for 11 GM values over the same range, but in steps 

of 2.5 yg/dL. 

Figure 22 shows that the Expert A risk distributions are zero for all GM values 

because Expert A judged that Hb level < 9.5 g/dL cannot be attributed to lead exposure. 

The Expert D risk distributions are nonzero at GM = 7.5 yg/dL, and the 90% CIs of the 

Expert D risk distributions overlap the 90% CIs for the Experts C and E at GM values > 

7.5 yg/dL. The 90% CIs for the Expert C and E risk distributions overlap for all GM 

values considered. The Expert E risk distributions exhibit the largest uncertainty, 

indicated by the comparatively long CIs, which increase in length as GM increases. 

5.4 OVERVIEW OF THE RISK RESULTS FOR IQ 

Judgments regarding IQ effects were obtained in a manner that allowed 

consideration from two perspectives. The first of these is mean IQ decrement 

•The greater sensitivity of heme synthesis to lead effects in the presence of iron 

deficiency was accounted for in this study by excluding the age group in which iron 

deficiency is most prevalent. Recent analyses (EPA, 1986c) indicate that more direct 

control for iron status results in different dose-response relationships for PbB and EP at 

different iron levels. 

The phrase "Expert A risk distributions" means the risk distributions based on the 

judgments of Expert A. 
P.58 

6O-1 

50-

fc* 40 -

"5 

ac 

© 30-

w 

c 

o 

Q . 

OT 

© 20-

10-

T 

T 

\\ ft 

T 

i 

a. 1 

-•—p -

A C D E 

5 

J . I il l ?! . 1 

i 

I i i 1 

-i—•—i—i—i—i—•— r 

ACO E ACO E 

15 

-•—I—I— i i 

ACO E 

-•— i 1—i—i—•— i 1— r 

A C D E ACD E 

— 25 35 — 

PbB Level (/xg/dL) 

•45 55 

FIGURE 22 Risk Results for the Occurrence of Hb Level < 9.5 g/dL among Children 

Aged 0-3 (median values are indicated by geometric symbols and 90% CIs by bars 

extending above and below the median values) 

(A-rrr). The second is more complicated, involving the lead-induced increase in the 

percentage of children having IQs below a specified critical level denoted by IQ*. (The 

details of these calculations are provided in App. C.) For both perspectives, the PbB 

level of interest was that measured at the 36th month of life; the IQ of interest was that 

measured on the seventh birthday. 

Judgments about dose-response functions were combined with PbB distributions 

to produce risk distributions for each of the IQ effects. Results for mean IQ decrement 

among low SES children (lowest 15% of the population, based on family income) are 

presented in Sec. 5.4.1. Complete results for low and high SES children are given in 

Table D.3. Section 5.4.2 presents results for an IQ* value of 70 for low SES children. 

This value corresponds to two standard deviations below 100. Other values of IQ* could 

have been used. Results for all four combinations of IQ* (70 and 85) and SES level (low 

and high) are given in Table D.4. 
47 

5.4.1 Risk Distributions over Mean IQ Decrement 

A risk distribution for mean IQ decrement is calculated by combining a PbB 

distribution with an individual's judgments about mean IQ decrements (relative to a 

control group of children sheltered from lead) at different PbB levels. Figure 23, which 

is based in part on functions fit to the judgments of Experts F through K, gives median 

values for mean IQ decrement and 90% CIs around those values for PbB distributions 

having GM values of 2.5-27.5 yg/dL (in steps of 5 yg/dL) and a GSD of 1.42 yg/dL. The 

90%-CI bars are of various textures to help readers distinguish the results of individual 

experts. 

At GM = 2.5 yg/dL, a mean IQ decrement of zero results for Experts F, I, and 

K. The Expert F risk estimates are nonzero for GM > 12.5 yg/dL, but are comparatively 

small, even at GM = 27.5 yg/dL. Over the entire range of GM values, the Expert I and K 

risk distributions are quite similar; the same is true for those of Experts H and J. Above 

GM = 7.5 yg/dL, the medians of the Expert G risk distributions are close to those of 

either Expert I or K. The 90% CIs for the Expert G risk distributions are generally larger 

(i.e., display more uncertainty) than those for the Expert I and K distributions. Above 

"1 

10-

«4 

£ « H 

4 - | 

2-

T 

T 

T 

I 

i ! T 

I 

I 

I 

! l 1 ii ! 1 1 

0-!-•--— 

F 6 H 

•D—r 

I J 

-•—r -

F 6 

5 I i I 

HIT 

i i 

T i ii 

i i 

If' 7 

i 

i i 

H I J X 

-•-T -

F 6 i K 

-f-rF 6 

T 

H I 4 t t Q H I J K r s 

i i i 

M I i 

2.5 •7.5- 12.5 •17.5 22.5 27.5 

Geometric Mean PbB Level (/xg/dL) 

FIGURE 23 Risk Results for Mean IQ Decrement in Low SES Children (median values 

indicated by geometric symbols and 90% CIs by bars extending above and below the 

median values) 

are 
48 

P.60 

GM = 7.5 yg/dL, all the 90% CIs overlap, except that for Expert F. The 90% CIs for the 

Expert H risk distributions are larger than those for the other experts at all GM values. 

5.4.2 Increased Probability of Lead-Induced IQ Levels Being £ IQ* 

The uncertainties in (1) mean IQ of children sheltered from lead, (2) within-group 

IQ standard deviation, and (3) mean IQ decrement at different PbB levels were combined 

to calculate the lead-induced increase in probability (expressed as a response rate, in 

percent) of children having IQs < IQ* for IQ* values of 70 and 85. These results were 

then combined with the PbB distributions described earlier. The resulting risk 

distributions are analogous to dose-response functions. 

Figure 24 shows the results for low SES children and IQ* = 70. As was true for 

IQ decrement, the Expert F risk distributions are different from those of all the other 

experts, except at GM = 2.5 yg/dL, where the Expert K risk distribution is also zero. At 

GM > 7.5 yg/dL, the 90% CIs for Experts G, H, J, and K overlap. The Expert K medians 

are larger than all others at GM > 12.5 yg/dL because Expert K judged the mean IQ levels 

TJ 

© 

w O © 

u 

o 

c 

12-i 

10-

8 -

6 -

O 

QC 

© 

in 

C 4 

O 

CL 

V) 

© 

OC 

2 

TT 

T 

4 

o-i-» 

F G 

1

 • I 

ii 1 i

1

? i ^ 

! f 

• l a 

1 il ! I" 

i i 

H J 

2.5-

- • i i i i i 

F G H J K 

••— i 1 1 rF G H J K 

-•— i —i—i—r -

F G H J K 

I 

IT 

I 

F G H J K 

•7.5 12.5— 17.5 — 

Geometric Mean PbB Level (/xg/dL) 

F G H J K 

— 22.5— —27.5 — 

FIGURE 24 Response Rates for IQ Level < 70 among Low SES Children (median values 

are indicated by geometric symbols and 90% CIs by ban extending above and below the 

median values) 
P.61 

49 

among low SES children sheltered from lead to be quite low (around 85). No estimates 

are given for Expert I because that individual did not provide the needed judgments about 

mean IQ levels for children sheltered from lead exposure or for IQ standard deviation. 

5.5 SBHSnTvTTY ANALYSIS 

Two sensitivity analyses were conducted to study the effects of (1) having doseresponse distributions on intervals smaller than 10 yg/dL and (2) changing the GSD value 

assumed for the PbB distributions. We considered the Hb risk assessment for the first 

sensitivity analysis and the EP, Hb, and IQ risk assessments for the second sensitivity 

analysis. 

We chose the Hb judgments for the first sensitivity analysis because the log-odds 

transformation resulted in functions with approximately equal slopes. This "common 

slope" allowed interpolation with a high degree of confidence between the probability 

distributions encoded for Experts C, D, and E. The IQ judgments were less suitable for 

this type of analysis because the slopes of the transformed distributions were not equal. 

Furthermore, we chose to consider children aged 0-3 because they are the most sensitive 

to lead exposure and their dose-response distributions display the largest variations, 

which tends to accentuate any sensitivities that may be present. 

Twenty-one dose-response distributions were specified for Experts C and E (six 

distributions on 10-yg/dL intervals were encoded) by plotting the median values of the 

transformed distributions versus the six PbB levels and drawing a smooth curve through 

the points. The smooth curve allowed estimation of median values in steps of 2.5 yg/dL 

from 5 yg/dL to 55 yg/dL. (Eighteen distributions were specified for Expert E because 

only five distributions, beginning at PbB = 15 yg/dL, were encoded in his case.) These 

values, along with the common slope value, completely specified the dose-response 

distributions. These distributions were then combined with PbB distributions in a fashion 

identical to that used to produce the results described in Sees. 5.2-5.4. 

For Experts C, D, and E, the risk distributions based on the larger number of PbB 

levels are virtually identical to those based on the smaller number of PbB levels. The 

differences between the two sets of calculations are very small, but systematic, for each 

expert. For Experts C and E, the risk distributions based on fewer PbB levels are about 

0.1% closer to the origin than are the corresponding risk distributions based on more PbB 

levels. In other words, the risk estimates we reported are slightly smaller than those 

that would have been produced by a finer-grained analysis. The opposite is the case for 

Expert Ds the risk distributions based on more PbB levels are about 0.2% closer to the 

origin. These results strongly indicate that encoding at only five or six PbB levels was 

adequate, at least for Hb effects. 

The second sensitivity analysis was simpler than the first. We repeated the risk 

calculations for EP, Hb, and IQ effects (performed assuming a GSD of 1.42 yg/dL for the 

PbB distribution) for two additional GSD values; 1.3 yg/dL and 1.5 yg/dL. The chosen 

values bound those reported in the literature and summarized in the CD for lead (EPA, 

1986a). Geometric standard deviation values for PbB distributions in populations of 

children are extensively discussed in the EPA staff paper that reviews NAAQS for lead 

(EPA, 1986b). The 1.42-g/dL value is reported in NHANES II (Annest et al., 1982). 

ma^__\__w^__\\\\\\\\\\^mmmMmm 
P.62 

For EP level 2 53 yg/dL, risk results are virtually unchanged at low (< 7.5 yg/dL) 

GM PbB values. Differences are greatest at GM = 15 yg/dL: results at GSD = 1.3 yg/dL 

are about 28% lower (i.e., a response rate of 4% versus 5.5%), and results at GSD ,= 

1.5 yg/dL are about 22% higher than those assuming GSD = 1.42 yg/dL. At GM = 

27.5 yg/dL, results for GSD values of 1.3 yg/dL and 1.5 yg/dL are within 11% of those 

assuming a GSD of 1.42 yg/dL. The threshold for lead-induced EP effects, which was 

calculated by Piomelli et al. (1982) to be at a PbB level of about 16.5 yg/dL, probably 

explains the observation that results are most sensitive to GM PbB values around 

15 yg/dL. 

Results for Experts C and E are virtually unaffected by the GSD value for Hb 

level < 9.5 yg/dL and children aged 0-3. For Expert D, differences in mean values of the 

risk distributions are about 10% for GM values > 15 yg/dL (e.g., median response rates at 

GM = 27.5 yg/dL are 4.6%, 5.3%, and 5.7% for GSD = 1.3, 1.42, and 1.5 yg/dL, 

respectively). The difference beginning at 15 yg/dL can probably be attributed to Expert 

D's judgment that a threshold exists for lead-induced Hb effects in the 15-25 yg/dL PbB 

range. 

For IQ decrement among low SES children, the different GSD values have 

essentially no effect on the risk distributions for any of the six IQ experts (Experts F 

through K). The differences are generally less than 0.1 mean IQ points. The same is true 

for the IQ response rate at IQ* = 70 and low SES children. Differences between GSD = 

1.42 yg/dL and the other two GSD levels are less than 0.2% (in terms of response rate) 

for Experts H, J, and K, and less than 0.1% for Expert G. Risk distributions for Expert F 

are unaffected. 
--•- — 5T"~ " * 

6 CONCLUDING REMARKS 

Formal risk assessments were conducted to aid the EPA Administrator in 

determining an adequate margin of safety for the current review of the NAAQS for 

lead. The risk assessments focus on three potentially adverse effects of exposure to lead 

in children from birth through the seventh birthday: EP elevation, Hb decrement, and IQ 

effect. The same general strategy was followed in all three cases: for two levels of 

each effect, probability distributions over population response rate were estimated at a 

series of PbB levels. These distributions were estimated from data for the EP 

assessment and from expert judgments for the Hb and IQ assessments. These estimates 

are of interest in their own right; however, they were also combined with PbB 

distributions to yield probability distributions over the estimated percentages of children 

experiencing the particular health effect. 

For each of two levels of EP elevation, the dose-response probability 

distributions were calculated directly from the data of a large study. Because 

appropriate data were unavailable for the Hb and IQ assessments, it was necessary to 

obtain probability judgments from experts. For each effect, a protocol was developed to 

standardize and document the procedures used to encode the judgmental probabilities. 

Dose-response probability judgments were obtained from four Hb experts. Five IQ 

experts provided probability judgments regarding expected IQ decrements caused by lead 

exposure, expected IQ in the absence of lead exposure, and within-group IQ variability; a 

sixth provided judgments with respect to the first variable only. Dose-response 

probability distributions over the occurrence of IQ levels below 70 and 85 points were 

calculated from the judgments of the first five IQ experts. For both Hb and IQ, the 

judgments of each person were treated and presented separately for all analyses. 

Additional analyses indicated the extent of agreement among experts. 

Probability distributions are presented in graphical and tabular form for expected 

lead-induced IQ decrement and for dose-response functions for two levels of each of the 

three effects. For Hb, judgments were obtained separately for children aged 0-3 and 

4-6. Judgments of three of the four experts display substantial agreement. For IQ, 

judgments were obtained separately for children of low and high SES groups. The 

judgments of one expert differed considerably from those of the other five, which are 

relatively similar but fall into two distinguishable groups. 

Blood-lead distributions are expressed as lognormal distributions with geometric 

means over a wide range and a geometric standard deviation of 1.42. Final risk 

estimates, therefore, are presented in terms of probability distributions over the 

percentage of children experiencing particular effects as a function of geometric mean 

PbB level. 
-wzr 

REFERENCES 

Annest, J.L., et al., Blood-Lead Levels for Persons 6 Months - 74 Years of Age: United 

States, 1976-80, U.S. Department of Health and Human Services, Advance Data from 

Vital and Health Statistics of the National Center for Health Statistics, No. 79 (May 12, 

1982). 

EPA, Air Quality Criteria for Lead, draft (1986a). For copies, contact Center for 

Environmental Research Information, USEPA/ORD Publications, 26 W. St. Clair, 

Cincinnati, Ohio 45268, (513) 569-7562. 

EPA, Review of the National Ambient Air Quality Standards for Lead: Assessment of 

Scientific and Technical Information, Office of Air Quality Planning and Standards, draft 

staff paper (1986b). For copies, contact Jeff Cohen, USEPA/OAQPS, MD-12, Research 

Triangle Park, N.C. 27711, (919) 541-5655. 

EPA, Lead Effects on Cardiovascular Function, Early Development, and Stature: An 

Addendum to US. EPA Air Quality Criteria for Lead (1986c). For copies, contact Center 

for Environmental Research Information, USEPA/ORD Publications, 26 W. St. Clair, 

Cincinnati, Ohio 45268, (513) 569-7562. 

Hammond, P., R. Bornschein, and P. Succop, Dose-Effect and Dose-Response 

Relationships of Blood Lead to Erythrocyte Protoporphyrin in Young Children, 

Environmental Research, 33:187-196 (1985). 

Kaufman, A.S., and J.E. Doppelt, Analyst's of WISC-R Standardization Data in Terms of 

the Stratification Variables, Child Development, 47(1):165-171 (1976). 

Piomelli, S., et al., Threshold for Lead Damage to Heme Synthesis in Urban Children, 

Proc. National Academy of Sciences (Medical Sciences), 79:3335-3339 (1982). 

Ruckleshaus, W.D., Risk in a Free Society, Risk Analysis, 4:157-162 (1984). 

Sattler, J.M., Assessment of Children's Intelligence and Special Abilities, 2nd Ed., Allyn 

and Bacon, Boston (1982). 

Schwartz, J., personal communication, U.S. Environmental Protection Agency, 

Washington, D.C. (1986). 

Seaman, C, personal communication, New York University Medical Center, New York 

(1985). 

Wallsten, T.S., and D.V. Budescu, Encoding Subjective Probabilities: A Psychological and 

Psychometric Review, Management Science, 29:151-173 (1983). 

Wallsten, T.S., B.H. Forsyth, and D.V. Budescu, Stability and Coherence of Health 

Experts? Upper and Lower Subjective Probabilities about Dose-Response Functions, 

Organizational Behavior and Human Performance, 31:277-302 (1983). 
53 

Whitfield, R.G., and T.S. Wallsten, Estimating Risks of Lead-Induced Hemoglobin 

Decrements under Conditions of Uncertainty: Methodology, Pilot Judgments, and 

Illustrative Calculations, Argonne National Laboratory Report ANL/EES-TM-276 (Sept. 

1984). 

Winkler, R.L., An Introduction to Bayesian Inference and Decision, Holt,. Rinehart and 

Winston, New York (1972). 

^m 
P.66 

55 

APPENDIX A 

FITTING FUNCTIONS TO DATA ON LEAD-INDUCED 

ELEVATED EP LEVELS 
T T 

APPENDIX A 

FITTING FUNCTIONS TO DATA ON LEAD-INDUCED 

ELEVATED EP LEVELS 

Section 2 discusses dose-response relationships between PbB and elevated EP 

levels. Because the data published in Piomelli et al. (1982)* are complete and reliable, 

probability encoding of expert judgments was unnecessary. These data (see Fig. 1), when 

combined with sample-size data for that study (see Table 3), are sufficient to develop the 

following expressions for the mean dose-response curves for the two EP levels (> 33 ug/dL 

and > 53 yg/dL) of interest. 

i10.7, for L < 16.4 yg/dL 

FP

 = \ -1 

(100* [0.103U - 16.4) - 1.24], for L > 16.4 yg/dL 

for EP > 33 yg/dL, and 

(2.4 , for L < 16.6 yg/dL 

REP = ) 100*"1

[0.103(L - 16.6) - 1.98], for L > 16.6 yg/dL 

for EP > 53 yg/dL, where: 

R = population response rate (percentage) of children having 

EP levels greater than or equal to the specified value, 

L = PbB level (yg/dL), and 

100«~ [•] = inverse of the cumulative distribution function (CDF) of a 

standardized normal random variable. 

The Piomelli et al. (1982) data indicate a threshold for EP effects at a PbB level of about 

16.5 yg/dL. (As discussed in Sec. 5.2, new analyses indicate a somewhat different doseresponse relationship when direct adjustments are made for iron status.) Further, 

response rates of 2.4% and 10.7% were found to be "natural frequencies" (response rates 

at PbB levels < 15.5 yg/dL) for the occurrence of EP levels > 53 yg/dL and > 33 yg/dL, 

respectively. 

Probability distributions over the population response rate determined for 10 

PbB-EP combinations are summarized in Table A.l. These distributions are either beta 

BtR ; - ( x . !),( „ - X - 1)1

 CR J U R ' 

•Piomelli, S., et al., Threshold for Lead Damage to Heme Synthesis in Urban Children, 

Proc. National Academy of Science (Medical Sciences), 79:3335-3339 (May 1982). 
TABLE A.1 Probability Distributions and Parameters for EP Levels among New York City Children 

PbB 

Level 

(yg/dL) 

2-17 

17-21 

21-31 

31-41 

41-98 

Functional 

Form 

Normal 

Normal 

Normal 

Normal 

Beta 

EP > 33 yg/dL 

Parameter 

E[R]a = 10.7 

E[R] = 14.9 

E[R] = 37.5 

E[R] = 76.1 

X = 42 

Values 

SD[R]b = 1.1 

SD[R] = 1.6 

SD[R] = 2.1 

SD[R] = 4.1 

N = 43 

Funct ional 

Form 

Normal 

Normal 

Normal 

Normal 

Beta 

EP > 53 yg/dL 

Parameter 

E(R] = 2.4 

E[RJ = 3.8 

EfR] = 14.6 

E[R] = 49.0 

X = 40 

Values 

SD(R] = 0.5 

SD[R] = 0.9 

SD[R] = 1.5 

SD[R) = 4.8 

N = 43 

o 

aE(R) denotes the expected value of R, in percent. . 

SD(R) denotes the standard deviation of R, in percent. 

Source: Data are from Piomelli et al. (1982). 
59 

or normal at each PbB level, where: 

N = number of children at a specific PbB level, 

X = number of children having EP levels > 33 yg/dL or > 53 yg/dL, and 

R' = 0.01R. 

The CDF B(R') for the beta distribution is 

R' 

B(R') = J B(R')dR' 

R=0 ° ° 

o 

• X C>"' 

The mean E[R] and standard deviation SD[R] of the beta distribution and, where 

appropriate, its normal approximation are 

„,„.!§!. [SJ-^i] 

For most PbB-EP combinations, the quantity NR'(1 - R') was large enough (> 5) to justify 

using the normal approximation. 
61 

APPENDIX B 

FITTING FUNCTIONS TO ENCODED JUDGMENTS 

RELATING TO LEAD-INDUCED Hb DECREMENT 

"1 
P.71 

63 

APPENDIX B 

FITTING FUNCTIONS TO ENCODED JUDGMENTS 

RELATING TO LEAD-INDUCED Hb DECREMENT 

Appendix B is organized as follows: Sec. B.l reproduces the protocol used for the 

Hb encoding sessions; Sec. B.2 details the mathematical formulations for the doseresponse models; Sec. B.3 tabulates encoded judgments, specifications for functions fit to 

those judgments, and CIs for encoded judgments and fitted functions; and Sec. B.4 

summarizes the discussions held with each of the experts. Because Hb experts are 

generally knowledgeable about EP, significant portions of these discussions focus on the 

significance of elevated EP levels, an additional topic of interest to EPA. 

B.1 Hb PROTOCOL 

B.l.l Introduction 

The U.S. Environmental Protection Agency is charged by the Clean Air Act with 

setting and revising 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 CDs. 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 CD 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 

the health risks associated with various potential standards will aid the EPA 

Administrator in selecting that standard which, in his or her 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 uncertain lead-exposure estimates, 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 probability estimates for 

dose response and exposure. 

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 
P.72 

64 

from the data to make the 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 CD, two populations have been identified as 

being most susceptible to the effects of lead intoxication. One is children from birth 

through the seventh birthday, and the other is pregnant women, or more precisely, the 

fetuses carried by 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.1.2 Lead-Induced Hb 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 Hb 

reduction in the population of U.S. children from birth 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. 

There are differences of opinion, of course, as to what degree of reduction in Hb 

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 Hb level 

considered to be adverse may be different for regulatory purposes than for clinical 

action. Since it is generally agreed for children that a Hb level of about 12 g/dL is 

normal and about 9 g/dL is anemic, we will specify two Hb levels in that interval, namely 

9.5 g/dL and 11 g/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. 

•In this report, we focus only on children aged 0-6. 
P.73 

65 

B.1.3 Population at Risk 

We are defining the most susceptible group as all United States children from 

birth' through their seventh birthdays. However, you may believe on various grounds that 

younger and older children in this group have different dose-response functions for leadinduced Hb reduction. If so, then we will elicit your judgments separately for age groups 

0-3 and 4-6. 

B.l.4 Exposure Conditions 

We will be asking your judgment about population response rates at various PbB 

levels. Assume that the PbB 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.1.5 Physiological Conditions 

Because the effect of lead on Hb 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 aged 0-3 than aged 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 also well established that EP level is positively correlated with PbB level. 

However, the correlation is not perfect, and there is a range of EP values at any given 

PbB level. You may believe that the effect of lead varies with EP level. If so, assume 

that EP is distributed at each PbB level as you believe it in fact is. 

B.1.6 Factors to Consider 

In order tb 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 Hb 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 Hb 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 
P.74 

effects of lead? EP level increases with iron deficiency, but it also increases with PbB 

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 PbB and Hb 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 

exposure and increased susceptibility? Are there other factors to consider in thinking 

about the dose-response functions for lead-induced Hb 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 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. 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 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. 
67 

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 personally significant. 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. 

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 that is consistent with one's beliefs and expectations, results are 

overgeneralized, and contradictory evidence is ignored or underestimated. 

B. 1.7.4 Relation between Event Importance and Probability 

Sometimes the importance of events, or their possible costs or benefits, 

influences judgments about the certainty of the events when, rationally, importance 

should not affect probability. In other words, one's attitudes toward 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; 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. 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. . 

B. 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. Do not 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 measurement, and 

subjective evaluation and interpretation. In addition, the farther 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 that 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. 
— • P.77 

69 

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 

an 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 0.005. 

