ANL/AA-32
Assessing the Risks to Young Children
of Three Effects Associated with
Elevated Blood-Lead Levels
T. S. Wallsten and R. G. Whitfield
ARGONNE NATIONAL LABORATORY
Energy and Environmental Systems Division
Operated by
THE UNIVERSITY OF CHICAGO for U. S. DEPARTMENT^ OF ENERGY
under Contract W-31 -109-Eng-38
-------
Argonne National Laboratory, with facilities in the states of Illinois and Idaho, is
owned by the United States government, and operated by The University of Chicago
under the provisions of a contract with the Department of Energy.
DISCLAIMER
This report was prepared as an account of work sponsored by an
agency of the United States Government. Neither the United
States Government nor any agency thereof, nor any of their
employees, makes any warranty, express or implied, or assumes
any legal liability or responsibility for the accuracy, com-
pleteness, or usefulness of any information, apparatus, product,
or process disclosed, or represents that its use would not infringe
privately owned rights. Reference herein to any specific com-
mercial product, process, or service by trade name, trademark,
manufacturer, or otherwise, does not necessarily constitute or
imply its endorsement, recommendation, or favoring by the
United States Government or any agency thereof. The views and
opinions of authors expressed herein do not necessarily state or
reflect those of the United States Government or any agency
thereof.
Printed in the United States of America
Available from
National Technical Information Service
U. S. Department of Commerce
5285 Port Royal Road
Springfield, VA 22161
NTIS price codes
Printed copy: A08
Microfiche copy: A01
-------
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
*L.L. Thurstone Psychometric Laboratory, University of North Carolina, Chapel Hill
-------
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
111
-------
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
-------
TABLES (Cont'd)
A.I Probability Distributions and Parameters for EP Levels among New York
City Children 58
B.I 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.I 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.I 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 < 11 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
-------
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, Hb < 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 for 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%-CI Judgments about CJTQ, 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, I, 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
VI
-------
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 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
VI1
-------
VI11
-------
SYMBOLS
E[R] expected value of R
FJ encoded cumulative probability value
F. cumulative probability value that results from fitting a regression line to
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
9
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— mean IQ decrement
y mean of Y
OTQ within-group IQ standard deviation
a1 estimate of a obtained by pooling data across several blood-lead levels
P J
a standard deviation of Y
a variance of Y
y
$(X) cumulative distribution function for the standardized normal random
variable
-------
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
is
-------
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.
-------
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 Air 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
*A11 acronyms used in this report are listed alphabetically on pp. ix and x.
-------
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 dose-
response 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 lead-
induced 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
-------
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
-------
that fewer than 1% of the population will TABLE 1 Probability of Suffering a
suffer it, and so forth. (Equivalently, 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
4 provides the greatest degree of protection n Probability under
. ,, . f u • , *. . t Response NAAQS Alternatives
in that a greater chance exists that fewer Ratg < R 3
people will suffer the health effect. (%) ° 1 2 3 4
Output of the sort illustrated in
Table 1 would presumably be helpful to EPA o.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 each 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
-------
TABLE 2 Probabilities of Suffering a Specified Health Effect
under Alternative NAAQS, Given Incomplete Information
Response
Rate < Rn
(%)
0.5
1.0
1.5
Probability Ranges for NAAQS Alternatives
1
0.01-0.02
0.01-0.05
0.29-0.41
2 3
0.02-0.06 0.11-0.19
0.04-0.11 0*15-0.23
0.40-0.53 0.53-0.64
4
0.26-0.38
0.49-0.60
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
-------
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 dose-
response 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 dose-
response functions for EP effects, although the data were somewhat uncertain because of
sampling and mesurement errors. In the Hb and 1Q 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.
-------
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
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 dose-
response 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).
-------
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 dose-
response 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.I 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-
£S 95-
£ 90-
D
w 75-
c
O
Q. 50-
tn
c 25-
D
CD
2 10-
1-
EP > 33
10 20 30
PbB Level
40
—r~
50
FIGURE 1 Mean Response Rate vs. Dose for EP > 33
and > 53 yg/dL (Source: Adapted from Piomelli et al., 1982)
-------
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 yg/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 yg/dL (66-80% and
37-52% for EP > 33 yg/dL and > 53 yg/dL,
respectively) because there were fewer
children.
TABLE 3 Sample
Sizes for the EP Data
PbB
Level Number of
(yg/dL) Children
2-17
17-21
21-31
31-41
41-98
829
479
544
109
43
Source: Based on
data from Piomelli
et al., 1982
(Seaman, 1985).
99-
95-
§ 90-
0)
75'
50-
o
Q.
S 25-
10-
5-
1-
10
20 30
PbB Level
90% CI
Median
40
50
FIGURE 2 Median Response Rate and 90% CI vs. Dose for EP
> 33 yg/dL
-------
10
99-
95-
90-
Q)
I
<0
50-
o
Q.
25-
10-
/ /> 90% Cl
Median
10 20 30
PbB Level
40
50
FIGURE 3 Median Response Rate and 90% CI vs. Dose for EP
> 53 yg/dL
-------
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 func-
tions 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.
-------
12
TABLE 4 Consultants for the Hb Protocol
Consultant
Affiliation
Julian Chisolm
Jeff Cohen
Anita Curran
Thomas Feagans
Lester Grant
John Haines
Paul Hammond
Robert Kellam
Paul Mushak
Johns Hopkins University
EPA, OAQPS3
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.I 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
the 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 dose-
response 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
-------
14
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,
for R. > R., F(Rj|L) = 0.25 and F(R-|L) = 0.75 imply that the true response rate is equally
likely to fall either inside the (Rj, R-) interval or outside it. If the expert disagreed with
this or any of several other implications, adjustments were made. When the expert was
satisfied that the encoded distribution represented his probabilistic judgment, another
PbB level was selected and the process was repeated.
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
-------
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-log-
odds (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 = TOOT' for 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 L-, where j = 1, ..., m (m = 6). This fitting was accomplished by deriving least-
squares estimates of the parameters y • and a-, 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 Lg is greater
than L,.
Equal-variance NOLO distributions were derived by (1) obtaining a least-squares
estimate of the standard deviation pooled over PbB levels, a', (2) setting all the
o'. equal too', 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 L-, thatJhas 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 L. 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
-------
17
generally close to that of the best-fitting NOLO distributions. Because the equal-
variance 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
-------
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.
40
30-
CD 20-
C
o
CL
in
CD
10---
\90%
Cl
50%
45
55 65 75
PbB Level (//g/dL)
FIGURE 4 Dose-Response Functions, Hb < 11 g/dL, Ages 0-3,
Expert A
-------
19
Figure 5 represents the probabilistic judgments of Experts A, C, D, and E rather
completely regarding the dose-response function for Hb level < 11 g/dL in U.S. children
aged 0-3. (With Expert C's 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 C's 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 pg/dL, and that it rises to
between 26% and 33% at PbB = 55 yg/dL.
40-|
30-|
20-
10-
Expert D
60-
50-
40-
30-
20-
10-
Expert E
15 25 35
PbB Level
15 25 35 45 55
PbB Level (yu-g/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)
45 55
-------
20
60-i
T T
su-
^ 40-
— '
0)
D
i:
q> 30-
w
c
o
CL
W
J—
10-
l
~[~
- i ITJ
n? i.
-ji i-
ACDE ACDE
5 — 15-
r
i -p
"^
'
R
\ J't :lt ^j
L ui M
i
ACDE ACDE ACDE
- — 25 — — 35 — — 45-
B
t 1
. i
If'1
0
ACDE
55-
1
.
<
A
1
1
C D E A
-65— -
1
C D E
-75 —
PbB Level
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 90% 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 < 11 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
.10-
8
....-• 0.75
/ ,'*
ft / —0.5
/' '..' ' /~~\^.. 0.25
* >^ * ' " "
X/>''^ 0.05
"i I i
5 55 65 75
40-1
30-
20-
10
Expert C
i i i i i
5 15 25 35 45 55
-------
22
4U-
30-
— x
•~s
4_
D
3^
-------
23
O>
"5
0>
W
c
o
Q.
V>
0)
12-j
10-
8-
6
4-
2-
0
Expert C
,-0.95
15
25 35 45 55
40 -i
30-
IX.
-------
24
D
o;
c
o
Q.
W
60-,
50-
40-
30-
20-
10
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 C's 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
W
C
o
CL
w
Q)
CfL
9H
6-
3^
Expert C
-0.95
I I I I I
5 15 25 35 45 55
30-,
PbB Level
40-i
30-
20-
10-
Expert E
I I I 1 I
5 15 25 35 45 55
PbB Level
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.
-------
26
30-
25-
£
d>
"5 20-
o;
Q>
W
Q_
W
CD
cc
10-
5-
4 ;
^ m
w -|- - ™ -
ACDE
O e:
t *J
_^_ ._. Q 1 H ,
j jf | a i
ACDE
7 c:
T
T
~r
I
'
0
I ' iJ il
T
! .
tJ
T
1
[.
ACDE ACDE ACDE ACDE
1O R 1V £; OO K O7 C
Geometrlc Mean PbB Level (yu-g/dL)
FIGURE 12 Comparison of Judgments, Hb < 9.5 g/dL, Ages 4-6, Experts A, C, D, and E
-------
27
4 PROBABILISTIC DOSE-EFFECT AND DOSE-RESPONSE
FUNCTIONS FOR LEAD-INDUCED IQ DECREMENTS
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
-------
28
probabilistic judgments about mean IQ decrement, control-group mean IQ, and within-
group 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.
-------
29
TABLE 6 Consultants for the IQ Protocol
Consultants
Affiliation
Vernon Benignus
Robert Bornshein
Jeff Cohen
Anita Curran
Gerri 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.
-------
30
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 disserta-
tion. 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.I 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 pro-
vide 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 lead-
exposure 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 (9896-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.
-------
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
-------
34
they are discussed separately for the two SES levels.
repeated for comparison purposes.
Expert F's judgments will be
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
115-
110-
105-
100-
O
0
95-
90-
85-
80-
i
T T
1
JJT,
; i i
j j x i i ^
T
T i T
j T
X
v
1 1 1 1 1 r r— ^ 1 1 1 r- .
F G H J K
— Low SES —
F G H J K
— High SES —
FIGURE 13 Median Values and 90% CIs for Func-
tions 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-
12-
11-
10
T
T T
1
i !
F G H J K
— Low SES —
F G H J K
— High SES —
FIGURE 14 Median Values and 90%-CI Judg-
ments about OJQ, Experts F, G, H, J, and K
-------
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, it
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
3-
1-
Expert F
•0.95
^>^''':"---~ 0.05
0+-//-T
5 25 35 45 55 65
15
12-
9-
6-
3-
Expert G
i \ \ i i
5 15 25 35 45 55
16-1
12-
4-
Expert H
—i 1 1 1 r~
5 15 25 35 45 55
9-
6-
3-
Expert
I I T I I
5 15 25 35 45 55
10-
5-
Expert J
i i i i i
5 15 25 35 45 55
PbB Level
15-,
12-
9-
6-
3-
Expert K
i i T r i^ i
5 15 25 35 45 55 65
PbB Level
FIGURE 15 Judgments about Lead-Induced IQ Decrements, Low 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)
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
-------
38
T
JT
i i >
Tit 6
illi -
, 1 1 y
1 j_ J.
n
—
1
1
1 _^.
i A •
1 ! *J
1 t
Li;
¥
'
1 ^
' |
j
r '
.
T
*
1 1 1 1 T 1
"
I
r
}\
L
-
1
t
.J
{
V
_
T
1
i
'_
L
T
i-
.lv
-
T
I
1 1 1 1 1 1 1 r
FGHJK FGHJK FGHJK FGHJK FGHJK FGHJK FGHJK
15
25
35-
45-
-55
PbB Level
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. Calcula-
tions 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 vg/dL; with the
-------
39
3-
f >-
1-
Expert F
-0.95
.-0.75
0—//-
1 I I I I
5 25 35 45 55 65
10-
8-
6-
4-
Expert G
i i i i i
5 15 25 35 45 55
10-.
