Investigation of Cancer Risk
Assessment Methods
Volume 3. Analyses
Clement Associates, Inc., Ruston, LA
Prepared for
Environmental Protection Agency. Washington, DC
Sep 87
PB88rl27139
L
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-'••' TECHNICAL REPORT DATA
/Please read Inuructions on the went before completing/
1 REPORT NO. . 12.
EPA/600/6-87/007d |
4. TITLE ANO SUBTITLE
.Investigation of Cancer Risk Assessment Me
Volume 3. Analyses
3 PB88-127139
5. REPORT DATE .,
thods: September 1987
6. PERFORMING ORGANIZATION CODE
-/AUTHOR*. Bruce c> Allen, Annette M. Shipp, Kenny S. B.PERFORM.NGOR
Crump, Bryan Kill an, Mary Lee Hogg, Joe Tudor,
Barbara Keller
9 PERFORMING ORGANIZATION NAME AND ADDRESS
Clement Associates, Inc.
-1201 Gaines Street
Ruston, LA 71270
3ANIZATION REPORT NO.
10. PROG-AM ELEMENT NO.
11. CONTRACT /GRANT NO.
68-01-6807
12. SPONSORING AGENCY NAME AND ADDRESS . 13; TYPE OF REPORT AND PERIOD CO VERED
Office of Health and, Environmental Assessment
Carcinogen Assessment Group (RD-689)
U.S. Environmental Protection Agency
Washington, DC 20460
14. SPONSORING AGENCY CODE
EPA/600/21
15. SUPPLEMENTARY NOTES £pA pr0ject officer: Chao Chen, Carcinogen Assessment Group
Office of Health and Environmental Assessment, Washington, DC (382-5719)
i6. ABSTRACT jne major focus of this study is upon making quantitative comparisons of
carcinogenic potency in animals and humans for 23 chemicals -for which suitable
animal and human data exists. These comparisons are based upon estimates of risk
related doses (RRDs) obtained from both animal and human data. An RRD represents
the average daily dose per body weight of a chemical that would result in an extra
cancer risk of 25%. Animal data on these and 21 other chemicals of interest to the
EPA and the DOD are coded into an animal data base that permits evaluation by
computer of many risk assessment approaches.
This report is the result of a two-year study to examine the assumptions,
other than those involving low dose extrapolation, used in quantitative cancer risk
assessment. The study was funded by the Department of Defense [through an inter-
agency transfer of funds to the Environmental Protection Agency (EPA)J, the EPA,
the Electric Power Research Institute and, in its latter stages, by the Risk Science
Institute.
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DISCLAIMER :
This document has been reviewed in accordance with the U.S. Environmental
Protection Agency's peer and administrative review policies and /approved for
pufolication. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use. The information in thisi-document has
been funded by the U.S. Environmental Protection Agency, the Department of
Defense (through Interagen^y Agreement Number RW97Q751Q1), the Electric
Power Research Institute, and the Risk Science Institute.
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CONTENTS
Section Poqe
1 METHODOLOGY
Introduction 1-1
Analysis of Bioassay Data 1-2
Definition of Analysis Methods 1-3
Description of Approaches to Components 1-7
Definition of Standard Methods 1-8
Sieve 1-10
Comparison With Epidemiological Results 1-13
Correlation Analysis 1-13
Prediction Analyses 1-16
Uncertainty 1-2<»
2 RESULTS
Correlation Analysis 2-1
Evaluation of Sieve 2-3
Analyses that Use Combination of 2-5
All Significant Individual Responses
Analyses That Utilize Malignant Neoplasms Only 2-6
Adjustment for Early Deaths by Considering Only 2-7
Animals Alive at the Time of Occurrence of the
First Tumor
Analyses That Utilize Only Long Studies 2-7
Analyses That Use Same Tumor Response in 2-8
Animals as in Humans
Comparison of Correlations from Data from 2-8
Specific Animal Species
Choice of Dose Units 2-9
Identification of Analyses Yielding Higher 2-10
Correlations
Prediction Analysis '•' > 2-12
Sieve 2-13
Predictors 2-1 «*
Comparison of Analysis Methods 2-16
Asymmetric Loss 2-20
Animal-to-Human Conversion 2-22
Uncertainty 2-26
3 DISCUSSION
Positive Correlation 3-1
Data Quality and Data Screening 3-3
Application of Analysis Results in Extrapolating 3-6
from Animals to Humans
Identification of Good Methods 3-7
Predictors 3-7
Analysis Methods 3-9
Coraponent-Speci.'ic Uncertainty 3-15
Options for Presenting a Range of Risk Estimates 3-18
Option 1 3-19
Options 2 and 3 3-19
Comparison of Option* 3-21
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Section Page
Example* 3-2^
General Considerations and Major Conclusions 3-26
Directions for Future Research 3-30
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ILLUSTRATIONS
1-1 Final RRD Estimate
2-1 Correlation Analysis :
2-2 Correlation Analysis :
2-3 Correlation Analysis :
2-4 Correlation Analysis :
2-5 Correlation Analysis:
2-6 Correlation Analysis:
2-7 . Correlation Analysis:
2-8 Correlation Analysis:
2-9 Correlation Analysis:
2-10 Correlation Analysis:
2-11 Correlation Analysis:
2-12 Correlation Analysis:
2-13 Correlation Analysis:
Experiment (5)
2-14 Correlation Analysis:
2-15 Correlation Analysis:
Responses (8a)
2-16 Correlation Analysis:
2-17 Correlation Analysis:
2-18 Correlation Analysis:
2-19 Correlation Analysis:
2-20 Correlation Analysis:
2-21 Correlation Analysis:
2-22 Correlation Analysis:
2-23 Correlation Analysis:
2-24 Correlation Analysis:
2-25 Correlation Analysis:
2-26 Correlation Analysis:
2-27 Correlation Analysis:
2-28 Correlation Analysis:
and Species (12)
2-29 Correlation Analysis:
and Species (12)
2-30 Correlation Analysis:
and Species (12)
2-31 Correlation Analysis:
and Species (12)
2-32 Correlation Analysis:
Significant Response
2-33 Correlation Analysis:
Animals (20)
2-34 Correlation Analysis:
2-35 Prediction Analysis:
Predictor
2-36 Prediction Analysis:
Predictor
Standard Analysis (0) 2-58
Standard Analysis (0) 2-59
Standard Analysis (0) 2-60
Standard Analysis (0) 2-61
Long Experiment Only (1) 2-62
Long Dosing Only (2) 2-63
Long Dosing Only (2) 2-64
Route That Humans Encounter (3a) 2-65
Any Route of Exposure (3b) 2-66
Any Route of Exposure (3b) 2-67
Any Route of Exposure (3b) 2-68
Any Route of Exposure (3b) 2-69
Average Dose Over BOH of 2-70
Malignant Tumors Only (7) 2-71
Combination of Significant 2-72
Total Tumor-Bearing Animals (8b) 2-73
Response That Humans Get (8a) 2-74
Average Over Sex (9) 2-75
Average Over Sex (9) 2-76
Average Over Study (10) 2-77
Average Over Study (10) 2-78
Average Over All Species (11a) 2-79
Average Over All Species (Ha) 2-80
Average Over Rats and Mice (11b) 2-81
Average Over Rats and Mice (11b) 2-62
Rat Data Only (11c) 2-83
Mouse Data Only (11d) 2-84
Average Over Sex, Study, 2-85
Average Over Sex, Study, 2-86
Average Over Sex, Study, 2-87
Average Over Sex, Study, 2-88
Average Over All: Combination of 2-89
(16)
Average Over All: Total Tumor-Bearing 2-90
Route and Response Like Humans (25) 2-91
Analysis 17, Median Lower Bound 2-92
Analysis 17, Median Lower Bound 2-93
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ILLUSTRATIONS
2-37 Prediction Analysis: Analysis 3b, Median Lower Bound 2-94
Predictor
2-38 Prediction Analysis: Analysis 20, Median Lower Bound 2-95
Predictor
2-39 Prediction Analysis: Analysis 3b, Median Lower Bound; 2-96
Best-Fitting Lines with Increasing Degrees of Asymmetry
2-40 Prediction Analysis: Analysis 20, Median Lower Bound; 2-9.'
Best-Fitting Lines with Increasing Degrees of Asymmetry
2-41 Prediction Analysis: Analysis 22, Median Lower Bound; 2-98
Best-Fitting Lines with Increasing Degrees of Asymmetry
2-42 Component-Specific Uncertainty; Ratios of RRDs for 2-99
Analysis 31 (mg/m^/doy) to RRDs for Analysis 30
2-'»3 Component-Specific Uncertainty; Ratios of RRDs for 2-99
Analysis 32 (ppm diet) to RRDs for Aoalysiu 30
2-44 Component-Specific Uncertainty; Ratios of RRDs for 2-100
Analysis 33 (ppm air) to KRDs for Analysis 30
2-45 Component-Specific Uncertainty; Ratios of RRDs for 2-100
Analysis 34 (mg/kg/lifetime) to RRDs for Analysis 30
2-46 Component-Specific Uncertainty; Ratios of RRDs for 2-101
Analysis 35 (Long Experiments Only) to RRDs for Analysis 30
2-47 Component-Specific Uncertainty; Ratios of RROs for 2-101
Analysis 36 (Long Dosing Only) to RRDs for Analysis 30
2-48 Component-Specific Uncertainty; Ratios of RRDs for 2-102
Analysis 37 (Route Like Humans) to RRDs for Analysis 30
2-49 Component-Specific Uncertainty; Ratios of RRDs for 2-102
Analysis 38 (Inhalation, Oral, Gavage, Route Like Humans)
to RRDs for Analysis 30
2-50 Component-Specific Uncertainty; Ratios of RRDs for 2-103
Analysis 41 (Malignant Tumors Only) to RRDs for Analysis 30
2-51 Component-Specific Uncertainty; Ratios of RRDs for 2-103
Analysis 42 (Combination of Significant Responses)
to RROs for Analysis 30
2-52 Component-Specific Uncertainty; Ratios of RRDs for Analysis 2-104
43 (Total Tumor-Bearing Animals) to RRDs for Analysis 30
2-53 Component-Sp»cific Uncertainty; Ratios of RRDs for 2-104
Analysis 44 (Response Like Humnas) to RRDs for Analysis 30
2-54 Component-I.pecific Uncertainty; Ratios of RRDs for 2-105
Analysis 45 (Average Ovsr Sex) to RRDs for Analysis 30
2-55 Component-Specific Uncertainty; Ratios of RROs for 2-105
Analysis 46 (Average Over Study) to RRDs for Analysis 30
2-56 Component-Specific Uncertainty; Ratios of RRDs for Analysis 2-106
47 (Average Over All Species) to RRDs for Analysis 30
2-57 Component-Specific Uncertainty; Ratios of RROs for Analysis 2-106
48 (Average Over Rats and Mice) to RROs for Analysis 30
2-58 Component-Specific Uncertainty; Ratios of RROs for Analysis 2-107
49 (Rat Data Only) to RRDs for Analysis 30
2-59 Component-Specific Uncertainty; Ratios of RRDs for 2-107
ti« 50 fmauma Oatn Onlv^ to RRDm for Analvmia 30
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TABLES
Toble Poge
1-1 Approaches to Risk Assessment Components 1-30
1-2 Approaches Used For Initial Thirty-Eight Analyses i-32
1-3 Standard Values Used in Analysis of Animal Bioassay Data 1-33
1-4 Approaches Used for Supplemental Analyses 1-34
1-5 Descriptions of All Analyses 1-35
1-6 RanKs Based on Length of Experiment 1-77
and Number of Treated Animals
2-1 Correlation Coefficients and Associated p-Values, 2-33
by Analysis Method and Sieve
2-2 Abbreviations for Chemicals Tncluded in the Study 2-34
2-3 Average Loss as Determined by the Symmetric DISTANCF2 2-35
Loss Function, by Analysis Method, Predictor, and Sieve
2-4 Average Loss as Determined by the Symmetric CAUCHY 2-36
Loss Function, by Analysis Method, Predictor, and Sieve
2-5 Average Loss as Determined by the Symmetric TANK 2-37
Loss Function, by Analysis Method, Predictor, and Sieve
2-6 Comparison of Analyses; Five Best Analyses, 2-38
by Predictor and Loss Function
2-7 Comparison of Analyses; Five Best Analyses, Excluding 2-39
Analyses 6, 18, and 19, by Predictor and Loss Function
2-8 Total Incremental Normalized Losses, by Analysis and Sieve 2-40
2-9 Average Loss for Restricted Sets of Chemicals 2-41
for Analyses 3b, 17, ana 20, by Loss Function
2-10 Average 'Loss as Determined by the Asymmetric TANH Loss 2-42
Function for LM. by Analysis and Degree of Asymmetry
2-11 Average Loss as Determined by the Asymmetric TANH Loss 2-43
Function for L2Q, by Analysis and Degree of Asymmetry
2-12 Y-Intercept Values for Best-Fitting Lines, LM Predictor, 2-44
By Analysis, Sieve, and Loss Function
2-13 Y-Intercept Values for Best-Fitting Lines, L2Q Predictor, 2-45
By Analysis, Sieve, and Loss Function
2-14 Y-Intercept Values for Best-Fitting Lines, MLEM Predictor, 2-46
By Analysis, Sieve, and Loss Function
2-15 Y-Intereept Values for Btst-Fitting Line-, MLE2Q Predictor, 2-47
By Analysis, Sieve, and Loss Function
2-16 Average Loss for Supplemental Analyses With the LJQ 2-48
Predictor, By Analysis, Stive, and Loss Function
2-17 Y-Intercept Values for Best-Fitting Lines, Among 2-49
Supplemental Analyses, by Analysis, Sieve, and Loss Function
2-18 Average Loss, by Dose Units, Sieve and Loss Function 2-50
2-19 Y-Intercepts by Dose Units, Sieve, and Loss Function 2-51
2-20 Conversion Factors for All Dose Units, by Method of 2-52
Analysis and Sieve
2-21 Uncertainty Factors for Analyses Without the Sieve 2-53
2-22 Uncertainty Factors for Analyses With the Sieve 2-55
2-23 Component-Specific Uncertainty: Modes and Dispersion 2-57
Factors for Ratios of RRDs, by Supplemental Analysis
3-1 Comparison of Selected Results for Selected Analyses 3-35
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TABLES
Trhle Page
3-2 Median Lower Bound RRO Estimate*, by Chemical 3-36
and Analysis Method
3-3 RRO Predictions, by Jhemical and Analysis Method 3-37
3-4 Uncertainty Intervals for RRD Predictions, by 3-38
Chemical ant Analysis Method
3-5 Ranges of Human RROs Dorived from the Recommended 3-39
Set of Analyses
3-6 Ranges of Human RRDs Derived from the Recommended 3-40
Set of Analyses Ignoring Analysis 43
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Section 1
METHODOLOGY
INTRODUCTION
One goal of this project is to examine various methods for analyzing
bioassay data to determine which methods produce results that correlate
well with the results obtained from epidemiologica] data and to
characterize the uncertainties involved. For this to be possible,
reasonable, alternotive methods of analysis need to be defined. Recall
that in the introductory section (in Volume 1 of this report) were
listed the components of risk assessment and several approaches for each
component; that list is reproduced in Table 1-1. Consider Figure 1-1,
which depicts the process of risk assessment based on bioassay data: for
several experiments in each of a few species, particular carcinogenic
responses yield estimates of RRDs that are combined in some way to yield
the final estimate. The components listed in Table 1-1 correspond to
the different levels in the tree shown in Figure 1-1 and the approaches
specify how to handle the corresponding level. The basic method for
defining analysis methods has been to select different combinations of
the approaches, as is described in this section.