B.l.8 Possible Adverse Health Effe.cts of Elevated EP Levels 

It seems well established that there is a positive dose-response relationship 

between PbB and 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 Hb/PbB 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 central nervous system (CNS) functions, 

2. Liver detoxification capabilities, or 

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 PbB 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 are 

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 CD 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 
P.78 

70 

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 PbB concentrations can be represented 

probabilistically, and 

2. Uncertainty about the PbB 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 PbB 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 

Hb response. 

Now, in order for us to determine your uncertainty about the percentages of the 

population that would be affected by given PbB levels, we must introduce a definition. 

Let C be the PbB concentration in question. 

Definition: R(C) is the percentage of the population for which a PbB level of C 

would cause the defined Hb health effect. 

Thus, R(C) is precisely the percent of the population that would show a response if the 

entire population had PbB 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 PbB 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: 

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)? 
P.79 

71 

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 on blue, or 

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 the first response. 

Other wheel settings will have a large enough relative area of blue that you will feel 

confident making the second response. 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 the third response. 

Once we have determined the point at which you are most comfortable with the 

third response, and still focusing on the given PbB concentration 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. 

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 

CD 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 PbB concentration necessary to produce the effect in a given percentage of 

the population r, if the entire population had the same PbB 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 PbB level that would cause the defined Hb health effect 

in R percent of the population. 
P.80 

_ , p j 

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, or 

3. You cannot judge either event as more probable than the other. 

After determining the wheel setting at which you feel most comfortable with the third 

response, 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. After basic definitions and the 

notation are introduced, the NOLO 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 NOLO distribution and for 

assessing the goodness of fit. The family of equal-variance NOLO distributions is 

presented next, along with methods for obtaining least-squares estimates of its 

parameters and assessing its goodness of fit. Although this family may sacrifice some 

goodness of fit to the judgments, it meets all the specified criteria. 

B.2.1 Definitions and Notation 

Readers are 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 fx(x)

 = judgmental probability density function 

(PDF) for X, and Fx(x) = judgmental CDF for X. By definition 

x 

FY(x) = J fv(x )dx 
P.81 

Thus, Fx ( x ) is the judgmental probability* that X is less than or equal to x. 

Furthermore, let y = E[X], or the expected value of X. Then 

x 

K = J"

 x

«

f Y( x

«

)dx

o - X o o 

—TM 

And, let o 2 = V[X], the variance of X. Then 

CD 

o

2

 = J (x - E[X]) 2f Y ( x )dx 

x

 J *• o ' X o o 

—°> 

The uncertain quantities of interest in this risk assessment are population 

response rates, denoted R, at each of several PbB levels, denoted L. During encoding 

sessions with the experts, judgments representing a CDF for a response rate R given a 

population PbB level L (i.e., judgments representing Fn n [R]) will be elicited for a 

number of PbB 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 PbB level of L, for a specific adverse health effect, population, and exposure 

conditions. 

As already discussed, calculating risk generally requires interpolation between 

assessed points. Such interpolation is best accomplished by fitting a function to the 

judged probabilities. 

B.2.2 NOLO Function 

Because probabilistic judgments about dose-response relationships generally form 

an S-shaped curve over the closed [0%, 100%] interval, they can be difficult to represent 

with closed-form mathematical functions. One function that is relatively easy to work 

with is the NOLO distribution, which is obtained by fitting a normal distribution to the 

natural log of the odds implied by the population response rates R. Thus 

x = Torn* °K

-

x K

- -

Y • ln(X) , — < Y < « 

where X is the odds variable and Y is the log-odds variable. The variable Y is assumed to 

be normally distributed with mean y and variance a . The degree to which this 

assumption is appropriate can be tested with each set of judgments. If Y is normally 

distributed, X is lognormally distributed. Although no closed-form expression is readily 

•All probabilities hereafter referred to are judgmental probabilities, even if they are not 

so specified. 
P.82 

available for the distribution on R, all probabilistic and statistical results of interest on 

R can be obtained through the distribution on Y since 

i 

FR(r) = pr[R < r] 

and 

- pr [l * Cr^)] 

fv(y) - rHi * yl 

" P' zs(y

-^ 

= • 

y - u. 

where pr[>] denotes probability, and Z is the unit normal random deviate for which *(Z) is 

extensively tabulated and available in computer libraries. Thus 

FR(r )

 " FX [TH 

• F, [«rH)] 

• F„ 

l

»(rH)" \ 

m {^ri\ - , 

Table B.l summarizes the quantities of interest for these variables. 

The parameters y and a 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 o 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 o, and 
T T 

TABLE B.1 Variables Pertaining to the NOLO Function 

Variable 

Quantity 

of Interest 

Defining Y = ln(X) X = eY = * D R =

 100X 

equations 

100 - R 1 • X 

2 2 

Distribution* N(y ,o ) A(y ,o ) 

y y y y 

y +o2/2 

Mean y„ y = e y y 

y x 

2 2 

2 2 

2y *o a 

A 

2 

y -o 

e y y 

100e

 y 

2 

y - o 

lOOe

 y y 

2 

y - o 

i • e y y 

Variance o o = e y yfe

 y - l) 

y x 

Median y 

Mode y 

aN(y ,o ) denotes the normal PDF and h[u ,o ) denotes the 

lognormal PDF. The PDF for R cannot be expressed in closed 

form. 

^lean and variance expressions for R are obtained using 

numerical methods. 

y is the y-intercept (i.e., value of y corresponding to z = 0 in the regression equation). 

Since m judgmental distributions are assessed, one for each PbB level j for j = 1, ..., m, 

there are m means (ui, •.. , 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 PbB level is 

given by the standard regression r statistic obtained by regressing the F^ on Fif where 

r • 1 -

•z.2 

n-i - z) 
and F- denotes the estimated F values (i.e., F^ = *((y£ - y)/o}), and by obtaining the 

r value of this regression. If the r value is sufficiently high, the NOLO distribution 

with parameters y: and o; describes the judgments well for lead level j. This 

distribution can then be used for interpolation. 

To summarize, formulas were presented for calculating the parameters of a 

NOLO distribution, which can be used to represent a judged probability distribution over 

a population response rate for a given PbB level. Goodness of fit is given by a regression 

r statistic. The NOLO variable and its PDF can be used to estimate judgmental 

probabilities for the response rate variable R and to estimate risk. 

B.2.3 Representing a Probabilistic Dose-Response Surface with a Family 

of Equal-Variance NOLO Distributions 

If the oj are approximately equal, it is desirable to set them equal to a single 

pooled value before proceeding further (i.e., set o; = op = o for all j). This step ensures 

that the fitted distributions for two different PbB levels never cross one another. 

(Crossed distributions would imply that exceeding a specified response rate is more 

probable at PbB level L, than at L,» where L« is greater than Lj.) A pooled estimate of 

o , denoted op, can be obtained by first subtracting the mean y • for each set of assessed 

points 

y

j»i

 = yj»i " U3' £or i * l' '"' n j an d

 J • It •••» • 

where n: is the number of assessed points for FR/L.

 an d vi i *s a n assesse d

 point on 

Fp/T,. The y'. . can then be used to calculate a mean (which should be very close to 

zerorand a variance (which will be the pooled, least-squares estimate o' ) by regressing 

P zi ; on y! .. The individual least-squares estimates of the means can be recalculated 

at each PbB level by finding the best-fitting line (in the least-squares sense) with a slope 

of l/o'. Under these conditions, the result is simply 

n. J 

JJ n. . . j i= l 

I y; ; 

= 1 J' 1 

The results of these last steps are denoted as y!, ... , y'. Goodness of fit^again can be 

obtained by regressing the recalculated estimates (which can be denoted as F! .) on the 

original F • j .

 J 'l 

If a functional relationship can be established between PbB levels and the y'., a 

judgmental PDF over R can be calculated for any PbB level, should that be necessary for 

interpolating between PbB levels. This continuum of density functions in essence is a 

probability surface over the dose-response plane. 

A PbB distribution can be combined with the dose-response curves to yield an 

estimate of the overall fraction of the population R suffering the adverse health effect. 

Such calculations result in the risk estimates summarized in Sec. 5 and described in 

detail in App. D. 
P.85 

77 

B.3 RESULTS 

Results are presented in three tables: Table B.2 presents the encoded judgments, 

Table B.3 summarizes the functions fit to the judgments, and Table B.4 compares the 

encoded judgments with the fitted functions. The tables are organized so that each 

expert/Hb-level/age-category combination is listed, beginning with Expert A and 

continuing alphabetically through Expert E. The tables are explained using .the judgments 

of Expert A as an example. 

Expert A chose to separate the population of U.S. children aged 0-6 into two 

subpopulations — children aged 0-3 and 4-6. This individual provided judgments only at 

the < 11 g/dL Hb level. Because his judgments indicated that the lead-induced Hb effect 

at PbB levels below 45 yg/dL is very small, it was unnecessary to obtain probabilistic 

judgments at the < 9.5-g/dL Hb level. 

Table B.2 gives the probabilistic judgments of Expert A regarding the occurrence 

of Hb level < 11 g/dL among U.S. children aged 0-3 and 4-6 at a series of PbB levels. The 

probability judgments are CDFs of judgmental probability; that is, for each PbB level L, 

the corresponding entries in the F column represent the judged probability that the true 

response rate R-p is less than or equal to the rate R shown in the R column. Expert A did 

not feel that there was a measurable, lead-induced Hb effect at PbB levels below 

45 yg/dL. The curves display a wider range of plausible population response rates at 

successively higher PbB levels, suggesting that Expert A is less certain about the actual 

response rates at higher PbB levels. The data do not indicate a threshold for an Hb 

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. The corresponding curves for the various PbB levels are 

guaranteed never to cross. They were obtained by fitting regression lines to the NOLO 

transformation of the judgments. It happens that this transformation leads to normal 

distributions, with a high degree of accuracy. These distributions are also convenient for 

subsequent analysis. The NOLO distributions are uniquely defined by the mean and 

variance of the underlying normal distributions and the transformation functions (see 

Sec. B.2). 

Table B.3 summarizes the relevant parameters for each of the conditional CDFs 

fit to the judgments of Expert A. Included in the table for each PbB 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 r2 values 

of regressions of the fitted functions on encoded judgments. In general, the r values are 

reassuringly high. 

Table B.4 summarizes and compares the probabilistic judgments and the fitted 

functions. The median is that population response rate that is exceeded with probability 

0.5. The 90% CI is a. set of population 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 

PbB levels of 55 yg/dL, the median encoded response rate is 9%, and the 90% CI is 

1-15%. In other words, with probability 0.05, the true response rate is less than or equal 

to 1% and with probability 0.05, it is greater than or equal to 15%. Parallel statements 
tOOtO^UON H 

OOOOOOO O 

....... . 

VOVOVOOOUI.*«M« — 

totoui m 

VO 

U l 

00 00 N | Ot U i * » N I > j o> i n t > U 

. . . . 

wn ui ui m 

9> 9 Ul ^ U U K> 

OOOOO O OOOOO O 000000 0 

vO VO 00 Ui O O VO SO -~l Oi O O to to - J m N> o o 

TO Vl Ul •— VO T4 u< J > 1— IO><U I W M H 

U U M M H 

m o m o u< 

oooo o 

K» K> •-• t-a •-• •-• 

m to 00 o» J> o 

ooooo o 

tSi I-. t-a t" 

H s j OJ K ) tO U l 

ooooo o 

Ot U l * > U M H 

U l 

ooooo o 

..... . 

vo vo - J Ui o o 

vO VO Ul M O 

vO •— 

K> t-a t-a t-a 

O NI *» t-. vo 00 Ui 

000000 0 

J> u> u> •-*»-• o 

. . . . 

Ul Ul Nl Ul 

ooooo o 

vO vO 00 Ul o o 

VO U l U l H 

Ui M to 00 o< u 

ooooo o 

VOVONIUI O to to vi Ui M O 

vO 00 M tO 00 ^-

VO 

vO tO NI Ul t— O tOtOt O OtUiN O tO to Ui Ul M o 

tO 00 t— O vO to •— U vO Ot 00 1— 

t—1 to 
Nl 

Ul 

(r W UMM H H 

omomomou i 

OOOOOOO O 

U l 

K> t-a t-a ,-. fa 

N> VO Ot Ut O N I JN 

O O O O O O O 

U l 

U l 

Ot U i NJ vO Ot U> t— 

O O O O O O O 

vOvONiOtUIJ>N> 0 

VO U l U l 

IO M •— I— 

m o ui o ui JN 

ooooo o 

VO 00 Ul JN l-a O 

00 Ul 

tOt O 0> t - U H O 

00 U l U l U l U l 

00 U l N> VO U l U l 

ooooo o 

t O Ot U l JN M O 

00 U l U l K) 

vo vo o> m J> H- o 

VO U l 0 0 U l 

OJ <r ui u M H 

ooooo o 

..... . 

t o t o vo U i JN O 

VO U l m 

o vo oo NI ot m 

ooooo o 

vo vO 00 U l O O 

VO U l U l t-a 

J r U U M M M H T 

o m o NI m o m 

o o o o o o o 

tO t o 00 U l U l O O 

t o 00 00 O 

VO t-a 
Ul 

Ul 

U M M H M 

U) Ui O Ot O 

oooo o 

U l 

M t-a t-a ¥-. 

Ul to Ot t— N I 

oooo o 

Ul H OOfft U 

oooo o 

U l 

Nl u> o 

Ul 

o o o 

tOMUIN O 

vo m m o VO I-, 

VO Nl Ul NJ O 

VO Ul Ul o 

VO •-

tO vl Ul M O 

vo m m o vo t— 

VO Ul o 

vO »-• 

vO 

o o 

. . 

vo Ul 

VO 

VO 

uiMOooo t 

oooo o 

M O 00 Ot JN 

oooo o 

00 Ot Ul M 

OOO O 

• - O O 

. . . 

Ul Ul O 

O 

U l 

O O O 

VO NI Ul M O 

to m m o 

tO t— 

JN JN U> N> M 

NI O O Ov UJ 

vo NI m M o 

vo ui m o 

vO t-' 

M M M »— t— 

VO Ot M vo NI 

vO NI Ul O 

VO Ul O 

VO t-a 

M M »— •-> t-a 

JN M 00 Ot Ul 

M 

t-a Nl 

to rn o 

VO O 

vO •— 

t-a t-a !-• 

Ul t-a t-a 

OOOO O oooo o oooo o 

oo 

oooo o 

UIMOtJNN ) »— O JN M 

. 

oo 

oooo o oooo o 

00 Nl Ul M I— 

N I Ul Ul M 

m ui 

Nl Ul JN M O 

m 

oooo o 

VO N I Ul M O 

m m m m 

• ot o oo 

o o o 

VO Nl Ul M O 

to m ui H 

JN O VO Nl 

Ul 

OOO O 

VO N I Ul M O VO N I Ui M O t o Nl Ul M O 

to ui m M torn m i— vo ui m H 

M 00 Nl Ul 

Ul 

OOO O 

tOUM H 

OOO O 

Ov M I— *-

OOO O 

vO NI Ul M O 

vO m Ul I-T 

vo m o VO t-a 

VO Nl Ul O 

VO Ul »-• 

to NJ m o 

vo Ui •-• 

tO Ul N> O 

tO Ul H 

VO Ul M O 

vO Ul •"
JN 

U l 

HHt O O (Mi l 

OOOOO O 

U l 

Ul 

M M »-* t-a 

Ot O U l O U l M 

OOOOO O 

M 

U i 

M K ) I— 

U1|->UIVON|JNU> 0 

U l U l 

OOOOOOO O 

ui vo ui •— NI u> o 

O O O O O O O 

to NI m NI o o 

tO U l Ot H 

M M * - HOt t-. Ot O Ot M 

ui m m m ui 

ooooo o 

t o 00 Ot JN t— o 

tO M U l 

">UNH H 

U l U l M Ot O Ot 

ooooo o 

vO N I u i M O O 

VO U l Ulvl H 

iji h3 H» t- t-a 

o ui o m o ui 

ooooo o 

VO 00 Ot JN t-. o 

vO U l U l 

vO 00 U i M O O 

oo t-. ov N I oo t-< 

UOOtU H 

U l 

oooo o 

vO 00 U l M I--

U l U l JN M 

U l M M HO U l O U l 00 JN 

ooooo o 

vo 00 U l M O O 

oo H ot vi oo H 

M I-T t-. !-• 

O Nl JN I— CD Ul 

ooooo o 

t o 00 U l M I-T o 

U l U l JN N l N l 

VOVONIUIMI-TO O 

vo ui ui u> H 

Ul O J> M 

VO VO 00 Ot Ul o o 

VO Ul I-T Ul H 

O Nl M I— 

OOO O 

VO vO m H-T 

tO Nl 

OOO O 

tO NI Ul I-T 

00 00 Ul 

M M I— t— 

00 Ui vO Ui tO Ot Ul 

O O O O O O O 

M M H* t-a !-• 

Ot M 00 JN O Ot Ul 

O O O O O O o 

Ui O Ul I— o 

oooo o 

. 9 . . . 

to to ui H o 

tO I-

to Ot •— o 

JN 

OOO O 

... . 

VO Nl Ul |-T 

00 00 U

KJ M I-T t-. 

JN O 0> K) 00 JN M 

O O O O O O O 

vO VO NI Ui M H- O 

VO Ul Ul t—• 

h3 t— t-a 

O Nl I-T 00 Ui 

oooo o 

vO vo Ul I1 O 

vO Ot Ot 

vo vO 00 Ov Ul I— o 

oo ui i— ui I-T 

at ui o NI JN t— 

ooooo o 

VO Nl Ul JN H-T O 

oo oo m NI m •— 

VO to 00 Ot Ul i— O 

0 0 U > I-T U l I-

JN i-- 00 Ui M 

oooo o 

VO Nl Ul JN I-

oo oo m N I u
P.90 

82 

TABLE B.2 (Cont'd) 

PbB 

Level 

(yg/dL) 

55 

0-

R 

5 

8 

22 

36 

AO 

A7 

Hb < 9 

-3 yr 

F 

0.01 

0.1 

0.5 

0.75 

0.9 

0.99 

Expe 

.5 g/dL 

AR 

6 

11 

15 

22 

26 

30 

-6 yr 

F 

0.05 

0.A 

0.5 

0.75 

0.9 

0.98 

rt E 

0-

R 

10 

20 

30 

AO 

50 

55 

Hb < 

•3 yr 

F 

0.01 

0.35 

0.5 

0.62 

0.9A 

0.99 

11 g/dL -

AR 

5 

10 

15 

20 

25 

30 

35 

•6 yr 

F 

0.01 

0.05 

0.A 

0.5 

0.75 

0.9 

0.98 

aR denotes population response rate (percentage having 

Hb levels < 9.5 g/dL or < 11 g/dL). 

bF denotes cumulative probability. 

could be made for the fitted functions. The encoded median values are fairly close to 

those of the fitted functions, differing by only 2-4%. However, the fitted functions 

exhibit more uncertainty than do the judgments. These features and differences were 

pointed out to Expert A, who finally concluded that the fitted functions better captured 

his best judgments about the effects of PbB on Hb levels among the two groups of U.S. 

children. 

B.4 DISCUSSION SUMMARIES CONCERNING ELEVATED EP AND Hb DECREMENTS 

The following summaries are based on notes taken during the interviews with the 

experts. At times, the points made are fragmentary and highly specialized. Each expert 

has had at least one opportunity to review his section. 

B.4.1 Expert A 

• There is absolutely no evidence that zinc protoporphyrin (ZPP) is 

toxic per se. 

• The biosynthesis of heme is regulated by a negative feedback 

process whose rate-limiting factors are heme, heme oxygenase, and 

6-aminolevulinic acid synthase (ALAS). The enzymes in the 
-gy 

TABLE B.3 Functions Fit to Judgments about Population Response Rates for 

Lead-Induced Hb Decrements 

P.91 

•- PbB 

Level 

(yg/dL) 

Expert A, 

A5 

55 

65 

75 

Expert A, 

55 

65 

75 

Expert C, 

5 

. 15 

25 

35 

A5 

55 

Expert C, 

5 

15 

25 

35 

A5 

55 

Functional 

Hi 

Hb 

Hb 

Hb 

Form 

< ii 

NOLO 

NOLO 

NOLO 

NOLO 

< 11 

NOLO 

NOLO 

NOLO 

< 9.5 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

< ii 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

g/dL, 

9/dL, 

Defini 

Paramet 

uy 

Ages 0-3 

-3.35A6 

-2.9338 

-2.072A 

-1.575A 

Ages 4-6 

-3.6826 

-2.2713 

-2.0617 

• g/dL, Ages 0-

9/dL, 

-3.9995 

-3.AA81 

-3.1298 

-2.9187 

-2.7A2A 

-2.5781 

Ages 0-6 

-3.6826 

-2.2713 

-2.0617 

-1.6965 

-1.3190 

-1.0A98 

ng 

ersa 

°y 

0.6820 

0.6820 

0.6820 

0.6820 

0.59A5 

0.5945 

0.59A5 

6 

0.2764 

0.276A 

0.276A 

0.276A 

0.2764 

0.2764 

0.2720 

0.2720 

0.2720 

0.2720 

0.2720 

0.2720 

Measures of 

Distrib 

over 

E[RHb] 

A.l 

6.0 

12.8 

19.0 

2.8 

10.5 

12.5 

1.8 

3.2 

4.3 

5.2 

6.2 

7.2 

2.5 

9.5 

11.5 

15.7 

21.3 

26.1 

ution 

R

b 

SD(RHb] 

2.5 

3.7 

7.1 

9.6 

1.6 

5.3 

6.1 

0.5 

0.9 

1.2 

1.4 

1.7 

1.9 

0.7 

2.4 

2.9 

3.8 

4.8 

5.6 

t^2 for 

Regression 

of F on F 

0.89 

0.84 

0.93 

0.94 

0.97 

0.90 

0.95 

0.98 

0.99 

0.99 

0.99 

0.99 

0.97 

0.97 

0.90 

0.95 

0.99 

0.97 

0.98 
m JN 

m m 

5S SS 

o o 

r* r* 

o o 

i i 

t-. M 

. . 

oo o 

u i t o 

N | v o 

U l U l 

o o 

. . I-T I-* 

N l N l 

N l N l 

N l N l 

u> 

m 

5S 

O 

ro 

i 

M 

. M 

J N 

J N 

O t 

o 

. t - . 

N l 

N | 

N | 

M 

U l 

ss 

o 

r* 

o 

i 

M 

. U l 

o 

J N 

VO 

o 

. I - T 

N | 

N l 

N l 

I - T 

U l 

ss 

o 

f 

o 

1 

U l 

• 

J N 

0 0 

Ov 

Ov 

o 

• J N 

oo 

VO 

J N 

U l 

9S 

o 

r* 

o 

i 

U l 

. 

0 0 

N l 

U l 

vo 

o 

• J > 

oo 

vO 

J N 

sr 

T J ert D, Hb I A 

K T 

K I 

vq 

ft 

4. 

<o 

ro 

in 

T U 

1 

Ch 

U l 

U l 

SB 

O 

t -

o 

1 

o 

N l 

M 

U l 

JN 

o 

• JN 

VO 

1— 

VO 

J N 

U l 

z 

O 

r« 

o 

i 

I - T 

M 

J* 

0 0 

U l 

o 

• 

JN 

vO 

•— 

VO 

u> 

U l 

ss 

o 

co 

1 

I - T 

J N 

a t 

U l 

U l 

o 

• J N 

VO 

t--

VO 

M 

U l 

as 

o 

f 

o 

1 

I—T 

N l 

J N 

J> 

I s ) 

o 

• J N 

VO 

H-r 

VO 

I - T 

m 

SS 

o 

f 

o 

i 

M 

N l 

o 

v O 

N l 

o 

• J N 

v O 

t—a 

VO 

U l 

5 

o 

r* 

o 

i 

U l 

I — I 

N l 

J N 

N l 

o 

• J N 

vo 

1—I 

v O 

s? er•o 

t D, Hb I A 

1-4 

fr~ 

VQ 

ft 

•* 

i> 

VQ 

ro 

CO 

o 

i 

U l 

U l 

U l 

SS 

o 

f 

o 

1 

M 

. M 

J N 

U l 

U l 

o 

. M 

K - T 

N | 

N | 

J N 

U l 

X 

o 

f 

o 

1 

M 

. U l 

1—I 

M 

U l 

O 

. M 

l - T 

N | 

N l 

U l 

U l 

X 

O 

t -

o 

1 

U l 

. 

o 

J N 

J N 

U l 

o 

• M 

• - T 

N | 

N l 

M 

U l 

X 

o 

r* 

o 

i 

Ov 

• 

J N 

Ov 

O 

J N 

1 — 

. O 

J N 

o 

VO 

s ert •o D, Hb I A 

VO 

U l 

•Q 

\ 

ft 

N 

*» 

VQ 

01 

in 

aU 

1 

Ot 

W*«UN H 

m m ui ui m 

U l O v O N I U l M 

..... . 