8-
6-
Expert H
i i i i i
5 15 25 35 45 55
5 15 25 35 45 55
6-
3-
Expert J
i i i i r
5 15 25 35 45 55
PbB Level
8-1
6-
4-
2-
0—//-
Expert K
5 25 35 45 55 65
PbB Level (yug/dL)
FIGURE 17 Judgments about Lead-Induced IQ Decrements, High
SES Population, Experts F, G, H, I, J, and K (A^Q and PbB scales
were selected to show the details of each expert's judgments)
-------
40
8-
<
2-
T
•
±
•
1
•J
4
X
F G ^
1
•
1
j J
•
^
1 j 1C F 6 h
1C;
r
I
""
J
>c
-r
I
4 <
I
/{^
J K PC
i
i
"
r
' \
j
H
7 =
-r
1
|
I -
•ll ,
111
I
J K F G
~r
i T
m 1
IT
i ! '
j
.,ii.
i
H 1 J K F G
A ^
\ ]
TTj
i |
fy
1 i
i 1
1 V
> i-
! *
L
i"
•
H 1 J K F G H 1 J K
=;<:; fie,
PbB Level
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
6H
n
c
o
Q- 2-\
a:
Expert F
xO.95 Fractlie
S
.--0.75 Fractlle
0.50 Fraotile
,.-•0.25 Fractile
ZZgZ--'' ___ 0.05 Fractile
"•""'"— —•
O-T-//-T , , 1 r-
5 25 35 45 55 65
40-i
30-|
~D
a:
-------
42
15-
12-
9-
6-
3-
-
T
T T
T T I
T ! 1
T_ ! I'll- .J
! T' * i U
ii |, V -
I A T-L • 1
1J- I t 1 Y -i- i - T
6 j. 6 J. _ i
_L -L e i
F G H i J K ' F G H i' J K ' F e H ' J K FGt
c; . . .. IR .. . o^
r
.
i
T.I
I
~
.
'
J
•
.
V
^ I
_L
K F C
-
g
j
•>
L
P
"
1
L
A*
\
I
A
r
iv c
\
[- j
I
1
J K F C
r-
'T*
i
iit
5L
1
H 1 J K FGHIJK
cc: cc;
PbB Level
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 right. However, they will be combined in Sec. 5 with PbB
distributions (which represent different levels of exposure) to yield risk distributions.
-------
43
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 health 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.
-------
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 the "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-.
30-
£S
_Q>
~o
0>
OT
CL
w
ct:
10-
5-
T
T
1
T
T
1
0 5 10 15 20 25 30
Geometric Mean PbB Level (jug/dL)
FIGURE 21 Risk Results for the Occurrence of EP Level > 53 ug/dL
(median values are indicated by circles and 90% CIs by bars
extending above and below the median values)
-------
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.
-------
46
60-
50-
^? 40-
_Q)
"5
0) 30-
w
c
o
Q.
v>
Q) 20-
10-
T
T
i Tt
{ Hi
1 I
1}
I
t
ACDE ACDE
25- ^35
ACDE ACDE
. A C CC
*tu OO
PbB Level
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—)» 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
12-1
0-
8-
6-
4-
2-
I
0
F G H
r
T
In
' f _'
1 J K F G H 1 J
> C T C
T'
' ij
L t
j.
V
K F G f
1
r
' •
T -
i
I J
9 C.
_
T
I
{
.
7
K F G K
1
I ,
L|.
i
7 c.
r
I
T <
U
j
T
K r G
^
i
J
i
.
H
-9
-
|
J
T
j
i j
9 =,-
"
—
<:
j
T
K F C
1
J
i
H
-9
T
1
i
T -
!
.
Y
i -
1 J K
7 R
Geometric Mean PbB Level (yu,g/dl_)
FIGURE 23 Risk Results for Mean IQ Decrement in Low SES Children (median values are
indicated by geometric symbols and 90% CIs by bars extending above and below the
median values)
-------
48
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
^/.-
10-
TJ
03
0 8~
-------
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 SENSITIVITY ANALYSIS
Two sensitivity analyses were conducted to study the effects of (1) having dose-
response 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 D: 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).
-------
50
For EP level > 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.
-------
51
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.
-------
52
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 LT.S. 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, 38:187-196 (1985).
Kaufman, A.S., and J.E. Doppelt, Analysts 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 Bayesion Inference and Decision, Holt, Rinehart and
Winston, New York (1972).
-------
54
-------
55
APPENDIX A
FITTING FUNCTIONS TO DATA ON LEAD-INDUCED
ELEVATED EP LEVELS
-------
56
-------
57
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 PSomelli 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 yg/dL
and > 53 yg/dL) of interest.
REP
10.7, for L < 16.4 yg/dL
100$~1[0.103(L - 16.4) - 1.24], for L > 16.4 yg/dL
for EP > 33 yg/dL, and
REP
2.4, for L < 16.6 yg/dL
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 dose-
response 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.I. These distributions are either beta
' -
"
-------
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
EP > 33 yg/dL
EP > 53 yg/dL
Functional
Form Parameter Values
Normal E[R]a = 10,7
Normal E[R] = 14.9
Normal E[R] = 37.5
Normal E[R] = 76.1
Beta X = 42
SD[R]b = 1.1
SD[R] = 1.6
SD[R] = 2.1
SD[R] = 4.1
N = 43
Functional
Form Parameter Values
Normal E[R] =2.4
Normal E[R] = 3.8
Normal E[R] = 14.6
Normal E[R] = 49.0
Beta X = 40
SD[R] =
SD[R] =
SD[R] =
SD[R] =
N = 43
0.5
0.9
1.5
4.8
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).
Ul
03
-------
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 ug/dL, and
R' = 0.01R.
The CDF B(R') for the beta distribution is
R1
B(R') = J 6(R')dR'
R =0 ° °
o
X-l /N-l\ . xr . .
= 1 - I I R'^l - R')*-1-1
i=0 \ i /
The mean E[R] and standard deviation SD[R] of the beta distribution and, where
appropriate, its normal approximation are
E[R] = ^~ and
SD[R] = ig° ['<;;*)]*
For most PbB-EP combinations, the quantity NR'(1 - R') was large enough (> 5) to justify
using the normal approximation.
-------
60
-------
61
APPENDIX B
FITTING FUNCTIONS TO ENCODED JUDGMENTS
RELATING TO LEAD-INDUCED Hb DECREMENT
-------
62
-------
63
APPENDIX B
FITTING FUNCTIONS TO ENCODED JUDGMENTS
RELATING TO LEAD-INDUCED Hb DECREMENT
Appendix B is organized as follows: Sec. B.I reproduces the protocol used for the
Hb encoding sessions; Sec. B.2 details the mathematical formulations for the dose-
response 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.I.I 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 dose-
response 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
-------
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.
-------
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 lead-
induced Hb reduction. If so, then we will elicit your judgments separately for age groups
0-3 and 4-6.
B.I.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.I.6 Factors to Consider
In order to help you bring to mind the relevant evidence so that you may consider
it systematically, and also in order to help us to interpret your judgments, we would like
to ask you to discuss briefly your interpretations of various aspects of the literature.
First of all, could you tell us something about how, in your judgment, lead and iron
interact to reduce 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
-------
66
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.I.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.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 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.I.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.I.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.
-------
68
B.I.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.I.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.
-------
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.1.8 Possible Adverse Health Effects 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
-------
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 probabil-
istically 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)?
-------
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 r1 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.
-------
72
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
F (x) = J f (x )dx
X X o o
-------
73
Thus, FX(X) is the judgmental probability* that X is less than or equal to x.
Furthermore, let yx = E[X], or the expected value of X. Then
CO
y = J x fv(x )dx
x J o X o o
2
And, let a = V[X], the variance of X. Then
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 FR/L[R]) wiU 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 ' Too^T' o < x < ~
Y = ln(X), -co < 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 o . 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
*A11 probabilities hereafter referred to are judgmental probabilities, even if they are not
so specified.
-------
74
available for the distribution on R, all probabilistic and statistical results of interest on
R can be obtained through the distribution on Y since
FR(r) = pr[R < r]
and
- pr
[Y S L.Cj-t
FY(y) = pr[Y < y]
= pr
z <
= $
y - y
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["H-
= F,
= $
in
Table B.I summarizes the quantities of interest for these variables.
The parameters y and o can be estimated in a least-squares sense from an
assessed distribution. Let the n assessed points for a CDF be denoted (Rj, Fj) for i = 1»
..., n, where Rj is the population response rate and Fj is the associated cumulative
judgmental probability.
Least-squares estimates y and a for y and o can be obtained by linearly re-
gressing the Zj on the yj. The reciprocal of the slope of the regression equation is o, and
-------
75
TABLE B.1 Variables Pertaining to the NOLO Function
Variable
Quantity
of Interest
Defining
equations
Y = Ln(X) X = eY = R
Distribution3 N(y ,a^
Mean
Variance
A(y ,
y y
100 - R
2,
y +a2/2
y y
= e
2 2
2y +o o
a2 =e y y(ey- l)
x *• '
R =
100X
1 + X
Median yw
y
Mode y
yy lOOe y
y
1 * e y
2
2 y -o
y y lOOe
6 2
y -a
1 + e y y
3Nfy ,a ) denotes the normal PDF and Afy ,a ) denotes the
y y y y
lognormal PDF. The PDF for R cannot be expressed in closed
form.
Mean and variance expressions for R are obtained using
numerical methods.
is the y-intercept (i.e., value of y corresponding to z = 0 in the regression equation)
noo m ijirlcrmontnl Hictrihiitinna ar«» nsspsspri. nnp for each PbB level i for 1 = 1 m
y-intercept (i.e., value of y corresponding to z = 0 in the regression equation).
judgmental distributions are assessed, one for each PbB level j^for j = 1, ..., m,
e m means (yj_, ..., ym) and standard deviations (o]_, ..., om), one pair for
:he judged distributions.
there are m means (yj_, ...,
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 r2 statistic obtained by regressing the F± on Fi? where
= 1 -
-------
76
and F- denotes the estimated F values (i.e., F^^ = ${(yi - y)/o}), and by obtaining the
r2 value of this regression. If the r2 value is sufficiently high, the NOLO distribution
with parameters y^ and a; 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
r2 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 a; are approximately equal, it is desirable to set them equal to a single
pooled value before proceeding further (i.e., set o; = ai = a 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 L2> where lj^ is greater than^L^.) A pooled estimate of
a , denoted al, can be obtained by first subtracting the mean y • for each set of assessed
points
yj,i = yj,i ~ yj> for i = lj •••' nj and J = *' •••» m
where n- is the number of assessed points for Fp/T and yj : is an assessed point on
FP/L.. 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
z- • on y1. . . The individual least-squares estimates of the means can be recalculated
j» i
at each PbB level by finding the best-fitting line (in the least-squares sense) with a slope
of I/a1 . Under these conditions, the result is simply
n .
J
^ 1
yl =i- I y. .
j n. .^ yjfl
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 F1. . ) on the
original F • • .
J J x
J '
,
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.
-------
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.J, 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 r 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
-------
78
TABLE B.2 Encoded Judgments about Population Response Rates for
Lead-Induced Hb Decrements
Expert A
Hb < 11 g/dL Hb < 9.