Also in this section is a description of the methods used to compare the
bioassay-based results to the epidemiologically derived estimates. A
nonparametric generalizea rank test is used to evaluate the correlation
between the two sets of estimates. When specific point estimates from
the bioassay analyses are employed as predictors, their performance i."
compared on the basis of tf.e fit of a straight line with slope of one to
the data. Three approaches (loss functions) used to fit the line are
described.
1-1
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ANALYSIS OF BIOASSAY DATA
For each chemical being analyzed, the procedure described here is
followed to derive the RRDs of interest. For each carcinogenic response
coded from a study testing the chemical of interest, the multistage
mod»l that best describes the response rates from all dose groups is fit
tc the dose-respopse data. The multistage model has the form
P(d) - 1 - exp<-(q0 v q-|d + ... + qkdk)}, (1-1)
where P(d) is the probability of cancer when exposed to average daily
dose d; qQ, q-|, . . . ,qk > 0 and K is equal to one less than the number of
dose groups. The model is fit by an updated version of GLOBAL82 Q)
that gives maximum likelihood, lower bound, and upper bound estimates
for the dose 0 such that
PCD) - P(0) - 0.25,
1 - P(0)
i.e. D is the dose corresponding to an extra risk of one in four. This
dose will be called a risk related dosa (RRD) corresponding to a risk of
one in four. Similar definitions of doses corresponding to the
particular levels of risk can be found in the literature. Sawyer et al.
(2), for example, discuss "TD50", the daily dose required to halve the
probability of remaining tumorless.
Actually, the model is fit to each combination 3f dose and response
values that might arise by combination of the approaches listed in Table
1-1. In particular, the components that affect the fitting of the model
are numbered 4, 5, and 6 in that table; 20 combinations of the
approaches to these components are possible. Hsnce, as many as 20
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models hove been fit to each response. (Many responses have been fit by
only 10 models since tne data needed to analyze only the affective
number of animals, approach b to component 6, are not generally
available in the published literature.) The triple of estimates
composed of the 95Jf lower bound, the MUE, and the 95* upper bound for
the RRD corresponding to an extra risk of 0.25, which is labeled (DL,
. is available for each of the models fit to each response.
Definition of Analysis Methods
Each analysis mathod specifies which soecies of animal to consider, what
criteria the experiments on those species must satisfy, wf oh responses
within those experiments to consider, and which of the 20 model results
to use. (Throughout this report, "experiment" denotes the data from all
dose groups in a single bioassay of one species and one sex of test
animal, except when results for two sexes are reported together and
cannot be separated. ) In every case, the first step is to assign one
triple to each experiment, selecting the triple from the responses that
are eligible for that method (components 7 and 8). The tr pie that is
selected is the one that has the smallest DL, lower limit on RRD. This
procedure is adopted because we are interested in the evidence for
carcinogenicity and the manipulation of that evidence. The eligible
response with the smallest DL is the one that is consistent with tf-«
highest carcinogenic potential and may, therefore, provide the best
evidence of carcinogenicity from th* experiment une'er consideration
Given this method of assignment of RRO triples to experiments, and given
the approaches listed in Table 1-1, 88320 possible analysis methods
could be defined. Thirty-eight analyses were run as the first set
(Table 1-2). The thirty-eight analysis methods fall into five
categories that are defined by the manner in which the data from
individual experiments ore combined to yield the twelve values that are
1-3
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of interest in tlie investigation. Those twelve values are the minimum,
the first quartile, the median, and the third quartile of the lower
bounds, MLEs and upper bounds. The five categories are described below.
No Averaging. The first category of analyses includes those that treat
each species, each study within species, and each sex within study
separately (approach a for component 9, a for 10, and d for 11; see
Table 1-1). Let Ykj be the ith lower bound for RRD in species k, and
assume that the Ykj values are ordered with Yk-| the smallest and Ykn(k)
the largest; n(k) is the number of experiments in species k. Define the
species-specific quartile values as follows:
Yk1Q - Yk! for n(k) 1 * (1-2)
for n i 5
Yk2Q - Yk! for n(k) 1 2
yk3Q • Ykn(k) f°r "CO i *
Ykn(k)-l(n(k)/<*J for n(k) i 5
Then the minimum and quartile values of the lower bounds for the
analysis are defined by
Ymin • -"in (Yk,) (1-3)
k
Y1Q - min (Yk10)
k
Y2Q • median (Yk2Q)
k
Y3Q - max (Yk30).
k
The minimum and maximum over species are adequate to define the first
and third quartiles, respectively, because rarely are there more than
1-4
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four specie* tested for any chemical. The MLE and upper bound value*
are defined in exactly the same manner. Analyses 0 through Be, He,
11d, and 25 are in this category.
Averaging Over Sex. The second category of analyses is represented by
analysis 9, where the results from different sexes tested in the same
study are combined. A study may include as many as two experiments.
Two experiments are considered to be from tft* same study only if tn.»y
were carried out in the same laboratory by the same experimenters, the
same moiety of chemical was used, the same strain of animal was tested,
the numbers of animals initially on test were nearly identical, and the
study protocols ware nearly identical. If that is the case, this
analysis methods calls for harmonically averaging the values from the
two experiments, lower bound with lower bound, MLE with MLE, and upper
bound with upper bound. The weights for the average are equal to the
initial numbers of animals on test in each experiment. After the
averaging, one triple is associated with each study. These can be
ordered, the species-specific quartiles defined, and the minimum and
quart.ile values for the analysis defined in exactly the same manner as
the first category.
Averaging Over Study. The third category entails combining studies
within species (Analysis 10). Note that different experiments falling
under the same study are not averaged, so each study may contain more
than one triple of estimates. Once again, let Yki be the ith ordered
lower bound from an experiment testing species k (the same procedure is
followed for MLEs and upper bounds). Species-specific minimum values
are obtained by harmonically averaging the smallest Y*i values from each
study. Species-specific quartiies are obtained by randomly sampling a
single Yk^ value from each study and then harmonically averaging the
values selected. A total of 100 samples is taken for each jpecies so
that when the averages are ordered, the 25th, 50th, and 75th estimate
1-5
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the first, second, and third quartiles, respectively. The weight
attached to each study for the harmonic averages is the total number of
animals initially on test from all experiments under that study. The
minimum value associated with the analysis is the smallest of the
species-specific minimums and the quartiles associated with the analysis
are defined from the species-specific quartiles as shown in Eq. 1-3.
Averaging Over Species. Examples of the fourth category of analyses are
provided by Analyses 11a and 11b, in which results from different
species are averaged. Once again, species-specific results are averaged
harmonically; in this case an unweighted average *s used. To obtain the
minimum average lower bound, one selects the smallest lower bound found
among experiments in each species, then these species minimjms are
averaged. The lower bound quartile values associated with the analysis
are estimated by random sampling: 100 times, a lower bound is randomly
selected from each species and the average computed. When ordered, the
25th, 50th, and 75th avernge represent the first, second, and third
quartile, respectively. The same procedure is followed for MLEs and
upper bounds.
Averaging Over Sex. Study, and Species. The final category of analyses
includes Analyses 12 through 2<>d. In this category, results are
sequentially averaged over experiment within study, over study within
species, and finally, over species. Note that at each step, one triple
(averaged) is associated with each study, species, and analysis,
respectively. Consequently, only one average lower bound, one average
MLE, and one average upper bound is associated with such on analysis.
As a result, the minimum and all quartiles of the lower bounds are the
same, i.e. the one overall average of lower bounds. The same is tri
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all experiments contained within a study when averaging over study
within species, and the constant 1 when averaging over species.
Description of Approaches to Components
The previous discussion has described the manner in which the different
analysis methods are definod. In so doing, it has described the
approaches to several of the components of risk assessment. In
particular, it has been shown how the approaches to components
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possible, experiment-specific, indeed dose-group-specific, body weights
and food intake* have b«».i used to convert among the unit*. Standard
value* (Table 1-3) have been u*ed when nece**ary.
Calculation of Average Dose. Component 5 relate* to the calculation of
average doses for each do*e group. Either all dosing is considered
(approach a), in which case the average is calculated over the entire
experiment, or only dosing over the first 800 of the experiment is
considered (approach b), in which case average daily dose is based on
that time period as well. The 60% figure is predicated on the
assumption that exposures during the last 20% of the life of an animal
are unlikely to affect cancer incidence due to the latency period.
Crump and Howe (ft) observe that 'chemically induced tumors are apt to
have a latent period of about 1/5 of the life span of the species.*
(The »'jme assumption is used when specifying approach b to component 2,
i.e., when restricting experiments to those with "long" dosing of 80* or
more.) As an example of the difference between the approaches to
component 5, consider a 100-week study with a dose group receiving 1
mg/kg/day for 90 weeks. In approach a, average daily dose is calculated
as
(90-1 + 10-0)/100 • 0.9 mg/kg.
For approach b, the average daily dose is
(80-1)/80 • 1 mg/kg.
Tumor Type to U«e. A* discussed in Volume 2 of this report, special
codes have been designated for two types of response, all tumors and the
combination of all significantly increased tumors. The codes used, in
general, are based on the International Classification of Diseases for
1-8
-------
Oncology (5). The tcpoiogy-mor ->hology cod* applied for all tumors is
1000-8000; for the combination of significantly increased tumorm it is
1000-7000. These are the responses included in approaches b and a,
respectively, to component B.
Definition of Standard Method*
Analyst* 0 resembles the procedure employed by EPA'a carcinogenic
Assessment Group in many respects: ing/m2/day are the units assumed to
yield human and animal equivalence; species, studios, and experiments
are not combined so that the minimum lower bound comes from the most
sensitive species and sex and from the experiment- yielding the smallest
RRO lower bound (largest upper bcund on risk); and route of exposure is
limited to the more common routes, inhalation, gavage, and oral, unless
humans are exposed by some other route. Of course, no automatic
procedure can exactly duplicate the decision-laden process of risk
assessment. Nevertheless Analysis 0 is one reasonable procedure and,
more importantly for this project, is the one that serves as a template
for defining other analyses.
Another standard method nas been defined. It is called Analysis 30 and
has been used as a template to define an additional set of twenty
analysis methods (Table !-*•). Analysis 30 differs from Analysis 0 in
that mg/kg/day rather than mg/m^/day are the units assumed to yielri
equivalence between humaits and animals for extrapolation of RRO
estimates. Moreover, the route of administration of the test chemicals
is not limited to any particular route; injection and instillation
studies are included olong with gavoge, oral, or inhalation experiments.
The eighteen methods that are single-component variations of
Analysis 30, i.e. Analyse* 31 through 50 (Analyses 39 and *0 were not
performed), are not duplicated in Analyses 1 through 25, except for
1-9
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Analysis 31 which is the •am* as Analysis 3b and Analysis 38 which is
the sanw as 4a.
This alternative standard and its single-component variants are not used
in the majority of the analyses performed for this project. That set of
methods was defined only after the bulk of the analysis was completed.
Its purpose is to provide information on the uncertainty associated with
single components of the risk assessment process. It is used to
investigate component-specific uncertainty or variability in the manner
described later in this section. However, information on the
predictiveness of the estimates from vhe supplemental analyses is
considered when the best mnthod(s) ore identified.
Table 1-5 gives a verbal description of the 38 initial analyses and the
19 supplemental analyses.
Sieve
In addition to criteria restricting the type of experiments that are
used in some analyses, another procedure hae been set up to select ,
subsets of the data for analysis. This procedure is called a sieve and
operates as follow*. Criteria are defined that rank experiments in
terms of preference for analysis. Say a rank of 1 is preferred over 2.
2 over 3. etc. The experiments and responses that are used in any
specific analysis are those that nave the lowest rank; if there are any
rank 1 data sets those and only those are used, if no rank 1 data sets
are available all the rank 3 data sets are used, etc. This procedure is
an attempt to use the best data that are available but yat to do
something when the best type of data is unavailable.
The sieve may have more than one 3evel. That is, a selection from among
the experiments may tit made on the basis of one criterion and then the
1-10
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selected bioassay* may be subjected to further screening on the basis of
another criterion. In each case, the best, the lowest rank, data cets
survive the screening and become available for analysis. If one
criterion is based on properties of the carcinogenic responses (e.g.,
rank 1 is given to responses that show a significant relationship to
dosing) as opposed to another criterion that is based on features of
the entire experiment (e.g., rank 1 is given to experiments that have at
least 50 dosed animals) the former screening is applied first. In that
way, the greatest amount of data passes from one level of the sieve to
the other; individual responses, not entire experiments, are eliminated
at the first stage. Also, for the example given above, a significant
response (i.e. evidence of carcinogenicity) is to be preferred, no
matter how many animals are teuted. This is not guaranteed to happen if
the fir»t screening is based on nunber of dosed animals.
The sieve technique is designed to work *ith any of the analyses defined
in terms of the components of risk assessment as described above. The
sieve is applied only after any inclusion criteria specific to an
analysis. For example. in Analysis 1, only experiments that lasted at
least 90* of the standard experiment length are included; the sieve is
applied after that selection is made. Note also that the selections
that define the analyses are unlike the selection procedure for the
sieve. The analysis-defining selections do not rank studies. If there
are not experiments that-lasted at least 90* of the standard experiment
length for a Chen-leal, that chemical is not included in Analysis 1. The
sieve technique does rank experiments so that the best can be used; a
chemical cannot be excluded from an analysis because of the action of
the sieve.
The sets of analyses that employ a sieve use one or both of two screens.