U i t O O t O t U > M 

K> M I-T I-T I-T H-T 

..... . 

JN o oo JN m o 

U l M I- * t— 

U l U l VO U l O t J N 

M U l 0 0 0 0 0 0 J N 

O 0 0 N I o v U l M 

Ov J N U l U > O O 

v O N I J N O 

... . 

N I Ov O t U l 

M H - I- T O 

... . 

t— N l O U l 

X X X X X 

oooo o 

f f f f f 

oooo o 

I I I I I 

I - T !- • M U l J N 

J N N l J N 0 0 U l 

O N l VO N l Crr 

to Ov vo ui v.-

v l V D H I O M 

OOOO O 

.... . 

U l U l U J U l U l 

ui m m m m 

m m U l U l U l 

O J N N l M H -

HtOtOH H 

U i J N M O O 

N I m O t N I J N 

ooooo o 

VO v o v O 

N I J N N | 

t O t O t o 

Ov VO J N 

ooooo o 

vO vO v O v o vO v O 

N I t o N I N I O t U l 

o o o o 

v o v O v o 0 0 

0 0 J N U l J N 

oooo o 

t o VO t O 0 0 t O 

t O N I 0 0 J N t O 
P.93 

85' 

TABLE B.3 (Cont'd) 

• 

PbB 

••Level 

(yg/dL) 

Expert E, 

5 

15 

25 

35 

45 

55 

Function! 

Hb 

Form 

< 9.5 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

Defining 

Parameters 

il 

uy 

g/dL, Ages 0-

-3.7820 

-2.7992 

-2.4725 

-1.9602 

-1.5643 

-1.4002 

°y 

•3 

0.9600 

0.9600 

0.9600 

0.9600 

0.9600 

0.9600 

Measures of 

Distribution 

over 

E[RHb] 

3.3 

8.1 

10.6 

15.8 

21.0 

23.4 

• R 

SD[RHb] 

3.3 

7.2 

8.9 

12.0 

14.5 

15.5 

r

2 for 

Regression 

of F on F 

0.98 

0.96 

0.96 

0.96 

0.99 

0.99 

Expert E, Hb < 9.5 g/dL, Ages 4-6 

5 

15 

25 

35 

45 

55 

Expert E, 

5 

15 

25 

35 

45 

55 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

Hb < 11 g/dL 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

-4.1623 

-3.6856 

-3.3376 

-3.0218 

-2.1141 

-1.9121 

, Ages 0-3 

-2.3463 

-2.1130 

-1.9311 

-1.6552 

-1.3014 

-0.9199 

0.8224 

0.8224 

0.8224 

0.8224 

0.8224 

0.8224 

0.5991 

0.5991 

0.5991 

0.5991 

0.5991 

0.5991 

2.1 

3.3 

4.6 

6.1 

13.2 

15.5 

9.9 

12.1 

14.1 

17.6 

23.0 

29.9 

1.8 

2.8 

3.7 

4.8 

9.2 

10.3 

5.3 

6.3 

7.1 

8.4 

10.1 

11.8 

0.98 

0.99 

0.98 

0.95 

0.98 

0.93 

0.98 

0.99 

0.98 

0.95 

0.98 

0.93 

Expert E, Hb < 11 g/dL, Ages 4-6 

5 NOLO 

15 NOLO 

25 NOLO 

35 NOLO 

45 NOLO 

55 NOLO 

aY = ln[R/(l - R)] 

deviation o„. 

-2.8545 

-2.6381 

-2.2151 

-1.9784 

-1.7096 

-1.5286 

is normally 

0.5912 

0.5912 

0.5912 

0.5912 

0.5912 

0.5912 

distributed 

6.3 

7.6 

11.1 

13.5 

16.8 

19.4 

with 

3.5 

4.2 

5.8 

6.8 

8.1 

8.9 

mean y and 

0.90 

0.95 

0.97 

0.94 

0.97 

0.98 

standard 

Using y 

y . 

and numerical methods, values can be calculated for 

the mean E[R] and the standard deviation SD[R] of the responserate distribution (which is NOLO) over R. R is expressed as a 

percentage. 
P.94 

86 

TABLE B.4 Comparison of Judgments and Fitted Functions 

Concerning Population Response Rates for Lead-Induced Hb 

Decrements 

Response Rate8 at PbB Level j_ 

Index 45 yg/dL 55 yg/dL 65 yg/dL 75 yg/dL 

Expert A, Hb < 11 g/dL, Ages 0-3 

Encoded Judgments 

Median 

502 CIb 

902 CI 

5 

2, 7 

1, 9 

tted Functions 

Median 

502 CI 

902 CI 

982 CI 

3 

2, 5 

1, 10 

1, 15 

9 

A, 13 

1, 15 

5 

3, 8 

2, 14 

1, 21 

14 

9, 18 

A, 21 

11 

7, 17 

A, 28 

3, 38 

20 

11, 31 

5, 35 

17 

12, 25 

6, 39 

A, 50 

Expert A, Hb < 11 g/dL, Ages 4-6 

Encoded Judgments 

Median 

502 CI 

902 CI 

Fitted Functions 

Median 

502 CI 

902 CI 

982 CI 

3 

2, A 

1, 6 

2 

2, 4 

1, 6 

1, 9 

11 

6, 16 

3, 18 

9 

6, 13 

A, 22 

3, 29 

15 

8, 19 

A, 2A 

11 

8, 16 

5, 25 

3, 3A 
"W 

TABLE B.4 (Cont'd) 

Response Rate at PbB Level 

Index 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL A5 yg/dL 55 yg/dL 

Expert C, Hb < 9.5 g/dL, Ages 0-6 

Encoded Judgments 

Median 

502 CI 

902 CI 

2 

1, 3 

1, A 

3 

2, A 

2, 5 

A 

A, 5 

3, 6 

5 

A, 6 

A, 7 

6 

5, 7 

5, 8 

7 

6, 8 

6, 9 

Fitted Functions 

Median 

502 CI 

902 CI 

982 CI 

2 

1, 2 

1, 3 

1, A 

3 

3, A 

2, 5 

2, 6 

A 

A, 5 

3, 6 

2, 8 

5 

A, 6 

3, 8 

3, 9 

6 

5, 7 

A, 9 

3, 11 

7 

6, 8 

5, 11 

A, 13 

Expert C, Hb < 11 g/dL, Ages 0-6 

Encoded Judgments 

Median 

502 CI 

902 CI 

8 

6, 10 

3, 10 

9 

8, 12 

5, 13 

12 

10, IA 

7, 15 

16 

IA, 19 

11, 20 

20 

17, 26 

15, 27 

27 

2A, 29 

18, 31 

Fitted Functions 

Med] 

502 

902 

982 

Lan 

CI 

CI 

CI 

6, 

5, 

A, 

1 

9 

11 

13 

10 

8, 

6, 

5, 

11 

IA 

17 

12 

10, 

8, 

6, 

IA 

17 

20 

15 

13, 

10, 

9, 

18 

22 

26 

21 

18, 

15, 

12, 

2A 

29 

33 

26 

23, 

18, 

16, 

30 

35 

40 
TABLE B.4 (Cont'd) 

Response Rate at PbB Level 

P.96 

Index 5 yg/dL 15 yg7dL 25 yg/dL 35 yg/dL A5 yg/dL 55 yg/dL 

Expert D, Hb < 9.5 g/dL, Ages 0-3 

Encoded Judgments 

Median 

502 CI 

902 CI 

Fitted Functions 

Median 

502 CI 

902 CI 

982 CI 

Expert D, Hb < 9.5, Ages 4-6 

Encoded Judgments 

Median 

502 CI 

902 CI 

Fitted Functions 

Median 

502 CI 

902 CI 

982 CI 

1 

c, 2 

c, 3 

1 

1, 1 

1, 2 

0, 2 

3 

2, 5 

1, 7 

2 

2, 3 

1, A 

1, A 

8 

6, 11 

A, IA 

8 

6, 9 

A, 13 

3, 16 

16 

11, 19 

8, 2A 

IA 

12, 18 

9, 23 

7, 28 

20 

16, 25 

11, 31 

20 

16, 24 

12, 30 

12, 36 

0.5 

0, 1 

0, 1 

0.2 

0, 0 

0, 1 

0, 2 

5 

3, 6 

2, 8 

5 

A, 5 

3, 6 

3, 7 

8 

6, 10 

A, 12 

7 

7, 9 

5, 10 

5, 12 

10 

8', 11 

6, 14 

10 

8, 11 

7, 13 

6, 15 
TABLE B.4 (Cont'd) 

Response Rate at PbB Level 

Index 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL A5 yg/dL 55 yg/dL 

• L • • • IH-1-MI I •! • I • — ^ HI ! • • 11 I •! I I I II I !• II III • I • • • '• • •' " _ ••••••••--lll l 

Expert D, Hb < 11 g/dL, Ages 0-3 

Encoded Judgments 

Median 

502 CI 

902 CI 

A 

2, 10 

1, 3 

6 

A, 12 

2, 15 

15 

11, 18 

11, 21 

18 

16, 22 

IA, 26 

22 

19, 26 

17, 29 

30 

26, 40 

21, 52 

Fitted Functions 

Median 

502 CI 

902 CI 

982 CI 

4 

3, 6 

2, 9 

1, 12 

6 

5, 8 

3, 13 

2, 17 

15 

11, 20 

7, 28 

5, 35 

19 

14, 24 

9, 34 

7, 42 

22 

17, 29 

11, 39 

8, 47 

33 

26, 40 

18, 52 

13, 60 

Expert D, Hb < 11 g/dL, Ages 4-6 

Encoded Judgments 

Median 

502 CI 

902 CI 

2 

1, A 

1, 6 

3 

2, 6 

1, 9 

7 

6, 9 

5, 11 

9 

8, 11 

7, 13 

10 

9, 13 

8, 16 

14 

12, 16 

10, 17 

Fitted Functions 

Median 

502 CI 

902 CI 

982 CI 

2 

1, 3 

1, A 

1, 6 

3 

2, A 

1, 6 

1. 9 

8 

7, 8 

6, 10 

5, 11 

10 

9, 11 

7, 12 

7, IA 

11 

10, 12 

8, 14 

7, 16 

14 

12, 15 

10, 17 

9, 19 
^__ _ P.98 

TABLE B.4 Cont'd) 

Response Rate at PbB Level 

Index 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Expert E, Hb < 9.5 g/dL, Ages 0-3 

Encoded Judgments 

Median 

502 CI 

902 CI 

3 

2, 7 

1, 12 

tted Functions 

Median 

502 CI 

902 CI 

982 CI 

2 

1, 4 

0, 10 

0, 18 

7 

5, 13 

3, 21 

6 

3, 10 

1, 23 

1, 36 

9 

6, 15 

3, 23 

8 

4, 14 

2, 29 

1, 44 

14 

9, 19 

4, 24 

12 

7, 21 

3, 41 

1, 57 

19 

11, 31 

5, 39 

17 

10, 29 

4, 50 

2, 66 

22 

13, 36 

6, 44 

20 

11, 32 

5, 54 

3, 70 

Expert E, Hb < 9.5 g/dL, Ages 4-6 

Encoded Judgments 

Median 

502 CI 

902 CI 

1 

1, 5 

0, 9 

tted Functions 

Median 

502 CI 

902 CI 

982 CI 

1.5 

1, 3 

0, 6 

0, 10 

2 

1, 6 

0, 10 

2.4 

1, 4 

1, 9 

0, 15 

4 

1, 7 

0, 11 

3.4 

2, 6 

1, 12 

1, 19 

6 

3, 9 

1, 13 

5 

3, 8 

1, 16 

1. 25 

13 

8, 20 

3, 25 

11 

7, 17 

3, 32 

2, 45 

15 

9, 22 

6, 29 

13 

8, 21 

4, 36 

2, 50 
TABLE B.4 (Cont'd) 

Response Rate at PbB Level 

Index 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Expert E, Hb < 11 g/dL, Ages 0-3 

Encoded Judgments 

Median 

502 CI 

902 CI 

8 

5, 14 

3, 22 

10 

7, 16 

4, 24 

15 

9, 19 

5, 26 

Fitted Functions 

Median 

502 CI 

902 CI 

982 CI 

9 

6, 13 

3, 20 

2, 28 

11 

7, 15 

4, 24 

3, 33 

13 

9, 18 

5, 28 

3, 37 

19 

14, 24 

6, 28 

16 

11, 22 

7, 34 

5, 44 

Expert E, Hb < 11 g/dL, Ages 4-6 

Encoded Judgments 

Fitted Functions 

22 

16, 35 

9, 43 

30 

17, 44 

11, 51 

21 

15, 29 

9, 42 

6, 52 

28 

21, 37 

13, 52 

9, 62 

Median 

502 CI 

902 CI 

6 

3, 10 

1, 14 

8 

5, 12 

2, 16 

11 

9, 15 

4, 19 

13 

10, 16 

4, 20 

16 

12, 24 

6, 29 

20 

13, 25 

10, 33 

Median 

502 

902 

982 

CI 

CI 

CI 

< 

4, 

2, 

1, 

8 

13 

19 

5, 

3, 

2, 

7 

10 

16 

22 

10 

7, 

4, 

3, 

14 

22 

30 

12 

8, 

5, 

3, 

17 

27 

35 

15 

11, 

6, 

4, 

21 

32 

42 

18 

13, 

8, 

5, 

24 

36 

46 

aThe response rate is expressed as a percentage. 

CI denotes credible interval. 

cLower CI limits could not be calculated because Expert D did not make 

probability judgments on response rate values less than the median at this 

PbB level. 
P.100. 

92 

pathway from 6-aminolevulinic acid dehydrase (ALAD) to 

ferrochelatase are present in substantial excess. There is normally 

a substantial excess of these intermediary enzymes. For example, 

there is 16 times as much ALAD as is necessary to metabolize the 

amount of ALA produced by ALAS. Overall, for every 10,000 

molecules of heme produced, the equivalent of one molecule is lost 

as ALA, coproporphyrin, and protoporphyrin. 

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, increased free EP 

(FEP) levels are observed to 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. 

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 cell function, and lead 

inhibits heme synthesis in most cells of the body, including those in 

the liver, kidney, and brain. The heme enzymes in these cells may 

have very short half-lives. These enzymes are probably quite 

important in studying the effects of lead. One of these is the P-450 

family of enzymes. In the liver, they are essential in the 

metabolism of drugs. Also of concern is the activation rate of an 

enzyme in the kidney, which may be inhibited to a harmful level by 

lead. 

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 the PbB 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 it may be related to an effect of lead on the production of 

P-450 enzymes in the 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. 

A new disease related to the virtual absence of ALAD has been 

described. A genetic disorder, it is transmitted as a recessive 

trait. The people affected have symptoms similar to those 

associated with acute intermittent porphyria, another genetic 

disorder of porphyrin metabolism. It is extremely doubtful that this 

disease has anything to do with low-level lead exposure, although at 

high PbB levels (70-80 yg/dL and higher), it is possible that lead 

inhibits ALAD to the same extent as found in this new disease. In 
p.1 

93 

this new disease, ALAD activities are about 1% of normal. 

Furthermore, people with ALAD levels at about 20% of normal have 

been identified, and these people are healthy and without any 

symptoms whatsoever. 

Clinically speaking, children with PbB levels about 40 pg/dL, 

elevated EP levels, and other evidence of iron deficiency can be 

treated with iron, and this anemia or iron deficiency can be 

corrected, even though no specific treatment for lead is given. The 

symptoms associated with anemia would be the same, regardless of 

whether the cause was lead exposure or iron deficiency. However, 

iron deficiency increases the absorption of lead from the gut. 

Another possible effect involves tryptophan pyrrolase, which is a 

heme-dependent enzyme in the liver. It has been postulated that 

the reduced level of heme in porphyria may be responsible for some 

of the symptoms seen in acute intermittent porphyria (Litman and 

Correia, 1983). 

Regarding the possible effects of ALA itself, effects are not likely 

because ALA does not readily cross the blood-brain barrier. 

Bull et al. (1983) have found delay of myelinization of the nerve 

sheaths in the brain in conjunction with PbB levels 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 

the delay in mylenization. 

Patients with sickle-cell anemia appear to be more susceptible to 

the toxic effects of lead, although the mechanisms responsible are 

not understood. 

In general, evidence seems to be good that an elevated EP level 

indicates an increased risk of adverse health effects. It seems to be 

a good indicator of both iron deficiency and lead exposure. The EP 

level is useful for monitoring long-term exposure. 

Epidemiological studies should be based on data acquired by 

extraction techniques rather than by the hematofluorometer. 

Extraction techniques are used to calibrate hematofluorometers. 

Data show that hematofluorometers give readings that are 

systematically low; therefore, it would appear that they should be 

recalibrated at the factory every three months or so. The technical 

difficulties with the hematofluorometer have not yet been resolved. 
_ .._ __P.2_ 

94 

B.4.2 Expert B 

• A child with a high PbB level and no reduction in Hb level can die of 

neurological toxicity. Thus, Hb level is not a very useful index for 

the adverse health effects of lead, at least from a clinical point of 

view. 

• Neurological and behavioral effects (e.g., aggression and 

hyperactivity) occur much more quickly in children than hematological effects, and at much lower PbB levels (about 40 ug/dL). 

• The body can compensate for reduced Hb. Oxygen begins to be 

transported other ways, offsetting to some degree the possible 

adverse effects of reduced Hb. 

• Anemia only becomes a problem when the body's ability to 

compensate is lost. 

• Damage to the heme synthetic pathway is crucial, but this damage 

cannot be attributed to reduced Hb. The inhibition of heme 

synthesis has broad implications for a variety of organs and systems, 

especially in the developing child. Beside its role in the 

erythropoetic system in forming Hb, heme is active in liver 

function, vitamin D metabolism, and the CNS, all of which are 

affected by low-level exposure to lead. 

• A rough dose-effect relationship between PbB and Hb levels was 

expressed — one for iron-deficient children and one for nonirondeficient children. Expert B estimated that, on the average, 

noniron-deficient children with PbB levels of about 10 ug/dL and 

50 ug/dL would have Hb levels of about 12 g/dL and 10.5 g/dL, 

respectively. For iron-deficient children, he estimated Hb levels of 

10 g/dL and 6.5-7.0 g/dL for PbB levels of 10 ug/dL and 50 ug/dL, 

respectively. However, Expert B believed that it was quite possible 

that Hb levels could be even lower for the iron-deficient children at 

PbB levels of 50 yg/L, but just could not be sure. He could not 

express these feelings quantitatively, despite efforts to assist him 

using judgmental probability encoding techniques. 

B.4.3 Expert C 

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. 
-JJ^~ r -

There is no evidence that a lead-induced elevated EP level itself 

causes health problems; it is simply a marker, or indicator, of 

adverse health effects due possibly to lead exposure. EP levels 

larger than one standard deviation above the mean should be 

followed by a look at PbB levels. 

Since changes in EP levels tend to lag changes in PbB levels, jt is 

important to be looking at both over time to get a good idea of what 

is going on. The rate of rise in EP versus an increase in PbB is 

greater than linear, but lagged in time. A plot of the natural log of 

EP values versus PbB would be roughly linear under chronic, 

relatively constant lead-exposure conditions. 

A lead-induced elevated EP level is an indicator of interference 

with heme synthesis, which may be compensated for by derepression 

of ALAS, the rate-limiting enzyme involved in heme systhesis, 

depending on the degree of lead exposure. 

It is possible that an elevated EP level is an indicator of 

interference by lead in the body's ability to produce 1,25 

dihydroxyvitamin D. The cytochrome P-450 enzymes, of which 

there are more than 50 different isozymes, are related to the 

synthesis of 1,25 dihydroxyvitamin D. There are strong indications 

that lead reduces synthesis of the P-450 enzymes, which may in turn 

reduce the metabolism of 25-(OH)D, a necessary ingredient in the 

biosynthesis of 1,25 dihydroxyvitamin D (Fraser, 1980). 

There is also suggestive evidence, but not proof, that elevated EP 

levels indicate 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. 

Furthermore, elevated EP levels may indicate sufficient exposure to 

lead or other metals to accelerate the destruction (i.e., reduce their 

half-lives) of the hemoproteins (Maines, 1976). 

Regarding the CNS, it is not clear whether elevated EP levels per se 

cause any effects. Some animal studies have been conducted 

concerning CNS effects when very large doses of the EP precursor 

ALA are administered. Some report CNS effects and others not 

(Moore and Meredith, 1976; Edwards et al., 1984). 

In a study of lead workers, Hammond et al. (1980) determined that 

ALA in plasma and urine was as good a marker of the degree of 

toxicity of lead as PbB; that ALA was as good a marker as EP for 

hematopoietic system damage; and that ALA and PbB were better 

indicators of damage than EP for other effects (e.g., neurological 

and renal). Another study (Lillis et al., 1977) showed that EP was a 

P.3 
P.4 

T6 ~ 

better indicator of hematopoietic effects than ALA and PbB. The 

differences between the two studies can probably be attributed to 

the differential measurement reliabilities of the two laboratories. 

• There is no evidence of an EP versus Hb relationship in children at 

PbB levels < 50 ug/dL. Also, there are factors other than lead that 

affect EP level. 

• The possibility of lead exposure causing hypertension is a new issue. 

• To summarize, evidence is lacking that elevated EP levels per se 

related to lead exposure cause adverse health effects. 

B.4.4 Expert D 

FEP 

Elevated EP levels caused by lead exposure indicate the direct toxic 

effect of lead on heme, a basic physiological system that is common 

to many organs and cell types. 

Piomelli et al. (1982;) and Silbergeld and Lamon (1980) have both 

suggested that some of the effects of lead on the CNS may be 

attributable to altered metabolism of porphyrin compounds. Others 

have proposed that perturbations may occur in CNS intracellular 

calcium metabolism. 

Liver 

At PbB levels of 30-40 ug/dL, evidence has shown that liver 

metabolism of model compounds (e.g., Cortisol) is altered, thereby 

implying a reduced ability to detoxify the blood stream. Since many 

drugs have metabolic pathways that are similar to that of Cortisol, 

their metabolism may also be affected by PbB levels. 

Calcium 

• There is evidence that the calcium-mediated basic enzymatic 

systems in all mammalian cells are affected at PbB levels above 

about 5 micromolar. Any disruption of these systems may have 

pervasive effects. For example, calcium from calmodulin can be 

displaced by lead, calmodulin being a central component of the 

normal chemistry of cells. 

1,25 Dihydroxyvitamin D 

• A complex enzyme system is responsible for production of 1,25 

dihydroxyvitamin D hormone. Lead is known to impair several 
P.5 

97 

aspects of this enzyme system, including electron transport, 

mitochondrial function, and the cytochrome P-450 family of 

enzymes. Impairment in the production of 1,25 dihydroxyvitamin D 

hormone in lead-toxic children has been confirmed in experimental 

studies in vivo and in vitro. 

At PbB levels of 33-55 ug/dL, there is evidence of an approximately 

66% decrease in the kidney's ability to produce 1,25 dihydroxyvitamin D hormone. 

At PbB levels above 62 ug/dL, there is evidence of a decrease in 

1,25 dihydroxyvitamin D levels to a degree comparable to that 

reported in children with inborn errors in metabolism. 

At PbB levels of 12-120 ug/dL, there is a statistically significant 

negative correlation between 1,25 hihydroxyvitamin D and PbB 

levels. 

At PbB levels above 55 ug/dL, chelation therapy is immediately 

used. At 25-55 ug/dL, the results of the ethylenediaminetetraacetate (EDTA) provocative test are used to determine which 

children would benefit from chelation therapy. 

1,25 dihydroxyvitamin D affects the maturation of cells and 

enhances the differentiation of cells. Rats and mice having 

leukemia were treated with picomolar concentrations of 1,25 

dihydroxyvitamin D, which resulted in their lifespans being 

extended. In vitro experiments using a variety of human cells (e.g., 

lymphoma, myeloid leukemia cells, and monocytes) have replicated 

these findings. 

Recent research shows that 1,25 dihydroxyvitamin D evidences 

some immuno-regulatory functions like other steroid hormones. 

There is early, evolving evidence that 1,25 dihydroxyvitamin D has a 

role in controlling insulin secretion from the pancreas. 