PbB 0-3 yr 4-6 yr 0-6
Level
(ug/dL) Ra Fb R F R
5 0.5
1
1.75
3
3.5
4.5
15 1.5
2
3
4
5
6
25 2.5
3
3.5
4
5
6
6.75
35 3.5
4
5
6
7
7.5
45 1 0.1 4.5
2 0.25 5
4 0.4 6
5 0.5 7
7 0.8 8
9 0.95 8.5
Expert
5 g/dL
yr
F
0.01
0.05
0.5
0.8
0.95
0.99
0.001
0.02
0.5
0.75
0.99
0.999
0.01
0.02
0.25
0.5
0.75
0.97
0.99
0.01
0.04
0.5
0.75
0.97
0.99
0.01
0.05
0.5
0.8
0.97
0.99
C
Hb
R
3
6
8
9
12
15
5
8
9
11
14
17
20
5
9
12
13
17
21
10
14
16
18
22
25
15
20
25
30
35
< 11 g/dL
0-6 yr
F
0.01
0.28
0.5
0.5
0.96
0.99
0.03
0.2
0.5
0.6
0.91
0.99
0.999
0.001
0.11
0.5
0.7
0.98
0.99
0.01
0.2
0.5
0.7
0.98
0.99
0.01
0.5
0.7
0.98
0.999
10
19
0.99
0.999
-------
79
TABLE B.2 (Cont'd)
Expert A
Hb < 11 g/dL
PbB
Level
(yg/dL)
55
65
75
0-3
Ra
1
3
6
9
12
15
16
4
7
10
13
16
19
22
5
10
15
20
25
30
35
40
yr
Fb
0.05
0.18
0.4
0.5
0.6
0.95
0.99
0.05
0.15
0.35
0.45
0.6
0.9
0.98
0.05
0.2
0.4
0.5
0.6
0.7
0.95
0.99
4-6
R
1
2
3
5
6
8
3
5
9
12
15
18
4
5
10
15
20
25
Expert C
Hb < 9.5 g/dL
yr 0-6 yr
F R F
0.05 5 0.01
0.4 6 0.05
0.5 7 0.5
0.9 8 0.8
0.95 9 0.95
0.99 10 0.99
0.02
0.2
0.45
0.55
0.6
0.98
0.05
0.1
0.4
0.5
0.8
0.98
Hb < 11 g/dL
0-6 yr
R F
15 0.001
20 0.08
25 0.3
27 0.5
30 0.8
35 0.98
40 0.999
-------
80
TABLE B.2 (Cont'd)
Expert D
Hb < 9.5 g/dL
PbB
Level
(yg/dL)
5
15
25
35
45
55
0-3
R
1
3
0.5
3
7
3
6
8
11
15
7
11
16
19
25
10
16
20
25
33
yr
F
0.5
0.999
0.01
0.5
0.999
0.001
0.25
0.5
0.75
0.999
0.001
0.25
0.5
0.75
0.999
0.001
0.25
0.5
0.75
0.999
4-6
R
0.005
0.5
1.5
2
5
6
8
4
6
8
10
12
6
8
10
11
15
yr
F
0.001
0.5
0.999
0.001
0.5
0.75
0.999
0.001
0.25
0.5
0.75
0.999
0.001
0.25
0.5
0.75
0.999
0-3
R
1
2
4
10
11.8
2
4
6
12
15
11
11.5
15
17.8
21
15
16
18
22
24
17
19
22
26
29
23
26
30
40
47
Hb < 1
yr
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
0.05
0.25
0.5
0.75
0.95
0.125
0.25
0.5
0.75
0.875
1 g/dL
4-6
R
1
1
2
6
1
2
3
9
5
7
8.5
12
7
9
10.5
14
8
10
16
10
12
14
15.5
17
yr
F
0.01
0.25
0.5
0.99
0.01
0.25
0.5
0.99
0.01
0.5
0.75
0.99
0.01
0.5
0.75
0.99
0.01
0.5
0.99
0.01
0.25
0.5
0.75
0.99
-------
81
TABLE B.2 (Cont'd)
Expert E
Hb < 9.
PbB
Level
(yg/dL)
5
15
25
35
45
0-3
R
0.1
1
3
10
15
0.2
3
7
11
15
19
23
0.3
3.5
4
7
9
15
21
25
2.5
5
10
15
20
26
3
6
10
19
31
41
yr
F
0.01
0.1
0.5
0.9
0.99
0.01
0.05
0.5
0.61
0.83
0.9
0.99
0.01
0.05
0.1
0.25
0.5
0.75
0.9
0.99
0.01
0.08
0.27
0.56
0.81
0.98
0.01
0.06
0.2
0.5
0.75
0.99
,5 g/dL
4-6
R
0.4
1
6
9
1
2
7
10
2
4
10
13
1.5
3
6
10
13
2
6.5
10.5
16.5
21.5
26.5
Hb < 11
yr
F
0.15
0.5
0.78
0.98
0.15
0.5
0.78
0.98
0.17
0.5
0.9
0.99
0.1
0.22
0.54
0.85
0.95
0.03
0.1
0.42
0.6
0.8
0.99
0-3
R
2
4
8
12
16
20
24
3
6
10
14
18
22
26
3.5
6
9.5
15
19.5
25
28
4
8
15
20
25
30
6
10
16
22
35
45
yr
F
0.01
0.15
0.5
0.61
0.83
0.9
0.98
0.01
0.15
0.5
0.61
0.83
0.9
0.98
0.01
0.1
0.25
0.5
0.75
0.9
0.99
0.01
0.08
0.27
0.56
0.81
0.98
0.01
0.07
0.25
0.5
0.75
0.99
g/dL
4-6
R
2
5
8
11
14
1
4
7
10
13
16
5
8
11
17
20
5
8
11
14
17
20
5
10
15
20
25
30
yr
F
0.15
0.47
0.55
0.78
0.98
0.01
0.15
0.47
0.55
0.78
0.98
0.06
0.16
0.5
0.9
0.99
0.07
0.1
0.27
0.54
0.85
0.95
0.03
0.1
0.43
0.6
0.8
0.99
-------
82
TABLE B.2 (Cont'd)
Expert E
Hb < 9.5 g/dL Hb < 11 g/dL
PbB
Level
(yg/dL)
55
0-3
R
5
8
22
36
40
47
yr
F
0.01
0.1
0.5
0.75
0.9
0.99
4-6
R
6
11
15
22
26
30
yr
F
0.05
0.4
0.5
0.75
0.9
0.98
0-3
R
10
20
30
40
50
55
yr
F
0.01
0.35
0.5
0.62
0.94
0.99
R
5
10
15
20
25
30
35
4-6 yr
F
0.01
0.05
0.4
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).
F 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
-------
83
TABLE B.3 Functions Fit to Judgments about Population Response Rates for
Lead-Induced Hb Decrements
PbB
Level
(yg/dL)
Expert A,
45
55
65
75
Expert A,
55
65
75
Expert C,
5
15
25
35
45
55
Expert C,
5
15
25
35
45
55
Defining
Parameters3
Functional
Form
Hb < 11 g/dL,
NOLO
NOLO
NOLO
NOLO
Hb < 11 g/dL,
NOLO
NOLO
NOLO
Hb < 9.5 g/dL
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
Hb < 11 g/dL,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
yy
°y
Measures of
Distribution
over Rb
E[RHb]
SD[R
Hbl
r2 for
Regression
of F on F
Ages 0-3
-3
-2
-2
-1
.3546
.9338
.0724
.5754
0
0
0
0
.6820
.6820
.6820
.6820
4
6
12
19
.1
.0
.8
.0
2.
3.
7.
9.
5
7
1
6
0
0
0
0
.89
.84
.93
.94
Ages 4-6
-3
-2
-2
.6826
.2713
.0617
0
0
0
.5945
.5945
.5945
2
10
12
.8
.5
.5
1.
5.
6.
6
3
1
0
0
0
.97
.90
.95
, Ages 0-6
-3
-3
-3
-2
-2
-2
.9995
.4481
.1298
.9187
.7424
.5781
0
0
0
0
0
0
.2764
.2764
.2764
.2764
.2764
.2764
1
3
4
5
6
7
.8
.2
.3
.2
.2
.2
0.
0.
1.
1.
1.
1.
5
9
2
4
7
9
0
0
0
0
0
0
.98
.99
.99
.99
.99
.97
Ages 0-6
-3
-2
-2
-1
-1
-1
.6826
.2713
.0617
.6965
.3190
.0498
0
0
0
0
0
0
.2720
.2720
.2720
.2720
.2720
.2720
2
9
11
15
21
26
.5
.5
.5
.7
.3
.1
0.
2.
2.
3.
4.
5.
7
4
9
8
8
6
0
0
0
0
0
0
.97
.90
.95
.99
.97
.98
-------
TABLE B.3 (Cont'd)
84
PbB
Level
(yg/dL)
Expert D,
15
25
35
45
55
Expert D,
25
35
45
55
Expert D,
5
15
25
35
45
55
Expert D,
5
15
25
35
45
55
Defining
Parameters
Functional
Form y a
Hb < 9.
NOLO
NOLO
NOLO
NOLO
NOLO
Hb < 9.
NOLO
NOLO
NOLO
NOLO
Hb < 11
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
Hb < 11
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
Measures of
Distribution
over R
E[RHb]
SD[RHb]
r2 for
Regression
of F on F
5 g/dL, Ages 0-3
-4.5852
-3.8759
-2.4991
-1.7769
-1.4097
0.3557
0.3557
0.3557
0.3557
0.3557
1.1
2.1
7.9
14.9
20.1
0.4
0.7
2.6
4.5
5.7
0.99
0.84
0.98
0.97
0.99
5 g/dL, Ages 4-6
-6.4604
-3.0443
-2.5123
-2.2433
g/dL, Ages 0-3
-3.1747
-2.7097
-1.7442
-1.4655
-1.2485
-0.7254
g/dL, Ages 4-6
-3.8759
-3.4866
-2.5049
-2.2446
-2.0993
-1.8573
1.0409
0.2177
0.2177
0.2177
0.4919
0.4919
0.4919
0.4919
0.4919
0.4919
0.4894
0.4894
0.1777
0.1777
0.1777
0.1777
0.3
4.6
7.6
9.7
4.4
6.8
15.8
19.8
23.3
33.2
2.2
3.3
7.6
9.6
10.9
13.5
0.3
1.0
1.7
2.1
2.0
3.0
6.3
7.5
8.4
10.6
1.0
1.5
1.4
1.8
2.0
2.4
0.84
0.95
0.94
0.98
0.93
0.96
0.97
0.97
0.99
0.97
0.94
0.99
0.96
0.97
0.94
0.97
-------
85
TABLE B.3 (Cont'd)
PbB
Level
(vg/dL)
Expert E,
5
15
25
35
45
55
Expert E,
5
15
25
35
45
55
Expert E,
5
15
25
35
45
55
Expert E,
5
15
25
35
45
55
Defining
Parameters
Functional
Form
Hb < 9.5 g/dL
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
Hb < 9.5 g/dL
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
Hb < 11 g/dL,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
Hb < 11 g/dL,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
yy
, Ages 0-3
-3.7820
-2.7992
-2.4725
-1.9602
-1.5643
-1.4002
, Ages 4-6
-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
Ages 4-6
-2.8545
-2.6381
-2.2151
-1.9784
-1.7096
-1.5286
ay
0.9600
0.9600
0.9600
0.9600
0.9600
0.9600
0.8224
0.8224
0.8224
0.8224
0.8224
0.8224
0.5991
0.5991
0.5991
0.5991
0.5991
0.5991
0.5912
0.5912
0.5912
0.5912
0.5912
0.5912
Measures of
Distribution
over R
E[RHb]
3.3
8.1
10.6
15.8
21.0
23.4
2.1
3.3
4.6
6.1
13.2
15.5
9.9
12.1
14.1
17.6
23.0
29.9
6.3
7.6
11.1
13.5
16.8
19.4
SD[RHb]
3.3
7.2
8.9
12.0
14.5
15.5
1.8
2.8
3.7
4.8
9.2
10.3
5.3
6.3
7.1
8.4
10.1
11.8
3.5
4.2
5.8
6.8
8.1
8.9
r2 for
Regression
of F on F
0.98
0.96
0.96
0.96
0.99
0.99
0.98
0.99
0.98
0.95
0.98
0.93
0.98
0.99
0.98
0.95
0.98
0.93
0.90
0.95
0.97
0.94
0.97
0.98
aY = ln[R/(l - R)] is normally distributed with mean y and standard
deviation
b,
V
DUsing
j , a , and numerical methods, values can be calculated for
the mean E[R] and the standard deviation SD[R] of the response-
rate distribution (which is NOLO) over R.
percentage.