The first examines each response to tee if a significant dose-related
effect on response rates is evident. Priority (i.e., the lowest rank)
1-11
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is given to those responses that do «how such a significant
relationship. The second screen is based on a combination of two
features of each experiment, the length of observation and the number of
dosed animals.
Significance of a relationship between dose and response rates is
assessed by use of the Fisher's exact test (6) and the Cochran-Armitoge
trend test (7). If the response rate in any treated group is
significantly greater than that in the control group at the 0.05 level
as determined by Fisher's exact test or if the trend of response rates
is significant at the 0.05 level as determined by the Cochran-Armitage
trend test, then the response is considered significant and is given
lower rank. Otherwise, the higher rank is assigned. This screening is
called the significance screening.
The ranking scheme based on experimental protocol, i.e. on length of
experiment and number of treated animals, is depicted in Table 1-6.
Note that this is just one of infinitely many ranking schemes possible.
Of the two features (experiment length and number of dosed animals)
slightly more weight, in terms of the perceived quality of the study,
has been given to length of observation. This part of the sieve is
labeled the quality screen.
Given the two screens described above, four sets of analyses have been
defined, one with no screenings, one with the significance screen alone,
one with the quality screen alone, and one with both screens. As
described earlier, when both screens are used, the significance screen
applied to individual responses operates before the quality screen. Of
course, the entire sieve procedure comes into play only after the
application of the exclusion criteria that define each analysis method.
1-12
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COMPARISON WITH EPIDEMIOLOGICAL RESULTS
Onca the bioassay data have been analyzed by the many methods defined,
one wishes to use the results to compare and evaluate those methods.
The techniques that have been selected to do this use the RRO estimates
obtainad from the epidemiological data as the basis for comparison. A
method of bioassay analysis that yields estimates "close to* the
epidemiologically derived estimates is judged to be satisfactory. The
following describes the techniques for determining how close a set of
bioafcsay-basbd estimates is to the human-based estimates.
Correlation Analysis
In the onalysi* of the epidemiological data, we have produced a "best"
estimate of the RRD corresponding to a one-in-four risk, RRO^, and upper
and lower bounds on that dose, RRD^u and RRD^Lt respectively. The
interval [RRDHL, RRDHij] represents the range of estimates that are in
some sense consistent with the epidemiological data because of data
uncertainty or statistical variability.
Because of the many bioassays for any given chemical and because of
statistical variability within each bioassay, the bioassay analysis
results may also be reasonably characterized by a range of RRO
estimates The interval selected in the correlation analysis to
represent that range is defined by the median RRDs; it extends from the
median of the lower bour.d estimates to the median of the upper bound
estimates. That choice of interval considers statistical variability in
the sense that both lower and upper statistical confidence limits are
used in its definition. Moreover, the use of median values avoids some
difficulties with outliers and behaves properly in on asymptotic sense.
Should anomalous results appear in some bioassays, estimators of the
1-13
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appropriate range such as that from the minimum lower bound to the
maximum upper bound are adversely affected. Such "minimum-to-maximum"
ranges are highly sensitive to outliers and once outliers appear, those
estimators are not self-correcting. As more bioassays of a particular
chemical are performed (and so as the chance of outliers increases) the
minimum lower bound and maximum upper bound estimates can only get more
extreme. Median values, on the other hand, should behave more properly
in the sense of discounting truly anomalous results and converging to
the "true" value. Let [LjQ. U2Q] be the interval fron the median
(second quartile) of the lower bound RRD estimates to the median of the
upper bound RRD estimates obtained for any given chemical.
We are interested in the correlation between the epidemiologically based
estimates and the bioassay-based estimates. That is, we wish to know if
chemicals with larger estimated human RROs also tend to have larger
estimated animal RROs. In the absence of known or suspected
distributions for the RRD estimate.1!, nonparametric tests of correlation
are appropriate. The standard nonparametric measures of correlation
(notably Spearman's rho) use the ranks of point estimates without
consideration of variabilities. When the variability or uncertainty
about point estimates is not the same for each observation, as is the
case with the data in the present analysis, such a method may be
inappropriate. Ng (8) has proposed a concept of generalized ranks that
does consider variabilities as reflected in the intervals surrounding a
point estimate. That concept is used to rank the human intervals,
(RRDm.. RRDmj). and, separately, t.o rank the animal intervals, (LJQ,
1>2Q)> '-"ia to determine the degree of correlation between the two sets of
intervals.
A partial ordering for the intervals is defined as follows (the
definition is given in terms of the animal intervals; exactly equivalent
definitions hold for the human intervals). Let interval i,
-------
corresponding to chemical i, be labelled (L^Qi, u"2Qi) * *i- Then 1^ is
less than Ij if l-20i < L2Qj and U2Qi < U2Qj (if UJQI • UJQJ • «, then l
is less than I j if LJQI < l-2Qj ) • l± is greater than I j if I j is less
than Ij,. Otherwise, 1^ and Ij cannot be ordered (we will say they are
-tied").
A ranking of the intervals can be defined on the basis of the partial
ordering. Let nj be the number of intervals less than intervol Ij and
let mi be the number of intervals tied with 1^. Define the rank of Ij,
R, to be
i ' ni
We will use RI to denote the rank of the ith chemical when based on the
animal intervals and 3j to denote the rank of the ith chemical when
based on the human intervals. Ng (8) has shown that the ranks so
defined have desirable properties including the fact that the sum of the
ranks, ER^ or ES^, is N-(N+1)/2 (i.e. the sum of the ordinary ranks of N
numbers) and that these generalized ranks reduce to ordinary ranks if
the partial ordering is also a total or daring. The R^ and S^ values are
used hare to estimate correlations.
By analogy to Spearman's rho, a correlation coefficient, p, is defined
as follows:
Note that R » S • (N+1)/2. The statistic p behaves appropriately for
a measure of correlation (-1 < p < 1; larger positive (negative) values
indicate more positive (negative) correlation; etc.).
1-15
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The significance of p i* assessed by simulation. The Ri'» are held fixed
at their observed values while the S^'s are permuted over che set of
observed S^'s. That is. each permutation •- ts p(i), i - 1,2,....,N,
from the set {1,2 N) such that p(i) / p{j) for i f. j. Let 3^' •
Sp(i). The correlation coefficient is evaluated for each permutation
(in the numerator of equation 1-4, RI is paired with Si')- If among a
total of M permutations, K of them yield coefficiertm at least as large
as the observed p, then the probability of observing a coefficient as
large as or larger than p under the null hypothesis of no correlation is
estimated to be K/M. The null hypothesis is rejected in favor of the
alternative, f > 0, for small values of K/M. In the present analysis,
10,000 permutations were created (M • 10,000).
Prediction Analyses
The correlation analysis just discussed concentratos on intervals of
RRO estimates to determine whether or not the human and animal estimates
generally behave in the same way (i.e., RRDs for chemical i are lower
when estimated from the epidemiology when they ore lower when based on
the bioassay). If that correlation analysic is positive, then it is
reasonable to go on to ask if particular points obtained via bioassay
analysis are good predictors of the results that are chained directly
from epidemiological investigation. At this stage also, one can examine
the magnitude of errors, i.e. the uncertainty that results from the use
of any predictor. The following is a description of the methods
employed to compare and evaluate various predictors.
Unlike the correlation analysis, the prediction analy .is selects a
single point from the bioassay analysis results as the estimate of RRD
for each chemical. Each of the 38 analyses descriaed in Table 1-2 could
supply any number of predictors. The four that have been investigated
are the minimum of the lower bound estimates, L^, the median of the
1-16
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lower bound estimates, I-2Q, and the minimum and median of the maximum
likelihood estimates, Ml- EM and ML t2Q. respectively. Theso values are
available for each chemical analyzed by each of the thirty-eight
methods .
The behavior and properties of the predictors are assessed, again, by
comparison with the epidemiologically derived estimates. Those human
estimates are not distilled to a single point. Instead the best
estirate, RRD^, and/or the interval from RRDm. to RRDmj form the basis
for evaluating the predictors. In particular, a straight line with
slope of 1 is fit to the base ten logarithmic transform of predictor
values and the logarithmic transform of the human estimates. That is,
the bioassay-based estimate of the human RRD corresponding to a risk of
one in four, HA. is given by
log-io(HA) - logi0(Pi) -f C, '
where P^ is the predictor from the analysis (either L^, I-2Q' ML(^M> or
MLE2g) for chemical i and C is the y-intercept to oe estimated. This
relationship implies that
HA
i.e. that a linear relationship exists between the untransformed
estimates. Consequently, the potency of chemicals as determined from
bioassay data relative to the estimates of human potency is not related
to their absolute potency, which seems reasonable.
Suppose that A^ • log-|n(pi) + C, where PJ is one of the predictors for
chemical i from the bioassay data as described above, for any given
value of C. The y-intercept, C*. is determined (i.e. the line is i~it to
the data) by minimizing the sum of the losses for each chemical
1-17
-------
associated with the predicted RRD, A£, and the estimates derived from
the epidemiological data. Clearly, a loss function must be defined in
order to carry out this procedure.
Three different forms of loss function are considered. The first and
simplest, called DISTANCED, defines th«i loss associated with tha
prediction for chemical i to be proportional to the square of the
distance from the predicted value to the interval defined by the lower
and upper endpoints of the epidemiologically derived RROs. Though this
formulation of loss is straightforward, it does have some disadvantages.
First, it does not consider the oest estimates of RRD* obtained from the
epidemiological analysis, the RRO^s. Moreover, it cannot be applied
when the animal predictors can have infinite values. Since MLE^ and
MLEjQ can be infinite, but L^ and LgQ cr>:tnot, DISTANCED can be used co
evaluate only the latter two predictors. This some difficulty with
infinite values arises when the loss function utilizes the RRD^
estimates, which may indeed be infinite. Because cf these limitations
of DISTANCE? and because we wish to consider possibly infinite
estimates (particularly in RROji since we made a point of including in
•these analyses chemicals that may not be carcinogenic as determined by
epidemiological investigation, i.e. for which RRD^ is infinite) two
other loss functions have been developed. These ere called CAUCHY and
TANH. All three forms of loss function are described in detail below.
DISTANCED Los:* Function. Loss associated with chemical i is defined
solely in terms of the interval (RROHL.i- RRDHU,i)- That loss is
given by
Jl.i " 0 if log1o(RPDHL,i) < *i < l"3lo(RRDHU,i).
d* if Ai < log10(RRDHL.i).
k-d2 if Ai > log10(?RDHu,i).
1-18
-------
Here d is the absolute distance between A^ and the closest of
login(RRDnL.i) anti 109lo(RRDHU,i)- Tn* constant k is the asymmetry
parameter .
If, :* appears reasonable, it is worse to overpredict RROs, then k > 1
can be used to reflect the belief about the degree of asyrmetry.
Nevertheless, this approach to fitting tr,» line is essentially
equivalent to determining the line that is closest to the intervals
defined by the lover and upper endpoints of the human estimates. The
total loss associated with a particular analysis is the unweighted sum
of the looses associated with each chemical in the analysis.
A simple extension of the reasoning presented in the discussion of the
loss function I-j allows definition of a fitting algorithm for results
expressed as intervals in both the horizontal and vertical directions.
Such results are obtained in the correlation analyses. The extended l-\
routine has been run with the same intervals used to determine
correlations. Such a procedure allows us to identify individual
chemicals whose intervals of RRO estimates are far from the fitted line
and, therefore, may be thought of as outliers and may, in fact, detract
from the correlation.
CAUCHY and TANH Loss Functions. Suppose H^ » log-jo (RRD^i), the
logarithmic transform of the best estimate from the epidemiological
analysis for chemical i. Then, recalling that A^ - logio (Pi) + C, we
wish to find C that minimizes
EI(Ai. Hi) • Wt (1-6)
where !(-,-) is a nonnegative loss function, W^ is the weight attached
to the loss for chamical i, and the sum runs over all chemicals in the
analysis. Considering that A^ or H^ may be infinite, these are
properties that we considered it desirable for 1 to have:
1-19
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PI: J(A,H) - 0 if A - H
P2Q: !(<*>. H) < * and 1(A,°°) < oo
P2b: l(oo, «) - 0
P3: I(A-|, ao) > i(A2, OB) if A-| < A2
P*: I(A, H) < 2(A, oo) for A, H < oo
P5: KA-I, H) > I(A2, H) if A-, > A2 > H or A-, < A2 < H
P6: 1(A-|. H) < J(A2, H) for H - A; - A2 - H > 0.
These properties can be interpreted as stating that loss is minimized
only when the prediction matches the observation (PI); that loss is
finite *ven for infinite RRC estimates (P2a) and that predictions of
infinite RROs are good (i.e., have zero loss) when the observed RRDs are
infinite (P2b); that the loss is lees if the prediction is larger when
the observed RRD is infinite (Pi); that the loss is greater when the
observed RRD is infinite than when the observation is finite if the
prediction is finite (P<»); that the farther away from the observed RRO
one goes in one direction the greater is the loss (PS); and that the
loss from underestimating an observed RRO by a certain amount is no
greater than the loss from overestimating by that amount (P6). The last
property allows one to choose an asymmetric loss function if one wants
to reflect the belief that it is worse to overestimate RRDs than to
underestimate them.
Unfortunately, it is easy to show that the properties P1 through P6 are
mutually inconsistent. Two approaches have bean taken to get a set of
consistent properties to motivate vhe choice of loss function. The
first approach is to drop property 3. This is the only property that
prevents the loss function from being expressed as a function of the
distance (A-H). Consequently, we defined 12 ac follows:
J2(A.H) - 1 - <1/(H-f(
-------
where ?(-) it the sign function and f(-) is some positive function
allowing the introduction of asymmetry. It i* clear that 1% satisfies
Pi, P2a, P2b, and PA - P6. Moreover, once we are given a set of H^'s
end PI'S, then we can approximate P3 but retain the other properties.
To do so, infinity must be approximated by some large number. That
number must be chosen large enough so tnat P.
The set of properties obtained by replacing P<» with P J(A2. H) even though H-A1-A2-H>0
(in violation of P6).
1-21
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Consequently. we or* led to try a slightly different loss:
K'". H) - g(H) - g(A), A < H
«Cg(H) - g(2H-A)]. A > H.
where g is *ome monotone increasing function and m > 1 . When this is
the case, 1(A-|. H) - g(H) - g(A1) and 1(A2. H) - m[g(H) - g(2H - A2)]
m[gCH> - g(A'i)] when H-AT - A2-H > 0. and BO P6 is not violated.