The actions of 1,25 dihydroxyvitamin D hormone involve not only 

mineral absorption, bone remodeling, and calcium homeostasis in 

virtually all mammalian cells, but recently reported information 

indicates that it 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 evidence, together with that discussed in the sixth through 

eighth points above, suggests that a decrease of 1,25 

dihydroxyvitamin D hormone is likely to have pervasive effects on 

the function of other organs. 
P3_ 

98 

B.4.5 Expert E 

There does not seem to be any evidence that an elevated EP level is 

itself an adverse health effect. However, it could be because there 

is a risk of damage to other organs or functions anytime the balance 

of an essential metabolite is upset. For example, although an 

essential amino acid, phenylalanine is toxic at high levels. This 

toxicity is seen in the disease phenylketonuria, in which excess 

phenylalanine cannot be metabolized. Thus, in the absence of a 

special diet, the phenylalanine builds up and affects the developing 

CNS, causing mental retardation. Also, excess levels of fluoride 

cause teeth to become brittle, even though proper levels increase 

the hardness of teeth. Thus, future research may show that 

elevated EP is an adverse health effect. 

Elevated EP is a valuable index of adverse effects of lead in 

systems and organs (e.g., CNS, liver, and kidney). 

The body can compensate for lead insult up to a point. For 

example, at low PbB levels, the inhibition of EP is compensated for, 

but not at slightly higher levels. Piomelli et al. (1982) report a 

threshold in the range of 16-17 ug/dL. ALAD shows no threshold. 

Regarding measurement of EP, care must be taken if the 

hematoflurometer is used because the amount of EP that is ZPP 

decreases proportionately as total EP rises. Because the 

hematoflurometer measures ZPP, it may be underestimating total 

EP. Below 35 ug/dL, there is good agreement between EP 

(extraction) and ZPP (hematofluorometer). Above 35 ug/dL, there 

appears to be a 30% difference between ZPP (lower) and FEP 

(higher). 

In assessing the need for treatment, both EP and PbB levels should 

be considered, as the Centers for Disease Control do. 

Critical PbB 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. 

B.5 APPENDIX B REFERENCES 

Bull, R.J., et al., The Effects of Lead on the Developing Central Nervous System of the 

Rat, Neurotoxicology, 4:1-18 (1983). 

Edwards, S., et al., Neuropharmacology of Delta-Aminolaevulinic Acid, H. Effect of 

Chronic Administration in Mice, Neuroscience Letters, 50:169-173 (1984). 
Fraser, D.R., Regulation of the Metabolism of Vitamin D, Physiological Reviews, 

60:551-613 (1980). 

Hammond, P.B., et al., The Relationship of Biological Indices of Lead Exposure to the 

Health Status of Workers in a Secondary Lead Smelter, J. Occupational Medicine, 22:475-

484 (1980). 

Lilis, R., et al., Prevalence of Lead Disease among Secondary Lead Smelter Workers and 

Biological Indicators of Lead Exposure, Environmental Research, 14:255-285 (1977). 

Litman, D.A., and M.A. Correia, L-tryptophcm: A Common Denominator of Biochemical 

and Neurological Events of Acute Hepatic Porphyrias?, Science, 222:1031-1033 (1983). 

Maines, M.D., and A. Kappas, The Induction of Heme Oxidation in Various Tissues byTrace Metals: Evidence for the Catabolism of Endogenous Heme by Hepatic Heme 

Oxygenase, Annals of Clinical Research, 8(Suppl. 17):39-46 (1976). 

Moore, M.R., and P.A. Meredith, The Association of Delta-Aminolevulinic Acid with the 

Neurological and Behavioral Effects of Lead Exposure, in Trace Substances in 

Environmental Health - X, University of Missouri-Columbia, pp. 363-371 (1976). 

Piomelli, S., et al., Threshold for Lead Damage to Heme Synthesis in Urban Children, 

Proc. National Academy of Science (Medical Sciences), 79:3335-3339 (May 1982). 

Silbergeld, E.K., and J.M. Lamon, Role of Altered Heme Synthesis in Lead Neurotoxicity, 

J. Occupational Medicine, 22:680-684 (1980). 

P.7 
P.8 

APPENDIX C 

FITTING FUNCTIONS TO ENCODED JUDGMENTS 

RELATING TO LEAD-INDUCED IQ EFFECTS 
P.9 

APPENDIX C 

FITTING FUNCTIONS TO ENCODED JUDGMENTS 

RELATING TO LEAD-INDUCED IQ EFFECTS 

The organization of this appendix is similar to that of App. B.. Section C.l 

reproduces the IQ protocol, and Sec. C.2 summarizes the mathematical formulations. 

Section C.3 tabulates encoded judgments, specifications for functions fit to those 

judgments, data concerning CIs, and comparisons of encoded judgments and fitted 

functions. Finally, Sec. C.4 summarizes the discussions held with each of the experts. 

C I IQ PROTOCOL 

C.l.l Introduction 

The U.S. Environmental Protection Agency is charged by the Clean Air Act with 

setting and revising 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 CDs. 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 CD 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 

the health risks associated with various potential standards will aid the EPA 

Administrator in selecting that standard which, in his or her 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 uncertain lead-exposure estimates, 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 probability estimates for 

dose response and exposure. 

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 the best decision for the patient. Here, too, it is necessary to use 

scientific judgment to extrapolate from the available data. The extrapolation is not 
P.10 

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 CD, two populations have been identified as 

being most susceptible to the effects of lead intoxication. One is children from birth 

through the seventh birthday, and the other is the fetuses 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 CD suggest that there are numerous 

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 welldefined 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 electroencephalogram 

(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 emerge that are obviously adverse and for which a substantial 

•In this report, we focus only on children aged 0-6. 
P.11 

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 a hypothetical ideal experiment. If you agree with the 

assumptions on which the hypothetical experiment is 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 PbB levels. Then we will use your judgments to derive 

probabilistic statements about the percent of children at each PbB level whose IQ scores 

are below any value of interest, such as, for example, below IQs of 70, 80, 90, or 100. 

C.1.2.3 Hypothetical Ideal Experiment 

Assume that at birth, subjects are randomly assigned to groups differentiated by 

PbB level targeted for the third birthday. Members of each treatment group are exposed 

to lead from birth until their seventh birthdays, while members of a control group are 

sheltered from lead from birth 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 PbB level. 

Thus, groups differ in terms of mean PbB on the third birthday. Environmental lead 

levels necessary to yield a given PbB 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 PbB levels on their third birthdays. 
P.12 

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, PbB 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 condftions, then we 

will consider separate hypothetical experiments for the two subpopulations. Otherwise, 

we will consider only a single such experiment. 

SES is a complex variable. For simplicity, if we divide the population into low 

SES and high SES categories, let us define low SES as those children coming from 

households with incomes in the lowest 15%. 

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 PbB level, and we will only have to encode your probabilistic judgment about the mean IQ at age seven for each of several PbB 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 PbB 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 PbB (the control 

group) and children at each of several elevated PbBs at age three (the treatment groups). 

The following sections specify further the conditions to be assumed in this 

hypothetical experiment. 

C.1.3 Population at Risk 

Based on the CD, we can specify the most susceptible population as all U.S. 

children from birth through their seventh birthdays. We have already defined the effect 

as being measured on the seventh birthday. However, as already discussed, you may 

consider IQ effects of lead to be different for low SES than for high SES subpopulations 

of children, resulting in different experimental outcomes for the two groups. If so, then 

we will elicit your judgments separately for low SES children and for high SES children. 
P.13 

C.1.4 Exposure Conditions 

We will be asking your judgment about mean IQ values on the seventh birthdays 

at various PbB levels. Assume that the PbB 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, PbB levels were not necessarily constant 

from birth to age seven, but exposure and behavioral factors were such that at age three, 

PbB was at a specific level. Finally, assume that the changes in PbB 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). 

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 (home 

observation for measurement of the environment) scale, 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.l.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 
___ ^ P.14 

108 

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 

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 fewer 

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 leadrinduced IQ effects that we should discuss now? 

C.l.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 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. 

C.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 

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. 
P. 15 

109 

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 personally significant. 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. 

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 that is consistent with one's beliefs and expectations, results are 

overgeneralized, 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, 

influences judgments about the certainty of the events when, rationally, importance 

should not affect probability. In other words, one's attitudes toward 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; similarly, many smokers underestimate the probability of 

adverse consequences of smoking, because they feel that the odds do not apply to 

themselves personally. 
P.16 

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. 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.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. Do not 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 Vie 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 measurement, and 

subjective evaluation and interpretation. In addition, the farther 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 that 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 

an 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 0.005. 

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, 

please think carefully about the relevant information reviewed in the CD, 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 the mean IQ of children sheltered from PbB exposure) 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 PbB concentration. 

2. Uncertainty about the PbB 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 

PbB level, while everyone in the zero PbB population has negligible PbB, as described 

above. Then, in order for us to determine your uncertainty about the mean IQ decrement 

of the exposed group with a given PbB level relative to the negligible PbB group, we must 

introduce a definition. Let L be the given PbB concentration in question, then 

Definition: D(L) is the mean IQ decrement of the exposed group with PbB 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 your 
P.18 

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 PbB 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, or 

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 the 

first response. Other wheel settings will have a large enough relative area of blue that 

you will feel confident making the second response. The intermediate settings will be 

more difficult to judge. However, for a fixed PbB L, and mean IQ decrement d, we will 

manipulate the wheel settings to find the one for which you feel most comfortable 

making the third response. 

Once we have determined the point at which you are most comfortable with the 

third response, and still focusing on the given PbB concentration 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 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 PbB level. We will obtain the probabilistic 

representation of your uncertainty for 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 the-, to you for your consideration and comparison. At 

these times you may wish to change some of the judgments you gave 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 
P.19 

exhibit some incoherences. That is another reason we will consider together the graphs 

of your judgments. Our objective is to obtain a coherent set of judgments that 

represents your opinions well by the end of this elicitation process. You are not expected 

to giye 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 

CD or other sources as you wish as you formulate your judgments. 

(Encode judgments for two PbB concentrations, then continue with instructions.) 

Recall that uncertainty about the experimental outcomes can also be expressed 

in terms of the PbB concentration necessary to produce a given mean IQ decrement D, if 

the entire exposed population had the same PbB concentration, established in the manner 

discussed earlier. More specifically, proceeding as before, let us introduce a definition: 

Definition: L(D) is the PbB 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 I and ask you to consider how 

likely it is that the L(D) is less than the specified 1. 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 I, 

2. You judge it more probable that the wheel would stop with the 

pointer on blue, or 

3. You cannot judge either event as more probable than the other. 

After determining the wheel setting at which you feel most comfortable with the 

third response, we will specify a new I 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 a negligible PbB level under the exposure 

conditions described previously. We start with a definition: 

Definition: Le£ y be the true population mean IQ for children with negligible 

PbB. (Or, let y . be the true population mean IQ for children with negligible PbB 

in SES group i.) 
_ _ _ P.20 

114 

* ie 

The value of y or u . 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 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 PbB 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 o. be the true IQ standard deviation for SES group i. 

* 

The value of o. 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 a 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 FURTHER MATHEMATICAL FORMULATIONS FOR IQ ASSESSMENTS 

NOLO probability functions were fit to all of the judgments of the Hb 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 is an intermediate step 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 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 that designated Y. 

Distributions for response rate (increased occurrence of IQs less than or equal to 

a critical level IQ*) were derived from the distributions for IQ , oTO, and Aypr that 

were encoded from the IQ experts. Numerical methods were used to obtain the 

distributions. The first step was to change the PDFs for IQ , a , and A^o into discrete 

probability mass functions (PMFs) with a reasonable number of points (seven were used in 

most cases). 

For one expert, one SES level, and one PbB level, and for a specific combination 

of mean IQ, standard deviation, and IQ decrement, the increased probability (converted 

to a response rate, expressed in percent) of having IQ values < IQ* was calculated. The 

response rate and the probability for the particular values of IQ , oT_, and A-— were 

recorded. This process, which was repeated for each possible combination of IQ , 

OJQ, and A—, resulted in a set of points to which a distribution function (either normal 
•a a-3' 

P.21 

or NOLO) was fit in order to facilitate further calculations. One function was obtained 

for each PbB and SES combination. The process was repeated for each of the experts 

except Expert I. 

To illustrate the process, consider the following hypothetical example. Let 

= 95 

! 105 

0.5, for IQ = 

0.5, for IQ = 

(0.5 , for o = 14 

P(0 I Q ) = ) 

IQ

 (0.5 , for oIQ u 1C 

(0.5, for AJQ = 

i y

 (0.5 , for A— = 

IQ = 15 

= 5 

10 IQ 

These are discrete PMFs having only two possible outcomes in each case, each of which 

is equally likely. There are eight combinations of the three variables to consider, and 

each combination is equally likely. For IQ = 95, o = 14, and A— = 5, the 

increased probability of having IQs < 70 is 

AP = •( 70 - 95 • 5 

14 ) -• ( 

= 0.077 - 0.037 

= 0.04 

70-95 -

14 

which corresponds to a response rate of 4%. In a similar fashion, a response rate can be 

calculated for each of the other seven combinations. The results are response rates of 

0.1%, 1.2%, 3.1%, 3.8%, 4.3%, 10.5%, and 11.1%. These values, along with their 

associated probabilities, define a probability distribution having a mean of 4.9% and a 

standard deviation of 3.6%. 

C.3 RESULTS 

The results, which are presented in Tables C.1-C.8, are explained using the 

judgments of Expert F as an example. Expert F believed that SES level does not 

significantly influence the effects of lead on IQ; therefore, he or she provided only one 

set of judgments. Expert F judged a 0.5 probability that the mean IQ of the unexposed 

group would be < 100.5, a 0.8 probability that it would be < 101.5, and so on (see 

Table C.l). Expert F also believed that using a probability distribution to characterize 

population standard deviation was unnecessary and simply gave a point estimate of 15 for 

OJQ (see Table C.2). As shown in Table C.3, Expert F provided judgments on IQ 

differences at five PbB levels. For example, at a PbB level of 65 yg/dL, Expert F judged 
P.22 

TABLE C.l Encoded Judgments about the Mean IQ of Children 

Unexposed to Lead 

Expert F 

lQ0

a Fb 

Both SES Level 

100 0.01 

100.5 0.05 

101 0.65 

101.5 0.80 

102 0.99 

Low SES Level 

High SES Level 

Expert G 

IQo

 F 

s 

90 

93 

94 

96 

98 

100 

100 

104 

106 

108 

110 

0.01 

0.25 

0.50 

0.76 

0.92 

0.99 

0.01 

0.15 

0.50 

0.85 

0.99 

Expert H 

iQ0

 F 

92 

94 

98 

99 

102 

100 

102 

104 

106 

108 

UO 

0.01 

0.20 

0.50 

0.65 

0.99 

0.02 

0.11 

0.30 

0.49 

0.75 

0.96 

Expert J 

^ 0 

90.0 

93.5 

95.0 

96.0 

98.0 

100 

102 

104 

106 

108 

110 

F 

0.01 

0.25 

0.50 

0.75 

0.90 

0.001 

0.1 

0.77 

0.90 

0.99 

0.999 

Expert K 

iQ0*

 F 

78 0.01 

83 0.25 

85 0.50 

88 0.75 

91 0.99 

100 0.01 

102 0.17 

104 0.42 

106 0.60 

108 0.85 

110 0.99 

aIQ denotes mean IQ of children unexposed to lead. 

F denotes cumulative probability. 

a 0.95 probability that the mean IQ difference would be < 3.7 points. Figure 15 shows 

that Expert F is increasingly uncertain about the magnitude of IQ differences as PbB 

level increases. Also, Expert F did not provide judgments on IQ differences having 

cumulative probabilities less than 0.5 at the lowest three PbB levels (see Table C.3), 

indicating that he or she experienced difficulty in providing judgments on what would 

have been very small IQ differences. 

For the reasons presented in Sec. 1, mathematical functions were fit to the 

judgments of Expert F. They were obtained by fitting regression lines to transformations 

of the judgments. The transformation used was the natural log (In) transformation. As 
TABLE C.2 Encoded Judgments about Population Standard Deviation 

Expert F 

°IQ

 F 

Expert G 

"IQ

 F 

Expert H 

°IQ

 F 

Expert J 

°IQ

 F 

Expert K 

aIQ F 

Both SES Levels 

15 1 

Low SES Level 

14 10 

11 

12 

13 

14 

0.04 

0.1 

0.35 

0.5 

0.85 

11 

12 

13 

14 

15 

0.001 

0.125 

0.5 

0.875 

0.999 

10 

11 

12 

13 

14 

0.01 

0.05 

0.14 

0.53 

0.93 

15 0.999 15 0.999 

High SES Level 

14 1 13 

13.5 

14 

14.3 

15 

15.5 

0.04 

0.07 

0.275 

0.5 

0.9 

0.99 

11 

12 

13 

14 

15 

0.001 

0.125 

0.5 

0.875 

0.999 

12 

13 

13.5 

14 

15 

0.02 

0.25 

0.5 

0.75 

0.99 

a oT n denotes standard deviation in IQ values. 

'IQ 

F denotes cumulative probability. 

was true for the Hb case, this transformation led to distributions that are normal 

distributions, with a high degree of accuracy. For Expert F, the mathematical 

representations of the CDFs for IQ differences conditional on PbB level are guaranteed 

never to cross. 

The fitted distributions are lognormal distributions, which are uniquely defined 

by the mean and variance of the underlying normal distributions and the transformation 

function. The properties of the lognormal distributions 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 fit of the distributions 

to the judgments of the experts. Table C.4 identifies the functional form; the defining 

parameters y and a, if a transformation is used; the mean E[IQ ] and standard 

deviation SD[IQ ] of the IQ distributions; and r for the regression of fitted cumulative 
P.24 

TABLE C.3 Encoded Judgments about Mean IQ Decrements of 

Children Exposed to Lead 

PbB 

Level 

(ug/dL) 

5 

15 

25 

35 

45 

55 

65 

Expert F 

Both SES 

*IQ 

0. 

1 

0. 

2 

0. 

1 

2 

3 

1 

2 

3 

4 

1 

2 

3 

4 

5 

25 

5 

9 

F 

0.5 

0.999 

0.5 

0.999 

0.5 

0.55 

0.93 

0.99 

0.2 

0.8 

0.95 

0.99 

0.15 

0.5 

0.9 

0.96 

0.99 

Low 

*TQ 

0.2 

0.3 

0.5 

1 

3 

O.S 

0.7 

1.5 

2 

5 

1 

1.3 

3 

4 

8.5 

2 

2.5 

3.5 

5 

10 

3.5 

4 

5 

7 

12 

4 

5 

7 

10 

IS 

Exp 

SES 

F 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

(.99 

0.01 

0.25 

O.S 

0.75 

0.99 

ert C 

High 

4lQ 

0.3 

0.4 

0.5 

1 

3 

0.5 

0.7 

1 

2 

4 

1 

1.5 

2.5 

4 

8 

2 

2.5 

3.5 

5 

10 

3.5 

4 

5 

7.5 

12 

SES 

F 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

0.99 

Low 

*IQ 

1 

2 

3 

4 

5 

2 

3 

4 

5 

6 

2 

4 

6 

8 

10 

4 

6 

8 

10 

12 

6 

8 

10 

12 

14 

8 

10 

12 

14 

16 

Expert H 

SES 

F 

0.03 

0.4 

0.55 

0.9 

0.99 

0.06 

0.5 

0.6 

0.75 

0.93 

0.01 

0.35 

0.6 

0.84 

0.99 

0.02 

0.25 

0.46 

0.79 

0.95 

0.02 

0.35 

0.55 

0.85 

0.95 

0.02 

0.4 

0.77 

0.9 

0.95 

High 

4lQ " 

0.5. 

1 

1.5 

1 

2 

2.5 

3 

3.5 

4 

2.4 

3.4 

4.4 

4.5 

5.4 

6.4 

7.4 

3.8 

4.8 

5.5 

5.8 

6.8 

8.3 

4.8 

5.8 

6.5 

6.8 

7.8 

8.8 

6 

7 

8 

9 

10 

SES 

F 

0.45 

0.8 

0.98 

0.03 

0.3 

0.5 

0.6 

0.73 

0.93 

0.02 

0.13 

0.47 

0.5 

0.7 

0.93 

0.99 

0.04 

0.3 

0.5 

0.61 

0.86 

0.99 

0.01 

0.09 

0.5 

0.7 

0.85 

0.99 

0.01 

0.1 

0.5 

0.85 

0.99 
TIT 

TABLE C.3 (Cont'd) 

' 

PbB 

Level 

(ug/dL) 

5 

15 

25 

35 

45 

SS 

65 

Low 

m 

0.001 

0.5 

0.7 

1.1 

2 

1 

1.9 

2.3 

3.2 

5 

2 

3.1 

3.6 

5.1 

7 

3 

4.5 

S.3 

6.9 

10 

4 

5.5 

6.3 

8.2 

12 

Expert 

SES 

F 

0.025 

0.25 

0.5 

0.75 

0.975 

0.025 

0.25 

0.5 

0.75 

0.975 

0.025 

0.25 

0.5 

0.75 

0.975 

0.025 

0.25 

0.5 

0.75 

0.975 

0.025 

0.25 

O.S 

0.75 

0.975 

I 

High SES 

4IQ 

0.2 

0.3 

0.5 

1 

0.7 

1 

2 

3 

1 

1.9 

2.3 

3.2 

5 

2 

3.1 

3.6 

4.7 

7 

2 

3.5 

4.3 

5.8 

9 

F 

0.25 

0.5 

0.75 

0.975 

0.25 

0.5 

0.75 

0.975 

0.025 

0.25 

0.5 

0.75 

0.975 

0.025 

0.25 

0.5 

0.75 

0.975 

0.025 

0.25 

0.5 

0.75 

0.975 

Low 

m 

0.001 

1 

2 

3 

5 

0.002 

2.25 

3.5 

4.5 

6.5 

0.003 

4 

5 

5.75 

8 

2 

6 

7 

8 

10 

4 

7.5 

9 

10.5 

12 

6 

9 

11 

12.5 

14 

Expert 

SES 

F 

0.0001 

0.25 

0.5 

0.75 

0.995 

0.001 

0.25 

0.5 

0.75 

0.995 

0.001 

0.25 

0.5 

0.75 

0.99 

0.001 

0.25 

0.5 

0.75 

0.99 

0.001 

0.25 

0.5 

0.75 

0.99 

0.001 

0.25 

O.S 

0.75 

0.99 

J 

High 

*IQ 

0.5 

1.25 

2.3 

2.75 

3.5 

3.5 

4.5 

5.75 

8 

5 

6.5 

7 

7.5 

10 

SES 

F 

• 

0.014 

0.14 

0.25 

0.5 

0.75 

0.95 

0.99 

0.999 

0.01 

0.25 

0.5 

0.75 

0.999 

0.05 

0.25 

0.5 

0.75 

0.999 

0.005 

0.25 

0.5 

0.75 

0.99 

0.01 

0.25 

0.5 

0.75 

0.99 

Low 

*TQ 

0.25 

1 

1.5 

2 

0.5 

1 

2 

3 

4 

5 

1 

2 

3 

4 

5 

6 

4 

5 

6 

7 

8 

9 

5 

6 

7 

8 

9 

10 

7 

8 

10 

12 

14 

Expert K 

SES 

F 

0.01 

0.36 

0.5 

0.97 

0.01 

0.06 

0.27 

0.47 

0.8 

0.98 

0.01 

0.05 

0.18 

0.5 

0.86 

0.99 

0.02 

0.11 

0.5 

0.64 

0.82 

0.99 

0.02 

0.1 

0.28 

0.47 

0.82 

0.97 

0.01 

0.09 

0.5 

0.79 

0.99 

High 

4lQ 

0.5 

1 

1.5 

1 

1.0 

1.5 

2.0 

2.5 

3 

2 

3 

3.5 

4 

5 

3 

4 

4.5 

5 

6 

4 

5 

6 

7 

8 

SES 

F 

0.01 

0.35 

0.5 

0.99 

0.01 

0.11 

0.5 

0.9 

0.99 

0.01 

0.2 

0.5 

0.75 

0.99 

0.02 

0.25 

0.5 

0.78 

0.98 

0.01 

0.17 

0.5 

0.82 

0.99 

*4J:Q denotes the mean IQ decrement among children with the specified PbB Levels, referenced to 

unexpose ne9 x d children. 

*F denotes cumulative probability. 
P.26 

..,.,. . wwr ^—• 120 

TABLE C.4 Functions Fit to Judgments about Mean IQ Levels among 

Children Unexposed to Lead 

Functional 

Expert Form 

Defining 

Parameters3 

Measures of 

Distribution 

over IQQ

b 

E[IQJ SDUQJ 

r

2 for 

Regression 

of F on F 

Both SES Levels 

F Lognormal 

Low SES Level 

4.61 0.005 100.9 0.5 0.88 

G 

H 

J 

K 

Lognormal 

Lognormal 

Normal 

Normal 

4.55 

4.58 

0.02 

0.02 

94.6 

97.2 

94.8 

85.0 

2.2 

2.4 

1.9 

2.9 

0.99 

0.97 

0.99 

0.99 

High SES Level 

G 

H 

J 

K 

Lognormal 

Lognormal 

Lognormal 

Normal 

4.66 

4.66 

4.65 

0.02 

0.03 

0.02 

105.6 

105.6 

104.1 

104.9 

2.2 

2.8 

1.7 

2.4 

0.99 

0.99 

0.96 

0.99 

*The function Y = ln(IQ0 ) is normally distributed with mean y and 

standard deviation a . There are no entries in these columns 

when IQ is normally distributed. 