R is expressed as a
-------
86
TABLE B.4 Comparison of Judgments and Fitted Functions
Concerning Population Response Rates for Lead-Induced Hb
Decrements
Response Ratea at PbB Level
Index 45 yg/dL 55 yg/dL 65 yg/dL 75 pg/dL
Expert A, Hb < 11 g/dL,
Encoded Judgments
Median 5
50% CIb 2, 7
90% CI 1, 9
Fitted Functions
Median 3
50% CI 2, 5
90% CI 1, 10
98% CI 1, 15
Expert A, Hb < 11 g/dL,
Encoded Judgments
Median
50% CI
90% CI
Fitted Functions
Median
50% CI
90% CI
98% CI
Ages 0-3
9
4, 13
1, 15
5
3, 8
2, 14
1, 21
Ages 4-6
3
2, 4
1, 6
2
2, 4
1, 6
1, 9
9
4
7
4
3
6
3
6
4
3
14
, 18
, 21
11
, 17
, 28
, 38
11
, 16
, 18
9
, 13
, 22
, 29
20
11, 31
5, 35
17
12, 25
6, 39
4, 50
15
8, 19
4, 24
11
8, 16
5, 25
3, 34
-------
87
TABLE B.4 (Cont'd)
Response Rate
Index
5 yg/dL 15 yg/dL
25 yg/dL
at PbB Level
35 yg/dL
45 yg/dL
55 yg/dL
Expert C, Hb < 9.5 g/dL, Ages 0-6
Encoded Judgments
Median
50% CI
90% CI
2
1, 3
1, *
3
2,
2,
4
5
4
3
4
, 5
, 6
4
4
5
, 6
, 7
5
5
6
, 7
, 8
6
6
7
, 8
, 9
Fitted Functions
Median
50% CI
90% CI
98% CI
2
1, 2
1, 3
1, 4
Expert C, Hb < 11 g/dL,
Encoded
Median
50% CI
90% CI
Judgments
8
6, 10
3, 10
3
3,
2,
2,
Ages
9
8,
5,
4
5
6
0-6
12
13
4
3
2
10
4
, 5
, 6
, 8
12
, 14
7, 15
4
3
3
14
11
5
, 6
, 8
, 9
16
, 19
, 20
5
4
6
, 7
, 9
3, 11
17
15
20
, 26
, 27
6
7
, 8
5, 11
4, 13
24
18
27
, 29
, 31
Fitted Functions
Median
50% CI
90% CI
98% CI
7
6, 9
5, 11
4, 13
10
8,
6,
5,
11
14
17
10
12
, 14
8, 17
6, 20
13
10
15
, 18
, 22
9, 26
18
15
12
21
, 24
, 29
, 33
23
18
16
26
, 30
, 35
, 40
-------
TABLE B.4 (Cont'd)
Response
Index 5 yg/dL 15 yg/dL
Expert D, Hb < 9.5 g/dL, Ages 0-3
Encoded Judgments
Median 1
50% CI c, 2
90% CI c, 3
Fitted Functions
Median 1
50% CI 1, 1
90% CI 1, 2
98% CI 0, 2
Expert D, Hb < 9.5, Ages 4-6
Encoded Judgments
Median
50% CI
90% CI
Fitted Functions
Median
50% CI
90% CI
98% CI
Rate
25 yg/dL
3
2,
1,
2
2,
1,
1,
0.
o,
o,
0.
o,
o,
o,
5
7
3
4
4
5
1
1
2
0
1
2
at PbB Level
35 yg/dL
8
6,
4,
8
6,
4,
3,
5
3,
2,
5
4,
3,
3,
11
14
9
13
16
6
8
5
6
7
45 yg/dL
11
16
, 19
8, 24
12
14
, 18
9, 23
7,
6,
4,
7
5,
5,
28
8
10
12
7
, 9
10
12
55 yg/dL
16
11
16
12
12
8,
20
, 25
, 31
20
, 24
, 30
, 36
10
11
6, 14
8,
7,
10
11
13
6, 15
-------
89
TABLE B.4 (Cont'd)
Response Rate at PbB Level
Index
Expert D, Hb
5 yg/dL
< 11 g/dL,
15 yg/dL
Ages
0-3
25 yg/dL
35 yg/dL
45 yg/dL
55 yg/dL
Encoded Judgments
Median
50% CI
90% CI
4
2, 10
1, 3
6
4,
2,
12
15
15
11, 18
11, 21
18
16, 22
14, 26
19
17
22
, 26
, 29
26
21
30
, 40
, 52
Fitted Functions
Median
50% CI
90% CI
98% CI
Expert D, Hb
4
3, 6
2, 9
1, 12
< 11 g/dL,
6
5,
3,
2,
Ages
8
13
17
4-6
15
11, 20
7, 28
5, 35
19
14, 24
9, 34
7, 42
22
17, 29
11, 39
8, 47
26
18
13
33
, 40
, 52
, 60
Encoded Judgments
Median
50% CI
90% CI
2
1, 4
1, 6
3
2,
1,
6
9
7
6, 9
5, 11
9
8, 11
7, 13
10
9, 13
8, 16
12
10
14
, 16
, 17
Fitted Functions
Median
50% CI
90% CI
98% CI
2
1, 3
1, 4
1, 6
3
2,
1,
1,
4
6
9
8
7, 8
6, 10
5, 11
10
9, 11
7, 12
7, 14
11
10, 12
8, 14
7, 16
14
12, 15
10, 17
9, 19
-------
90
TABLE B.4 Cont'd)
Response Rate
Index
Expert E, Hb
5 yg/dL 15 yg/dL 25 yg/dL
< 9.5 g/dL,
at PbB Level
35 yg/dL
45 yg/dL
55 yg/dL
Ages 0-3
Encoded Judgments
Median
50% CI
90% CI
3
2,
1,
7
12
7
5,
3,
13
21
9
6, 15
3, 23
14
9,
4,
19
24
19
11, 31
5
, 39
22
13, 36
6
, 44
Fitted Functions
Median
50% CI
90% CI
98% CI
Expert E, Hb
2
1,
o,
o,
4
10
18
< 9.5 g/dL,
6
3,
1,
1,
10
23
36
8
4, 14
2, 29
1, 44
12
7,
3,
1,
21
41
57
17
10, 29
4
2
, 50
, 66
20
11, 32
5
3
, 54
, 70
Ages 4-6
Encoded Judgments
Median
50% CI
90% CI
1
1,
o,
5
9
2
1,
o,
6
10
4
1, 7
0, 11
6
3,
1,
9
13
8
3
13
, 20
, 25
9
6
15
, 22
, 29
Fitted Functions
Median
50% CI
90% CI
98% CI
1.
1,
o,
o,
5
3
6
10
2.
1,
1,
o,
4
4
9
15
3.4
2, 6
1, 12
1, 19
5
3,
1,
1,
8
16
25
7
3
2
11
, 17
, 32
, 45
8
4
2
13
, 21
, 36
, 50
-------
91
TABLE B.4 (Cont'd)
Response Rate
Index
5 yg/dL 15 yg/dL 25 yg/dL
Expert E, Hb < 11 g/dL,
Encoded Judgments
Median
50% CI
90% CI
8
5, 14
3, 22
Ages
0-3
10
7,
4,
16
24
9
5
15
, 19
, 26
at PbB Level
35 vg/dL
19
14, 24
6
, 28
45 yg/dL
55 yg/dL
22
16,
9,
35
43
17
11
30
, 44
, 51
Fitted Functions
Median
50% CI
90% CI
98% CI
Expert E,
Encoded
Median
50% CI
90% CI
9
6, 13
3, 20
2, 28
Hb < 11 g/dL,
Judgments
6
3, 10
1, 14
11
7,
4,
3,
Ages
8
5,
2,
15
24
33
4-6
12
16
9
5
3
9
4
13
, 18
, 28
, 37
11
, 15
, 19
16
11, 22
7
5
, 34
, 44
13
10, 16
4
, 20
21
15,
9,
6,
29
42
52
21
13
28
, 37
, 52
9, 62
16
12,
6,
24
29
13
10
20
, 25
, 33
Fitted Functions
Median
50% CI
90% CI
98% CI
5
4, 8
2, 13
1, 19
7
5,
3,
2,
10
16
22
7
4
3
10
, 14
, 22
, 30
8
5
3
12
, 17
, 27
, 35
15
11,
6,
A,
21
32
42
13
18
, 24
8, 36
5, 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.
-------
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 ferrochela-
tase. 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 dihydroxy-
vitamin 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
-------
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 yg/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.
-------
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 hematolog-
ical effects, and at much lower PbB levels (about 40 yg/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 noniron-
deficient children. Expert B estimated that, on the average,
noniron-deficient children with PbB levels of about 10 yg/dL and
50 yg/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 yg/dL and 50 yg/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.
-------
95
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, it 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
-------
96
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 yg/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 yg/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 DUiydroxyvitamin D
• A complex enzyme system is responsible for production of 1,25
dihydroxyvitamin D hormone. Lead is known to impair several
-------
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 yg/dL, there is evidence of an approximately
66% decrease in the kidney's ability to produce 1,25 dihydroxy-
vitamin D hormone.
At PbB levels above 62 yg/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 yg/dL, there is a statistically significant
negative correlation between 1,25 hihydroxyvitamin D and PbB
levels.
At PbB levels above 55 yg/dL, chelation therapy is immediately
used. At 25-55 yg/dL, the results of the ethylenediamine-
tetraacetate (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.
-------
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 yg/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 yg/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, II. Effect of
Chronic Administration in Mice, Neuroscience Letters, 50:169-173 (1984).
-------
99
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-tryptophan: 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 by
Trace 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).
-------
100
-------
101
APPENDIX C
FITTING FUNCTIONS TO ENCODED JUDGMENTS
RELATING TO LEAD-INDUCED IQ EFFECTS
-------
102
-------
103
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.I
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.I.I 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 dose-
response 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
-------
104
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 well-
defined effect if a sufficient amount of pertinent data could be collected, our first task
is to select one CNS or behavioral effect that is of acknowledged importance and that
can be well specified.
The search for lead-induced effects has included studies of electroencephalogram
(EEC) 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.
-------
105
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. 1.2.2 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.l.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.
-------
106
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 conditions, 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 probabil-
istic 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.
-------
107
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 con-
stant 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.I.5.1 Physiological Conditions
The effect of lead in the system depends on the person's nutritional and meta-
bolic 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.I.5.2 Environmental Conditions
The effect of lead on IQ also may depend on numerous environmental and care-
giving 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.I.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
-------
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 lead-induced IQ effects that we should discuss now?
C.I.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. 1.7.1 Sequential Consideration of Information
Generally, the order in which evidence is considered influences the final
judgment, although logically that should not be the case. Of necessity, pieces of
information are considered one by one in a sequential fashion. However, those
considered first and last tend to dominate judgment. In part, initial information has its
undue influence because it provides the framework that subsequent information is then
tailored to fit. For example, people usually search for evidence to confirm their initial
hypotheses; they rarely look for evidence that weighs against them. The later evidence
has its undue effect simply because it is fresher in memory.
-------
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. 1.7.2 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.I.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.
-------
110
C.I.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.I.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.
-------
Ill
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
-------
112
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 them 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
-------
113
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 give us such a set immediately. All of this will become clearer as we go along.
We should emphasize that the judgments we are asking you to make are not
simple ones, nor of course are there known correct answers. Rather, we want your best
and most considered judgment in light of the available relevant scientific data.
Therefore, please reflect on the available data carefully, feeling free to consult the lead
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 8, and ask you to consider how
likely it is that the L(D) is less than the specified a. 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 £ 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 moije probable that L(D) is less than 8,,
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 a and repeat the process. As before, for each D we
will elicit your comparative judgments for various values of «,.
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.)
-------
114
The value of y" or y". is uncertain, and we will obtain your judgment about its possible
values. Analogously to what we have already done, we will specify a mean y and 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.
i
The value of a. is uncertain, and we will obtain your judgment about its possible values.