If w* adopt this form of the Iocs function, then both lim g(x) and
X-««
lira g(x) must be finite (by P2a). A monotone increasing function that
X—oc
has all these nice properties is
g(*) - tanh (c,x) - (e^* - e-c,*)/^6!* * e'C,*}.
The constant c<| > 0 can be thought of as a scaling factor. The
resulting loss function (called TANH) is
IS(A.H) - tanh(c-|H) - tonh(ciA). A < H (1-8)
m[tanh(c-|H) - tanh(c1(2H-A))], A > H.
The factor m is chosen to reflect the desired degree of asymmetry. For
this investigation, asymmetry considerations have been examined by
setting m equal to 1.5, 2, 5. 10, 50, and 100. Larger values of m
reflect stronger beliefs about the undesirobility of overestimating
RRDs. Small c-j shrinks everything (except infinity) toward zero where
tanh is more nearly ".inear, so that loss when an infinite value is
observed or predicted is exaggerated compared to the loss when both
observed and predicted ore finite. Small enough c-| may also moke Pi»
true for any given set of observations and reasonable values of C. A
value of 0.1 has been assigned to c-\ throughout these analyses.
1-22
-------
Given the alternative* 1% and Jj. we can calculate the loss contributed
by any given chemical. What remains is to specify the weights. W^, that
allow accumulation of the individual losses into an overall loss value
as shown in Eq. (1-6). It seems clear that less weight should be given
to chemicals whose human RRD estimates are less certain, i.e. to those
whose intervals surrounding H^ are longer. Once again, the problem of
infinite values exists, in this case infinite interval lengths.
Consequently one should consider positive, monotone decreasing functions
that go to a positive limit as the representation for the W^'s.
Let D • log<)o(RM>HU) " lofl1o{RROHl)- *• wimn to
where lim h(x) • r > 0. The function selected is
X-HOO
h(x) - coth2(x) - ((e* + e-*)/(e* - e'*))2.
Note that lim coth2(v) - 1. Also consider the following. If we were
X-«o
doing ordinary weighted least squares, we would want the weights
proportional to the inverses of the variances. In our case, we have
quasi-war ionce represented by the intervals from RROm_ to RRO^u- In the
ordinary situation, the intervals would be proportional to the standard
deviations and so woights could be formulated in terms of the inverses
of the interval lengths squared. Note that coth(x) behaves like 1/x for
x close 1.0 zero, so that coth2(x) would behave like 1/x2. That is, if
wo choot * to use coth2{D^), we have a function that mimics ordinary
least soaares for small DI but that allow* us to consider infinite-
valued D^.
Tor each analysis method and for eoih predictor, lines have been fit to
the results using ;>ot.h loss functions ^2 and 23- In both cases
1-25
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Wl • coth2(Di) it the weighting scheme employed. For thorn* predictors
that or* guaranteed to be finite (L^ and L2tj) the lost defined by l-\
(distance to the interval) with w^'s set equal to 1 have also provided
estimates of the beet fitting line*. Average Iocs for any analysis and
for any loes function is the total loss (weighted cum of the chemieal-
•pecifie losses) divided by the sum of the weight*.
Uncertainty
Two type* of uncertainty are investigated in thi* project, what we have
called residual uncertainty and component-specific uncertainty. The
methods for quantifying these uncertainties are described below.
Residual Uncertainty. The lines fit to the data using any of the loss
functions described above will not eliminate all uncertain*. y. That is,
there will remain differences between the values predicted on the basis
of the best-fitting line ord the observed epidemiologically derived
estimates. The DISTANCE2 loss function is used to quantify those
differences.
Let At be the prediction (in this case from the DISTAWE2-fitted line}
for chemical i in any particular analysis. Let G± be defined as
follows:
Ot - 1 if log10(RRDHLii) < Ai < log10(RRDHu.i).
10Ai/RRDHU.i if *i > logia(RRDHu.i>
' *i
Then the average of the Gj/* over all the chemicals in the analysis
yields a result coiled the residual uncertainty factor, it is the
average factor by which the predicted values must be multiplied or
divided in order to yi-,ld predictions that lie within the intervals
-------
defined by th* RRDm.,1'1 ond th*
Alternatively, on* can *xomin* s*parot*ly thos* chemicals for which the
human RRO« or* overestimated by th« be»t-fitting line
[Aj > logio(RRDHu, *)] and thorn* for which they or* underestimated
[A} < login(RRDHL,i)3' Th*«* or* th* two group* of chemicals fcr which
th* best-fitting lin* does not intersect th* interval of human PRO
estimates. Factors analogous to th* uncertainty factor defined obovv
but pertinent to on* or th* other of these two group* , or* defined in a
slightly different manner.
For those chemicals whose human intervals li* completely below the line
[A£ > log
-------
Coi*ponent-Specific Uncertointy. A histogram approach ho* been u««d to
investigate the uncertainty associated with any one component of risk
assessment. Only the supplemental analyses (Analyses 30 through 50) are
used in this investigation. However, all chemicals with relevant animal
bioassay v-»ta can be used since epidemiological data is not required.
For any given predictor (eg., the median lower bound PRO estimate) each
analysis results in a single result for each chemical, P^. Let us
denote the dependence of the results on the analysis by letting PX,I be
the result for chemical i in Analysis X. Component-specific uncertainty
addresses the issue of how the Px.i values change with the analyses, X.
The investigation of this uncertainty is limited to analyses that differ
from a standard analysis (Analysis 30) in only one component. Analyses
31 through 30 are such single-component variants of Analysis 30. The
ratios Rx.i • Px,i/P30,i' wnare X • 31,32,...,50, ore the row data for
this component-specific uncertainty investigation.
For each Analysis, X, for X between 31 and 50, inclusive, there is a
corresponding histogram of the ratio*, "x,i- The cut points of the
histogram are 0, 0.01. 0.02, 0.05. 0.10. 0.20. 0.50. 0.80, 1.25, 2.0.
5.0, 10.0, 20.0, 50.0, 100.0, and <*>. Each ratio is located in one of
the subintervols defined by the te cut points. Its location indicates
how the results for the corresponding chemical change when the component
associated with the analysis (the one that differs from the standard
choice, that In Analysis 30) is changed.
For each histogram, the mode is determined. moreover, a dispersion
factor (> 1) is defined that indicates how spread out the ratios are.
Let I be the subinterval containing the mode of the distribution and let
GI be the geometric mean of the encpoints of interval I. For example,
if I • [0.8. 1.25], then Gj - ((0.08)•(1.25))1/? . 1. Generally, let J
1-26
-------
be any subinterval with geometric mean Gj. For the intervals on the
ends of the histogram?, [0, 0.01] and [100, »]. the geometric means are
determined from the ratios that fall within them. If, for instance, two
ratios are greater than 100, soy *»00 and 1000, then the geometric mean
for the interval [100, *>] in the histogram in question is
((*00)-(1000)1/2 . 632. This procedure is followed since the entries in
the intervals on the ends of the histograms may vary over many orders of
magnitude, unlike the entries in any other interval. It does not appear
reasonable or consistent to fix means in these cases.
The dispersion factor for any histogram is defined as
where Nj is the number of ratios (chemicals) in interval J and the sums
run over all intervals.
The dispersion factor indicates the average factor by which the ratios
differ from the mode. A dispersion factor of 1 corresponds to a
histogram with oil the ratios in one subinterval. Since the moae can be
construed as an indication of the direction and magnitude of the change
in RRO estimates when the approach to a single component is changed, the
dispersion factor indicates trow consistent that change in estimates is.
It is the average factor by which the RRD estimates from the altered
(nonstandard) analysis must be multiplied or divided to yield ratios in
the interval of the mode. Since the altered analyses differ from the
standard in only one component and a histogram corresponds to one
altered analysis, a dispersion factor is associated with one component
and indicates how well-determined are the changes that result froir a
change in approach to that component.
1-27
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REFERENCES
1. Howe, R. and Crump. K. (1982). GLOBAL 82: A Computer Program to
Extrapolate Quanta! Animal Toxicity data to Low Doses. Prepared for
the Office of Carcinogen Standards, OSHA, U. S. Department of Labor,
Contract 41USC252C3.
2. Sawyer, C., Peto, R., Bernstein, L., and Pike, M. C. (1984).
Calculation of carcinogenic potency from long-term animal
carcinogenesis experiments. Biometrics 40:27-40.
3. Freireich, E., Gehan. £., Rail, 0., Schmidt, L., and Skipper, H.
(1966). Quantitative comparison of toxicity of anti-cancer agents
in mouse, rat, hamster, dog, monkey, and man. Cancer Chemotherapy
Reports 50:219-244.
4. Crump, K. and Howe, R. (1980). A Small Sample Study of Some Multi-
variate and Dose Response Permutation Tests for Use with
Teratogenesis or Carcinogenesis Data. Prepared for the Food and
Drug Administration under contract to Ebon Research Systems, 34
pages.
5. International Classification of Diseases for Oncology (1976).
World Health Organization. Geneva, Switzerland.
6. Bickel, P. J. and Doksum, K. A. (1977). Mathematical Statistics.
Holden-Day, Inc., San Francisco.
7. Armitage, P. (1955). Tests for linear trends in proportions and
frequencies. Biometrics "5:375-386.
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S. Ng, T-H. (1965). A Generalized Ranking on Partially Ordered Set!
and Its Applications to Multivariate Extensions to Some
Nonparametric Tests. (unpublished report).
1-29
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Table 1-1
APPROACHES TO RISK ASSESSMENT COMPONENTS
1. Length of the experiment
a. Use data from any experiment but correct for short observation
periods.
b. Use data from experiments which last no less then 90* of the
standard experiment length of the test animal.
2. Length of dosing
a. Use data from any experiment, regardless of exposure duration.
b. Use data from experiments that expos* animals to the test
chemical no less than 80* of the standarc experiment length.
3. Route of exposure
a. Use data from experiments for which route of exposure is most
similar to that encountered by humans.
b. Use data from any experiment, regardless of route of exposure.
c. Use data from experiments that exposed animals by gavage,
inhalation, any oral route, or by the route most similar to
that encountered by humans.
-------
Table 1-1 (continued)
APPRO\CHES TO RISK ASSESSMENT COMPONENTS
7. Malignancy status to consider
a. Consider malignant tumors only.
b. Consider both benign and malignant tumors.
8. Particular tumor type to use
a. Use combination of tumor types with significant dose-response.
b. Use total tumor-bearing animals.
c. Use the response that occurs in hunans.
d. Use any individual response.
9. Combining data from males and females
a. Use data from each sex within a study separately.
b. Average the results of different sexes within a study.
10. Combining data from different studies
a. Consider every study within a species separately.
b. Average the result* of different studies within a species.
11. Combining data from different species
a. Average results from all available species.
b. Average results from mice and rats.
c. Use data from a single, preselected species.
d. Use all species separately.
NOTE: Underlines indicate c,Broach used in Initial Standard
(Analysis 0).
1-31
-------
Tob\» 1-2
APPROACHES USED FOR INITIAL THIRTY-EIGHT ANALYSES
Component
Analysis
0
1
2
3a
3b
risk marks those approaches that differ from those in
Analysis 0, the first standard.
1-32
-------
Table 1-3
STANDARD VALUES USED IN ANALYSIS OF ANIMAL BIOASSAY DATA
3ody Food Inhalation
Surface Area Weight Consumption Rate
Animal Coefficient0 (kg) (mg/day) (m3/day)
Dog
Guinea
Hamster
Monkey
Mouse
Rabbit
Rat
10.1
9.5
9.0
11.8
9.0
10.0
9.0
12.7 508000 1.5
0.43 12900 0.074
0.12 9600 0.037
3.5 140000 1.4
0.03 3900 0.05
1.1J 33900 1.6
0.35 17500 0.26
Drinking
Water Rate
(mg/dav)
350000
145000
30000
450000
6000
300000
35000
Experi-
ment
Length
(weeks)
312
104
104
364
104
156
104
"Surface area in m2 is calculated as KW2/3/100 where W is weight in
kilograms and K is the surface area coefficient (2).
1-33
-------
Table 1-4
APPROACHES USED FOR SUPPLEMENTAL ANALYSES
Component
Analysis
31
33
34
35
36
37
38
40
41
42
43
44
45
tc
HO
47
48
49
50
1
a
a
a
b"
a
a
a
a
a
a
a
a
a
a
Q
a
a
a
a
2
a
a
a
o
b"
a
a
o
a
a
a
a
a
a
a
a
a
a
a
3
b
b
b
b
b
a"
c"
b
b
b
b
b
b
b
b
b
b
4
c"
d"
a
a
a
a
Q
a
a
a
a
a
a
c
a
a
a •
a
5
a
a
a
a
a
a
a
a
a
a
a
a
o
a
a
o
a
6
a
a
a
a
a
a
a
a
b"
a
a
a
a
a
a
a
0
a
7
b
b
b
b
b
b
b
b
a'
b
b
b
b
b
b
b
b
8
d
d
d
d
d
d
d
d
d
a"
b"
c"
d
d
d
d
d
9
a
a
a
a
a
a
a
a
a
a
a
a
o
b"
a
a
a
a
10
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
11
ct
d
d
d
d
d
d
d
d
d
d
d
d
a"
b"
e-b
c*b
°The letter* in this table correspond to the labeling of approaches in
Table 1-1.
"Analyses 49 and 50 differ in that the single species considered in 49
is rats and in 50 it is mice.
"An asterisK marks those approaches thct differ from those in
Analysis 0, the first standard.
1-34
-------
Table 1-5
DESCRIPTIONS OF ALL ANALYicS
Analysis Template0 Differed >«s&_
0 Initial Standard mg/m^/day, no averaging of results; oral,
gavage, inhalation or route like humans
1 0 limited to experiments of long
observation
2 C limited to experiments of long dosing
3a 0 route like human route only
3b Q any route
-------
Table 1-5 (continued)
DESCRIPTIONS OF ALL ANALYSES
Analysis
Template0
Differences6
2
24b
24c
24d
25
30
31
32
33
34
35
36
37
38
41
42
43
44
45
46
47
48
49
50
12
12
12
12
0
Alternative
itcn^ard
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
mg/kg/doy
ppm diet
ppm air
mg/kg/ lifetime
route and response that humans gek. only
mg/kg/day; no averaging; any route
mg/m2/doy
ppni di*t
ppm air
mg/kg/lifetime
limited to experiments of long
observation
limited to experiments of long dosing
route like humans only
oral, gavage, inhalation, or route ? -ke
humans
malignant responses only
combination of significant responses only
total tumor-bearing animals only
response that humans get only
results averaged over sex within study
results averaged over study within
species
results averaged over all species
results averged over rats and mica only
rot data only
mouse data only
°The template is the analysis which most closely resembles and on which
is based the analysis in question. Analyses 0 and 30 are the two
standards; they have no template but rathwr are the bases for defining
the other analyses.
bThe differences listed are the ways in which the analysis in question
differs from its template. For Analyses 0 and 30, for which there ore
no templates, no "differences" are defined. In these two cases the
approaches for several prominent components are listed.