5

For lognormal distributions, y , o , and the equations in Table 

B.l are used to calculate the mean E[IQ ] and the standard 

deviation SD[IQ ] of the distribution over IQ . 

o o 

probability values P versus encoded values F. In Table C.5, E[OJQ] denotes the mean 

and SD[OJQ] denotes the standard deviation of the distribution for population standard 

deviation. In Table C.6, E[A-=Q] and SD[AYQ] denote the mean and standard deviation of 

probability distributions for the IQ decrements for different PbB levels. 

For Expert F, the fitted distribution of the uncertain mean IQ of the unexposed 

group is a lognormal distribution with a mean value of 100.9, a standard deviation of 

0.47, and an r value of 0.883 (see Table C.4). The defining parameters y and o are 

4.61 and 0.005, respectively. These values are needed to calculate points on a CDF for 

the mean IQ variable. 
X

rx*ur* 

TABLE C.5 Functions Fit to Judgments about Population Standard Deviation 

for IQ Levels 

Expert 

Functional 

Form 

Defining 

Parameters* 

y o 

y y 

Measures of 

Distribution 

over o I Q

b 

E[oI Q] SD[oIQ] 

r

2 for 

Regression 

of F on F 

BotA SES Levels 

Point 15.0 

Low SES Level 

G 

H 

J 

K 

Point 

Lognormal 

Normal 

Normal 

2.5056 0.0915 

14.0 

12.3 

13.0 

12.6 

1.1 

0.7 

0.9 

0.95 

0.99 

0.97 

High SES Level 

G 

H 

J 

K 

Point 

Lognormal 

Normal 

Normal 

2.6541 0.0416 

14.0 

14.2 

13.0 

13.5 

0.6 

0.7 

0.7 

0.99 

0.99 

0.99 

aThe function Y = ln(ojQ> is normally distributed with mean y and 

standard deviation a . There are no entries in these columns for 

normal or point distributions. 

For lognormal distributions, yy, oy, and the equations in Table B.l 

are used to calculate the mean E[OJQ ] and the standard deviation 

SD[oI Q ]. 

Lognormal distributions provided the best fits of Expert F's judgments about IQ 

differences. Thus, all of the columns in Table C.6 have entries. The mean values of the 

distributions over IQ decrement vary from 0.3 at a PbB level of 25 yg/dL to 1.9 at 

65 yg/dL. In general, the fitted functions represent the judgments quite well, having r 

values of 0.99. 

Table C.7 compares encoded judgments and corresponding points on the functions 

fit to the judgments of each expert. It can also be used to compare the judgments of the 

different experts. Tables like this one were used to help the experts understand the 

implications of their judgments and to choose the mathematical functions that best 

represented those judgments. 
P.28 

TABLE C.6 Functions Fit to Judgments about Mean IQ Decrements among Children 

Exposed to Lead3 

PbB 

Level 

(yg/dL) 

Functional 

Form 

Defining 

Parameters 

Measures of 

Distribution 

over A^ c 

E[AJQ] SD[AJQ] 

r* for 

Regression 

of F on F 

Both SES Levels 

Expert F 

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 

0.3 

0.5 

1.1 

1.6 

1.9 

0.1 

0.3 

0.5 

0.8 

0.9 

0.99 

0.99 

0.99 

0.99 

0.99 

Low SES Levels 

Expert G 

5 

15 

25 

35 

45 

55 

Expert H 

5 

15 

25 

35 

45 

55 

Expert I 

15 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

-0.4816 

0.3316 

0.9775 

1.3548 

1.7359 

1.9905 

0.8268 

1.2481 

1.5860 

2.0323 

2.2422 

2.4045 

-0.3276 

0.8495 

1.3361 

1.7009 

1.9041 

0.6422 

0.5429 

0.5229 

0.3807 

0.3011 

0.3174 

0.4037 

0.3989 

0.3749 

0.3087 

0.2366 

0.1887 

0.5351 

0.4110 

0.3282 

0.3088 

0.2845 

0.8 

1.6 

3.0 

4.1 

5.9 

7.7 

2.5 

3.8 

5.2 

8.0 

9.7 

11.3 

0.8 

2.5 

4.0 

5.7 

7.0 

0.5 

0.9 

. 1.7 

1.6 

1.8 

2.5 

1.1 

1.6 

2.0 

2.5 

2.3 

2.1 

0.5 

1.1 

1.4 

1.8 

2.0 

0.98 

0.98 

0.97 

0.98 

0.97 

0.98 

0.97 

0.98 

0.88 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 

0.99 
TABLE C.6 (Cont'd) 

' 

PbB 

Level 

(yg/dL) 

Expert J 

5 

15 

25 

35 

45 

55 

Functional 

Form 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

Defining 

Parameters 

y o 

My O y 

-Measures of 

Distribution 

over 

EIAIQ] 

2.4 

3.5 

4.8 

6.8 

8.8 

10.7 

*IQ 

SD[AJQ] 

0.9 

1.2 

1.5 

1.5 

1.6 

1.6 

Reg 

of 

r

2 for 

ression 

F on F 

0.96 

0.99 

0.99 

0.99 

0.99 

0.98 

Expert K 

15 

25 

35 

45 

55 

65 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

1.3 

2.9 

3.8 

6.4 

7.8 

10.4 

0.4 

1.1 

1.1 

1.2 

1.3 

1.6 

0.95 

0.99 

0.99 

0.98 

0.99 

0.99 

High SES Levels 

Expert G 

15 

25 

35 

45 

55 

Expert H 

5 

15 

25 

35 

45 

55 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

-0.3430 

0.2059 

0.9575 

1.3548 

1.7497 

-0.5767 

0.8960 

1.4785 

1.6873 

1.8859 

2.0688 

0.5671 

0.5045 

0.4847 

0.3807 

0.3068 

0.5207 

0.4498 

0.2607 

0.1955 

0.1297 

0.1103 

0.8 

1.4 

2.9 

4.2 

6.0 

0.6 

2.7 

4.5 

5.5-

6.6 

8.0 

0.5 

0.8 

1.5 

1.6 

1.9 

0.4 

1.3 

1.2 

1.1 

0.9 

0.9 

0.95 

0.97 

0.99 

0.98 

0.96 

0.99 

0.98 

0.99 

0.99 

0.98 

0.99 
P.30 

TABLE C.6 (Cont'd) 

PbB 

Level 

(yg/dL) 

Expert I 

15 

25 

35 

45 

55 

Expert J 

15 

25 

35 

45 

55 

Expert K 

25 

35 

45 

55 

65 

Functional 

Form 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Lognormal 

Normal 

Normal 

Normal 

Normal 

Normal 

Defining 

Parameters 

uy 

-1.1800 

0.0637 

0.8495 

1.3198 

1.4719 

0.4542 

1.0069 

1.3082 

1.6280 

1.9489 

°y 

0.6191 

0.6022 

0.4110 

0.3293 

0.3839 

0.4502 

0.3640 

0.2762 

0.1991 

0.1466 

Measures of 

Distribution 

over 

EUTQ] 

0.4 

1.3 

2.5 

3.9 

4.7 

1.7 

2.9 

3.8 

5.1 

7.1 

1.3 

2.0 

3.5 

4.5 

6.0 

AIQ 

SD[Ajp] 

0.3 

0.8 

1.1 

1.3 

1.9 

0.8 

1.1 

1.1 

1.0 

1.0 

0.3 

0.4 

0.6 

0.7 

0.9 

- r2 for 

Regression 

of F on F 

0.99 

0.99 

0.99 

0.99 

0.99 

0.96 

0.94 

0.96 

0.99 

0.99 

0.93 

0.99 

0.99 

0.99 

0.99 

The distributions are either normal or lognormal in form. 

If the distribution over AJQ is lognormal, then the function Y = ln(AYg) 

is normally distributed with mean y and standard deviation o . There are 

no entries in these columns when A-=-r is normally distributed. 

cFor lognormal distributions, y , a , and the equations in Table B.l are 

used to calculate the mean E[A— ] and the standard deviation SD[A—] of 

the response-rate distribution over ATQ. Calculations involving normal 

distributions over A-=r» are more straightforward. 
TABLE C.7 Comparison of Judgments and Fitted Functions Concerning Lead-Induced IQ Effects 

AJQ at PbB Level 

Index . IQ. 'IQ 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 65 yg/dL 

Expert F, Both SES Levels 

Encoded Judgments 

Median 

50Z CIa 

90% CI 

100.5 

100.2, 101.3 

100.1, 101.9 

15 0.25 

b, 0.6 

b, 0.9 

0.5 

b, 1.2 

b, 1.9 

0.9 

b, 1.5 

b, 2 

1.5 

1.1, 1.9 

b, 3 

2 

1.3, 2.6 

b, 4 

Fitted Functions 

Median 

50Z CI 

90Z CI 

98Z CI 

100.9 

100.6, 101.2 

100.1, 101.7 

99.8, 102 

15 0.25 

0.2, 0.3 

0.1, 0.5 

0.1, 0.7 

0.5 

0.4, 0.7 

0.2, 1.1 

0.2, 1.4 

1.0 

0.7, 1.3 

0.5, 2.1 

0.3, 2.8 

1.4 

1.0, 1.9 

0.7, 3.0 

0.5, 4.1 

1.7 

1.3, 2.4 

0.8, 3.7 

0.6, 5.1 
TABLE C.7 (Cont'd) 

Index IQ, 'IQ 

AJQ at PbB Level 

5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Expert G, Low SES Level 

Encoded Judgments 

Median 

50% CI 

90% CI 

94 

93, 96 

91, 99 

Fitted Functions 

14 0.5 

0.3, 1 

0.2, 3 

1.5 

0.7, 2 

0.5, 5 

3.0 

1.3, 4 

1, 8.5 

3.5 

2.5, 5 

2, 10 

5.0 

4, 7 

3.5, 12 

7.0 

5, 10 

4, 15 

Median 

50% CI 

90% CI 

98% CI 

94.6 

93.1, 96.1 

91.0, 98.3 

89.6, 99.8 

14 0.6 

0.4, 0.9 

0.2, 1.8 

0.1, 2.8 

1.4 

1. 2 

0.6, 3.5 

0.4, 4.9 

2.7 

1.9, 3.8 

1.1, 6.3 

0.8, 9 

3.9 

3, 5 

2.1, 7.3 

1.6, 9.4 

5.7 

4.6, 7 

3.5, 9.3 

2.8, 11.4 

7.3 

5.9, 9.1 

4.3, 12.3 

3.5, 15.3 

Expert G, High SES Level 

Encoded Judgments 

Median 

50% CI 

90% CI 

106 

105, 107 

103, 109 

Fitted Functions 

Median 

50% CI 

90% CI 

98% CI 

105.5 

104.1, 107.0 

102.0, 109.2 

100.6, 110.7 

14 

14 

0.5 

0.4, 1 

0.3, 3 

1.0 

0.7, 2 

0.5, 4 

2.5 

1.5, 4 

1, 8 

3.5 

2.5, 5 

2, 10 

5.0 

4, 7.5 

3.5, 12 

0.7 

0.5, 1 

0.3, 1.8 

0.2, 2.7 

1.2 

0.9, 1.7 

0.5, 2.8 

0.4, 4 

2.6 

1.9, 3.6 

1.2, 5.8 

0.8, 8 

3.9 

3, 5 

2.1, 7.3 

1.6, 9.4 

5.8 

4.7, 7.1 

3.5, 9.5 

2.8, 11.7 
TABLE C.7 (Cont'd) 

AJQ at PbB Level 

Index IQQ oI Q 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Expert H, Low SES Level 

Encoded Judgments 

Median 

50% CI 

90% CI 

98 

95, 100 

92, 102 

13 

12, 14 

10, 15 

2.6 

1.6, 3.4 

1.1, 4.5 

3.0 

2.6, 5 

1.9, 6.1 

5.2 

3.4, 7.2 

2.4, 9.2 

8.2 

6, 9.7 

4.2, 12 

9.5 

7.4, 11.3 

6.2, 14 

10.5 

9.7, 11.8 

8.2, 16 

Fitted Functions 

Median 

50% CI 

90% CI 

98% CI 

97.2 

95.5, 98.8 

93.3, 101.2 

91.7, 102.9 

12.3 

11.5, 13.0 

10.5, 14.2 

9.9, 15.2 

2.3 

1.7, 3 

1.2, 4.5 

0.9, 5.9 

3.5 

2.7, 4.6 

1.8, 6.7 

1.4, 8.8 

4.9 

3.8, 6.3 

2.6, 9 

2, 11.7 

7.6 

6.2, 9.4 

4.6, 12.7 

3.7, 15.7 

9.4 

8, 11 

6.4, 13.9 

5.4, 16.3 

11.1 

9.7, 12.6 

8.1, 15.1 

7.1, 17.2 

Expert H, High SES Level 

Encoded Judgments 

Median 

50% CI 

90% CI 

106 

104, 108 

101, 110 

14.3 

13.8, 14.7 

13.2, 15.2 

0.6 

b, 0.9 

b, 1.3 

2.5 

1.8, 3.5 

1.2, 4.1 

4.5 

3.8, 5.6 

2.7, 6.7 

5.5 

4.4, 6.4 

3.9, 7.8 

6.5 

6.1, 7.1 

5.3, 8.4 

8.0 

7.4, 8.7 

6.4, 9.6 

Fitted Functions 

Median 

50% CI 

90% CI 

98% CI 

105.6 

103.7, 107.5 

101.1, 110.3 

99.3, 112.3 

14.3 

13.8, 14.6 

13.3, 15.2 

12.9, 15.6 

0.6 

0.4, 0.8 

0.2, 1.3 

0.2, 1.9 

2.4 

1.8, 3.3 

1.2, 5.1 

0.9, 7 

4.4 

3.7, 5.2 

2.9, 6.7 

2.4, 8 

5.4 

4.7, 6.2 

3.9, 7.5 

3.4, 8.5 

6.6 

6, 7.2 

5.3, 8.2 

4.9, 8.9 

7.9 

7.3, 8.5 

6.6, 9.5 

6.1, 10.2 
TABLE C.7 (Cont'd) 

Index IQQ oI Q 

Expert I, Low SES Level 

Encoded Judgments 

Median 

50% CI 

90% CI 

Fitted Functions 

Median 

50% CI 

90% CI 

98% CI 

Expert J, High SES Level 

Encoded Judgments 

Median 

50% CI 

90% CI 

Fitted Functions 

Median 

50% CI 

90% CI 

98% CI 

5 yg/dL 15 yg/dL 

0.7 

0.5, 1.1 

0, 2 

0.7 

0.5, 1.0 

0.3, 1.7 

0.2, 2.5 

0.3 

0.2, 0.5 

0, 1 

0.4 

0.2, 0.5 

0.1, 0.9 

0.1, 1.3 

AJQ at 

25 yg/dL 

2.3 

1.9, 3.2 

1, 5 

2.3 

1.7, 3.1 

1.2, 4.6 

0.9, 6.1 

1.0 

0.7, 2 

0, 3 

1.1 

0.6, 1.7 

0.1, 2.8 

0.1, 4.3 

1 

PbB Level 

35 yg/dL 

3.6 

3.1, 5.1 

2, 7 

3.8 

3.0, 4.7 

2.2, 6.5 

1.8, 8.2 

2.3 

1.9, 3.2 

1, 5 

2.4 

1.8, 3.2 

1.2, 4.5 

0.9, 6.1 

45 yg/dL 

5.3 

4.5, 6.9 

3, 10 

5.5 

4.4, 6.7 

3.3, 9.1 

2.7, 11.3 

3.6 

3.1, 4.7 

2, 7 

3.8 

3.1, 4.7 

2.2, 6.3 

1.8, 7.9 

.• 

55 yg/dL 

6.3 

5.5, 8.2 

4, 12 

6.7 

5.5, 8.1 

4.2, 10.7 

3.5, 13.1 

4.3 

3.5, 5.8 

2, 9 

• 

4.5 

3.4, 5.7 

2.3, 8.0 

1.8, 10.6 

0 
TABLE C.7 (Cont'd) 

AJQ at PbB Level 

Index iQc OJQ 5 yg/dL 15 yg/dL 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 

Expert J, Low SES Level 

Encoded Judgments 

Median 

50% CI 

90% CI 

95 

94, 96 

91, 99 

13 

12, 14 

11, 15 

2 

1, 3 

0.2, 5 

3.5 

2.3, 4.5 

0.4, 6.4 

5 

4, 5.8 

1, 8 

7 

6, 8 

3, 9.6 

9 

7.5, 10.5 

5, 11.7 

11 

9, 12.5 

6.6, 13.7 

1 Fitted Functions 

Median 94.8 

50% CI 93.5, 96.1 

90% CI 91.6, 98.0 

98% CI 90.3, 99.3 

Expert J, High SES Level 

Encoded Judgments 

Median 103.1 

50% CI 102.5, 103.9 

90% CI 100.5, 107.0 

Fitted Functions 

Median 104.1 

50% CI 103.0, 105.2 

90% CI 101.4, 106.8 

98% CI 100.4, 108.0 

13 

12.5, 13.5 

11.9, 14.1 

11.4, 14.6 

13 

12, 14 

11, 15 

13 

12.5, 13.5 

11.9, 14.1 

11.4, 14.6 

1. 

0. 

0. 

2. 

8, 

9, 

3, 

4 

3.0 

3.9 

4.5 

3.5 

2.7, 4.3 

1.5, 5.4 

0.7, 6.2 

2 

1.3, 2.3 

0.7, 3 

1.6 

1.2, 2.2 

0.7, 3.4 

0.5, 4.6 

4.8 

3.8, 5.8 

2.3, 7.2 

1.3, 8.2 

3 

2.8, 3.5 

1.4, 6.4 

2.7 

2.1, 3.5 

1.5, 5.0 

1.2, 6.4 

6.8 

5.8, 7.8 

4.4, 9.3 

3.3, 10.3 

4 

3.5, 5 

2, 6.7 

3.7 

3.0, 4.4 

2.3, 5.8 

1.9, 7.0 

8.8 

7.8, 9.9 

6.3, 11.4 

5.2, 12.5 

5 

4.5, 5.8 

3.3, 7.6 

"' 

5.0 

4.4, 5.8 

3.6, 7.0 

3.2, 8.0 

10.7 

9.7, 11.8 

8.1, 13.4 

7.0, 14.5 

7 

6.5, 7.5 

5.3, 9.7 

i 

7.0 j 

6.4, 7.8 ' 

5.5, 8.9 

5.0, 9.9 

; 
TABLE C.7 (Cont'd) 

Index IQQ 

Expert K, Low SES Level 

Encoded Judgments 

Median 85 

50% CI 83, 88 

90% CI 79, 90.4 

Fitted Functions 

Median 85 

50% CI 83.0, 87.0 

90% CI 80.2, 89.8 

98% CI 78.2, 91.8 

°IQ 

13 

12.2, 13.5 

11, 14 

12.6 

12.0, 13.2 

11.1, 14.1 

10.4, 14.8 

15 yg/dL 

1.5 

0.8, 1.7 

0.3, 2 

1.3 

0.7, 1.6 

0.5, 1.8 

0.2, 2.3 

25 yg/dL 

3.1 

2, 3.8 

1, 4.8 

2.9 

2.1, 3.6 

1.1, 4.7 

0.3, 5.5 

AIQ 

35 yg/dL 

4 

3.2, 4.7 

2, 5.8 

3.8 

3, 4.5 

2, 5.5 

1.3, 6.3 

at PbB Level 

45 yg/dL 

6 

5.4, 7.5 

4.5, 8.8 

6.4 

5.6, 7.3 

4.4, 8.4 

3.6, 9.3 

55 yg/dL 

8.1 

6.8, 8.6 

5.5, 9.8 

7.8 

6.9, 8.6 

5.6, 9.9 

4.7, 10.8 

65 yg/dL 

10 

8.8, 11.8 

7.5, 13.7 

10.4 

9.3, 11.4 

7.8, 13 

6.7, 14 

Expert K, High SES Level 

Encoded Judgments 

Median 

50% CI 

90% CI 

104.9 

102.6, 107.2 

100.6, 109.4 

tted Functions 

Median 

50% CI 

90% CI 

98% CI 

104.9 

103.3, 106.5 

101, 108.8 

99.4, 110.4 

13 

13, 

12.2, 

13 

13, 

12.3, 

11.9, 

.5 

14 

14.8 

.5 

14 

14.6 

15.1 

1.5 

0.8, 1.7 

0.6, 1.9 

1.3 

1, 1.5 

0.7, 1.9 

0.5, 2.1 

2 

1.6, 2.3 

1.2, 2.9 

2 

1.7, 2.3 

1.3, 2.7 

1, 3 

3.5 

3.1, 4 

2.2, 4.8 

3.5 

3.1, 4 

2.5, 4.6 

2, 5 

4.5 

4, 4.8 

3.1, 5.9 

4.5 

4, 5. 

3.3, '5.7 

2.8, 6.2 

6 

5.2, 6.8 

4.3, 7.8 

6 

5.4, 6.6 

4.5, 7.5 

3.9, 8.1 

aCI denotes credible interval. 

Lower CI limit could not be calculated because Experts F and H did not make probability judgments on 

A-TTT values less than the median at this PbB level. IQ 
Ui JJ> OJ iV» HUl UI UI UI UI UI 

as * at as as as 

o o o o o o 

r r* f r t- r; 

o o o o o o 

i i i i i i 

N> ro ts> *s> OJ ui 

..... . 

o to ui oo *» o 

OJ so ui o ui vo 

K> VO O J> O O 

KJ O SO O 00 00 

o o o o o o 

..... . 

K> 0J OJ *» Ui Os 

IO H M M vO U 

~J *» O 00 -J 00 

0J J> J> IsJ ««l *» 

H- vO *J Os OJ O 

..... . 

00 J> Os •-• Os -J 

OJ K> N> NI NI O 

..... . 

N> *J Os *> O *» 

h 

o 

IA 

oo 

UI 

OQ 

tr 

CA 

PI 

CA 

f 

ft 

< 

it 

UI *» 0J |SJ H-" 

UI UI UI UI UI UI 

o o o o o o 

SO VO sO vO vO sO 

sO vO VO so -J Ui 

as se as as as as 

o o o o o o 

c c r* r

1

 r* r* 

o o o o o o 

i i i i i i 

O H H H M N 

..... . 

^J O OJ VO 0J 00 

VO *» 0J OJ Os «»l 

Ui K» Os VO -J 4S 

vl(T>0>UiM H 

o o o o o o 

..... . 

OJ J> J> UI UI UI 

UI 00 0 U M H 

ui oo oo oo oo K> 

00 UI OJ UI OJ SO 

UNM H 

H- Os l— OJ SO Ul 

*• Os 00 «»J J > VO 

v l V 00 0> {> M 

. o . . . . 

OOiOOOUv l 

o o o o o o 

vo vO vO vO vO vO 

vO vO VO 00 00 00 

?> X 

•o 

rt 

h 

rt 

a: 

^ 

H 

O 

IA 

oo 

U I 

"• 

f 

o 

« 

M 

P I 

CA 

r 

ft 

< 

a 

!-• 

U I 

U I 

as 

o 

c 

o 

1 

N> 

• 

*» 

U I 

as 

o 

f 

o 

1 

ls> 

• 

jJN VO 

O J 

K> 

K> 0.4721 

oo 

->J 

O J 

SO 

oo 0.5311 U I 

Os 

OJ 

U I 

as 

o 

t -

o 

1 

U> 

. OJ 

00 

U I 

^ j 0.6215 OJ 

oo 

N» 

U i 

as 

o 

tr

1 

o 

1 

J > 

. K l 

K> 

Os 

J > 0.5954 H -

» J 

H -

U I 

as 

o 

f 

o 

1 

*• 

. 

oo 

K> 

SO 

SO 0.6663 •— 

o 

tfl 

X 

•o 

rtt 

h 

rt 

O 

N 

H 

"O 

IA 

00 

U i 

" 

s 

H « 

OQ 

ET 

CA 

PI 

W 

f 

ft 

< 

m 

U I 

U I 

as 

o 

i 

3 

to 

K> 

H -

O J 

J > 

U I 

as 

o 

i 

a 

0> 

•— 

Os 

• 

o 

O J 

U I 

as 

o 

i 

g 

• — • 

•— 

U I 

K> 

U I 

SS 

o 

1 

g 

SO 

¥-. 

t-> 

U I 

as 

o 

i 

3 

to 

• 

SO 

U I 

as 

o 

i 

3 

to 

*> 

tq 

X 

tJ 

rt 

h 

rt 

O 

% 

H 

O 

IA 

oo 

U I 

*• 

f 

o 

< 

CA 

P I 

CA 

f 

ft 

< 

m 

!-• 

o« UI *» OJ IS* 

UI UI UI UI U

as as ss ss as 

o o o o o 

1111 1 

g g g g g 

U K) N) H O 

.... . 