Analogously to what we have already done, we will specify a standard deviation o and ask
you to consider how likely it is that o. is less than o. We will elicit your judgments
about various values of a 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 TQ , a , and A— 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 , cr , and A—- into discrete
o ly IQ
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 , a , and Ay^r 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
-------
115
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
!0.5, for IQ = 95
_°
0.5, for IQQ = 105
0.5, for o = 14
(0.5, for AjQ =
P(A-) =j ^
^ (0.5, for A™ =
— = 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, a = 14, and A— = 5, the
increased probability of having IQs < 70 is
= 0.077 - 0.037
= 0.04
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.I). 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
-------
116
TABLE C.I Encoded Judgments about the Mean IQ of Children
Unexposed to Lead
Expert F Expert G Expert H Expert J Expert K
IQ0a Fb IQQ F IQQ F IQQ F IQ0 F
Both SES Levels
100 0.01
100.5 0.05
101 0.65
101.5 0.80
102 0.99
Low SES Level
90
93
94
96
98
100
High SES Level
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
92
94
98
99
102
100
102
104
106
108
110
0.01
0.20
0.50
0.65
0.99
0.02
0.11
0.30
0.49
0.75
0.96
90.0
93.5
95.0
96.0
98.0
100
102
104
106
108
110
0.01
0.25
0.50
0.75
0.90
0.001
0.1
0.77
0.90
0.99
0.999
78
83
85
88
91
100
102
104
106
108
110
0.01
0.25
0.50
0.75
0.99
0.01
0.17
0.42
0.60
0.85
0.99
aIQ0 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
-------
117
TABLE C.2 Encoded Judgments about Population Standard Deviation
Expert F Expert G
°iqa Fb OIQ F
Expert H
°IQ F
Expert J Expert K
JJ1 — C1
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 0.04 11 0.001 12 0.02
13.5 0.07 12 0.125 13 0.25
14 0.275 13 0.5 13.5 0.5
14.3 0.5 14 0.875 14 0.75
15 0.9 15 0.999 15 0.99
15.5 0.99
ao-TQ denotes standard deviation in IQ values.
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.I. 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_fprm; the defining
parameters y and a, if a transformation is used; the mean E[IQ 1 and standard
deviation SD[IQ ] of the IQ distributions; and r2 for the regression of fitted cumulative
-------
118
TABLE C.3 Encoded Judgments about Mean IQ Decrements of
Children Exposed to Lead
Expert F
PbB Both SES
Level
(gg/dL) AYQ
5
15
25 0.25
1
35 0.5
2
45 0.9
1
2
3
55 1
2
3
4
65 1
2
3
4
5
'
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
AlQ
0.2
0.3
0.5
1
3
0.5
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
15
Expert C
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
f .99
0.01
0.25
0.5
0.75
0.99
High SES
AlQ
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
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
Expert H
Low SES
AIQ
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
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 SES
AIQ
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
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
-------
TABLE C.3 (Cont'd)
119
Expert I
PbB
Level
(pg/dL)
5
15
25
35
45
55
65
Low
AIQ
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
5.3
6.9
10
4
5.5
6.3
8.2
12
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
0.5
0.75
0.975
High
ATQ
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
SES
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
ATQ
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 J
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
0.5
0.75
0.99
High
AIQ
0.5
1
1.25
2
2.3
3
4
6
1
2.75
3
3.5
7
2
3.5
4
5
7
3
4.5
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
AiQ
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
AiQ
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
aAjQ denotes the mean IQ decrement among children with the specified PbB levels, referenced to
unexposed children.
F denotes cumulative probability.
-------
120
TABLE C.4 Functions Fit to Judgments about Mean IQ Levels among
Children Unesposed to Lead
Measures of
Distribution
Expert
Defining
Parameters3
Functional
Form yy oy
over IQ 2 c
0 r for
Regression
E[IQ0] SD[IQQ] of F on F
Both SES Levels
F Lognormal
Low SES Level
4.61 0.005
100.9
0.5
0.88
G Lognormal
H Lognormal
J Normal
K 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 Lognormal
H Lognormal
J Lognormal
K Normal
4.66 0.02
4.66 0.03
4.65 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
aThe function Y = ln(lQo) is normally distributed with mean y and
standard deviation a . There are no entries in these columns
when IQ is normally distributed.
3For lognormal distributions, u , o , and the equations in Table
B.I are used to calculate the mean E[IQ ] and the standard
deviation SD[IQ ] of the distribution over LQ .
o xo
In Table C.5, E[OIQ] denotes the mean
probability values F versus encoded values F.
and SD[O-[.Q] denotes the standard deviation of the distribution for"1 population standard
deviation. In Table C.6, E[AYQ] 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 r2 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.
-------
121
TABLE C.5 Functions Fit to Judgments about Population Standard Deviation
for IQ Levels
Measures of
Distribution
Expert
Defining
Parameters3
Functional
Form yy ay
over oTr.
IQ r2 for
Regression
E[aIQ] SD[aIQ] of F on F
Both SES Levels
F Point
Low SES Level
G Point
H Lognormal
J Normal
K Normal
High SES Level
2.5056 0.0915
15.0
14.0
12.3
13.0
12.6
1.1
0.7
0.9
0.95
0.99
0.97
G
H
J
K
Point
Lognormal 2.6541 0.0416
Normal
Normal
14.0
14.2
13.0
13.5
0.6
0.7
0.7
0.99
0.99
0.99
aThe function Y = ln(aIO) is normally distributed with mean y and
standard deviation a . There are no entries in these columns for
normal or point distributions.
5For lognormal distributions, y ,
are used to calculate the mean E[a
SD[aIQ].
a , and the equations in Table B.I
and the standard deviation
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 rz
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.
-------
122
TABLE C.6 Functions Fit to Judgments about Mean IQ Decrements among Children
Exposed to Leada
PbB
Level
(ug/dL)
Functional
Form
Defining
Parameters
Measures of
Distribution
over A" c
r for
Regression
of F on F
Both SBS Levels
Expert F
25
35
45
55
65
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
Lognormal
Lognormal
Lognormal
Lognormal
Lognormal
•1.4059
-0.7127
•0.0329
0.3350
0.5574
•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
0.4628
0.4628
0.4628
0.4628
0.4628
0.6422
0.5429
0.5229
0.3807
0.3011
0.3174
0.4087
0.3989
0.3749
0.3087
0.2366
0.1887
0.5351
0.4110
0.3282
0.3088
0.2845
0.3
0.5
1.1
1.6
1.9
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
0.1
0.3
0.5
0.8
0.9
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
0.99
0.99
0.99
0.99
0.99
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)
123
Measures of
Distribution
PbB
Level
(yg/dL)
Defining over A
Parameters
Functional
Form y o E[A!Q]
IQ 2 ,
r tor
Regression
SD[AJQ] of F on F
Expert J
5
15
25
35
45
55
Expert
15
25
35
45
55
65
High SES
Expert
15
25
35
45
55
Expert
5
15
25
35
45
55
Normal
Normal
Normal
Normal
Normal
Normal
K
Normal
Normal
Normal
Normal
Normal
Normal
Levels
G
Lognormal
Lognormal
Lognormal
Lognormal
Lognormal
H
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
2.4
3.5
4.8
6.8
8.8
10.7
0.9
1.2
1.5
1.5
1.6
1.6
0.96
0.99
0.99
0.99
0.99
0.98
1.3
2.9
3.8
6.4
7.8
0.4
0.4
1.1
1.1
1.2
1.3
1.6
0.95
0.99
0.99
0.98
0.99
0.99
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
-------
TABLE C.6 (Contsd)
124
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
Defin:
Paramel
Py
-1.1800
0.0637
0.8495
1.3198
1.4719
0.4542
1.0069
1.3082
1.6280
1.9489
aThe distributions are either normal
If the distribution over
Measures of
Distribution
Lng over A™
oy E[A
0.6191
0.6022
0.4110
0.3293
0.3839
0.4502
0.3640
0.2762
0.1991
0.1466
or lognormal
A™ is lognormal, then
IQl
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
in
the
so(^
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
form.
function Y
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
= In(Ajg)
is normally distributed with mean \i and standard deviation a .
no entries in these columns when ATT^; is normally distributed.
There are
For lognormal distributions, y , a , and the equations in Table B.I are
used to calculate the mean E[A—] and the standard deviation SD[A—] of
the response-rate distribution over A—. Calculations involving normal
distributions over A— are more straightforward.
-------
TABLE C.7 Comparison of Judgments and Fitted Functions Concerning Lead-Induced IQ Effects
™ at PbB Level
Index IQQ OIQ 25 yg/dL 35 yg/dL 45 yg/dL 55 yg/dL 65 yg/dL
Expert F, Both SES Levels
Encoded Judgments
Median
50% CIa
90% CI
100
100.2,
100.1,
.5 15
101.3
101.9
0
b,
b,
.25
0.6
0.9
0.
b,
b,
5
1.2
1.9
0
b,
b,
.9
1.5
2
1.
1.1,
b,
5
1.9
3
2
1.3,
b,
2.6
4
Fitted Functions
Median
50% CI
90% CI
98% CI
100
100.6,
100.1,
99.8,
.9 15
101.2
101.7
102
0
0.2
0.1
0.1
.25
, 0.3
, 0.5
, 0.7
0.
0.4,
0.2,
0.2,
5
0.7
1.1
1.4
1
0.7,
0.5,
0.3,
.0
1.3
2.1
2.8
1.
1.0,
0.7,
0.5,
4
1.9
3.0
4.1
1.
1.3,
0.8,
0.6,
7
2.4
3.7
5.1
Ln
-------
TABLE C.7 (Cont'd)
- at PbB Level
Index
IQ
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 94 14
50% CI 93, 96
90% CI 91, 99
Fitted Functions
Median 94.6 14
50% CI 93.1, 96.1
90% CI 91.0, 98.3
98% CI 89.6, 99.8
Expert G, High SES Level
Encoded Judgments
Median 106 14
50% CI 105, 107
90% CI 103, 109
Fitted Functions
Median 105.5 14
50% CI 104.1, 107.0
90% CI 102.0, 109.2
98% CI 100.6, 110.7
0.5 1.5 3.0 3.
0.3, 1 0.7, 2 1.3, 4 2.5
0.2, 3 0.5, 5 1, 8.5 2,
0.6 1.4 2.7 3.
0.4, 0.9 1, 2 1.9, 3.8 3,
0.2, 1.8 0.6, 3.5 1.1, 6.3 2.1,
0.1, 2.8 0.4, 4.9 0.8, 9 1.6,
0.5 1,0 2.
0.4, 1 0.7, 2 1.5
0.3, 3 0.5, 4 1,
0.7 1.2 2.
0,5, 1 0.9, 1.7 1.9,
0.3, 1.8 0.5, 2.8 1.2,
0.2, 2.7 0.4, 4 0.8
5 5.0
,5 4, 7
10 3.5, 12
9 5.7
5 4.6, 7
7.3 3.5, 9.3
9.4 2,8, 11.4
5 3.5
, 4 2.5, 5
8 2, 10
6 3.9
3.6 3, 5
5.8 2.1, 7.3
, 8 1.6, 9.4
7,
5,
4,
7,
5.9,
4.3,
3.5,
5
4,
3.5
5
4.7,
3.5,
2.8,
,0
10
15
.3
9.1
12.3
15.3
.0
7.5
, 12
.8
7.1
9.5
11.7
ho
CTN
-------
TABLE C.7 (Cont'd)
at PbB Level
Index IQQ OIQ 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 98
50% CI 95, 100
90% CI 92, 102
Fitted Functions
Median 97.2
50% CI 95.5, 98.8
90% CI 93.3, 101.2
98% CI 91.7, 102.9
Expert H, High SES Level
Encoded Judgments
Median 106
50% CI 104, 108
90% CI 101, 110
Fitted Functions
Median 105.6
50% CI 103.7, 107.5
90% CI 101.1, 110.3
98% CI 99.3, 112.3
13
12,
10,
12
11.5,
10.5,
9.9,
14
13.8,
13.2,
14
13.8,
13.3,
12.9,
14
15
.3
13.0
14.2
15.2
.3
14.7
15.2
.3
14.6
15.2
15.6
2.
1.6,
1.1,
2.
1.7
1.2,
0.9,
0.
6
3.4
4.5
3
, 3
4.5
5.9
6
b, 0.9
b,
0.
0.4,
0.2,
0.2,
1.3
6
0.8
1.3
1.9
3.0
2.6, 5
1.9, 6.1
3.5
2.7, 4.6
1.8, 6.7
1.4, 8.8
2.5
1.8, 3.5
1.2, 4.1
2.4
1.8, 3.3
1.2, 5.1
0.9, 7
5.2
3.4, 7.2
2.4, 9.2
4.9
3.8, 6.3
2.6, 9
2, 11.7
4.5
3.8, 5.6
2.7, 6.7
4.4
3.7, 5.2
2.9, 6.7
2.4, 8
8
6,
4.2
7
6.2,
4.6,
3.7,
5
4.4,
3.9,
5
4.7,
3.9,
3.4,
.2
9.7
, 12
.6
9.4
12.7
15.7
.5
6.4
7.8
.4
6.2
7.5
8.5
9.5
7.4, 11.3
6.2, 14
9.4
8, 11
6.4, 13.9
5.4, 16.3
6.5
6.1, 7.1
5.3, 8.4
6.6
6, 7.2
5.3, 8.2
4.9, 8.9
10.