1-36
-------
Toble 1-6
RANKS BASED ON LENGTH OF EXPERIMENT
AND NUMBER OF TREATED ANIMALS
Length of
Experiment0
> 75*
50-75*
< 50*
Number
50+
1
3
6
of Dosed Animals
15-*9 <
2
*
8
15
5
7
9
°These values are expressed as percentages of the standard experiment
length of the test soecies. Table 1-3 lists the standard experiment
lengths.
1-37
-------
Figure 1-1
Final mo Estimate
I
u
OB
[Species ij
i
[Species II]
[Species "TYTj
-------
Section 2
RESULTS
This section describes the results of the evaluation of the animal
bioassay data and of its comparison with the epidemiologicolly derived
risk estimates. Tho evaluation is logically divided into two steps.
The first is a correlation analysis, the goal of which is to determins
whether or not the estimates of risk-related doses obtained from
analysis of the biiassay data (the animal estimates) are correlated with
the estimates obtained from epidemiology (the human estimates). If no
correlation is found, thon it may not be appropriate to attempt to
estimate human ris'v from animal data. If, on the other hand, a positive
correlation does exist, then it seems reasonable to assume that the
animal models are relevant to human risk estimation and to proceed to
the second step, that of identification of useful predictors. The goal
of that process in to determine which particular point estimates
calculated from the bioassay data can be satisfactorily employed as
predictors of the human RRDs, and to evaluate the variability (the
remaining uncertainty) associated with the identified predictors.
The correlation analysis reveals that there is, indeed, a significant
positive correlation between the human estimates and most of the animal
estimates. Thoie analysis methods that demonstrate the best
correlations provide viable alternatives for the choice of the
predictors. Thi» detailed results of the correlation and prediction
analyses are described below.
CORRELATION ANALYSIS
Table ?-1 pres»nts the correlation coefficient estimates (and their
associated p-values) corresponding to each method of analyzing the
bioassay data. The four columns of that table represent th«« four data
sieves we havi* defined. Graphs of animal RRDs vs. human r.RUs for many
of the analysis methods are contained in Figuret, 2-1 to 2-34.
(Abbreviations for all the chemicals considered in this project are
2-1
-------
given in Table 2-2).
Generolly speaking, the results in Taole 2-1 show a strongly positive
relationship between animal and human RRDs. The number of analyses
resulting in correlation coefficients greater than 0.6 ranges from 26 to
29 out of 38, depending on the sieve used. When the full sieve is used.
26 analyses yield results with t > 0.7. In no instance did a negative
value for f obtain. Out of the 38 p-values associated with the analyses
employing the full sieve, 28 were less than O.C1, and 35 less than 0.05.
Given these results, it is inconceivable thc.i these correlations are due
to chance. It is also highly unlikely that they are due to bias in the
methods employed. The coding of the animal data into the computerized
data base was made by individuals who were unaware of the results for
the RRO estimate* for the human data. The calculations for the animal
RROs were mode using jnifo.-m approaches implemented by an impartial
computer program. Although the calculations of the human RROs were made
individually and required judgements on the part of the analyst, they
also wer* made blindly without knowledge of animal RROs for any of the
chemicals.
Thus, by any reasonable standard, the animal RROs are substantially
correlated with the human RRDs. This correlation is very important
because it demonstrates that it is both possible and scientifically
appropriate to estimate human risk from animal data. The range of
finite, best RRO estimates from human data represented by these 23
chemicals spans roughly six orders of magnitude (from 10~3-5 mg/kg/day
for melphalan to lO^-B mg/kg/day for saccharin). Human and animal RRO
estimates are fairly consistent over this range considering the
rrudeness of much of the underlying data (see, for example, Figure
2-12).
These analyses are considered in greater detail below. Individual
analysis methods will be studied; methods that yield the best
correlations are identified and discussed. Similarly, methods that
yield the poorest correlations will be discussed. We begin with an
evaluation of the sieve.
2-2
-------
Evoluotion cf Sieve
The purpose of the sieve is to select only the better data for analysis
whenever data of varying quality are available, while at the same time
not excluding any chemicals from analysis on the basis of the sieve.
The sieve consists of two parts: a quality screen that discriminates
among data Bets on the basis of number of animals tested and length of
observation, and a significance screen that selects only data sets in
which a statistically significant response was found, whenever such deta
sets are available for a chemical (cf. Section 1). The idea behind the
sieve is that use of better data should improve the observed
correlations between the human and animal results. This desired result
is in fact achieved, since ? \* higher when the full sieve is used in 28
out of the 3B analyses (Table 2-1). The effect of the sieve can be
observed by comparing, for example, the graphs in Figures 2-1 through
2-k or in Figures 2-9 through 2-12. The data appear to be more closely
grouped about the best-fitting line when the screenings are applied
(especially when the full sievr is applied. Figures 2-4 and 2-12) than
when they are not applied (Figures 2-1 and 2-9). This improvement in
correlations when better data are used is further evidence that the
observed correlations between the animal and human RRDs are real.
Aside from Analyses 3b, 8a end 11a, almost all of the benefit obtained
from applying o sieve is seen when the significance screen is applied.
That screen limits attention to the carcinogenic responses that are
significantly dose-related when such responses are available. The
quality screen, which focuses on the number of animals tested and the
length of the experiment, does not appear to provide much of an
improvement over and above the significance screen for most analysis
methods (compare the third and fourth columns of Table 2-1). Such a
result is expected for analyses, like number 1, that already restrict
attention to a subut of the experiments, in this case the "long"
experiments. It is somewhat surprising in other cases, especially since
the majority of the carcinogenic responses in the data base are there
because of their apparent dose-related action. It is possible that the
criterion limiting attention to studies utilizing gavage, inhalation, or
oral routes of exposure (or the route most similar to human exposure), a
2-3
-------
criterion underlying every onolysis except 3D, also had the side effect
of eliminating many of the studies that woul'1 receive lower ranks in the
quality screening. This is conceivable if, for example, other methods
of dosing involved fewer animals (possibly because these routes are more
difficult to administer) or if other routes tend to involve bolus doses
that might cause early deaths (carcinogenic or non-carcinogenic) and
consequently shorten the duration of observation. It is possible that
experiments employing "nonstandord" routes of dosing were designed to
investigate special questions and so may not have been overly concerned
with number of animals or length of observation.
Also in relation to the action of the sieves, those analyses that
average RRD values at each stage (over sex within study, over study
within species, and finally across species; Analyses 12 through 2dd) are
relatively impervious to the application of any screenings. The
correlation coefficients within any of the rows in Table 2-1
corresponding to those analyses are very similar, no matter which sieve
is applied (cf. Figures 2-28 through 2-31). It seems likely that the
averaging that occurs in these onnlyw«*» acts in much the same way as the
screens are intended to work; much as a sieve acts to eliminate
outliers, so averaging works to pull outliers toward the "middle" of the
results. This effect is enhanced by the use of harmonic averaging which
severely limits the influence of infinite values. Since RRDs are
bounded beXow but not above, infinite-valued estimates are obvious
candidates for outliers. Similarly, the action cf both the quality
screen and the significance screen would tend to eliminate infinite-
valued estimates since experiments that are too short or employ too few
animals would tend to find no carcinogenicity of a chemical (i.e. , give
infinite RRD estimates) and responses not significantly related to dose
generally also produce infinite-valued RRDs.
Analyses other than 12 through 2<»d employ averaging, but not at every
level. Analysis 9 averages only across sex within study. Analysis 10
only across study within species; Analysis 11a only across species; and
Analysis lib only across the species rets and mice. Since the
experiments employing species other than rats and mice do not appear to
be as "clean" as those using ruts and mice (compare the first columns in
the rows corresponding to Analyses 11a and 11b and note the sizable
2-
-------
increase m p when a quality screen is applied to Analysis 11a), let us
concentrate on Analyses 9, 10, and 11b (cf. Figures 2-18 through 2-25}.
In those cases, one notes a similar but slightly lessened independence
from the sieve. Especially when averaging across sex or across study,
an effect similar to that of the screenings may already be in operation.
In this connection note that Analysis 12, which averages at all levels
a'- that uses the same data as Analysis 0, results in larger correlation
coefficients than does Analysis 0 when the significance screen is not
used (columns 1 and 2 of Table 2-1). Correlation coefficients
associated with Analysis 12 are somewhat smaller than those associated
with Analysis 0 when the significance screen is employed (third and
fourth columns) and, moreover, the application of the significance
screen to Analysis 0 produces larger coefficients than the nonscreened
Analysis 12. This suggests that applicction of an appropriate sieve may
be a better approach than merely averaging at all levels. Since use of
a sieve appears to improve most analyses, and since use of the full
siev» is about as good or better for most analyses than use of cither
screen by itself, the remaining discussion will emphasize analyses that
employ the full sieve.
Analyses that Use Combination of All Significant Individual Responses
Two of the endpoints defined and included in the bioassay data base
whenever possible are the combination of all individual carcinogenic
responses that are significantly dose-related and the combination of all
such responses that are malignant. Analyses that use the first of
these, combination of significant responses, i.e. Analyses 8a, 16, and
17, provide relatively poor correlations (p < 0.6) no matter which data
screening procedure is implemented (cf. Figures 2-14 and 2-32). The
p-values associated with these correlations range betweon 0.02 and 0.05
which, given the number of comparisons performed, might reasonably be
considered only marginally significant. The response, combination of
significant responses, could not be defined for every study or every
chemical; only 13 of the 23 chemicals had one or more experiments
presenting data that allow calculation of this endpoint. it is the case
that the experiments that do provide the necessary information in this
2-5
-------
regard are generally more complete and better studies, notably the NTP
bioassays. This is indicated by the fact that rank 1 studies (those
observing over 50 dosed animals for at least 754 of the standard
observation period) are available for 12 of the 13 chemicals included in
Analyses 8a one1 16. That being the case, it is less likely that the
relatively poor correlation is due to use of data of poorer quality.
Interestingly, the analyses using the combination of malignant
statistically dose-related responses. Analyses 18 and 19, provide very
good (and in some cases, th» largest) correlation coefficients, ranging
from 0.73 to 0.79. However, the difficulty of defining the response is
even more severe with this endpoint than with the previous one. No more
than 10 chemicals included studies with the necessary information. Note
that the p-values associated with these chemicals range between 0.003
and 0.009; such p-values are associated with i's on the order of 0.61
when more chemicals are included (cf. Analysis 2, no screens). So,
while use of this endpoint may well be appropriate, more data would have
to be made available before any stronger conclusion would be warranted.
Analyses That Utilize Malignant Neoplasms Only
Analysis 7 is identical to Analysis 0 except that the former analysis
utilizes animal data on malignant neoplasms only, where the latter
analysis permits data on benign neoplasms to be used as well; Analyses
12 and 14 have a similar relationship. Analyses 7 and 14, utilizing
data on malignant neoplasms, yield results that are quite similar to
those obtained from Analyses 0 and 12, respectively, analyses that used
data on both benign and malignant neoplasms. The graphs for Analyses 0
and 7 (Figures 2-4 and 2-14) are very similar, the major difference
being that data for benzidine are utilized in Analysis 0 but not
Analysis 7. It is important to note that inclusion of both benign and
malignant tumors does not degrade the correlations (in fact, it improves
them somewhat) despite the fact that the human results are for malignant
tumors exclusively.
2-6
-------
epidemiologically derived estimates even when no screening is used.
This may reflect an underlying difference in the overall quality of rat
and mouse experiments.
One of the few analyses that derives some benefit from the quality
screening, over and above that obtained by significance screening, is
11a. The same is not true for AncXysis 11b. This suggests that the
improvement obtained by screening the quality of the data in Analysis
11a is derived primarily from elimination of tixperimants in species
other than rats or mice that were too short or that tested too few
animals. Indeed, the correlation coefficients for Analyses 11a and lib
are nearly identical when the quality screen is applied (columns 2 and <*
of Table 2-1; cf. Figures 2-23 and 2-25). With that screening, either
of these two analyses compares favorably with the standard analysis
(Analysis 0) and are similar to the results obtained from rats alone or
mice alone. This is perhaps not surprising given the preponderance of
rat and mouse experiments in the data base and the previously noted
similarity of rat-alone and mouse-alone correlation coefficients when
the data is appropriately screened.
Choice of Dose Units
Analyses 0,
-------
prediction analyses.
Tdentificotion of Analyses Yielding Higher Correlations
Analysis 3b yields the highest correlation; when the fi-11 sieve is
applied, p - 0.90 (cf. Figure 2-12). This analysis method also yields
correlation coefficients that are among the best when less than the full
sieve is used. Interestingly, Analyris 3b is the Irost restrictive of
the methods examined. Whereas all other analyses are restricted to
experiments that expose animals by gavage, inhalation, oral, or the
route of exposure that humans oncounter, 3b also allows instillation,
injection, and implantation experiments. These additional routes are
often not considered in quantitative risk assessment.
This discussion of Analynis 3b provides an opportunity to consider the
effect that changes in the data have on the correlation coefficients.
Some changes in data are the result of changing the criteria used to
pick experiments and carcinogenic responses for particular analysis
methods. In this case, allowing all routes of exposure adds threo
chemicals that only have studies that expose animals by "nonstandard"
means, chlorambucil, chromium, and melphalan. Moreover, RRO estimates
for certain other chemicals change dramatically when all routes are
allowed. Arsenic is a prime example; note the change in location of the
animal lower bound for this chemical (compare Figure 2-4 to Figure 2-12).
The animal lower bound RRO for arsenic in Analysis 3b is derived from an
experiment in which exposure was accomplished via intratracheal
instillation and for which a dose-related increase in lung tumors was
found. Note that the animal upper limit RRO is infinite whether or not
all routes of exposure are included in the analysis, a fact consistent
with the commonly held view that arsenic has not been shown conclusively
to be carcinogenic in animals.
The correlation coefficient, f, is derived from the ranks determined by
the relative positions of the intervals. In Analysis 0, the human rank
of arsenic is 6 and its animal rank is 15, a major discrepancy. In
Analysis 3b, with the addition of the three chemicals, arsenic's human
rank increases to 9 but its animal rank, due to the reduction in the
lower bound discussed above, rises to only 16.5. So, while the values
2-10
-------
of the RRD« con and do change substantially, the rank* based on the RRDs
may be relatively insensitive to those changes.