Os «J K) O 0> 

O O O O O 

vo vO s o s o so 

00 00 ->J v j UI 

OS *» J> *• K) H-

..... . 

00 vO OJ o» Ui *» 

o o o o o o 

SO s o s o s o so so 

^ »J •M f> OS f> 

M J W H O 

.... . 

O K> t-• H- U

•— H-< O O O 

o . . . . 

00 J> SO UI OJ 

o o o o o 

SO s o s o s o s o 

UI 0> Os -»l Os 
O* UI *» OJ K) 

UI UI UI UI UI 

I 

It 

h 

rt 

3 P 3 3 3 

to to to to o> 

as as as as as 

O O O O O IA 

1111 1 

3 -J 

o 

CA 

P I 

CA 

r

1 

rt 

< 

it 

H- o o o o 

.... . 

o oo ui io Ho o o o o 

.... . 

UI J> OJ •— •— 

o o o o o 

vO SO SO s o s o 

U I v l v l v l CO 

Os Ui J> OJ IO 

UI UI UI UI UI 

as as as ss as 

o o o o o 

r

1

 n c r

1

 r* 

o o o o o 

IIII I 

IO K> OJ OJ * » 

.... . 

J> oo H» oo OJ 

NMUHU I 

r o i— * » vo oo 

u i ^ H-» J > O 

o o o o o 

.... . 

OJ OJ OJ OJ *• 

H- IO *» OS M 

vO ~J io *• 00 

UI H- OS Os UI 

00 Ui Ms ) H 

.... . 

*» 00 *<• OJ *» 

fO o- I— o o 

.... . 

Ui 00 *» 00 Os 

It 

1 

rt 

H 

"O 

0O 

UI 

00 

9* 

CA 

PI 

CA 

f 

It 

< 

ft 

Os Ui J> OJ to H ^ 

UI UI UI UI UI UI 

as as as as as ss 

o o o o o o 

11111 1 

3 3 3 3 3 3 

to to to to to to 

& 

.X 

•a 

it 

i 

rt 

>s 

H 

O 

IA 

00 

U I 

"• 

f 

O 

s 

CA 

PI 

CA 

r* 

ft 

< 

it 

>-• 

U I 

U I 

as 

o 

c 

o 

1 

ro 

. O 

«sl 

U I 

o 

o 

. N > 

~ J 

>»J 

O J 

J > 

U I 

as 

o 

f 

o 

1 

to 

. 

U I 

O J 

to 

• - • 

o 

• 

O J 

I O 

U I 

1—• 

O J 

U I 

as 

o 

f 

o 

1 

to 

. 

VO 

O J 

to 

to 

o 

• O J 

oo 

-o 

U I 

to 

U I 

as 

o 

r* 

o 

i 

O J 

. 

I O 

OS 

O J 

O J 

o 

• 

*» 

V J , 

o 

U I 

•— 

U I 

as 

o 

f 

o 

1 

O J 

. 

oo 

oo 

Os 

oo 

o 

. U I 

O J 

« J 

O J 

tfl 

X 

t l 

t 

1 

rt 

«H 

% 

H 

"O 

I A 

0 0 

U I 

•• 

as 

»-•• OQ 

XT 

CA 

PI 

(A 

frit 

< 

rt 

H-» 

UI J> OJ t o •— 

UI UI UI UI UI 

as as ss as as 

o o o o o 

11111 

3 3 3 3 3 

0) 0) 0) 0) 0) 

oo K> co H oo w 

t o IO -si vO 

J> J> OJ U> OJ H-> 

..... . 

00 O «J IO OJ J> 

H s i U I * > N 

.... . 

OJ OS OJ O OJ 

NMHH H 

.... . 

VO OJ VO oo t o 

OJ K> I— t— 

O J> 00 t o s o 

OJ - o 0 0 vO Isl 

* » J > * > j > U> 

• « . . . 

vo oo ui to OJ 

o o o o o 

vO s o s o VO s o 

sO 00 SO VO -O 

o o o o o o 

SO so so vO so so 

SO 00 00 so so vO 

o o o o o 

vO s o s o s o vO 

vO SO sO 00 -g 

o o o o o 

sO so so so vO 

SO so so 00 00 
TABLE C.8 (Cont'd) 

i 

PbB 

. Level 

"(yg/dL) 

Expert 

5 

15 

25 

35 

45 

55 

Expert 

15 

25 

35 

45 

55 

Expert 

5 

15 

25 

35 

45 

55 

Expert 

5 

15 

25 

35 

45 

55 

Expert 

5 

15 

25 

35 

45 

55 

o, 

G, 

H, 

H, 

J, 

Functional 

Form 

IQ < 70, 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

IQ S 70, 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

IQ < 70, 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

IQ S 70, 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

IQ * 70, 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

Low 

13T 

Defining 

Parameters 

wy 

SES Level 

-5.4123 

-4.5825 

-3.8201 

-3.3673 

-2.8823 

-2.4877 

°y 

0.7608 

0.7137 

0.7204 

0.5560 

0.4934 

0.5490 

High SES Level 

Low 

-6.8990 

-6.3072 

-5.4150 

-4.9164 

-4.3577 

SES Level 

-4.7645 

-4.2186 

-3.7332 

-3.0392 

-2.6958 

-2.3930 

0.7389 

0.7189 

0.7421 

0.6530 

0.6024 

0.7706 

0.7796 

0.7789 

0.7292 

0.6406 

0.5844 

High SES Level 

Low 

-7.1075 

-5.4439 

-4.7471 

-4.4666 

-4.1788 

-3.8790 

SES Level 

-4.4206 

-3.9207 

-3.4556 

-2.8627 

-2.4235 

-2.0625 

0.7947 

0.7860 

0.6348 

0.5795 

0.5290 

0.5071 

0.6652 

0.6087 

0.5718 

0.4528 

0.4076 

0.3779 

Measures of 

Distribution 

EI*IQ] 

0.6 

1.3 

2.7 

3.8 

5.8 

8.5 

0.1 

0.2 

0.6 

0.9 

1.5 

1.1 

1.9 

3.0 

5.6 

7.4 

9.4 

0.1 

0.6 

1.0 

1.3 

1.7 

2.3 

1.5 

2.3 

3.5 

5.8 

8.6 

11.7 

SD[RIQ] 

0.4 

0.9 

1.8 

1.9 

2.6 

4.1 

0.1 

0.2 

0.4 

0.6 

0.9 

0.8 

1.4 

2.2 

3.7 

4.1 

4.7 

0.1 

0.4 

0.6 

0.7 

0.9 

1.1 

0.9 

1.3 

1.9 

2.4 

3.1 

3.9 

r

2 for 

Regression 

of F on F 

0.94 

0.95 

0.97 

0.98 

0.99 

0.98 

0.96 

0.97 

0.98 

0.98 

0.99 

0.97 

0.97 

0.98 

0.98 

0.98 

0.98 

0.97 

0.98 

0.99 

0.99 

0.99 

0.99 

0.96 

0.97 

0.98 

0.99 

0.99 

0.99 . 

P.39 

"•- ^ 
P.40 

TABLE C.8 (Cont'd) 

PbB 

Level 

(yg/dL) 

Expert J, 

15 

25 

35 

45 

55 

Expert K, 

15 

25 

35 

45 

55 

65 

Expert K, 

25 

35 

45 

55 

65 

Functional 

Form 

IQ < 70, 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

IQ S 70, 

Normal 

Normal 

Normal 

Normal 

Normal 

Normal 

IQ S 70, 

NOLO 

NOLO 

NOLO 

NOLO 

NOLO 

Hi Lgh 

Low 

H] Lgh 

Defining 

Parameters 

yy °y 

SES Level 

-6.1838 

-5.5216 

-5.1690 

-4.7212 

-4.1927 

SES Level 

0.7171 

0.6529 

0.5887 

0.5191 

0.4751 

SES Level 

-6.5690 

-6.0268 

-5.2946 

-4.9459 

-4.4969 

0.6485 

0.6122 

0.5926 

0.5723 

0.5548 

Measures of 

Distribution 

EIRIQI 

0.3 

0.5 

0.7 

1.0 

1.6 

2.4 

5.9 

7.7 

14.0 

17.5 

24.9 

0.2 

0.3 

0.6 

0.8 

1.3 

SD[RIQ] 

0.2 

0.3 

0.4 

0.5 

0.7 

1.0 

2.7 

2.9 

4.2 

4.9 

6.2 

0.1 

0.2 

0.3 

0.5 

0.7 

r

2 for 

Regression 

6'f F on F 

0.88 

0.98 

0.98 

0.99 

0.99 

0.96 

0.95 

0.96 

0.98 

0.98 

0.99 

0.98 

0.98 

0.98 

0.98 

0.98 

The main point of the table is to show that the fitted functions match the 

judgments quite well. The fitted median values are generally quite close to the assessed 

median values. The 50%- and 90%-CI values are also quite close. For example, Expert 

G* judged the median value for the mean IQ level for unexposed children in the low SES 

category to be 94 (see Table C.l), 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% CIs (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 

•Because Expert F did not provide judgments at 0.25 cumulative probability for three of 

the five PbB levels, the following discussion of CIs is based on Expert G's judgments. 
P.41 

ends of the 50% CIs (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 the mean IQ of children unexposed to lead to be about 101 with a 

high .degree of certainty, which is indicated by a standard deviation of about 0.5. The 

other experts judged the mean IQ of the unexposed high SES group to be three to five 

points higher, but with much less certainty, which is indicated by standard deviations 

that- ranged from 1.7 to 2.8. Expert F also judged much smaller IQ decrements 

attributable to lead exposure than did the other experts. 

Table C.8 summarizes distributions for population response rate, in percent, for 

the occurrence of IQ levels below 70 and 85 (i.e., increased percentage of occurrence of 

IQ levels below 70 or 85 among children exposed to lead versus those sheltered from 

lead). This table is identical in format to earlier tables, and entries were obtained by 

combining information on IQ , a , and A—. The tabulated values are for functions fit 

to intermediate results obtained through the steps outlined in Sec. C.2. 

For Expert F, small response rates were calculated for both of these critical IQ 

levels. In addition, normal distributions provided the best fits at both IQ levels. For IQ = 

85, mean response rates ranged from 0.5% at PbB = 25 yg/dL to 4% at 65 yg/dL; for IQ = 

70, results ranged from 0.1% to 1% at the corresponding PbB levels. The r values for 

regressions of intermediate numerical results and corresponding fitted distributions are 

high (the smallest is 0.95). Uncertainties in these results are small, evidenced by the 

small (relative to the mean values) standard deviation values, and expected because of 

the small degree of uncertainty expressed by Expert F for I Q , o , and A—. 

While the judgments of the experts 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 DISCUSSION SUMMARIES 

The following summaries are based on notes taken during the interviews with the 

experts. At times, the points made are fragmentary and highly specialized. Each expert 

has had at least one opportunity to review his or her section. 

C.4.1 Expert F 

• Low PbB levels (< 30-40 yg/dL) do not have a discernible deleterious 

effect on IQ. Studies that purport to show such an effect have 

methodological and bias problems. 

• Although low PbB levels do not have independent effects on IQ, one 

cannot 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 PbB level. Related variables 
P.42 

might include general health status, mental health status, and other 

environmental factors. 

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. 

Behavioral, social, and cognitive measures have some degree of 

unreliability, which adds uncertainty to any conclusions. 

Cord PbB may be related to a few negative birth outcomes, but 

direction of causality cannot be inferred from such data. Perhaps a 

distressed fetus accumulates lead. 

There is a fairly strong correlation (about 0.8) between maternal 

PbB and cord PbB. 

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, may be able to compensate. 

The existence of a threshold level for the effects of lead on IQ is 

not indicated by the available evidence. 

The assumption of normal IQ distributions within exposure groups in 

the hypothetical experiment is reasonable, except that at high PbB 

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 Expert G 

• There are no data to suggest that the physiological response to lead 

varies as a function of SES level. 

• The effects of lead on the developing CNS are probably long lasting 

and irreversible. 

• If there is a threshold for the effects of lead on IQ, it is very low. 

• Animal models for risk assessment have limited usefulness because 

of the difficulty in extrapolating to humans in a quantitative 

manner. Their importance is in studying mechanisms of lead effects 

and topics such as the reversibility of effects and vulnerable periods 

of development, not in establishing dose-response relationships that 

are directly applicable to humans. 
TTF 

• Specific neurobehavioral effects of lead, such as attentional 

deficits, should not be overlooked. 

• It is reasonable to assume normally distributed IQ scores within 

exposure groups as in the hypothetical experiment. 

C.4.3 Expert H 

• Lead interacts with other factors to affect IQ. Such factors include 

SES, maternal stimulation, and nutrition. 

• The concept of critical developmental periods is crucial in 

understanding the effects of lead on IQ. When opportunities for 

intellectual development are lost, it is very hard to compensate for 

them later. This situation is especially true in low SES children. 

Furthermore, the effect can snowball, in that skills generally build 

on each other. 

• Children exposed to lead also tend to be exposed to cadmium, 

pesticides, etc. This pattern is especially true for low SES children. 

• No data exist on the minimum exposure time necessary to produce 

an effect. 

• At a given dose level, the cumulative effects are worse than the 

immediate effects. Exposures earlier in life have more effect than 

those later in life. 

• Some effects of lead are reversible and others are not. 

• Rat studies have indicated that the half-life of lead in the brain is 

very long. 

• Some recent research suggests that lead may be involved in 

senility. The amount of bone lead decreases with age. It may be 

eliminated or recirculated. In the latter case, lead may have 

neurobehavioral effects. 

• It is reasonable to assume that IQ is normally distributed within 

exposure groups as in the hypothetical experiment. 

• Important research related to behavioral toxicology is being 

conducted. 
P.44 

C.4.4 Expert I 

The meta-analyses occasionally done as part of studies on the 

effects of lead on IQ are inappropriate because the studies differ in 

so many ways — different ages of the subjects, different sorts of 

control groups, different methods, and different exposure 

conditions. 

It is reasonably certain that PbB levels above 30 yg/dL affect IQ, 

but it is less clear whether there is an effect at lower levels. 

There is an exposure-sensitivity interaction, in that children who 

suffer the greatest exposure to lead tend to be those who are most 

susceptible to its effects. 

Except for high acute exposures, neurobehavioral effects are more 

likely to result from chronic than from acute exposures. 

One should distinguish between the biological and functional effects 

of lead, but in either case there are no data suggesting that the 

effects are necessarily irreversible. 

The data are not clear on whether a threshold exists for the effects 

of lead on IQ. 

C.4.5 Expert J 

• Lead does have a deleterious effect on neurobehavioral 

development. In this regard, lead interacts with diet and SES 

factors. 

• Middle-class children are somewhat buffered against the negative 

effects of lead by virtue of their better diet, higher general health 

status, and richer intellectual resources. 

• Lead crosses the blood-brain barrier. Once in brain cells, it stays 

there and affects the neurotransmitters. It cannot be chelated 

out. The effects are irreversible. 

• Research with animals suggests that lead causes demyelination, but 

it is not clear whether this effect occurs in children. 

• The implications of the EEG data are not clear. The findings are 

somewhat inconsistent, and it is not known what the measures refer 

to. 
P.45 

Although some functional effects of lead may be reversible, 

morphological effects are not. 

There is probably no threshold for the effects of lead; if there is 

one, it is very low. Studies on primates suggest the absence of a 

threshold. 

The possibility of racial differences in terms of the effects of lead 

is a very complicated issue that remains to be untangled. 

The assumption that IQ scores are normally distributed within 

exposure groups in the hypothetical experiment is reasonable, with 

the possible exception of the 55-yg/dL group. 

C.4.6 Expert K 

• Children of all genotypes are vulnerable to the effects of lead. 

• Some neurobehavioral effects of lead, such as the effect on 

attention span, are reversible. These effects are generally 

associated with low levels of exposure. Even some perinatal effects 

can be reversed with proper treatment. 

• Other neurobehavioral effects are irreversible, including 

morphological changes and the effects on some behaviors that 

depend on critical developmental periods. 

• Blood-lead levels of 5-55 yg/dL have a deleterious effect on IQ in 

the presence of other factors. However, the interaction of lead 

with other factors is only in one direction, so that a multivariate 

analysis of variance would show both an interaction and a main 

effect. 

• Some of the factors that lead interacts with are physical and 

psychological hygiene, physiological status, parental IQ, nutritional 

and health status, organophosphates, and pesticides. 

• Early, long-term exposure to lead can lead to long-term effects; 

episodic exposure is more likely to lead to reversible effects, if the 

exposure is not too great. 

• A threshold exists for the effects of lead on IQ. 

• The assumption that IQ scores are normally distributed within 

exposure groups in the hypothetical experiment is reasonable. 
^^^p^^^^F^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^w^wrv^^^r^^^^^^^^^^^^^^^^^^^^^-T^i 

APPENDIX D 

RISK DISTRIBUTIONS 
143 

APPENDIX D 

RISK DISTRIBUTIONS 

The dose-response functions for the different health effects were combined with 

specified PbB distributions to estimate risk distributions. The PbB distributions, which 

are assumed to be lognormal with a GSD of 1.42 yg/dL, have one of 11 GM values that 

increase in steps of 2.5 yg/dL from 2.5 yg/dL to 27.5 yg/dL. Section D.l describes the 

method used to combine the PbB distributions and dose-response functions to obtain risk 

distributions. The next three sections present the resulting risk distributions for leadinduced EP, Hb, and IQ health effects, respectively. 

These last three sections consist mainly of tables that list fractiles (i.e., selected 

cumulative probability levels), means, and standard deviations of risk distributions for 

the lead-induced EP, Hb, and IQ health effects considered in this report. Details 

concerning the format of the tables are explained in the text. The tabular material 

provides the data points for Figs. 21-24 in Sec. 5 and for additional analysis. 

D.l METHOD FOR COMBINING PbB DISTRIBUTIONS WITH DOSE-RESPONSE 

FUNCTIONS TO CALCULATE RISK DISTRIBUTIONS 

The method used to combine a PbB distribution with a set of dose-response 

functions to calculate risk estimates is relatively simple but certain features need 

explanation. First, in calculating a set of PbB probabilities, the population PbB levels 

are assumed to be lognormally distributed, with specified GM and GSD values. Thus, for 

given GM and GSD values, the fraction F of a population having PbB levels < L is given 

by 

F(L) = •~1[ln(L/GM)/ln(GSD)] 

and the fraction F having PbB levels in the interval Lj to L2 is given by 

F(L, < L < L 2 > - F(L2) - F(LX) 

where • denotes the inverse of the CDF for the standardized normal distribution. For 

example, if GM = 15 yg/dL; GSD = 1.42 yg/dL; and the PbB intervals are 0-10, 10-20, 

30-40, 40-50, and 50-60 yg/dL (designated by their midpoints 5, ..., 55 yg/dL; then the 

cumulative probabilities are 0.12, 0.79, 0.98, 0.99, 1, and 1. The corresponding fractions, 

which are probabilities, are 0.12, 0.67, 0.19, 0.01, 0.01, and 0 for the six intervals. These 

PbB probabilities are denoted as p p ..., pg. 

To calculate the median overall response rate for a specific set of dose-response 

functions, the median response rate at each PbB level is multiplied by the corresponding 
P.48 

PbB probability and then summed across the PbB levels. Mathematically, this step can 

be written as 

R

0.5

 = X PiR

0.5,i

 f0 r i=1 ' 

i=l 

where Rg 5 denotes the median value of the overall response rate, and RQ^ J denotes the 

median response rate at PbB level i. For example, the median response rates of the 

functions fit to the judgments of Hb Expert E for children aged 0-3 at Hb level < 9.5 g/dL 

are 1.5%, 2.4%, 3.4%, 5%, 11%, and 13% (see Table B.4). Applying the last formula 

yields 2.5% for the median response rate based on the judgments of Expert E and a 

lognormal PbB distribution with GM = 15 yg/dL and GSD = 1.42 yg/dL. In a similar 

fashion, the response rate at any cumulative probability level can be calculated. Again 

for Expert E, the response rates at 0.95 cumulative probability are 6%, 9%, 12%, 16%, 

32%, and 36%, with a median response rate of 9.2%. At the 0.05 probability level, the 

result is 0.2%. Thus, the 90% CI is 0.2-9.2%. Repeated application of the formula at 

selected cumulative probabilities defines a CDF for the overall response rate. 

The above calculations assume that the dose-response distributions for a specific 

expert at the different PbB levels are perfectly and positively correlated. For example, 

if children with PbB level Lj have a response rate corresponding to cumulative 

probability 0.95, then the response rates at all other PbB levels will correspond to the 

0.95 cumulative probabilities. Thus, continuing the example with the judgments of 

Expert E, if the response rate for children having a PbB level of 5 yg/dL is assumed to be 

6%, then the response rates at the other PbB levels are assumed to be 9%, 12%, 16%, 

32%, and 36% (for PbB levels of 15, ..., 55 yg/dL, respectively). 

The independence assumption may not be exactly correct; however, to have 

explored the matter in any detail would have required more time with each expert than 

was available. Assessment of at least 5-10 conditional probability distributions for all 

but one of the PbB levels would have been required. For that level of effort, the likely 

result would be a family of distributions having a high degree of dependency and one that 

closely approximated the set of single distributions, one at each PbB level. 

The appropriateness of the approach can be further argued as follows. If probability distributions had been encoded at many more PbB levels (say at every 0.1 yg/dL 

instead of at every 10 yg/dL), then the adjacent curves would have been very close. For 

example, the curve at 10.6 yg/dL would have been shifted a little to the right of the 

curve at 10.5 yg/dL. The method would certainly have been more accurate but not 

necessarily more convincing. Considering a maximum of six curves means that the 

method is less accurate than it might have been. However, we argue, without proof, that 

six curves are sufficiently accurate for our purpose. The sensitivity analysis described in 

Sec. 5.5 supports this belief. 
TW 

D.2 ESTIMATES OF RISKS OF LEAD-INDUCED EP EFFECTS AMONG 

U.S. CHILDREN AGED 0-6 

Probabilistic dose-response functions for two EP levels considered to be adverse 

(> 33 yg/dL and > 53 yg/dL) were considered in Sec. 2 and App. A. Response-rate 

probability distributions for populations of children were estimated by combining the 

dose-response functions for particular PbB levels with PbB distributions in the manner 

described in Sec. D.l. The results for EP are listed in Table D.l. Entries in the table are 

response rates for the occurrence of EP levels above one of two risk levels among U.S. 

children aged 0-6. There is a column of numbers for each of the 11 GM PbB levels considered in this analysis. The first five numbers in each column are the 0.05, 0.25, 0.50, 

0.75, and 0.95 fractiles (cumulative probabilities) of the resultant risk distribution. The 

next two numbers are the mean and standard deviation. For example, for EP > 53 yg/dL 

and GM = 15 yg/dL, the fractiles are 4.1%, 4.9%, 5.5%, 6.0%, and 6.8%, the mean is 

5.5%, and the standard deviation is 0.8%. The 0.5 fractile is the median, the 0.25 and 

0.75 fractiles define the 50% CI, and the 0.05 and 0.95 fractiles define the 90% CI. 

At low GM PbB levels, the risk distributions converge on the response-rate 

probability distribution for the lowest PbB level considered (2-17 yg/dL) (see Table A.l). 