9.7,
8.2,
,5
11.8
16
11.1
9.7,
8.1,
7.1,
8.
7.4,
6.4,
7.
7.3,
6.6,
6.1,
12.6
15.1
17.2
0
8.7
9.6
9
8.5
9.5
10.2
-------
TABLE C.I (Cont'd)
A™ at PbB Level
Index IQQ a™ 5 yg/dL 15 yg/dL
Expert I, Low SES Level
Encoded Judgments
Median
50% CI
90% CI
Fitted Functions
Median
50% CI
90% CI
98% CI
Expert I, High SES Level
Encoded Judgments
Median
50% CI
90% CI
Fitted Functions
Median
50% CI
90% CI
98% CI
0.
0.5,
o,
0.
0.5,
0.3,
0.2,
0.
0.2,
o,
0.
0.2,
0.1,
0.1,
7
1.1
2
7
1.0
1.7
2.5
3
0.5
1
4
0.5
0.9
1.3
25 yg/dL
2.
1.9,
1,
2.
1.7,
1.2,
0.9,
1.
0.7
o,
1.
0.6,
0.1,
0.1,
3
3.2
5
3
3.1
4.6
6.1
0
, 2
3
1
1.7
2.8
4.3
35 yg/dL
3.
3.1,
2,
3.
3.0,
2.2,
1.8,
2.
1.9,
1,
2.
1.8,
1.2,
0.9,
6
5.1
7
8
4.7
6.5
8.2
3
3.2
5
4
3.2
4.5
6.1
45 yg/dL
5.
4.5,
3,
5.
4.4,
3.3,
2.7,
3.
3.1,
2,
3.
3.1,
2.2,
1.8,
3
6.9
10
5
6.7
9.1
11.3
6
4.7
7
8
4.7
6.3
7.9
55 yg/dL
6.
5.5,
4,
6.
5.5,
4.2,
3.5,
4.
3.5,
2,
4.
3.4,
2.3,
1.8,
3
8.
12
7
8.
2
1
10.7
13.1
3
5.
9
5
5.
8.
10,
8
7
0
.6
-------
TABLE C.7 (Cont'd)
Index
IQ0 OIQ 5 yg/dL 15 yg/dL
'15
25 yg/dL
at PbB Level
35 yg/dL 45 yg/dL
55 yg/dL
Expert J, Low SES Level
Encoded Judgments
Median
50% CI
90% CI
95
94,
91,
96
99
13
12, 14
11, 15
2 3.
1, 3 2.3,
0.2, 5 0.4,
5
4.5
6.4
5
4, 5.8
1,
8
7
6, 8 7.5,
3, 9.6 5,
9
10.5
11.7
11
9, 12.5
6.6, 13.
7
Fitted Functions
Median
50% CI
90% CI
98% CI
Expert J, High
94.
93.5,
91.6,
90.3,
8
96.1
98.0
99.3
13
12.5, 13.5
11.9, 14.1
11.4, 14.6
2.4 3.
1.8, 3.0 2.7,
0.9, 3.9 1.5,
0.3, 4.5 0.7,
5
4.3
5.4
6.2
4.
3.8,
2.3,
1.3,
8
5.8
7.2
8.2
6.8 8
5.8, 7.8 7.8
4.4, 9.3 6.3,
3.3, 10.3 5.2,
.8
, 9.9
11.4
12.5
10.7
9.7, 11.
8.1, 13.
7.0, 14.
8
4
5
SES Level
Encoded Judgments
Median
50% CI
90% CI
103
102.5,
100.5,
.1
103.9
107.0
13
12, 14
11, 15
2
1.3,
2.3
0.7, 3
3
2.8,
1.4,
3.5
6.4
4
3.5, 5 4.5
2, 6.7 3.3
5
, 5.8
, 7.6
7
6.5, 7.
5.3, 9.
5
7
Fitted Functions
Median
50% CI
90% CI
98% CI
104
103.0,
101.4,
100.4,
.1
105.2
106.8
108.0
13
12.5, 13.5
11.9, 14.1
11.4, 14.6
1.
1.2,
0.7,
0.5,
6
2.2
3.4
4.6
2.
2.1,
1.5,
1.2,
7
3.5
5.0
6.4
3.7 5
3.0, 4.4 4.4
2.3, 5.8 3.6
1.9, 7.0 3.2
.0
, 5.8
, 7.0
, 8.0
7.0
6.4, 7.
5.5, 8.
5.0, 9.
8
9
9
-------
TABLE C.I (Cont'd)
A™ at PbB Level
Index
Expert K, Low
ZQo
°IQ
15 yg/dL 25 yg/dL
35 yg/dL
45 yg/dL
55 yg/dL
65 yg/dL
SES Level
Encoded Judgments
Median
50% CI
90% CI
85
83,
88
79, 90.4
13
12.2,
11,
13.5
14
1.5 3.1
0.8, 1.7 2, 3.8
0.3, 2 1, 4.8
4
3.2, 4.7
2, 5.8
6
5.4,
4.5,
7.5
8.8
8.1
6.8, 8.6
5.5, 9.8
10
8.8, 11
7.5, 13
.8
.7
Fitted Functions
Median
50% CI
90% CI
98% CI
Expert K, High
85
83.0,
80.2,
78.2,
87.0
89.8
91.8
12.
12.0,
11.1,
10,4,
6
13.2
14.1
14.8
1.3 2,9
0.7, 1.6 2.1, 3.6
0.5, 1.8 1.1, 4.7
0.2, 2.3 0.3, 5.5
3.8
3, 4.5
2, 5.5
1.3, 6.3
6.
5.6,
4.4,
3.6,
4
7.3
8.4
9.3
7.8
6.9, 8.6
5.6, 9.9
4.7, 10.8
10.4
9.3, 11
.4
7.8, 13
6.7, 14
SES Level
Encoded Judgments
Median
50% CI
90% CI
104.9
102.6,
100.6,
107.2
109.4
13.
13,
12.2,
5
14
14.8
1.5
0.8, 1.7
0.6, 1.9
2
1.6, 2.3
1,2, 2.9
3.
3.1
2.2,
5
, 4
4.8
4.5
4, 4.8
3.1, 5.9
6
5.2, 6
4.3, 7
.8
.8
Fitted Functions
Median
50% CI
90% CI
98% CI
104.9
103.3,
106.5
101, 108.8
99.4, 110.4
13.
13,
12.3,
11.9,
5
14
14.6
15.1
1.3
1, 1.5
0.7, 1.9
0.5, 2.1
2
1.7, 2.3
1.3, 2.7
1, 3
3.
3.1
2.5,
2,
5
, 4
4.6
5
4.5
4, 5
3.3, 5.7
2.8, 6.2
6
5.4, 6
4.5, 7
3.9, 8
.6
~5
.1
aCI denotes credible interval.
bLower CI limit could not be calculated because Experts F and H did not make probability judgments on
A^=- values less than the median at this PbB level .
-------
131
TABLE C.8 Functions for Response Rate for IQ Levels below 85 and 70
PbB
Level
(yg/dL)
Functional
Form
Defining
Parameters
yy °y
Measures of
Distribution
E[RIQ] SD[RIQ]
r2 for
Regression
of F on F
Expert F, IQ < 85, All SES Levels
25
35
45
55
65
Expert G,
5
15
25
35
45
55
Expert G,
15
25
35
45
55
Expert H,
5
15
25
35
45
55
Expert H,
5
15
25
35
45
55
Normal
Normal
Normal
Normal
Normal
10 < 85,
Normal
Normal
Normal
Normal
Normal
Normal
IQ < 85,
NOLO
NOLO
NOLO
NOLO
NOLO
IQ < 85,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
IQ < 85,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
Low SES
Level
High SES Level
-4.
-4.
-3.
-2.
-2.
Low SES
-2.
-2.
-1.
-1.
-1.
-0.
8299
2264
3857
9398
4322
Level
8741
3672
9395
3366
0426
7957
0.6663
0.5954
0.6215
0.5311
0.4721
0.5129
0.5283
0.5385
0.4883
0.4085
0.3558
High SES Level
-5.
-3.
-2.
-2.
-2.
-2.
0908
4508
8040
5509
2990
0322
0.6384
0.5977
0.4282
0.3704
0.3144
0.2973
0.5
1.1
2.1
3.2
4.0
1.0
1.7
3.8
5.6
8.7
5.9
9.4
13.7
21.8
26.6
31.4
0.7
3.6
6.1
7.6
9.4
11.8
0.3
0.5
0.9
1.4
1.8
0.6
1.0
2.2
2.7
3.6
2.7
4.3
6.0
8.0
7.9
7.8
0.4
2.0
2.4
2.6
2.7
3.2
0.96
0.97
0.96
0.96
0.95
2.4
4.9
9.1
11.5
16.0
21.3
1.4
2.5
4.6
4.3
4.9
6.8
0.96
0.96
0.96
0.97
0.97
0.97
0.95
0.97
0.97
0.98
0.98
0.98
0.98
0.98
0.99
0.99
0.99
0.95
0.97
0.99
0.99
0.99
0.99
-------
TABLE C.8 (Cont'd)
132
PbB
Level
(yg/dL)
Expert J,
5
15
25
35
45
55
Expert J,
15
25
35
45
55
Expert K,
15
25
35
45
55
65
Expert K,
25
35
45
55
65
Expert F,
25
35
45
55
65
Defining
Parameters
Functional
Form yy oy
IQ < 85, Low SES Level
Normal
Normal
Normal
Normal
Normal
Normal
If? < 85, High SES Level
NOLO -3.8868 0.5373
NOLO -3.2633 0.4705
NOLO -2.9322 0.3875
NOLO -2.5321 0.3251
NOLO -2.0750 0.2773
IQ < 85, Low SES Level
Normal
Normal
Normal
Normal
Normal
Normal
IQ < 85, High SES Level
NOLO -4.3580 0.4285
NOLO -3.8194 0.3646
NOLO -3.1341 0.3426
NOLO -2.8214 0.3271
NOLO -2.4225 0.3195
IQ < 70, All SES Levels
Normal
Normal
Normal
Normal
Normal
Measures of
Distribution
E[RIQ]
6.2
9.2
12.9
18.8
24.7
30.3
2.3
4.0
5.3
7.6
11.3
3.9
8.7
11.3
18.7
22.2
28.2
1.4
2.3
4.4
5.8
8.4
0.1
0.2
0.5
0.8
1.0
SD[RIQ]
2.4
3.3
4.2
4.5
4.8
4.9
1.2
1.8
1.9
2.3
2.9
1.4
3.3
3.2
3.7
4.0
4.8
0.6
0.8
1.4
1.8
2.5
0.1
0.1
0.3
0.4
0.5
r2 for
Regression
of F on F
0.98
0.98
0.98
0.99
0.99
0.99
0.97
0.98
0.99
0.99
0.99
0.99
0.99
0.99
0.98
0.98
0.99
0.97
0.99
0.99
0.98
0.99
0.98
0.97
0.97
0.97
0.95
-------
133
TABLE C.8 (Cont'd)
PbB
Level
(vg/dL)
Expert G,
5
15
25
35
45
55
Expert G,
15
25
35
45
55
Expert H,
5
15
25
35
45
55
Expert H,
5
15
25
35
45
55
Expert J,
5
15
25
35
45
55
Defining
Parameters
Functional
Form y a
IQ < 70,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
IQ < 70,
NOLO
NOLO
NOLO
NOLO
NOLO
IQ < 70,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
IQ < 70,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
IQ < 70,
NOLO
NOLO
NOLO
NOLO
NOLO
NOLO
Low SES Level
-5.4123 0.7608
-4.5825 0.7137
-3.8201 0.7204
-3.3673 0.5560
-2.8823 0.4934
-2.4877 0.5490
High SES Level
-6.8990 0.7389
-6.3072 0.7189
-5.4150 0.7421
-4.9164 0.6530
-4.3577 0.6024
Low SES Level
-4.7645 0.7706
-4.2186 0.7796
-3.7332 0.7789
-3.0392 0.7292
-2.6958 0.6406
-2.3930 0.5844
High SES Level
-7.1075 0.7947
-5.4439 0.7860
-4.7471 0.6348
-4.4666 0.5795
-4.1788 0.5290
-3.8790 0.5071
Low SES Level
-4.4206 0.6652
-3.9207 0.6087
-3.4556 0.5718
-2.8627 0.4528
-2.4235 0.4076
-2.0625 0.3779
Measures of
Distribution
E[RIQ]
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
r2 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
-------
134
TABLE C.8 (Cont'd)
PbB
Level
(ug/dL)
Defining
Parameters
Functional
Form
Measures of
Distribution
E[RIQ]
SD[R
IQ
r for
Regression
of F on F
Expert J, IQ < 70, High SES Level
15
25
35
45
55
NOLO
NOLO
NOLO
NOLO
NOLO
-6.1838
-5.5216
1690
7212
-5,
-4,
-4.1927
0.7171
0.6529
0.5887
0.5191
0.4751
Expert K, IQ < 70, Low SES Level
15
25
35
45
55
65
Normal
Normal
Normal
Normal
Normal
Normal
0.3
0.5
0.7
1.0
1.6
2.4
5.9
7.7
14.0
17.5
24.9
Expert K, IQ < 70, High SES Level
0.2
0.3
0.4
0.5
0.7
1.0
2.7
2.9
4.2
4.9
6.2
0.88
0.98
0.98
0.99
0.99
0.96
0.95
0.96
0.98
0.98
0.99
25
35
45
55
65
NOLO
NOLO
NOLO
NOLO
NOLO
-6.5690
-6.0268
-5.2946
-4.9459
-4.4969
0.6485
0.6122
0.5926
0.5723
0.5548
0.2
0.3
0.6
0.8
1.3
0.1
0.2
0.3
0.5
0.7
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 9096-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.I), 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.