Nevertheless, ranks can be greatly t tered. Comparing the same two
Analyses. 0 and 3b, one notes a great change in the lower and upper
bounds associated with estrogen. This results in a change of rank, from
11.5 in Analysis 0 to 6 in Analysis 3b, despite the addition of three
more chemicals in the latter analysis. Estrogen has only two bioassays,
one an implantation study and the othor a feeding study. The feeding
study which was the only animal estrogen study utilized in Analysis 0,
failed to find any significantly dose-related responses (hence the
infinite MLE 'or estrogen in Analysis 0); however, the implantation
study entered Analysis Sb and included an increased incidence of kidney
tumors. So. while we are interested in changes in the underlying base
o* data and their effect on risk estimates, one must be aware that other
changes may be confounded with the changes in which we are interested.
Thus, with estrogen, including other routes (the implantation study)
actually eliminates the feeding study (because of the action of the
sieve), an unforeseen change in the underlying data. Another
manifestation of this is the fact that certain chemicals are eliminated
from some analyses because they lack the data to support those methods.
One can attempt to minimize such confounding data dependency. It is of
interest, for example, whether the high correlation obtained in Analysis
3b is due to the addition of the three chemicals mentioned earlier,
chlorombucil, chromium, and melphalon. The human and animal ranks of
chromium and melphalan are well matched, but those for chloromb>.icil are
7.5 and 3. respectively, showing moderate discrepancy. If these three
chemicals are not included in Analysis 3b, so that the only differences
between Analyses 0 and 3b are due to inclusion of additional routes of
exposure, then f • 0.88 when the full sieve is applied. This is very
close to the original p, 0.90, and is still notably better than the
correlation obtained from any other analysis.
Nevertheless, it is not possible to conclude unequivocally from these
analyses that the improved correlation due t-> inclusion of additional
routes of exposure will hold generally and is not simply a feature of
the particular data available for analysis. A substantial part of the
2-11
-------
improved correlation is due to a data-dependent change in one chemical
(emtrogen). This may, however, be on indication that inclusion of
additional routes may allow improved estimates for some human
carcinogens that, for some reason, or* not easily shown to be
carcinogenic in animals via routes through which humans are normally
exposed. Further investigation of this issue may be warranted.
Aside from Analysis 3b, no other analysis stands out as being superior
to the others based on the correlation analysis. The largest of the
remaining correlation coefficients is 0.81 (Analysis 25, full sieve) and
another 16 of the 38 analyses performed with the full sieve yield />'s
between 0.76 and 0.81. Those and perhaps many of the other analyses
provide ample indication that animal-based estimates of RRDs are
applicable to estimation of human RRDs and can be considered viable
alternative procedures for use in human risk assessment.
PREDICTION ANALYSIS
The three loss functions described in the discussion of methodology
(Section 1 of this volume) have been used to determine the lines of best
fit for 30
-------
provided notable ocMitisnal improvement in the correlation. Addition of
the quality screen ensurec that possibly questionable experiment* of
short duration or employing few ve*t animals do not conpronise the
results obtained from the lower ranked studies (the "better" studies).
This may be particularly important when extreme values, such as the
minimum lower bound or minimum MLL', are used as predictors.
Sieve
Examination of Tables 2-3 through 2-5 reveals that use of the sieve
generally does improve the predictive ability of the bioastay results.
No matter which loss function is used, the predictive power of those
analyses employing the minimum values (LR or MLE^) is improved (in the
sense of yielding smaller average loss) 74* to 82* of the time when the
sieve is applied. This effect is seen slightly more often among the
analyses that do not average over sex. study, and species (Analyses 0
through lid and 25) than among those that do average over sex, study,
and species (Analyses 12 through 2
-------
When the epidemiologicolly derived RRO ••titrates or* finite, the loss is
exacerbated. The sieve eliminates such data sets from consideration
when better ones are available.
The results for the median lower bound predictor, L^Q, are apparently
the most stable, os reflected in the fact that the action of the sieve
is neutral in a general sense. Note, however, that certain analyses
demonstrate definite improvement when the sieve is applied, even with
as the predictor.
Predictors
The four predictors that have been selected, L^, 1.20, Mil?*), W-E2Q, can
be compared on the basis of the average loss suffered when each
predictor is used in any particular analysis. Table* 2-3 through 2-5
clearly indicate that, no matter which loss function is employed, 1.20 is
the best predictor to use. In only 2 to 6 (depending on the loss
function) of the 76 analyses (38 pairs, with and without the sieve) does
that predictor fail to yield smaller loss than does LM. Analysis 2,
for example, appears to yield better prediction when LM is used instead
of 1-2;). Comparison of the . jss values among the analyses, however,
reveals that Analysis 2 in not one of the better methods of calculating
RRO estimate'*, so this observation has little bearing on the noted
superiority of LJQ. In three to five instances (again depending on the
choice of loss function) L2Q does not provide loss smaller than results
from using MLE2Q. Analyses 6 and 18 account for most of these
exceptions. Recall that these analyses could b» performed on only six
and ten cftomicols, respectively, «o again, the f'jct that MLEjQ yields
the smaller loss should not be given too much weight.
The superiority of LJQ is independent of the choice of loss function.
Also independent of loss function is the fact that MLEjQ is superior to
MlEpi among those analyses employing a sieve; the W.E2Q losses are
smaller in 17 or 18 of the 22 such analyses for which MLE^ and MLE2Q
differ. (Note that the analyses that average over sex, study, and
species, Analyses 12 through 2<*d, provide a single lower bound estimate
and a single maximum likelihood estimate. Consequently, LM - I-2Q and
-------
MLEM - MLE.2Q for those analyses and the losses associated with use of LM
are identical to those associated with use of \.^Q and similarly for MLEM
and MLEjQ.) Included in the set of 17 or 18 analyses are those that
yield the smallest losses when a maximum likelihood predictor is used so
the superiority of MLEjg over *LE- is clear when the sieve is applied.
The case is not so obvious when no sieve it applied. In this instance,
the results do depend on the choice of lost function. When fit is
measured by the CAUCHY loss function (Table 2-4) ML£20 is superior to
MLEM in 15 of the 22 no-sieve analyses. When the TANH loss function is
used (Table 2-5), MCEjQ is cuperior in only 10 of 22 no-sieve analyses.
Howevor, with both loss functions, MLE2Q is better than MLE^ for most of
those analyses that yield the smallest losses (Analyses 2 and 11c being
the oxceptiona). Thus, unless one wishes to analyze bioassays by method
2 (using only those experiments that dosed treated animals for at least
80* of the standard experiment length) or by lie (use rat experiments
only) without a sieve, one must conclude that in the case of the maximum
likelihood estimates, as well as in the case of the lower bounds, a
median predictor i* o better choice than a minimum predictor.
Interestingly, Analysis 2 (though not 11c) is also the method
consistently yielding smaller losses with L^ than with I-2Q-
One final observation will conclude this comparison of the predictors.
Since LJQ is better than LM and MLEjQ is better than MLt^, it is of
interest to determine whether LM is better than MLEjQ- The answer
depends to some extent on the choice of the two Iocs functions that nan
be used to compare these predictors, CAUCHY and TANH (Tables C-4 and
2-5, respectively). Among the 22 pairs of analysis • tthods that do not
average over sex, study, and species the CAUCHY loss function indicates
that LM produces smaller average loss than does KLE^Q *n 21 cases, i.e.
less than hal' the time. Among those same analyses, LM outperforms
ML£20 f°r **u analyses when measured by TANH loss. Both loss functions
indicate that Ml £20 is superior for Analyses 3b with and without th«
sieve (analyses providing some of tho oest correlations in the
correlation analysis) and for Analysis 6 with or without the sieve (tne
method applicable to only six chemicals). For those 32 analyses that do
average over sex, study, and species (Analyses 12 through 24d. with and
without the »ieve), LM is better in every casa but two (Analysis 18 with
2-15
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and without the sieve) no mo'.tar which loss function is used. Thus, LM
outperforms MLEjQ in th* "wjority of cases, especially when assessed by
the TANH loss function, but cny conclusion about the superiority of LM
may depend strongly on the analysis methods that are of interest.
Comparison of Analysis Methodn
The comparison of the analyses and the identification of the best ones
a'-e complicated because four separate predictors have been used and
three different loss functions have been defined. If the different
predictors or different loss functions result in distinct ordering* of
the methods, interpretation is more difficult. Table 2-6 presents the
five best analyses (those giving the smallest average losses) by
predictor and loss function.
Analyses 6. 18, and 19 dominate the list of methods giving smallest
losses. This is true no matter which predictor or v/hich loss function
is used. (Analysis 18 does not appear in any TANH list, however.)
Recall that these are the analyses cited in the discussion of correlation
analysis results as those that yield relatively large correlation
coefficients but that are applicable to few chemicals (six, ten, and
nine chemicals for 'nalyses 6, 18, and 19, respectively). So, as with
v.h« correlation results, the prediction results are suggestive for these
analysis methods, but no firm conclusions are warranted.
Table 2-7 lists the analyses that yield the smallest average losses
after eliminating Analyses 6, 1Q, and 19, which ore based on relatively
few chemicals. Analysis 17 appears on the list frequently. That method
uses the response that is the combination of significant individual
responses and is limited to experiments that dosed and observed the test
animals for a suitably long period. Furthermore, RRD estimates are
cveraged over sex, study, and species. That this method should appear
to provide good fit to the data is somewhat surprising since the
correlation coefficients associated with it are on the order of 0.58,
not among the better correlation results. Once again, however, the
number of chemicals that can supply data meeting the requirements of
this approach is limited; only 11 chwnicals had studies that dosed and
2-18
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observed animals long enough and for which the combination of
significant response* could be defined.
Analysis 16 is similar to Analysis 17 in that the endpoitit chosen is the
combination of significant responses and the estimates are averaged over
sex, study and species. It does not, however, exclude oxperii.wnts on
the basis of their length of observation and dosing, so that thirteen
chemicals can be analyzed by this method. Analysis IE also appears in
the list given in Table 2-7, predominantly when the CAUCHY loss function
is used. The analysis that does not average over sex, study, and
species but that rfoes use the combination of significant responses
(Analysis 8a) does not yield average losses that ore among the smallest,
for any loss function or predictor. Thus, it appears that averaging at
each level may be the most useful method whan the combination of all
significant responses is the endpoint used.
Analysis 20 is identified as a method yielding small losses, but only
when a lower bound predictor is used. That method is best when loss is
measured by the TANK function. This analysis method selects as the
endpoint of interest total tumor-bearing animals and overages estimates
over six, study, and speciea. The corresponding uoaveraged method
(Analysis 8b) does yield losses not much larger than those associated
with Analysis 20, 0.127 vs. 0.121 and 0.125 vs 0.121 for LM and LJQ,
respectively (measured by TANH). Consequently, use of total tumor-
bearing animals in conjunction with a lower bound estimate appears to be
an appropriate technique, if TANH is a suitable measure of loss.
Note that, of the twenty analyse* listed as providing the smallest
average losses determined by CAUCHY and TANH (the two functions that
consider the best epidemiological estimates of RRD) for the lower bound
predictors (L^ and LJQ), all but 'our use an endpoint that is a
combination of individual respcnses, either total tumor-bearing animals
or the combination of significant responses. Due to limitations in the
data available for analysis, not inherent limitations of the methods
themselves, some of these analyses were applicable to relatively few
chemicals. Nevertheless, the consistency with which these endpoints
yield small average Iocs indicates that they should be considered vnble
candidates for estimation of human risX.
2-17
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The DISTANCE2 loss function identifies a set of good methods that
intersects with the sets identified by CAUCHY and TANH infrequently.
All but one of the ten analyses listed in Table 2-7 under DISTANCE2 use
individual carcinogenic responses rather than a combined response. In
two coses (Analysis 25, the best when L^ is the predictor, and
Analysis 8c, also associated with the LM predictor) the response is
limited to those that are associated with human exposure. This response
may be identifiable when human data exist, but when such data are
absent, as would be the case for a new chemicol, then the appropriate
choice of endpoint is unknown and application of these methods
problematical.
The DISTANCE2 loss function identified Analysis 3b with the sieve as the
best method (in terms of average loss) when LJQ is the predictor. This
analysis was also clearly superior in the correlation analysis
(t » 0.90). It is not surprising that DISTANCE2 would tend to match the
results of the correlation analysis, especially when l_2Q is the
predictor. First, I-2Q was one end of the interval of animal RRDs used
in the correlation analysis. Second, DISTANCE2 does not consider the
location of the best estimate of RRD derived from the epidemiological
data and so is concerned only with the position of the human interval.
In any case. Analysis 3b yields the smallest loss with the DISTANCE2
function and reasonably small losses with CAUCHY and TANH, 0.4-13 and
0.140, respectively. (Note: it is not appropriate to compare the loss
values obtained using different loss functions. The fact that different
formulations of loss are used entails that the values in the different
columns of Table 2-7, for example, are not comparable.)
Since LJQ is the predictor that produces the best fit of the animal
results to the human results (a fact that is rei"forced by examination
of Table 2-7), wo concentrate on those analyses that perform best with
that predictor. Table 2-7 shows that Analyses 3b, 17, and 20 are the
analyses yielding the smallest average losses for one of the three loss
functions. One would like to have results that are independent of the
choice of loss function. That is, a good analysis method should be
robust with respect to differences in loss functions. To investigate
the analyses in this manner, we have defined what is called "total
•>- 18
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incremental normalized loss" as follows. For each loss function, the
difference between the smallest average loss and tne largest average
loss among the analyses (still ignoring Analyses 6, 18, and 19) when
is used is known. For each analysis the difference between the average
loss for that analysis a.id the minimum average loss, divided by the
difference between the minimum and maximum average losses, is defined as
the "incremental normalized loss". The sum of these across all three
loss functions gives the total incremental normalized loss (Table 2-8).
Normalization eliminates the difference in scale of the three loss
functions and should allow an overall oppraisal of the analyses.
Table 2-8 reveals that Analysis 17 (with the sieve) obviously adds least
to the average loss incurred. Analysis 17 without the sieve is nearly
as good. Analyser 3b with the sieve and 20 without the sieve, the other
two analyses picked as best by one of the three loss functions, yield
total incremental losses that are about the same, 0.555 and 0.558,
respectively, and follow the pair of Analysis 17 results, as the next
best methods of analysis.