Thus, the tabulated risk distributions for GM = 2.5-5.0 yg/dL are normal, with mean 2.4% 

TABLE D.l Risk Estimates for Lead-Induced Elevated EP Levels, U.S. Children Aged 0-6 

Fractiles, 

Mean, and 

Standard 

Deviation 

EP > 53 vg/dL 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

2.5 

1.5 

2.0 

2.4 

2.8 

3.3 

2.4 

0.5 

Response 

5.0 

1.5 

2.0 

2.4 

2.8 

3.3 

2.4 

0.5 

7.5 

1.6 

2.1 

2.4 

2.8 

3.3 

2.4 

0.5 

Rate (Z) 

10.0 

1.8 

2.3 

2.7 

3.1 

3.6 

2.7 

0.6 

at Ceometric 

12.5 

2.5 

3.2 

3.6 

4.0 

4.7 

3.6 

0.7 

15.0 

4.1 

4.9 

5.5 

6.0 

6.8 

5.5 

0.8 

Mean PbB Level 

17.5 

6.7 

7.8 

8.5 

9.2 

10.3 

8.5 

1.1 

20.0 

10.4 

11.8 

12.7 

13.6 

14.9 

12.7 

1.4 

in ug 

22.5 

15.0 

16.7 

17.9 

19.0 

20.6 

17.9 

1.7 

/dL 

25.0 

20.3 

22.5 

23.9 

25.2 

27.1 

23.8 

2.1 

27.5 

26.2 

28.7 

30.4 

32.0 

34.1 

30.3 

2.4 

EP > 33 ug/dL 

0.05 

0.25 

0.50 

• 0.75 

0.95 

Mean 

SD 

8.9 

10.0 

10.7 

11.4 

12.5 

10.7 

1.1 

8.9 

10.0 

10.7 

11.4 

12.5 

10.7 

1.1 

9.0 

10.1 

10.8 

11.5 

12.6 

10.8 

1.1 

9.5 

10.6 

11.4 

12.1 

13.2 

11.4 

1.1 

11.3 

12.4 

13.3 

14.1 

15.3 

13.3 

1.2 

14.5 

15.9 

16.8 

17.8 

19.1 

16.8 

1.4 

19.3 

20.8 

21.9 

23.0 

24.5 

21.9 

1.6 

25.1 

26.9 

28.1 

29.4 

31.1 

28.1 

1.8 

31.6 

33.6 

35.0 

36.4 

38.2 

35.0 

2.0 

38.3 

40.6 

42.1 

43.6 

45.6 

42.1 

2.2 

44.9 

47.5 

49.1 

50.7 

52.7 

49.0 

2.4 
P.50 

and SD = 0.5%. As GM increases, dose-response functions for PbB levels above the 

threshold (16.5 yg/dL) begin to influence the risk calculations. 

D.3 ESTIMATES OF RISKS OF LEAD-INDUCED Hb EFFECTS AMONG 

U.S. CHILDREN AGED 0-3 

The calculation of risk estimates for lead-induced Hb effects is almost identical 

to that for EP effects. The only difference is that normal and beta distributions were 

used to represent uncertainty about the EP dose-response functions, whereas NOLO 

distributions were used for the Hb functions. The NOLO distributions best represented 

the judgments of the experts consulted. Table D.2 presents the risk estimates for the 

occurrence of Hb levels below one of two critical levels. The format is the same as that 

in Table D.l, except that the results for individual experts are listed. 

Recall that Expert A judged that lead exposure would not cause Hb levels to be 

< 9.5 g/dL (see Fig. 22), so no results are listed for that level for Expert A. Expert B did 

not provide any probabilistic judgments, so no risk results could be calculated. Expert C 

provided judgments for children aged 0-6, explaining that the differences between 

children aged 0-3 and 4-6 were small and hard to distinguish. He agreed that his 

judgments could be used for both age categories. Experts D and E provided judgments 

for all four age-Hb combinations. 

As was true for EP, the risk distributions converge on the response-rate 

probability distribution for PbB = 5 yg/dL at low GM PbB values. Thus, the Expert C risk 

distributions at GM = 2.5 yg/dL and 5.0 yg/dL are NOLO distributed with a mean 

response rate of 1.9%, an SD of 0.5%, and a uv of -4 and a ov of 0.28 (see Table B.3). 

If desired, the distributions conditional on age can be combined to produce 

further risk distributions. That aeross-age calculation would be simple to perform if the 

relative proportion of children in the two age groups were specified. However, that 

proportion is site specific and was not considered in this analysis. 

D.4 ESTIMATES OF RISKS OF LEAD-INDUCED IQ EFFECTS AMONG 

U.S. CHILDREN AGED 7 

Two IQ health effects were considered: IQ decrement and the increased 

probability (expressed as a response rate in percent) of having IQ values less than a 

specified critical level IQ*. Calculations of the risk of IQ decrements are quite simple 

and similar to those for EP and Hb. The calculated risk distributions followed directly 

from the encoded judgments of the experts regarding IQ decrement. 

Calculating risk distributions of the second type is more complicated and 

includes the uncertainties in 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 low and high SES populations. The spirit of the calculation is as follows. 
P.51 

147 

TABLE D.2 Risk Estimates for Hb Levels < 9.5 and < 11 g/dL, U.S. Children Aged 0-3 

and 4-6 

Fractiles 

Mean, and 

Standard 

Deviation 

Expert C, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert D, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert E, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert C, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

> 

Hb 

Hb 

Hb 

Hb 

2.5 

< 9.5 

1.1 

1.5 

1.8 

2.2 

2.8 

1.8 

0.5 

< 9.5 

0 

0 

0 

0 

0 

0 

0 

< 9.5 

0.5 

1.2 

2.2 

4.2 

10.0 

3.3 

3.3 

< 9.5 

1.1 

1.5 

1.8 

2.2 

2.8 

1.9 

0.5 

Re 

5.0 

9/dL, 

1.2 

1.5 

1.8 

2.2 

2.9 

1.8 

0.5 

9/dL, 

0 

0 

0 

0 

. 0 

0 

0 

9/dL, 

0.5 

1.2 

2.3 

4.3 

10.3 

3.5 

3.4 

9/dL, 

1.2 

1.5 

1.8 

2.2 

2.9 

1.9 

0.5 

sponse Rate (Z) 

7.5 

Ages 0-3 

1.3 

1.7 

2.1 

2.5 

3.2 

2.1 

0.6 

Ages 0-3 

0.1 

0.2 

0.2 

0.3 

0.4 

0.2 

0.1 

Ages 0-3 

0.6 

1.6 

3.0 

5.5 

12.6 

4.3 

4.1 

Ages 4-6 

1.3 

1.7 

2.1 

2.5 

3.2 

2.1 

0.6 

10.0 

1.6 

2.1 

2.5 

3.0 

3.8 

2.6 

0.7 

0.3 

0.4 

0.5 

0.7 

1.0 

0.6 

0.2 

0.9 

2.2 

4.0 

7.4 

16.5 

5.8 

5.3 

1.6 

2.1 

2.5 

3.0 

3.8 

2.6 

0.7 

at Geometric 

12.5 

1.8 

2.4 

2.9 

3.4 

4.4 

3.0 

0.8 

0.5 

0.7 

0.9 

1.1 

1.6 

0.9 

0.3 

1.1 

2.7 

5.0 

9.1 

20.1 

7.1 

6.4 

1.8 

2.4 

2.9 

3.4 

4.4 

3.0 

0.8 

15.0 

2.0 

2.7 

3.2 

3.8 

4.9 

3.3 

0.9 

0.7 

1.0 

1.2 

1.6 

2.2 

1.3 

0.5 

1.3 

3.2 

5.8 

10.6 

22.8 

8.1 

7.2 

2.0 

2.7 

3.2 

3.8 

4.9 

3.3 

0.9 

Mean PbB Level 

17.5 

2.2 

2.9 

3.5 

4.1 

5.4 

3.6 

1.0 

1.0 

1.4 

1.7 

2.2 

3.0 

1.8 

0.6 

1.4 

3.6 

6.6 

11.8 

25.1 

9.1 

7.8 

2.2 

2.9 

3.5 

4.1 

5.4 

3.6 

1.0 

20.0 

2.4 

3.1 

3.7 

4.5 

5.8 

3.9 

1.0 

1.4 

1.9 

2.4 

3.0 

4.1 

2.5 

0.8 

1.6 

4.0 

7.4 

13.1 

27.3 

10.0 

8.4 

2.4 

3.1 

3.7 

4.5 

5.8 

3.9 

1.0 

in UR 

22.5 

2.6 

3.4 

4.0 

4.8 

6.2 

4.2 

1.1 

1.8 

2.6 

3.2 

4.0 

5.4 

3.4 

1.1 

1.8 

4.5 

8.2 

14.5 

29.5 

11.0 

9.0 

2.6 

3.4 

4.0 

4.8 

6.2 

4.2 

1.1 

/dL 

• 25.0 

2.8 

3.6 

4.3 

5.1 

6.6 

4.4 

1.2 

2.4 

3.4 

4.2 

5.2 

7.0 

4.4 

1.4 

2.1 

5.0 

9.1 

15.9 

31.8 

12.0 

9.6 

2.8 

3.6 

4.3 

5.1 

6.6 

4.4 

1.2 

27.5 

2.9 

3.8 

4.5 

5.4 

7.0 

4.7 

i.2 

3.1 

4.3 

5.3 

6.:. 

8.fe 

5.5 

1.8 

2.3 

5.6 

10.1 

17.4 

34.1 

13,1 

10.2 

2.9 

3.8 

4.5 

5.4 

7.0 

4.7 

1.2 
P.52 

TABLE D.2 (Cont'd) 

Fractiles, 

Mean, and 

Standard 

Deviation 

Expert D, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert E, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Hb 

Hb 

2.5 

< 9.5 

0 

0 

0 

0 

0 

0 

0 

< 9.5 

0.4 

0.9 

1.5 

2.6 

5.7 

2.1 

1.8 

Response 

5.0 

g/dL, 

0 

0 

0 

0 

0 

0 

0 

g/dL, 

0.4 

0.9 

1.6 

2.7 

5.8 

2.1 

1.8 

7.5 

Ages 4-

0 

0 

0 

0 

0 

0 

0 

Ages 4-

0.5 

1.0 

1.7 

3.0 

6.3 

2.3 

2.0 

Rate 

6 

6 

10. 

0 

0 

0 

0 

0 

0 

0 

0. 

1. 

2. 

3. 

7. 

2 

2 

(Z) 

0 

5 

2 

0 

5 

3 

7 

3 

at Geometric 

12.5 

0 

0 

0 

0.1 

0.1 

0.1 

0 

0.6 

1.3 

2.3 

3.9 

8.3 

3.1 

2.6 

15.0 

0.1 

0.1 

0.1 

0.2 

0.3 

0.2 

0.1 

0.7 

1.5 

2.6 

4.4 

9.3 

3.5 

2.9 

Mean PbB Level 

17.5 

0.2 

0.3 

0.4 

0.5 

0.7 

0.4 

0.2 

0.8 

1.7 

2.9 

4.9 

10.2 

3.8 

3.2 

20.0 

0.5 

0.6 

0.7 

0.9 

1.2 

0.8 

0.2 

0.9 

1.9 

3.2 

5.5 

11.3 

4.3 

3.5 

in ug/dL 

22.5 

0.8 

1.0 

1.2 

1.4 

1.9 

1.2 

0.4 

1.0 

2.1 

3.6 

6.1 

12.5 

4.8 

3.8 

25.0 

1.2 

1.5 

1.8 

2.1 

2.7 

1.8 

0.5 

1.1 

2.4 

4.1 

6.9 

13.9 

5.4 

4.2 

. 

27.5 

1.7 

2.1 

2.4 

2.8 

3.6 

2.5 

0.6 

1.3 

2.8 

4.7 

7.8 

15.5 

6.1 

4.7 

Expert A, Hb < 11 g/dL, Ages 0-3 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.1 

0.2 

0.1 

0.1 

0.1 

0.2 

0.3 

0.5 

0.9 

0.4 

0.3 

0.3 

0.5 

0.8 

1.2 

2.1 

0.9 

0.6 

0.5 

0.9 

1.4 

2.1 

3.8 

1.6 

1.1 

0.7 

1.3 

2.1 

3.2 

5.8 

2.5 

1.6 

1.0 

1.8 

2.9 

4.4 

7.8 

3.4 

2.2 

1.3 

2.4 

3.7 

5.6 

10.0 

4.4 

2.8 

1.6 

3.0 

4.6 

6.9 

12.1 

5.4 

3.4 

Expert C, Hb < 11 g/dL, Ages 0-3 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

1.6 

2.1 

2.5 

2.9 

3.8 

2.5 

0.7 

1.7 

2.2 

2.6 

3.1 

4.0 

2.7 

0.7 

2.5 

3.3 

3.9 

4.6 

5.9 

4.0 

1.0 

3.9 

5.0 

6.0 

7.0 

8.9 

6.1 

1.5 

5.1 

6.5 

7.7 

9.1 

11.5 

8.0 

2.0 

6.0 

7.6 

9.0 

10.6 

13.4 

9.3 

2.3 

6.6 

8.5 

10.0 

11.7 

14.7 

10.2 

2.5 

7.2 

9.2 

10.8 

12.7 

15.9 

11.1 

2.6 

7.8 

10.0 

11.7 

13.7 

17.1 

12.0 

2.8 

8.5 

10.8 

12.6 

14.8 

18.4 

12.9 

3.0 

9.2 

11.6 

13.6 

15.9 

19.7 

13.9 

3.2 
TABLE D.2 (Cont'd) 

i.HSFractiles 

Mean, and 

Standard 

Deviation 

Expert D, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert E, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert A, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert C, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

> 

Hb 

Hb 

Hb 

Hb 

2.5 

< 11 

1.8 

2.9 

4.0 

5.5 

8.6 

4.5 

2.1 

< 11 

3.5 

6.0 

8.7 

12.5 

20.4 

9.9 

5.3 

< 11 

0 

0 

0 

0 

0 

0 

0 

< 11 

1.6 

2.1 

2.5 

2.9 

3.8 

2.5 

0.7 

Re: 

5.0 

sponse Rate (Z) 

7.5 

g/dL, Ages 0-3 

1.9 

3.0 

4.1 

5.6 

8.7 

4.5 

2.2 

2.1 

3.3 

4.5 

6.1 

9.5 

5.0 

2.4 

g/dL, Ages 0-3 

3.5 

6.0 

8.8 

12.6 

20.5 

10.0 

5.4 

3.6 

6.3 

9.2 

13.1 

21.3 

10.4 

5.5 

g/dL, Ages 4-6 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

g/dL, Ages 4-6 

1.7 

2.2 

2.6 

3.1 

4.0 

2.7 

0.7 

2.5 

3.3 

3.9 

4.6 

5.9 

4.0 

1.0 

10.0 

2.5 

3.9 

5.3 

7.3 

11.2 

5.9 

2.7 

3.9 

6.8 

9.8 

14.0 

22.5 

11.1 

5.9 

0 

0 

0 

0 

0 

0 

0 

3.9 

5.0 

6.0 

7.0 

8.9 

6.1 

1.5 

at Geometric 

12.5 

3.0 

4.7 

6.5 

8.7 

13.3 

7.1 

3.2 

4.2 

7.2 

10.4 

14.9 

23.8 

11.7 

6.1 

0 

0 

0 

0 

0 

0 

0 

5.1 

6.5 

7.7 

9.1 

11.5 

8.0 

2.0 

15.0 

3.7 

5.8 

7.8 

10.5 

15.7 

8.5 

3.8 

4.4 

7.6 

11.0 

15.6 

24.8 

12.4 

6.4 

0 

0 

0 

0 

0 

0 

0 

6.0 

7.6 

9.0 

10.6 

13.4 

9.3 

2.3 

Mean PbB Level 

17.5 

4.5 

7.0 

9.4 

12.6 

18.5 

10.2 

4.4 

4.7 

8.1 

11.6 

16.4 

25.9 

13.0 

6.6 

0 

0 

0 

0 

0 

0 

0 

6.6 

8.5 

10.0 

11.7 

14.7 

10.2 

2.5 

20.0 

5.4 

8.3 

11.1 

14.7 

21.4 

12.0 

5.0 

5.0 

8.5 

12.3 

17.3 

27.1 

13.7 

6.9 

0 

0 

0 

0 

0 

0 

0 

7.2 

9.2 

10.8 

12.7 

15.9 

11.1 

2.6 

in pg 

22.5 

6.2 

9.6 

12.8 

16.8 

24.2 

13.7 

5.5 

5.3 

9.1 

13.0 

18.2 

28.4 

14.4 

7.2 

0 

0 

0 

0 

0.1 

0 

0 

7.8 

10.0 

11.7 

13.7 

17.1 

12.0 

2.8 

/dL 

25.0 

7.0 

10.8 

14.3 

18.8 

26.7 

15.3 

6.1 

5.7 

9.7 

13.8 

19.3 

29.8 

15.3 

7.5 

0 

0 

0.1 

0.1 

0.2 

0.1 

0 

8.5 

10.8 

12.6 

14.8 

18.4 

12.9 

3.0 

27.5 

7.8 

12.0 

15.8 

20.6 

29.1 

16.8 

6.5 

6.1 

10.4 

14.8 

20.5 

31.3 

16.2 

7.8 

0 

0.1 

0.1 

0.2 

0.3 

0.1 

0.1 

9.2 

11.6 

13.6 

15.9 

19.7 

13.9 

3.2 
P.54 

TABLE D.2 (Cont'd) 

Fractiles, 

Mean, and 

Standard 

Deviation 

Expert D, Hb 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert E, Hb 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

2.5 

< 11 

0.9 

1.5 

2.0 

2.8 

4.4 

2.3 

1.1 

< 11 

2.1 

3.7 

5.4 

7.9 

13.2 

6.3 

3.5 

Re 

5.0 

sponse Rate (Z) 

7.5 

g/dL, Ages 4-6 

0.9 

1.5 

2.1 

2.8 

4.5 

2.3 

1.1 

1.0 

1.6 

2.2 

3.1 

4.8 

2.5 

1.2 

g/dL, Ages 4-6 

2.1 

3.7 

5.5 

7.9 

13.3 

6.3 

3.5 

2.2 

3.9 

5.7 

8.3 

13.8 

6.6 

3.7 

10.0 

1.2 

1.9 

2.6 

3.6 

5.5 

2.9 

1.3 

2.4 

4.2 

6.1 

8.9 

14.7 

7.0 

3.9 

at Geometric 

12.5 

1.6 

2.4 

3.1 

4.2 

6.2 

3.4 

1.4 

2.6 

4.6 

6.7 

9.6 

15.8 

7.6 

4.2 

15.0 

2.2 

3.1 

3.9 

4.9 

6.9 

4.1 

1.5 

2.9 

5.0 

7.2 

10.4 

17.0 

8.2 

4.5 

Mean PbB Level 

17.5 

3.0 

3.9 

4.7 

5.7 

7.7 

4.9 

1.5 

3.2 

5.4 

7.9 

11.3 

18.4 

9.0 

4.8 

20.0 

3.8 

4.7 

5.5 

6.6 

8.5 

5.7 

1.4 

3.5 

6.0 

8.6 

12.3 

19.8 

9.7 

5.1 

in ug 

22.5 

4.5 

5.5 

6.4 

7.4 

9.2 

6.6 

1.4 

3.8 

6.5 

9.3 

13.2 

21.2 

10.5 

5.5 

/dL 

25.0 

5.2 

6.3 

7.1 

8.2 

9.9 

7.3 

1.4 

4.1 

7.0 

10.0 

14.2 

22.6 

11.3 

5.8 

27.5 

5.8 

6.9 

7.8 

8.9 

10.6 

8.0 

1.5 

4.4 

7.5 

10.8 

15.2 

23.9 

12.0 

6.1 

The numerical methods described in Sec. C.2 were used to obtain IQ doseresponse functions. The first step was to change each CDF for I Q , OJQ, and ATTT into a 

discrete PMF with a reasonable number of points. For every combination of the above 

three variables, a distribution for the increased probability of having IQ values less than 

or equal to IQ* was calculated at each PbB level for which IQ decrement judgments had 

been obtained. To facilitate further calculations, distribution functions (either normal or 

NOLO) were fit to the results, which were dose-response distributions conditional on PbB 

level. At this point, the calculations became quite similar to those for EP, Hb, and mean 

IQ decrement. These distributions were combined with PbB distributions using the 

method described in Sec. D.l to produce risk distributions for the two SES groups. 

Tables D.3 and D.4, respectively, present for each IQ expert consulted the risk 

distributions for mean IQ decrement and increased probability of children having IQ 

levels < 70 and < 85. Table D.3 has two main sections, one each for low and high SES 

children, while Table D.4 has four sections, one for each combination of IQ* (70 or 85) 

and SES level (low or high). 

If desired, the distributions conditional on SES can be combined across SES levels 

to produce further risk distributions. The across-SES calculation would be simple to 

perform if the relative proportion of low and high SES children were specified. However, 

that proportion is site specific and was not considered in this analysis. 
^ ^ ^ 

TABLE D.3 Risk Estimates for IQ Decrement, U.S. Children Aged 7 

Fractiles, 

' Mean, and 

Standard 

Deviation 

Expert F, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

2.5 

Low SES 

0 

0 

0 

0 

0 

0 

0 

5. 

0 

0 

0 

0 

0 

0 

0 

Re 

0 

sponse 

7.5 

0 

0 

0 

0 

0 

0 

0 

Rate 

10.0 

0 

0 

0 

0 

0 

0 

0 

(Z) at 

12.5 

0 

0 

0 

0 

0.1 

0 

0 

Geometric 

15.0 

0 

0 

0.1 

0.1 

0.1 

0.1 

0 

Mean 

17.5 

0 

0.1 

0.1 

0.1 

0.2 

0.1 

0.1 

PbB Level in 

20.0 

0.1 

O.i 

0.2 

0.2 

0.4 

0.2 

0.1 

22.5. 

0.1 

0.2 

0.2 

0.3 

0.5 

0.3 

0.1 

ug/dL 

25.0 

0.1 

0.2 

0.3 

0.4 

0.7 

0.3 

0.2 

27.5 

0.2 

0.2 

0.4 

0.5 

0.8 

0.4 

0.2 

Expert G, Low SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0.2 

0.4 

0.6 

1.0 

1.8 

0.8 

0.5 

0.2 

0.4 

0.6 

1.0 

1.8 

0.8 

0.5 

0.3 

0.5 

0.8 

1.2 

2.1 

0.9 

0.6 

0.4 

0.7 

1.0 

1.5 

2.7 

1.2 

0.7 

0.5 

0.9 

1.3 

1.9 

3.2 

1.5 

0.9 

0.7 

1.1 

1.6 

2.3 

3.8 

1.8 

1.0 

0.8 

1.3 

1.9 

2.7 

4.4 

2.2 

1.2 

1.0 

1.6 

2.2 

3.1 

5.0 

2.5 

1.3 

1.2 

1.9 

2.5 

3.5 

5.5 

2.9 

1.4 

1.4 

2.1 

2.9 

3.9 

6.1 

3.2 

1.5 

1.6 

2 J: 

3.2 

<.. ; 

v # _ 

3.6 

1.6 

Expert H, Low SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

1.2 

1.7 

2.3 

3.0 

4.5 

2.5 

1.0 

1.2 

1.8 

2.3 

3.0 

4.5 

2.5 

1.1 

1.3 

1.9 

2.5 

3.3 

4.9 

2.8 

1.1 

1.5 

2.2 

2.9 

3.8 

5.7 

3.2 

1.3 

1.7 

2.5 

3.3 

4.3 

6.4 

3.6 

1.5 

2.0 

2.8 

3.7 

4.8 

7.0 

4.0 

1.6 

2.2 

3.2 

4.1 

5.3 

7.7 

4.4 

1.7 

2.5 

3.6 

4.5 

5.8 

8.3 

4.9 

1.8 

2.8 

4.0 

5.0 

6.4 

9.0 

5.4 

1.9 

3.2 

4.4 

5.5 

7.0 

9.7 

5.9 

2.0 

3.6 

4.9 

6.1 

7.5 

10.3 

6.4 

2.1 

Expert I, Low SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.2 

0.2 

0.4 

0.2 

0.1 

0.2 

0.3 

0.4 

0.6 

0.9 

0.5 

0.2 

0.3 

0.5 

0.7 

1.0 

1.6 

0.8 

0.4 

0.5 

0.7 

1.0 

1.4 

2.2 

1.1 

0.5 

0.7 

1.0 

1.4 

1.8 

2.8 

1.5 

0.7 

0.9 

1.3 

1.7 

2.3 

3.4 

1.9 

0.8 

1.1 

1.6 

2.1 

2.8 

4.1 

2.3 

0.9 

1.4 

2.0 

2.5 

3.3 

4.7 

2.7 

1.0 

1.6 

2.3 

2.9 

3.7 

5.3 

3.1 

1.1 
P.56 

152 

TABLE D.3 (Cont'd) 