-------
135
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 ug/dL to 4% at 65 ug/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 IQ , a , 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
-------
136
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.
-------
137
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.
-------
138
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 EEC data are not clear. The findings are
somewhat inconsistent, and it is not known what the measures refer
to.
-------
139
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.
-------
140
-------
141
APPENDIX D
RISK DISTRIBUTIONS
-------
142
-------
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.I 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 lead-
induced 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.I 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(LX < L < L2) = F(L2) - F(LX)
where fl'1 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 pj_, ..., 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
-------
144
PbB probability and then summed across the PbB levels. Mathematically, this step can
be written as
&
RCL5 = .^ piR0.5,i for i = 1' •••' 6
where Rn c denotes the median value of the overall response rate, and Rg <- : 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 L^ 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 prob-
ability 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.
-------
145
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.I. The results for EP are listed in Table D.I. 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 con-
sidered 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.I).
Thus, the tabulated risk distributions for GM = 2.5-5.0 yg/dL are normal, with mean 2.4%
TABLE D.I Risk Estimates for Lead-Induced Elevated EP Levels, U.S. Children Aged 0-6
Fractiles,
Mean, and
Standard
Deviation
Response Rate (%) at Geometric Mean PbB Level in ug/dL
2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5
EP > 53 vg/dL
0.05
0.25
0.50
0.75
0.95
Mean 2.4 2.4 2.4 2.7 3.6 5.5 8.5 12.7 17.9 23.8 30.3
SD 0.5 0.5 0.5 0.6 0.7 0.8 1.1 1.4 1.7 2.1 2.4
EP > 33 \ig/dL
1.5
2.0
2.4
2.8
3.3
1.5
2.0
2.4
2.8
3.3
1.6
2.1
2.4
2.8
3.3
1.8
2.3
2.7
3.1
3.6
2.5
3.2
3.6
4.0
4.7
4.1
4.9
5.5
6.0
6.8
6.7
7.8
8.5
9.2
10.3
10.4
11.8
12.7
13.6
14.9
15.0
16.7
17.9
19.0
20.6
20.3
22.5
23.9
25.2
27.1
26.2
28.7
30.4
32.0
34.1
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
-------
146
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.I, 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 y of -4 and a o of 0.28 (see Table B.3).
If desired, the distributions conditional on age can be combined to produce
further risk distributions. That across-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.
-------
147
TABLE D.2 Risk Estimates for Hb Levels < 9.5 and < 11 g/dL, U.S. Children Aged 0-
and4-6
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
2.5
Hb < 9.5
1.1
1.5
1.8
2.2
2.8
1.8
0.5
Hb < 9.5
0
0
0
0
0
0
0
Hb < 9.5
0.5
1.2
2.2
4.2
10.0
3.3
3.3
Hb < 9.5
1.1
1.5
1.8
2.2
2.8
1.9
0.5
Response Rate (%) at Geometric
5.0
g/dL,
1.2
1.5
1.8
2.2
2.9
1.8
0.5
g/dL,
0
0
0
0
0
0
0
g/dL,
0.5
1.2
2.3
4.3
10.3
3.5
3.4
g/dL,
1.2
1.5
1.8
2.2
2.9
1.9
0.5
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
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 yg/dL
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
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
1.2
3.1
4.3
5.3
6.5
8.8
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
-------
TABLE D.2 (Cont'd)
148
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
Expert A, Hb
0.05
0.25
0.50
0.75
0.95
Mean
SD
Expert C, Hb
0.05
0.25
0.50
0.75
0.95
Mean
SD
Response Rate (%) at Geometric
2.5
< 9.
0
0
0
0
0
0
0
< 9.
0.4
0.9
1.5
2.6
5.7
2.1
1.8
< 11
0
0
0
0
0
0
0
< 11
1.6
2.1
2.5
2.9
3.8
2.5
0.7
5.0
5 g/dL,
0
0
0
0
0
0
0
5 g/dL,
0.4
0.9
1.6
2.7
5.8
2.1
1.8
g/dL,
0
0
0
0
0
0
0
g/dL,
1.7
2.2
2.6
3.1
4.0
2.7
0.7
7.5
Ages 4-6
0
0
0
0
0
0
0
Ages 4-6
0.5
1.0
1.7
3.0
6.3
2.3
2.0
Ages 0-3
0
0
0
0
0
0
0
Ages 0-3
2.5
3.3
3.9
4.6
5.9
4.0
1.0
10.0
0
0
0
0
0
0
0
0.5
1.2
2.0
3.5
7.3
2.7
2.3
0
0.1
0.1
0.1
0.2
0.1
0.1
3.9
5.0
6.0
7.0
8.9
6.1
1.5
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
0.1
0.2
0.3
0.5
0.9
0.4
0.3
5.1
6.5
7.7
9.1
11.5
8.0
2.0
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
0.3
0.5
0.8
1.2
2.1
0.9
0.6
6.0
7.6
9.0
10.6
13.4
9.3
2.3
Mean PbB Level in yg/dL
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
0.5
0.9
1.4
2.1
3.8
1.6
1.1
6.6
8.5
10.0
11.7
14.7
10.2
2.5
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
0.7
1.3
2.1
3.2
5.8
2.5
1.6
7.2
9.2
10.8
12.7
15.9
11.1
2.6
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
1.0
1.8
2.9
4.4
7.8
3.4
2.2
7.8
10.0
11.7
13.7
17.1
12.0
2.8
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
1.3
2.4
3.7
5.6
10.0
4.4
2.8
8.5
10.8
12.6
14.8
18.4
12.9
3.0
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
1.6
3.0
4.6
6.9
12.1
5.4
3.4
9.2
11.6
13.6
15.9
19.7
13.9
3.2
-------
149
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
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
t
2.5
Hb < 11
1.8
2.9
4.0
5.5
8.6
4.5
2.1
Hb < 11
3.5
6.0
8.7
12.5
20.4
9.9
5.3
Hb < 11
0
0
0
0
0
0
0
Hb < 11
1.6
2.1
2.5
2.9
3.8
2.5
0.7
Response Rate (%) at Geometric
5.0
g/dL, Ages
1.9
3.0
4.1
5.6
8.7
4.5
2.2
g/dL, Ages
3.5
6.0
8.8
7.5
0-3
2.1
3.3
4.5
6.1
9.5
5.0
2.4
0-3
3.6
6.3
9.2
12.6 13.1
20.5 21.3
10.0 10.4
5.4
g/dL, Ages
0
0
0
0
0
0
0
g/dL, Ages
1.7
2.2
2.6
3.1
4.0
2.7
0.7
5.5
4-6
0
0
0
0
0
0
0
4-6
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
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 in yg/dL
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
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
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
-------
150
TABLE D.2 (Cont'd)
Fractiles ,
Mean, and
Standard
Deviation
Response Rate (%) at Geometric Mean PbB Level in pg/dL
2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5
Expert D, Hb < 11 g/dL, Ages 4-6
0.05
0.25
0.50
0.75
0.95
Mean
3D
0.9
1.5
2.0
2.8
4.4
2.3
1.1
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
1.2
1.9
2.6
3.6
5.5
2.9
1.3
1.6
2.4
3.1
4.2
6.2
3.4
1.4
2.2
3.1
3.9
4.9
6.9
4.1
1.5
3.0
3.9
4.7
5.7
7.7
4.9
1.5
3.8
4.7
5.5
6.6
8.5
5.7
1.4
4.5
5.5
6.4
7.4
9.2
6.6
1.4
5.2
6.3
7.1
8.2
9.9
7.3
1.4
5.8
6.9
7.8
8.9
10.6
8.0
1.5
Expert E, Hb < 11 g/dL, Ages 4-6
0.05
0.25
0.50
0.75
0.95
Mean
SD
2.1
3.7
5.4
7.9
13.2
6.3
3.5
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
2.4
4.2
6.1
8.9
14.7
7.0
3.9
2.6
4.6
6.7
9.6
15.8
7.6
4.2
2.9
5.0
7.2
10.4
17.0
8.2
4.5
3.2
5.4
7.9
11.3
18.4
9.0
4.8
3.5
6.0
8.6
12.3
19.8
9.7
5.1
3.8
6.5
9.3
13.2
21.2
10.5
5.5
4.1
7.0
10.0
14.2
22.6
11.3
5.8
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 dose-
response functions. The first step was to change each CDF for IQ , OJQ, and A— 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.I 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.