Figures 2-35 through 2-38 display the plots of those four analysis
methods. One thing that is clear from these figures is that Analysis 17
derives much of its good performance from the specific subset of
chemicals to vhich it can be applied. For only three of those eleven
chemicals does the best fitting line fail to pass through the interval
of human RRD estimates, for any loss function. However, even when
Analyses 3b with the sieve and 20 without the sieve are limited to the
same eleven chemicals (Tablet 2-9), Analysis 17 with the sieve rs better
when measured by CAUCHY and T*NH. On tiie other hand, Analysis 3b with
the sieve, restricted to the seventeen chemicals to which Analysis 20
can be applied, yields smaller losses than does Analysis 20 as measured
by all three loss function.
Other analyses that yield relatively good, robust results can be
identified from Table 2-8. Those for which the total incremental
normalized losses are less than 1.0, for example, for at least one
member of the pair of results (with or without th» sieve) include
Analyses Ua through <*d (analyses that differ from the standard only with
respect to the Jose units used to extrapolate from animals to humans);
2-19
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8t>, utilising total tumor-bearing animals as the endpoint (as does
Analysis 20 discussed above); 8c, which is limited to carcinogenic
responses that humans got; 9, which average* results over sex within a
study; 11b, a method that averages the results from rats and mice; and
11c which uses rat data only. The best total incremental normalized
losses among these analyses range from 0.698 to 0.963.
Note, in passing, that an alternative ranking procedure that can be
applied is a minimax scheme. That is, for any analysis, the maximal
loss over the three loss function can be determined. The analyses that
have the smallest maximum* are best in a minimax framework. Since the
loss functions have different scales, this approach should also be based
on the incremental normalized lossos. If this is done, then
Analyses 17, 3b, and 20 remain the best three, in order, and several of
the others just cited, notably 8c and 8b, remain in the list of good
analyses. Analysis 22 also satisfies the minimax criterion well.
Asymmetric Loss
The discussion up to this point has concerned observations relating to
loss that is symmetric. That is, the loss functions employed reflected
the assumption that it is no worse to overestimate RRDs by a given
amount than to underestimate them by the same amount. In fact, it is
reasonable to think otherwise, i.e. to think and base our decisions on
the premise that overestimation is worse than underestimation. The
health considerations involved in cancer risk assessment make this a
prudent approach.
The effect of incorporating asymmetry into the loss calculations is
investigated in the following manner. The TANH loss function has been
used to fit a line to the results of each analysis method. In the
definition of TANH is a factor, m, called the asymmetry constant, that
reflects the degree of asymmetry thought to be pertinent. The symmetric
version has m • 1. The fitting is performed now with m equal to 1.5, 2,
5, 10, 50, and 100. Larger values of m reflect stronger beliefs about
the inadvisability of overestimating RRD-i. Tables 2-10 ana 2-11 display
the results for the lower bound predictors.
2-20
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Note trot the losses incurred when m • t>0 and m - ICO ore identical (to
three decimal places) for every analysis. Any high degree of asymmetry
drive* the line toward the chemicals in the lower right-hand corner of
the plots. Figure 2-39 displays this phenomenon for Analysis 3b, the
method applicable to the most chemicals.
As witti the symmetric ve.'Sion of the TANH loss function (cf. Table 2-5),
Analyses 6 and 19 perform well with moderate degrees of asymmetry.
Analysis 6 continues to be among the five best for larger degrees of
asymmetry whii? 19 does not. When the minimum lower bound is the
predictor, Analyses 20 (for moderate degrees of asymmetry) and Analysis
17 (for all degrees, with th» interesting exception of m • 5) perform
well, as they did with symmetric loss. When the predictor is I-2Q.
Analysis 17 is again good for all degrees of asymmetry, but Analysis 8b,
not Analysis 20, moves to the top five for moderate asymmetry constants.
For both predictors, Analysis 8c (which uses an endpoint that humans
get) produces small losses for m > 5. Most notable, however, is the
fact that Analysis 22 (using total malignancy-bearing animals and
averaging over sex, study, and species), a method moderately good with
no asymmetry, is second only to Analysis 6 (which is applicable to only
six chemicals) for high degrees of as\mmetry. This implies that, if it
is deemed necessary or desirable not to overestimate any RRD, method 22
is the best analysis to use (once agcin ignoring the suggestive results
of Analysis 6).
It is possible to characterize those analyses that will provide the
smallest losses with an asymmetric loss function. If those chemicals
that fall below the line fit with the symmetric function are nearly
colinear with slope equal to one, then a great reduction in asymmetric
loss can be achieved by moving the line to the right (decreasing the
y-intercept). Of course, if those chemicals that lie above the
symmetrically fit line also have this colinear relationship, then the
increase in loss for those chemicals when the line moves to the right
(as it always will with the introduction of asymmetry) can be minimized.
Hence, those analyses that do not produce outliers falling in the upper
left corner or, especially, in the lower right corner of the plots will
suffer relatively less loss than analyses thct do product such outliers.
2-21
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In this regard, compare Analyse* 20 and 22 (Figures 2- 50. In these cases the convention is driven by the chemicals
thai overestimate the most (cf. asbestos in Figures 2-40 and 2-41). If
one believes that it is not 50 times worse to overestimate than to
underestimate RROs, then conversions that are still protective (what has
been called "conservative") can be obtained. These correspond to
smaller values of m and tend to include more, though not necessarily
all, chemical* above the fitted line, the region where bioassays predict
larger risks than are obtained from the epidemiology for the given
conversion.
Since the question of asymmetric loss is closely linked to degrees of
belief about the relative desirability of underestimation and
overestimation of RROs, no further investigation of this issue is
undertaken. It should be borne in mind, however, that all of the
analyses reported in this document can be undertaken using asymmetric
loss. The remainder of the results and the discussion focus solely on
symmetric loss.
Animol-to-Humon Conversion
In the previous dijcuwsior of asymmetry, conversion of animal RRD
estimates to human RRO estimates was mentioned. This conversion is
based on the best-fitting line that relates the two sets of RRO
estimates. Specifically, it depends on the y-intercept, c, that defines
the line
Log10(RRDH) - Log-|0(RBOA) * c. (2-1)
2-22
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or
RRDH - 10C-RRDA (2-2)
which of course depends on the analysis method and predictor. This
conversion is over and above those that are used to equate the units
between humans and animals: recall that, for each of the possible
choices of units used to extrapolate doses from animals to humans,
species- and chemical-specific dose conversions were used to arrive at
the units mg/kg/day in humans, the units in which all RRD estimates are
expressed.
The conversion that is discussed here is a multiplicative factor i^ot is
the empirical result of fitting Eq. 2-1 to the ensemble of bioassay
data. The fitted line will rarely pass through a data point. That is,
for any given chemical used to fit the line, the conversion determined
by Eq. 2-1 rarely describes the exact relationship between RRDH and RRD&
for that chemical alone. Rather, all the study chemicals together
determine c, and this factor may then be applied to estimate RRD^ for
any other chemical without direct epidemiological estimates. Tables
2-12 through 2-15 display the y-intercept values for each analysis and
each predictor.
It is of r.ome interest to determine the conversion factor suggested by
the data that applies to the standard analysis, which is modelled after
the Carcinogen Assessment Group's (CAG's) usual procedure. That group
uses the minimum lower bound as its predictor. Table 2-12 shows that
Analysis 0 with CM yields y-intercepts between 0.51 and 1.71 when no
sieve is applied and between 0.83 and 1.07 when the full sieve is used.
The ratios, RRDn/RRDA (which we will call conversion factors), with
these intercepts range between 3.2<» (• 10°-51) and 51.7 or 6.71 and 11.7
without or with the sieve, respectively. These figures ore uniform in
suggesting that CAG's procedure is conservative, in th» sense of
underestimating RROs or overestimating risk and so being protective of
human health. Given that CAG screens its dnta to select the best
available studies, a process that may act like our sieve, the degree of
underestimation is likely to be about an ord»r of magnitude for the
2-23
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level of risk of interest here.
Since 1-2Q woe found to be the best predictor regardless of loss
function, the remainder of the discussion of conversion factors focuses
on that predictor (Table 2-13). Over all analyses and loss functions,
the ratio, RRDH/RRDA, determined by Eq. 2-2 ranges from 0.184 to 151.
Among those analyses that are based on extrapolation assuming mg/m^/day
human-and-animal equivalence (which include almost all of the analyses
since the standard analysis assumes such equivalence) tho -atio ranges
from 0.184 (from the CAUCHY loss function applied to Analysis 21 with
the sieve) to 74.6 (from the TANH loss function line fit to Analysis 6
with or without the sieve). Since Analysis 6 results are based on only
six chemicals, art alternative upper value that is more firmly supported
can be obtained from the CAUCHY line fit to Analysis 3a without the
sieve, 28.4. On the other hand, if we limit attention to those analyses
that appear to yield the smallest average losses with the LJQ predictor
and the loss functions for which they are best (cf. Table 2-7) than the
range is from 1.29 (Analysis 20 without the sieve, TANH loss function)
to 16.7 (Analysis 3b with the sieve. DISTANCE2 loss function).
At this point one can compare and contrast the results of the analyses
that are identical except for choice of the dose units assumed to yield
animal and human equivalence with respect to carcinogenic response
(component 4, cf. Table 1-1). To facilitate this comparison, the
supplemental analyses discussed in Section 1 are examined as well. The
results for these analyses are presented in Tables 2-1S and 2-17.
It is possible to identify three sets of five analyses each such that the
analysis within a set differ only with respect to the dose units assumed
to yield equivalence. These sets are (0, 4a, 4b, 4c.
-------
DISTANCE2 loss function and in the second set. (12, 2<»a-2<»d}, with the
DISTANCE2 and TANH loss functions. In oil these instances,
mg/kg/lifetime are the units producing the smallest average losses. The
units ing/kg/lifetime ore linear transformations of mg/kg/day dependent
only on the length of experiment, so a weight-based extrapolation
appears good when the sieve is used. For Analysis 30 with the sieve,
the analysis t'-at yields the smallest loss of any in Table 2-18, the
y-lntercepts (Table 2-19) indicate the ratio RRD;-i/RRDA is between 1.079
and 2.438, depending on which of th« loss functions is used. If
attention is restricted to the loss functions that base the fit of the
lines on the location of the bast epidemiological RRD estimates (i.e
CAUCHV and TANH) the range is narrowsd to between 1.079 and 1.698.
Thus, these calculations indicate that RRDs obtained from Analysis 30,
the least restrictive analysis using mg/kg/day, very slightly
underestimate human RRDs. This is interesting in light of the fact that
Analysis Aa, which is like Analysis 30 in every way except .that routes
of exposure ore limited to inhalation, gavage, oral, and.the route that
humans encounter, overestimates RRDs on average (note the negative
intercepts in Table 2-19). This is an instance of a general phenomenon:
no matter what units are used for extrapolation, the analysis that is
less r-ctrictivs w'th respect to routes of exposure yields larger
y-intercepts than the more restrictive analysis. The effect of
including all routes of exposure appears generally to be to decrease the
median lower bound. Using the restricted set of exposure routes but
averaging results over sex, study, and species has the same effect.
Conversion factor* (ratios) for an units of extrapolation are given in
Table 2-20.
To close out this discussion of conversion factors, it is of some
interest to compare conversion from rats to humans and from mice to
humans. The comparison can be made using Analyses 11c and 11d (rats
alone and mice alone, respectively, restricted routes of exposure, with
extrapolation based on mg/m2/day) and Analyses <*9 and 50 (rats alone and
mice alone, respectively, any route of exposure, with extrapolation
based on mg/kg/day). For the first pair of analyses, the rat bioassay
conversion factor ranges from 0.81 to 1.85 with no sieve and from 1.<»3 to
1.92 with the sieve whereas the mouse bioassay conversion factor may
vary between 1.78 and 11.67 without the sieve and between 3.72 and «».30
2-25
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with the sieve. Those results indicate that, unadjusted, the rat
results com* closer to the direct epidemiological results. (Average
losses are generally smaller with rat data also.) For the supplemental
pair, Analyses 49 and SO, rat data fits better only whcr the sieve is
not applied (Table 2-16) but tend to overestimate human RRDs whereas the
mouse data underestimate (Table 2-17). When no sieve is applied, the
degree of underestimation with mouse data is comparable to the degree of
overestimation with rat data. However, when the sieve is applied, the
underestimation with mouse data (conversion factors between 1.31 and
1.53) is less extreme than the overestimation with rat data (conversion
factors between 0.32 and 0.58). [All conversion factors are based on
the CAUCHY and TANH loss function, not DISTANCE2.]
Uncertainty
It is important to characterize the sources and amount of uncertainty
associated with any method of estimating human risks from animal data.
As described in Section 1, two approaches are taken to investigate
uncertainty. The first, which is referred to as residual uncertainty,
is the analog of the residual error aspect of statistical analyses. It
applies to each analysis method as a whole and delineates the degree of
uncertainty that remains even when the best unit-slope line describes
the data. The other uncertainty investigation attempts to say something
about the uncertainty associated with each of the components of risk
assessment. This investigation is more qualitative, but aids in
identification of major sources of uncertainty and in the degree of
variation attributable to those sources.
Residual Uncertainty. The DISTANCE2 loss function is ideally suited to
an investigation of residual uncertainty. This function finds the line
that minimizes the squared distances to the intervals defining the range
of epidemiologically derived RRD estimates. That being the case, the
contribution to the total loss of any individual chemical indicates how
far that line is from the chemical's interval end thus indicates
uncertainty over and above that associated with the epidemiologically
derived estimates. In this sense it is called residual uncertainty: it
is uncertainty remaining after the epidemiologicol uncertainty is
considered.
2-26
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For any analysis method, the DISTANCE2-fitted line determine* a
predicted dose, RRDp, for each chemical. If RRDp for any chemical lies
between the upper and lower bounds of the epidemiologically derived
estimates, RRD^u and RRDn(L. respectively, then no residual uncertainty
exists for that chemical. Otherwise, resirtuol uncertainty remains. T*e
residual uncertainties ore aggregated in two ways so as to indicate
something about tho uncertainty in terms of multiplicative factors that:
may be applied to the predictions to give a range of estimates about the
predicted value* which are consistent with the data (cf. the description
of the methods in Section 1 of this volume). Of course, larger factors
(wider ranges) indicate greater residual uncertainty.