Fractiles, 

Mean, and 

Standard 

Deviation 

Expert J, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

2.5 

Low SES 

0.9 

1.8 

2.4 

3.0 

3.9 

2.4 

0.9 

Re 

5.0 

0.9 

1.8 

2.4 

3.0 

3.9 

2.4 

0.9 

sponse 

7.5 

1.0 

2.0 

2.6 

3.3 

4.2 

2.6 

1.0 

Rate 

10.0 

1.2 

2.3 

3.0 

3.7 

4.7 

3.0 

1.0 

(Z) at 

12.5 

1.4 

2.5 

3.3 

4.1 

5.2 

3.3 

1.1 

Geometric 

15.0 

1.7 

2.8 

3.7 

4.5 

5.7 

3.7 

1.2 

Mean 

17.5 

1.9 

3.2 

4.0 

4.9 

6.1 

4.0 

1.3 

PbB Level in 

20.0 

2.2 

3.5 

4.4 

5.3 

6.6 

4.4 

1.3 

22.5 

2.6 

3.9 

4.8 

5.8 

7.1 

4.8 

1.4 

Ug/dL 

25.0 

2.9 

4.3 

5.3 

6.2 

7.6 

5.3 

1.4 

• 

27.5 

3.3 

4.8 

5.7 

6.7 

8.1 

5.7 

1.4 

Expert K, Low SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.2 

0.3 

0.3 

0.4 

0.3 

0.1 

0.3 

0.5 

0.7 

0.8 

1.1 

0.7 

0.2 

0.5 

0.8 

1.1 

1.4 

1.7 

1.1 

0.4 

0.6 

1.1 

1.5 

1.8 

2.3 

1.5 

0.5 

0.8 

1.4 

1.9 

2.3 

2.9 

1.9 

0.6 

1.0 

1.7 

2.2 

2.7 

3.5 

2.2 

0.8 

1.2 

2.0 

2.6 

3.2 

4.0 

2.6 

0.9 

1.5 

2.4 

3.0 

3.6 

4.5 

3.0 

0.9 

1.7 

2.7 

3.4 

4.1 

5.0 

3.4 

1.0 

Expert F, High SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0 

0 

0 

0 

0.1 

0.1 

0.1 

0.1 

0 

0 

0.1 

0.1 

0.1 

0.2 

0.1 

0.1 

0.1 

0.1 

0.2 

0.2 

0.4 

0.2 

0.1 

0.1 

0.2 

0.2 

0.3 

0.5 

0.3 

0.1 

0.1 

0.2 

0.3 

0.4 

0.7 

0.3 

0.2 

0.2 

0.3 

0.4 

0.5 

0.8 

0.4 

0.2 

Expert G, High SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.1 

0.2 

0.4 

0.2 

0.1 

0.1 

0.3 

0.4 

0.5 

0.9 

0.4 

0.3 

0.2 

0.4 

0.6 

0.8 

1.4 

0.7 

0.4 

0.3 

0.5 

0.8 

1.1 

1.9 

0.9 

0.5 

0.4 

0.7 

1.0 

1.4 

2.3 

1.1 

0.6 

0.5 

0.8 

1.2 

1.6 

2.7 

1.3 

0.7 

0.6 

1.0 

1.4 

1.9 

3.1 

1.6 

0.8 

0.8 

1.2 

1.7 

2.3 

3.6 

1.9 

0.9 

0.9 

1.4 

2.0 

2.6 

4.1 

2.2 

1.0 
--T--*Sd- ' "?7'**-*rr7firfwr~ 

TABLE D.3 (Cont'd) 

Fractiles 

Mean, and 

Standard 

Deviation 

Expert H, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

2.5 

High SES 

0.2 

0.4 

0.6 

0.8 

1.3 

0.6 

0.3 

Re 

5.0 

0.3 

0.4 

0.6 

0.9 

1.4 

0.7 

0.4 

sponse 

7.5 

0.4 

0.7 

1.0 

1.3 

2.1 

1.1 

0.5 

Rate 

10.0 

0.7 

1.1 

1.6 

2.1 

3.3 

1.7 

0.8 

(Z) at 

12.5 

1.1 

1.6 

2.1 

2.8 

4.3 

2.3 

1.0 

Geometric 

15.0 

1.4 

2.0 

2.6 

3.4 

5.0 

2.9 

1.1 

Mean 

17.5 

1.8 

2.5 

3.1 

3.9 

5.5 

3.3 

1.2 

PbB Level in 

20.0 

2.2 

2.9 

3.5 

4.4 

6.0 

3.7 

1.2 

22.5 

2.5 

3.3 

3.9 

4.8 

6.3 

4.1 

1.2 

Ug/dL 

25.0 

2.9 

3.7 

4.3 

5.1 

6.6 

4.5 

1.1 

27.5 

3.2 

4.0 

4.7 

5.5 

6.9 

4.8 

1.1 

Expert I, High SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.2 

0.1 

0.1 

0.1 

0.1 

0.2 

0.3 

0.5 

0.2 

0.1 

0.1 

0.2 

0.3 

0.5 

0.8 

0.4 

0.2 

0.2 

0.3 

0.5 

0.7 

1.2 

0.5 

0.3 

0.3 

0.4 

0.6 

0.9 

1.6 

0.8 

0.4 

0.4 

0.6 

0.9 

1.2 

2.1 

1.0 

0.6 

0.5 

0.8 

1.1 

1.6 

2.6 

1.3 

0.7 

0.7 

1.0 

1.4 

1.9 

3.1 

1.6 

0.8 

0.8 

1.2 

1.7 

2.3 

3.5 

1.9 

0.9 

Expert J, High SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0 

0 

0.2 

0.2 

0.3 

0.4 

0.7 

0.4 

0.2 

0.4 

0.6 

0.8 

1.1 

1.7 

0.9 

0.4 

0.6 

1.0 

1.3 

1.7 

2.6 

1.4 

0.6 

0.8 

1.2 

1.6 

2.2 

3.3 

1.8 

0.8 

1.0 

1.5 

2.0 

2.6 

3.8 

2.1 

0.9 

1.3 

1.8 

2.3 

2.9 

4.2 

2.4 

0.9 

1.5 

2.0 

2.6 

3.3 

4.6 

2.7 

1.0 

1.7 

2.3 

2.9 

3.6 

4.9 

3.0 

1.0 

2.0 

2.6 

3.2 

3.9 

5.2 

3.3 

1.0 

Expert K, High SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.1 

0.1 

0.2 

0.1 

0 

0.2 

0.2 

0.3 

0.3 

0.4 

0.3 

0.1 

0.3 

0.4 

0.5 

0.6 

0.7 

0.5 

0.1 

0.5 

0.6 

0.8 

0.9 

1.1 

0.8 

0.2 

0.6 

0.9 

1.0 

1.2 

1.5 

1.0 

0.2 

0.8 

1.1 

1.3 

1.5 

1.8 

1.3 

0.3 

1.0 

1.4 

1.6 

1.8 

2.2 

1.6 

0.3 
TABLE D.4 Risk Estimates for IQ Levels < 70 and < 85, U.S. Children Aged 7 

P.58 

Fractiles 

Mean, and 

Standard 

Deviation 

Expert F, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert G, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert H, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert J, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

i 

IQ 

10 

IQ 

IQ 

2.5 

* 70, 

0 

0 

0 

0 

0 

0 

0 

S 70, 

0.1 

0.3 

0.4 

0.7 

1.5 

0.6 

0.5 

< 70, 

0.2 

0.5 

0.8 

1.4 

2.9 

1.1 

0.9 

S 70. 

0.4 

0.8 

1.2 

1.8 

3.5 

1.5 

1.0 

Response 

5.0 

Low SES 

0 

0 

0 

0 

0 

0 

0 

Low SES 

0.1 

0.3 

0.5 

0.8 

1.6 

0.6 

0.5 

Low SES 

0.2 

0.5 

0.9 

1.4 

3.0 

1.1 

0.9 

Low SES 

0.4 

0.8 

1.2 

1.9 

3.5 

1.5 

1.0 

7.5 

0 

0 

0 

0 

0 

0 

0 

0.2 

0.3 

0.6 

0.9 

1.9 

0.7 

0.6 

0.3 

0.6 

1.0 

1.6 

3.4 

1.3 

1.1 

0.5 

0.9 

1.3 

2.1 

3.8 

1.6 

1.1 

Rate (Z) 

10.0 

0 

0 

0 

0 

0 

0 

0 

0.2 

0.5 

0.8 

1.2 

2.5 

1.0 

0.7 

0.3 

0.7 

1.2 

2.0 

4.1 

1.6 

1.3 

0.6 

1.1 

1.6 

2.4 

4.4 

1.9 

1.2 

at Geometric 

12.5 

0 

0 

0 

0 

0 

0 

0 

0.3 

0.6 

1.0 

1.6 

3.1 

1.2 

0.9 

0.4 

0.8 

1.4 

2.3 

4.8 

1.8 

1.5 

0.7 

1.2 

1.9 

2.8 

4.9 

2.2 

1.4 

15.0 

0 

0 

0 

0 

0 

0 

0 

0.4 

0.8 

1.2 

1.9 

3.8 

1.5 

1.1 

0.5 

1.0 

1.6 

2.7 

5.5 

2.1 

1.7 

0.8 

1.5 

2.1 

3.2 

5.5 

2.5 

1.5 

Mean PbB 

17.5 

0 

0 

0 

0.1 

0.1 

0 

0 

0.5 

0.9 

1.5 

2.3 

4.5 

1.8 

1.3 

0.5 

1.1 

1.9 

3.1 

6.3 

2.5 

1.9 

1.0 

1.7 

2.5 

3.6 

6.1 

2.9 

1.6 

Level 

20.0 

0 

0.1 

0.1 

0.1 

0.1 

0.1 

0 

0.6 

1.1 

1.8 

2.8 

5.2 

2.2 

1.5 

0.6 

1.3 

2.2 

3.6 

7.2 

2.9 

2.2 

1.2 

2.0 

2.9 

4.1 

6.8 

3.3 

1.8 

in ug 

22.5 

0 

0.1 

0.1 

0.2 

0.2 

0.1 

0.1 

0.7 

1.4 

2.1 

3.2 

5.9 

2.5 

1.7 

0.8 

1.6 

2.6 

4.2 

8.2 

3.3 

2.5 

1.4 

2.3 

3.3 

4.6 

7.5 

3.7 

1.9 

/dL 

25.0 

0 

0.1 

0.2 

0.2 

0.3 

0.2 

0.1 

0.9 

1.6 

2.4 

3.7 

6.6 

2.9 

1.8 

0.9 

1.9 

3.0 

4.8 

9.2 

3.8 

2.7 

1.7 

2.7 

3.8 

5.2 

8.3 

4.2 

2.1 

• 

27.5 

0 

0.1 

0.2 

0.3 

0.4 

0.2 

0.1 

1.1 

1.9 

2.8 

4.2 

7.3 

3.3 

2.0 

1.1 

2.1 

3.4 

5.4 

10.2 

4.2 

3.0 

2.0 

3.2 

4.3 

5.9 

9.1 

4.8 

2.2 
TABLE D.4 (Cont'd) 

I 

Fractiles 

Mean,' and 

Standard 

Deviation 

Expert K, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert F, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert G, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert H, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

» 

IQ 

IQ 

IQ 

IQ 

2.5 

i 70, 

0 

0 

0 

0 

0 

0 

0 

< 70, 

0 

0 

0 

0 

0 

0 

0 

S 70, 

0 

0 

0 

0 

0 

0 

0 

S 70, 

0 

0 

0.1 

0.1 

0.3 

0.1 

0.1 

Response 

5.0 

Low SES 

0 

0 

0.1 

0.1 

0.1 

0.1 

0 

High SES 

0 

0 

0 

0 

0 

0 

0 

High SES 

0 

0 

0 

0 

0 

0 

0 

High SES 

0 

0.1 

0.1 

0.2 

0.3 

0.1 

0.1 

7. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0. 

0 

0 

0 

0. 

0. 

0. 

0. 

0. 

0. 

5 

2 

4 

5 

6 

8 

5 

2 

1 

1 

2 

3 

6 

2 

2 

Rate (Z) 

10.0 

0.4 

0.9 

1.3 

1.7 

2.2 

1.3 

0.5 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.2 

0.1 

0.1 

0.1 

0.2 

0.3 

0.4 

0.9 

0.4 

0.3 

at Geometric 

12.5 

0.6 

1.5 

2.1 

2.7 

3.6 

2.1 

0.9 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.1 

0.3 

0.1 

0.1 

0.1 

0.2 

0.4 

0.6 

1.3 

0.5 

0.4 

15.0 

0.9 

2.1 

2.9 

3.7 

4.9 

2.9 

1.2 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.2 

0.4 

0.1 

0.1 

0.1 

0.3 

0.5 

0.8 

1.6 

0.6 

0.5 

Mean PbB 

17.5 

1.1 

2.6 

3.7 

4.7 

6.3 

3.7 

1.6 

0 

0 

0 

0.1 

0.1 

0 

0 

0 

0.1 

0.1 

0.2 

0.5 

0.2 

0.1 

0.2 

0.4 

0.6 

0.9 

1.8 

0.7 

0.5 

Level 

20.0 

1.4 

3.2 

4.5 ' 

5.8 

7.6 

4.5 

1.9 

0 

0.1 

0.1 

0.1 

0.1 

0.1 

0 

0.1 

0.1 

0.2 

0.3 

0.6 

0.2 

0.2 

0.2 

0.4 

0.7 

1.1 

2.0 

0.9 

0.6 

in ug 

22.5 

1.7 

3.8 

5.3 

6.8 

8.9 

5.3 

2.2 

0 

0.1 

0.1 

0.2 

0.2 

0.1 

0.1 

0.1 

0.1 

0.2 

0.4 

0.7 

0.3 

0.2 

0.3 

0.5 

0.8 

1.2 

2.2 

1.0 

0.6 

/dL 

25.0 

* 

2.1 

4.5 

6.2 

7.8 

10.2 

6.2 

2.4 

0 

0.1 

0.2 

0.2 

0.3 

0.2 

0.1 

. 0.1 

0.2 

0.3 

0.4 

0.9 

0.4 

0.3 

0.3 

0.6 

0.9 

1.3 

2.4 

1.1 

0.7 

27.5 

2.6 

5.2 

7.0 

8.8 

11.5 

7.0 

2.7 

0 

0.1 

0.2 

0.3 

0,4 

0.2 

0.1 

0.1 

0.2 

0.3 

0.5 

1.0 

0.4 

0.3 

0.4 

0.6 

1.0 

1.4 

2.6 

1.2 

0.7 
TABLE D.4 (Cont'd) 

P.60 

Fractiles 

Mean, and 

Standard 

Deviation 

Expert J, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert K, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert F, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert G, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

IQ 

IQ 

IQ 

IQ 

2.5 

S 70, 

0 

0 

0 

0 

0 

0 

0 

* 70, 

0 

0 

0 

0 

0 

0 

0 

S 85, 

0 

0 

0 

0 

0 

0 

0 

i 85, 

0.1 

1.5 

2.4 

3.3 

4.7 

2.4 

1.4 

5. 

High 

0 

0 

0 

0 

0 

0 

0 

High 

0 

0 

0 

0 

0 

0 

0 

Low 

0 

0 

0 

0 

0 

0 

0 

Low 

0. 

1. 

2. 

3. 

4. 

2. 

1 

Resp 

0 

SES 

SES 

SES 

SES 

1 

5 

5 

4 

8 

5 

4 

onse 

7.5 

0 

0 

0 

0.1 

0.1 

0.1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.3 

1.8 

2.9 

4.0 

5.6 

2.9 

1.6 

Rate (Z) 

10.0 

0 

0.1 

0.1 

0.2 

0.3 

0.1 

0.1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

O.S 

2.4 

3.7 

5.1 

7.0 

3.7 

2.0 

at Geometric 

12.5 

0.1 

0.1 

0.2 

0.3 

0.5 

0.2 

0.2 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.1 

0.1 

0 

0.7 

3.0 

4.6 

6.2 

8.5 

4.6 

2.4 

15.0 

0.1 

0.1 

0.2 

0.4 

0.7 

0.3 

0.2 

0 

0 

0 

0 

0.1 

0 

0 

0 

0.1 

0.1 

0.2 

0.2 

0.1 

0.1 

1.0 

3.6 

5.5 

7.4 

10.1 

5.5 

2.8 

Mean PbB 

17.5 

0.1 

0.2 

"0.3 

0.4 

0.8 

0.3 

0.2 

0 

0 

0.1 

0.1 

0.2 

0.1 

0 

0.1 

0.2 

0.2 

0.3 

0.4 

0.2 

0.1 

1.3 

4.3 

6.4 

8.6 

11.6 

6.4 

3.1 

Level 

20.0 

0.1 

0.2 

0.3 

0.5 

1.0 

0.4 

0.3 

0 

0.1 

0.1 

0.1 

0.3 

0.1 

0.1 

0.1 

0.2 

0.4 

0.5 

0.6 

0.4 

0.2 

1.6 

5.0 

7.4 

9.7 

13.1 

7.4 

3.5 

in ug 

22.5 

0.1 

0.3 

0.4 

0.6 

1.1 

0.5 

0.3 

0 

0.1 

0.1 

0.2 

0.3 

0.2 

0.1 

0.1 

0.4 

0.5 

0.7 

0.9 

0.5 

0.2 

2.1 

5.8 

8.3 

10.9 

14.5 

8.3 

3.8 

'dL 

25.0 

0.2 

0.3 

0.4 

0.7 

1.2 

0.5 

0.3 

0.1 

0.1 

0.2 

0.2 

0.4 

0.2 

0.1 

0.2 

0.5 

0.7 

0.9 

1.2 

0.7 

0.3 

2.6 

6.5 

9.3 

12.0 

15.9 

9.3 

4.0 

• 

27.5" 

0.2 

0.3 

0.5 

0.7 

1.3 

0.6 

0.4 

0.1 

0.1 

0.2 

0.3 

0.5 

0.2 

0.2 

0.2 

0.6 

0.8 

1.1 

1.5 

0.8 

0.4 

3.2 

7.3 

10.2 

13.0 

17.2 

10.2 

4.2 
T TT 

P.61 

TABLE D.4 (Cont'd) 

Fractiles, 

'Mean, and 

Standard 

Deviation 2.5 

Response Rate (Z) at Geometric Mean PbB Level in ug/dL 

5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 . 25.0 27.5 

Expert H, IQ < 85, Low SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert J, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

2.4 

3.8 

5.3 

7.4 

11.6 

6.0 

2.9 

IQ i 85, 

2.2 

4.5 

6.2 

7.8 

10.1 

6.2 

2.4 

2.4 

3.9 

5.4 

7.5 

11.8 

6.0 

2.9 

Low SES 

2.2 

4.6 

6.2 

7.9 

10.2 

6.2 

2.4 

2.7 

4.3 

6.0 

8.3 

13.0 

6.7 

3.2 

2.5 

5.0 

6.8 

8.5 

11.0 

6.8 

2.6 

3.1 

5.1 

7.1 

9.7 

15.1 

7.8 

3.8 

3.0 

5.8 

7.8 

9.7 

12.5 

7.8 

2.9 

3.6 

5.9 

8.1 

11.2 

17.3 

9.0 

4.3 

3.6 

6.6 

8.8 

10.9 

13.9 

8.8 

3.1 

4.1 

6.7 

9.2 

12.6 

19.3 

10.1 

4.7 

4.2 

7.4 

9.7 

12.0 

15.3 

9.7 

3.4 

4.7 

7.5 

10.4 

14.1 

21.3 

11.3 

5.2 

4.8 

8.3 

10.7 

13.2 

16.6 

10.7 

3.6 

5.4 

8.6 

11.7 

15.7 

23.4 

12.7 

5.6 

5.6 

9.3 

11.9 

14.4 

18.1 

11.9 

3.8 

6.2 

9.7 

13.1 

17.4 

25.5 

14.1 

6.0 

6.6 

10.4 

13.1 

15.7 

19.5 

13.1 

3.9 

7.1 

11.0 

14.6 

19.2 

27.6 

15.6 

6.3 

7.6 

11.6 

14.3 

17.1 

21.1 

14.3 

4.1 

8.1 

12.3 

16.1 

20.9 

29.7 

17.1 

6.6 

8.8 

12.8 

15.7 

18.5 

22.6 

15.7 

4.2 

Expert K, IQ < 85, Low SES 

0.05 

0.25 

0.5C 

0.75 

0.95 

Mean 

SD 

ert F, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

IQ i 85. 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0.1 

0.1 

0.1 

0.1 

0 

High SES 

0 

0 

0 

0 

0 

0 

0 

0. 

0. 

0. 

1. 

1. 

0. 

0. 

0 

0 

0 

0 

0 

0 

0 

3 

6 

8 

0 

3 

8 

3 

0.8 

1.6 

2.1 

2.6 

3.3 

2.1 

0.7 

0 

0 

0 

0 

0 

0 

0 

1.3 

2.5 

3.3 

4.1 

5.3 

3.3 

1.2 

0 

0 

0.1 

0.1 

0.1 

0.1 

0 

1.8 

3.4 

4.5 

5.6 

7.1 

4.5 

1.6 

0 

0.1 

0.1 

0.2 

0.2 

0.1 

0.1 

2.3 

4.3 

5.6 

6.9 

8.9 

5.6 

2.0 

0.1 

0.2 

0.2 

0.3 

0.4 

0.2 

0.1 

2.9 

5.2 

6.7 

8.3 

10.5 

6.7 

2.3 

0.1 

0.2 

0.4 

0.5 

0.6 

0.4 

0.2 

3.6 

6.1 

7.8 

9.6 

12.1 

7.8 

2.6 

0.1 

0.4 

0.5 

0.7 

0.9 

0.5 

0.2 

4.3 

7.1 

9.0 

10.9 

13.6 

9.0 

2.8 

0.2 

0.5 

0.7 

0.9 

1.2 

0.7 

0.3 

5.1 

8.1 

10.1 

12.1 

15.0 

10.1 

3.0 

0.2 

0.6 

0.8 

1.1 

1.5 

0.8 

0.4 
TABLE D.4 (Cont'd) 

P.62 

Fractiles, 

Mean, and 

Standard 

Deviation 2.5 

Response Rate (Z) at Geometric Mean PbB Level in ug/dL 

5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 

Expert G, IQ < 85, High SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0 

0 

0.1 

0.1 

0.2 

0.3 

0.5 

0.2 

0.1 

0.1 

0.3 

0.4 

0.6 

1.2 

0.5 

0.4 

0.2 

0.4 

0.7 

1.0 

1.9 

0.8 

0.5 

0.3 

0.6 

0.9 

1.3 

2.5 

1.1 

0.7 

0.4 

0.7 

1.1 

1.7 

3.0 

1.3 

0.9 

0.5 

0.9 

1.4 

2.1 

3.7 

1.6 

1.0 

0.6 

1.1 

1.7 

2.5 

4.4 

2.0 

1.2 

0.8 

1.4 

2.1 

3.0 

5.2 

2.4 

1.4 

1.0 

1.7 

2.4 

3.5 

6.0 

2.8 

1.6 

Expert H, IQ < 85, High SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

Expert J, 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0.2 

0.4 

0.6 

0.9 

1.7 

0.7 

0.5 

IQ $ 85, 

0 

0 

0 

0 

0 

0 

0 

0.2 

0.4 

0.7 

1.0 

1.9 

0.8 

0.5 

High SES 

0 

0 

0 

0.1 

0.1 

0.1 

0 

0.4 

0.7 

1.1 

1.7 

3.0 

1.3 

0.8 

0.2 

0.3 

0.4 

0.6 

1.0 

0.5 

0.3 

0.7 

1.3 

1.9 

2.8 

4.8 

2.2 

1.3 

0.4 

0.7 

1.0 

1.5 

2.4 

1.2 

0.6 

1.1 

1.8 

2.7 

3.9 

6.5 

3.1 

1.7 

0.7 

1.2 

1.6 

2.3 

3.8 

1.9 

1.0 

1.4 

2.4 

3.4 

4.7 

7.7 

3.8 

2.0 

0.9 

1.5 

2.1 

3.0 

4.8 

2.4 

1.2 

1.8 

2.9 

4.0 

5.5 

8.7 

4.5 

2.2 

1.2 

1.9 

2.6 

3.6 

5.6 

2.9 

1.4 

2.2 

3.4 

4.6 

6.2 

9.5 

5.0 

2.3 

1.4 

2.2 

3.0 

4.1 

6.4 

3.4 

1.5 

2.6 

3.9 

5.2 

6.8 

10.2 

5.6 

2.4 

1.7 

2.6 

3.5 

4.7 

7.0 

3.8 

1.7 

3.0 

4.4 

5.7 

7.4 

10.8 

6.1 

2.4 

2.0 

3.0 

3.9 

5.2 

7.7 

4.3 

1.8 

3.4 

4.8 

6.2 

8.0 

11.4 

6.7 

2.5 

2.3 

3.4 

4.4 

5.7 

8.3 

4.8 

1.9 

Expert K, IQ < 85, High SES 

0.05 

0.25 

0.50 

0.75 

0.95 

Mean 

SD 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0.1 

0 

0 

0.1 

0.1 

0.1 

0.2 

0.2 

0.1 

0.1 

0.1 

0.2 

0.3 

0.4 

0.6 

0.3 

0.1 

0.3 

0.4 

0.5 

0.7 

1.0 

0.6 

0.2 

0.4 

0.6 

0.8 

1.0 

1.5 

0.9 

0.3 

0.6 

0.8 

1.1 

1.4 

2.1 

1.2 

0.5 

0.8 

1.1 

1.4 

1.8 

2.6 

1.5 

0.6 

1.0 

1.4 

1.7 

2.2 

3.2 

1.9 

0.7