-------
151
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
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 I,
0.05
0.25
0.50
0.75
0.95
Mean
SD
2.5
Low SES
0
0
0
0
0
0
0
Low SES
0.2
0.4
0.6
1.0
1.8
0.8
0.5
Low SES
1.2
1.7
2.3
3.0
4.5
2.5
1.0
Low SES
0
0
0
o
0
0
0
Response Rate (%) at Geometric Mean
5.0
0
0
0
0
0
0
0
0.2
0.4
0.6
1.0
1.8
0.8
0.5
-
1.2
1.8
2.3
3.0
4.5
2.5
1.1
0
0
0
0
0
0
0
7.5
0
0
0
0
0
0
0
0.3
0.5
0.8
1.2
2.1
0.9
0.6
1.3
1.9
2.5
3.3
4.9
2.8
1.1
0.1
0.1
0.2
0.2
0.4
0.2
0.1
10.0
0
0
0
0
0
0
0
0.4
0.7
1.0
1.5
2.7
1.2
0.7
1.5
2.2
2.9
3.8
5.7
3.2
1.3
0.2
0.3
0.4
0.6
0.9
0.5
0.2
12.5
0
0
0
0
0.1
0
0
0.5
0.9
1.3
1.9
3.2
1.5
0.9
1.7
2.5
3.3
4.3
6.4
3.6
1.5
0.3
0.5
0.7
1.0
1.6
0.8
0.4
15.0
0
0
0.1
0.1
0.1
0.1
0
0.7
1.1
1.6
2.3
3.8
1.8
1.0
2.0
2.8
3.7
4.8
7.0
4.0
1.6
0.5
0.7
1.0
1.4
2.2
1.1
0.5
17.5
0
0.1
0.1
0.1
0.2
0.1
0.1
0.8
1.3
1.9
2.7
4.4
2.2
1.2
2.2
3.2
4.1
5.3
7.7
4.4
1.7
0.7
1.0
1.4
1.8
2.8
1.5
0.7
PbB Level in yg/dL
20.0
0.1
0.1
0.2
0.2
0.4
0.2
0.1
1.0
1.6
2.2
3.1
5.0
2.5
1.3
2.5
3.6
4.5
5.8
8.3
4.9
1.8
0.9
1.3
1.7
2.3
3.4
1.9
0.8
22.5
0.1
0.2
0.2
0.3
0.5
0.3
0.1
1.2
1.9
2.5
3.5
5.5
2.9
1.4
2.8
4.0
5.0
6.4
9.0
5.4
1.9
1.1
1.6
2.1
2.8
4.1
2.3
0.9
25.0
0.1
0.2
0.3
0.4
0.7
0.3
0.2
1.4
2.1
2.9
3.9
6.1
3.2
1.5
3.2
4.4
5.5
7.0
9.7
5.9
2.0
1.4
2.0
2.5
3.3
4.7
2.7
1.0
27.5
0.2
0.3
Oo4
0.5
0.8
0.4
0.2
1.6
2.4
3.2
4.3
6.6
3.6
1.6
3.6
4.9
6.1
7.5
10.3
6.4
2.1
1.6
2.3
2.9
3.7
5.3
3.1
1.1
-------
TABLE D.3 (Cont'd)
152
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
2.5
Low 5ES
0.9
1.8
2.4
3.0
3.9
2.4
0.9
Low SES
0
0
0
0
0
0
0
High SES
0
0
0
0
0
0
0
High SES
0
0
0
0
0
0
0
Response Rate (%) at Geometric Mean
5.0
0.9
1.8
2.4
3.0
3.9
2.4
0.9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7.5
1.0
2.0
2.6
3.3
4.2
2.6
1.0
0.1
0.2
0.3
0.3
0.4
0.3
0.1
0
0
0
0
0
0
0
0.1
0.1
0.1
0.2
0.4
0.2
0.1
10.0
1.2
2.3
3.0
3.7
4.7
3.0
1.0
0.3
0.5
0.7
0.8
1.1
0.7
0.2
0
0
0
0
0
0
0
0.1
0.3
0.4
0.5
0.9
0.4
0.3
12.5
1.4
2.5
3.3
4.1
5.2
3.3
1.1
0.5
0.8
1.1
1.4
1.7
1.1
0.4
0
0
0
0
0.1
0
0
0.2
0.4
0.6
0.8
1.4
0.7
0.4
15.0
1.7
2.8
3.7
4.5
5.7
3.7
1.2
0.6
1.1
1.5
1.8
2.3
1.5
0.5
0
0
0.1
0.1
0.1
0.1
0
0.3
0.5
0.8
1.1
1.9
0.9
0.5
17.5
1.9
3.2
4.0
4.9
6.1
4.0
1.3
0.8
1.4
1.9
2.3
2.9
1.9
0.6
0
0.1
0.1
0.1
0.2
0.1
0.1
0.4
0.7
1.0
1.4
2.3
1.1
0.6
PbB Level in yg/dL
20.0
2.2
3.5
4.4
5.3
6.6
4.4
1.3
1.0
1.7
2.2
2.7
3.5
2.2
0.8
0.1
0.1
0.2
0.2
0.4
0.2
0.1
0.5
0.8
1.2
1.6
2.7
1.3
0.7
22.5
2.6
3.9
4.8
5.8
7.1
4.8
1.4
1.2
2.0
2.6
3.2
4.0
2.6
0.9
0.1
0.2
0.2
0.3
0.5
0.3
0.1
0.6
1.0
1.4
1.9
3.1
1.6
0.8
25.0
2.9
4.3
5.3
6.2
7.6
5.3
1.4
1.5
2.4
3.0
3.6
4.5
3.0
0.9
0.1
0.2
0.3
0.4
0.7
0.3
0.2
0.8
1.2
1.7
2.3
3.6
1.9
0.9
27.5
3.3
4.8
5.7
6.7
8.1
5.7
1.4
1.7
2.7
3.4
4.1
5.0
3.4
1.0
0.2
0.3
0.4
0.5
0.8
0.4
0.2
0.9
1.4
2.0
2.6
4.1
2.2
1.0
-------
TABLE D.3 (Cont'd)
153
Fractiles
Mean, and
Standard
Deviation
Expert H,
0.05
0.25
0.50
0.75
0.95
Mean
SD
Expert It
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
Expert K,
0.05
0.25
0.50
0.75
0.95
Mean
SD
y
Response Rate (%) at Geometric Mean
2.5
High SES
0.2
0.4
0.6
0.8
1.3
0.6
0.3
High SES
0
0
0
0
0
0
0
High SES
0
0
0
0
0
0
0
High SES
0
0
0
0
0
0
0
5.0
0.3
0.4
0.6
0.9
1.4
0.7
0.4
0
0
0
0
0
0
0
0
0
0
0.1
0.1
0
0
0
0
0
0
0
0
0
7.5
0.4
0.7
1.0
1.3
2.1
1.1
0.5
0
0
0.1
0.1
0.2
0.1
0.1
0.2
0.2
0.3
0.4
0.7
0.4
0.2
0
0
0
0
0
0
0
10.0
0.7
1.1
1.6
2.1
3.3
1.7
0.8
0.1
0.1
0.2
0.3
0.5
0.2
0.1
0.4
0.6
0.8
1.1
1.7
0.9
0.4
0
0
0
0
0
0
0
12.5
1.1
1.6
2.1
2.8
4.3
2.3
1.0
0.1
0.2
0.3
0.5
0.8
0.4
0.2
0.6
1.0
1.3
1.7
2.6
1.4
0.6
0.1
0.1
0.1
0.1
0.2
0.1
0
15.0
1.4
2.0
2.6
3.4
5.0
2.9
1.1
0.2
0.3
0.5
0.7
1.2
0.5
0.3
0.8
1.2
1.6
2.2
3.3
1.8
0.8
0.2
0.2
0.3
0.3
0.4
0.3
0.1
17.5
1.8
2.5
3.1
3.9
5.5
3.3
1.2
0.3
0.4
0.6
0.9
1.6
0.8
0.4
1.0
1.5
2.0
2.6
3.8
2.1
0.9
0.3
0.4
0.5
0.6
0.7
0.5
0.1
PbB Level in ug/dL
20.0
2.2
2.9
3.5
4.4
6.0
3.7
1.2
0.4
0.6
0.9
1.2
2.1
1.0
0.6
1.3
1.8
2.3
2.9
4.2
2.4
0.9
0.5
0.6
0.8
0.9
1.1
0.8
0.2
22.5
2.5
3.3
3.9
4.8
6.3
4.1
1.2
0.5
0.8
1.1
1.6
2.6
1.3
0.7
1.5
2.0
2.6
3.3
4.6
2.7
1.0
0.6
0.9
1.0
1.2
1.5
1.0
0.2
25.0
2.9
3.7
4.3
5.1
6.6
4.5
1.1
0.7
1.0
1.4
1.9
3.1
1.6
0.8
1.7
2.3
2.9
3.6
4.9
3.0
1.0
0.8
1.1
1.3
1.5
1.8
1.3
0.3
27.5
3.2
4.0
4.7
5.5
6.9
4.8
1.1
0,8
1.2
U7
2.3
3.5
1.9
0.9
2.0
2.6
3.2
3.9
5.2
3.3
1.0
1.0
1.4
1.6
1.8
2.2
1.6
0.3
-------
154
TABLE D.4 Risk Estimates for IQ Levels < 70 and < 85, U.S. Children Aged 7
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
Response Rate (%) at Geometric
2.5
IQ < 70,
0
0
0
0
0
0
0
IQ ^ 70,
0.1
0.3
0.4
0.7
1.5
0.6
0.5
IQ ^ 70,
0.2
0.5
0.8
1.4
2.9
1.1
0.9
IQ < 70,
0.4
0.8
1.2
1.8
3.5
1.5
1.0
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
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
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 Level in ug/dL
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
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
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
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)
155
Fractiles,
Mean, and
Standard
Deviation
Expert K, IQ
0.05
0.25
0.50
0.75
0.95
Mean
SD
Expert F, IQ
0.05
0.25
0.50
0.75
0.95
Mean
SD
Expert G, IQ
0.05
0.25
0.50
0.75
0.95
Mean
SD
Expert H, IQ
0.05
0.25
0.50
0.75
0.95
Mean
SD
Response Rate (%) at Geometric
2.5
< 70,
0
0
0
0
0
0
0
< 70,
0
0
0
0
0
0
0
< 70,
0
0
0
0
0
0
0
< 70,
0
0
0.1
0.1
0.3
0.1
0.1
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
7.5
0.2
0.4
0.5
0.6
0.8
0.5
0,2
0
0
0
0
0
0
0
0
0
0
0
0.1
0
0
0
0.1
0.2
0.3
0.6
0.2
0.2
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
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 Level in yg/dL
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
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
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
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)
156
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
2.5
IQ < 70,
0
0
0
0
0
0
0
IQ < 70,
0
0
0
0
0
0
0
IQ < 85,
0
0
0
0
0
0
0
IQ ^ 85,
0.1
1.5
2.4
3.3
4.7
2.4
1.4
Response Rate (%) at Geometric
5.0
High SES
0
0
0
0
0
0
0
High SES
0
0
0
0
0
0
0
Low SES
0
0
0
0
0
0
0
Low SES
0.1
1.5
2.5
3.4
4.8
2.5
1.4
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
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
0.5
2.4
3.7
5.1
7.0
3.7
2.0
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 Level in yg/dL
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
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
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
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
-------
157
TABLE D.4 (Cont'd)
Fractiles
Mean, and
Standard
Deviation
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
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
Response Rate (%) at Geometric
2.5
IQ < 85,
2.4
3.8
5.3
7.4
11.6
6.0
2.9
IQ < 85,
2.2
4.5
6.2
7.8
10.1
6.2
2.4
JO < 85,
0
0
0
0
0
0
0
IQ < 85,
0
0
0
0
0
0
0
5.0
Low SES
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
Low SES
0
0.1
0.1
0.1
0.1
0.1
0
High SES
0
0
0
0
0
0
0
7.5
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
0.3
0.6
0.8
1.0
1.3
0.8
0.3
0
0
0
0
0
0
0
10.0
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
0.8
1.6
2.1
2.6
3.3
2.1
0.7
0
0
0
0
0
0
0
12.5
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
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
15.0
W
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
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
Mean PbB Level in ug/dL
17.5
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
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
20.0
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
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
22.5
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
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
25.0
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
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
27.5
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
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)
158
Fractiles ,
Mean, and
Standard
Deviation
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
Expert K,
0.05
0.25
0.50
0.75
0.95
Mean
SD
2.5
IQ < 85,
0
0
0
0
0
0
0
IQ < 85,
0.2
0.4
0.6
0.9
1.7
0.7
0.5
IQ < 85,
0
0
0
0
0
0
0
IQ < 85,
0
0
0
0
0
0
0
Response Rate (%) at Geometric
5.0
High SES
0
0
0
0
0.1
0
0
High SES
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
High SES
0
0
0
0
0
0
0
7.5
0.1
0.1
0.2
0.3
0.5
0.2
0.1
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
0
0
0
0
0
0
10.0
0.1
0.3
0.4
0.6
1.2
0.5
0.4
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
0
0
0
0
0.1
0
0
12.5
0.2
0.4
0.7
1.0
1.9
0.8
0.5
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
0.1
0.1
0.1
0.2
0.2
0.1
0.1
15.0
0.3
0.6
0.9
1.3
2.5
1.1
0.7
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
0.1
0.2
0.3
0.4
0.6
0.3
0.1
Mean PbB Level in yg/dL
17.5
0.4
0.7
1.1
1.7
3.0
1.3
0.9
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
0.3
0.4
0.5
0.7
1.0
0.6
0.2
20.0
0.5
0.9
1.4
2.1
3.7
1.6
1.0
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
0.4
0.6
0.8
1.0
1.5
0.9
0.3
22.5
0.6
1.1
1.7
2.5
4.4
2.0
1.2
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
0.6
0.8
1.1
1.4
2.1
1.2
0.5
25.0
0.8
1.4
2.1
3.0
5.2
2.4
1.4
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
0.8
1.1
1.4
1.8
2.6
1.5
0.6
27.5
1.0
1.7
2.4
3.5
6.0
2.8
1.6
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
1.0
1.4
1.7
2.2
3.2
1.9
0.7
------- |