Wr.en all the chemicals included in any analysis method, even those with
no residual uncertainty, are used to characterize uncertainty, a single
factor is estimated. This factor is the average amount by which the
predicted RROs must be multiplied or divided so as to eliminate residual
uncertainty. Alternatively, two sets of chemicals, those whose
epidemiological estimates lie completely above the line of predicted
values and those whose epidemiologically derived estimates lie
completely below that line, can be used separately to determine two
multiplicative factors, one to accommodate underprediction and one to
accommodate overprediction. Tables 2-21 and 2-22 present these factors
for all analyses (including the supplemental analyses) using the LJQ
predictor.
Analyses 6, 18, and 19 are the analyses yielding the smallest factors.
Tliese are the analyses with the fewest numbers of chemicals. As in
previous discussions, no more will ;>e said about these analyses.
The only other analyses for whicrt overall uncertainty factors (the
factors based on all chemicals included in an analysis) are less than
2.0 are Analyses 45 and 47, with the sieve. These supplemental analyses
average either over sex (45) or over all species (47). As can be seen
from Table 2-12, these two analyse, are two of the best of the
supplemental, indeed of all, analyses. Of course, the overall
uncertainty factors are closely tied to loss as determined by the
DISTANCE2 function. Consequently, those producing small average loss
2-i/
-------
(e.g. those in Table 2-6) also yield relatively small uncertoiity
factors.
The factors estimated using only those chemicals with positive residual
uncertainty (those for which the line does not intersect their vertical
interval) generally follow the same pattern as the overall uncertainty
Vactors. Since fewer chemicals are used to estimate these values, they
may be less stable than the overall factors, however. The usefulness of
separate "above the line* and "below the line" estimates can be
visualized if one considers that the chemicals completely below the line
are the ones of primary concern. They are the chemicals for which
bioassay data overestimate RRDs (even given the conversion factor
suggested by the best-fitting line). As long as one accepts that the
health implications are worse when RRDs are overestimated than when they
are underestimated, it may be reasonable to want to eliminate residual
uncertainty with respect to the former but not with respect to the
latter. One approach mentioned earlier is to use asymmetric loss
functions; high degrees of asymmetry do act to eliminate the residual
uncertainty of concern. Another approach, embodied here, is to estimate
an uncertainty factor tailored to those chemicals below the line.
That uncertainty factor can be seen to vary between 0.009 (Analysis 21
without the sieve) and 0.363 (Analysis 45 with the sieve), still
ignoring Analyses 6, 18, and 19. Generally, among the better analyses,
the values indicate that predictions would need to be divided by a
factor of 3 to 5 to account for the chemicals that overpredict RRDs.
Component-Specific Uncertainty. The supplemental analyses consist of an
alternative standard (Analysis 30) and 18 variations of the standard.
Each variant differs from the standard in only one respect, i.a. in the
approach taken to one of the components defining the analyses. This
supplemental set is used to investigate the uncertainty associated with
each of those components.
The alternative standard accepts any experiment and assumes a mg/kg/day
equivalence between humans and animals. This alternative is used in
place of Analysis 0 because the correlation analysis and certain of the
prediction analysis results suggest that allowing all routes of exposure
2-28
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(Analysis 3b) is preferable to restricting the routes to those that
humans encounter, gavoge, inhalation, or oral. Moreover, mg/kg/day
rather tha.i m/m^/day nwy be the preferred units for extrapolation when
t_2Q is the predictor. All component-specific uncertainty investigations
are limited to this predictor.
In such investigations, one is interested in how the RRC estimates
change when a component is changed. Consequently, it is not necessary
that there be epidemiologically derived estimates to use for comparison
end so all 44 chemicals (not only the 23 with human data) can b* used to
address this question.
It is usually the case that any change in an assumption underlying a
quantitative risk assessment will recult in a change in the risk
estimates. A component-specific uncertainty investigation should then
tell us two things: how the risk estimates change and how consistently
they change. A histogram approach has been used to address these
issues.
Figures 2-42 through 2-59 display the histograms resulting from this
investigation. Each histogram corresponds to one of the variations of
the alternative standard analysis. The entry for a chemical in any
histogram indicates the magnitude of the ratio of the RRD estimates
(l-2o) from the variant to that from the alternative standard. In this
way, the distribution of the changes among the chemicals can be
visualized.
Table 2-23 displays the mode of the distribution of each histogram.
Al?j presented in that table is a dispersion factor that is analogous to
the uncertainty factor used in the residual uncertainty analysis and
specifies the average factor by which the ensemble of chemicals differs
from the mode (cf. the Section 1 description of the methodology). This
factor is dependent on the specific cut points chaser for the
histograms, but because those cut points are the same for each analysis
method, it is a valid means of comparing the components with respect to
uncertainty. The greater the factor, the lesu consistent is the change
in RRD estimates that results from the component change corresponding to
the histogram. Less consistency (more chemical dependency) indicates
2-29
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more uncertainty is associated with the corresponding component.
Figures 2-42 through 2-4i pnrtain to tho ehoica of dose units used for
animal-to-humon extrapolation. These f-xguras snow relatively little
dispersion of the chemicals and heice indicate little uncertainty
associated with tha choice of cio?« units. That is not to say that the
resulting RRD estimates ora not dromoticolly affected by changes in
units. These are the only analyses for which tha mode is not in the
interval frcm 0.8 to 1.25 (Table 2-23). However, the dispersion factors
and the figures indicate that changing units has a relatively
predictable effect, one that is not chemical dependent. The plot in
Figure 2-42, for example, largely reflects the standard values (body
weight, surface area coefficient; cf. Table 1-3) used in the conversion
from mg/kg/day to mg/m^/day in rots and mice. When those standards are
used, the ratio of the RRD estimates (in all cases, the standard, using
mg/Kg/doy, is i" tne denominator) is, about 0.09 for mice and 0.21 for
rats. The chemicals falling between 0.1 and 0.2 in Figure 2-42 are the
result of using experiment-specific body weights or of cases in which
changing units also changes the ordering of the experiment* (due to
species-specific changes) and so changes the experiment yielding the
median estimate. Hence this figure, showing the greatest ("spersion of
the four because of the fairly even split between use of mice and rats,
may even exaggerate the uncertainty here.
The next two histograms (Figures 2-46 and 2-47) relate to criteria
placed on the length of observation and length of dosing, respectively.
The relatively large dispersion noted is due to extreme changes in one
or two chemical!,. Restriction to long experiments decreases the RRD
estimate for cigarette smoke by a factor over 1000. Similarly,
restriction to experiments that dosed the treated animals for at least
80< of the standard experiment length increases RRD estimates for
asbestos and cadmium by over three orders of magnitude.
No extreme changes are noted when experiments are limited to those using
the route of exposure by which humans encounter the chemicals in
question (Figure 2-48). However, for only 24 of the 44 chemicals were
there studies €>mploying that routb. When a less restrictive criterion
is used (the route just mentioned plus gavage, inhalation, and oral
2-30
-------
routes; Figure 2-49), moderately extreme values do appear,
benzo(a)pyrene and arsenic which change by factors of 847 and 410,
respectively. These chemicals were not included in Figure 2-48 but
account for the majority of the dispersion seen in Figure 2-49.
Otherwise Figure 2-49 is less disperse than Figure 2-48.
The next four histograms (Figures 2-50 through 2-53) relate to the
choice of endpoints to be analyzed. These are among the most disperse
of the figures in the sense of including several extreme changes
(Figures 2-50 and 2-53} and also in the sense of having less
dominant modes (Figures 2-51 through 2-53). If not for two extreme
changes (cigarette smoke and saccharin for which the ratios are
9.77x10-** and 8.69x10-6, respectively), Figure 2-50 (malignant tumors
only) would display much less dispersion, being on the order of 13
.-other than 291.
All of the histograms discussed above, except for those that relate to
choice of dose units, depict changes that occur because a subset of the
data are used.. They demonstrate the effect such selections have on the
location of the median lower bound RRD. A chemical with a ratio greater
than 1 is one for which the selection tends to eliminate snaller
estimates. Componentt such as the-.e that relate to bioassay or response
inclusion criteria can be very sensitive to the data that are available,
certainly more so than those components that relate to manipulation of
whatever data are available (s'-ich as the component related to the choice
of dose units). This sensitivity is reflected in the fact that for
these histograms fever than the maximum nu;v<5er of chemicals (44) are
addressable once the inclusion criteria are applied and may contribute
strongly to the appearance of the extreme changes that have been noted.
One must be aware that some confounding due to data availability may be
present in the histograms of Figures 2-46 through 2-53.
On the other hand, those analyses that dictate how the experiment-
specific RRDs are averaged are all based on the same data. In the
standard analysis no averaging is [.erformed. Analyses 45 through 47
(Figures 2-54 through 2-56) average results over sex alone, study alone,
and species alone, respectively. The uncertainty associated with any of
these procedures is small, the dispersion factors indicate that the
2-31
-------
average change in the RRD estimates is less than a factor of 2.2.
However, if we limit attention to rats and mice (Figures 2-57 through
2-59) uncertainty is again great. This, too, may be in part a
reflection of dependence on data availability. Consider the case of
saccharin which contains mouse and rat bioascays predominantly. Th9 rat
studies are of better quality (they get rank 1 by the quality screen)
than are the mouse studies (rank 3) so that when both are considered,
only the rat studies are analyzed (the full sieve is used in the
analyses represented in the histograms). Therefore, no change is seen
when rats alone or the average of rat and mouse data are used (Figures
2-47 and 2-46, respectively). The mouse results are over rive orders of
magnitude smaller than the rat results.
Nevertheless, some species-specific changes can be discerned. Cigarette
smoke is apparently more potent in rats than in other species. Arsenic
is less potent in rats and mice although this may also reflect some data
dependence. Overall, the choice of species appears to be a highly
uncertain component of risk assessment as indicated by the large
dispersion factors for Analyses 49 and 50, and by the difference in
dispersion between Analyses 47 and 48 (Figures 2-56 and 2-57) which
differ only in that species other than rats and mice are included in
Analysis 47. It is easy to see how data availability can affect the
estimates from any given species, above and beyond the question of the
most appropriate species for any given chemical.
2-32
-------
Table 2-1
CORRELATION COEFFICIENTS AND ASSOCIATED
p-VALUES. BY ANALYSIS METHOD AND SIEVE
Analysis
0
1
2
3o
3b
4a
4b
4C
4d
5
6
7
8a
8b
8c
9
10
11a
lib
lie
11d
12
13
14
15
16
17
18
19
20
21
22
23
24o
24b
24c
24d
25
# of
Chemi-
cals
20
18
19
17
23
20
20
20
20
20
6
19
13
17
18
20
20
20
20
19
13
20
18
19
18
13
11
10
9
17
13
15
13
20
20
20
20
16
NO
f
.68
.55
.61
.62
.80
.70
.67
.67
.68
.69
.96
.55
.50
.80
.76
.69
.71
.60
.66
.77
.62
.75
.48
.71
.48
.48
.57
.79
.79
.67
.43
.34
.18
.76
.73
.74
.73
.69
Screens
P-
volue
.0002
.0095
.0034
.0041
<.0001
.0008
.0004
.0008
.0004
.w003
.0028
.0079
.0379
.0050
.0004
. OOOn
.0004
.0025
.0009
.0002
.0121
.0005
.0240
.0005
.0267
.0489
.0358
.0036
.0062
.0020
.0715
.1078
.2832
<.0001
.0004
.0001
.0003
.0023
Quality
Screen
P
.73
.55
.55
.64
.77
.76
.73
.71
.7t
.74
.79
.64
.56
.60
.71
.70
.73
.73
.72
.74
.69
.75
.50
.75
.50
.49
.57
.76
.79
.64
.37
.34
.01
.76
.75
.76
.76
.64
P-
value
.0001
.0083
.0075
.0026
<.0001
<.0001
.0001
.0004
.0002
.0001
.0317
.0015
.0207
.0052
.0009
.0007
<.C001
.0002
.0001
.0001
.0046
.0001
.0172
.0001
.0177
.0472
.0369
.0046
.0057
.0035
.1046
. 1075
.4904
.0004
.0001
<.0001
.0002
.0042
Significance
Screen
p
.78
.68
.49
.74
.78
.77
.76
.77
.77
.78
.93
.72
.50
.66
.76
.77
.75
.69
.73
.79
.80
.73
.43
.70
.45
.49
.58
.74
.79
.65
.43
.35
.18
.72
.71
.72
.71
.79
P-
value
<.0001
.0013
.0187
.0005
<.0001
<.0001
<.0001
.0002
.0001
.0001
.0106
.0003
.0435
.0013
.0002
<.0001
.0001
.0011
. 0003
.0001
.0006
.0001
.0368
.0007
.0321
.0470
.0280
.0090
.0060
.0024
.0698
.1001
.2744
.0006
.0003
< .0001
.0001
.0001
Quality and
Significance
Screen
e
.78
.63
.49
.73
.90
.78
.76
.78
.78
.75
.79
.76
.56
.66
.76
.76
.77
.76
.73
.79
.76
.75
.43
.71
.46
.49
.58
.73
.79
.63
.38
.35
.18
.75
.74
.74
.75
.81
P-
value
.0001
.0015
.0153
.0007
<.0001
.0001
.0001
<.0001
<.0001
<.0001
.0342
.0001
.0214
.0022
.0001
.0003
.0002
<.0001
<.0001
<.0001
.0023
<.0001
.0416
.0005
.0316
.0436
.0301
.0090
.0058
.0043
. 1023
.1036
.2821
.0001
.0001
.0001
<.0001
.0002
2-33
-------
Table 2-2
ABBREVIATIONS FOR CHEMICALS INCLUDED IN THE STUDY
Thot><. with Suitable
Epideniolqical Data
Abbreviation
AB
AF
AS
BN
BZ
CB
CD
CR
CS
DS
EC
EO
ES
IS
MC
ML
NC
PC
PH
RS
SC
TC
VC
Chemical
Asbestos
Aflatoxin
Arsenic
Benzene
Benzidine
Chlorambucil
Cadmium
Chromium
Cigarette Smoke
DES
Epichlorohydrin
Ethylene Oxide
Estrogen
Isoniazid
Methylene Chloride
Melphalan
Nickel
PCBs
Phenacetin
Reserpine
Saccharin
Trichloroethylene
Vinyl Chloride
Abbreviation
AC
AL
AM
3A
CO
CT
DB
DE
DL
DP
ED
FO
HC
HY
LE
MU
NA
NT
TD
TE
TP
TO
Others
Chemical
Acrylonitrile
Allyl Chloride
^-Aminobiphenyl
Benzo(a)oyrene
Chlordane
Carbon Tetrachloride
3, 3-Dichloro-
benzidine
1 , 2-Dichloroethane
Vinylidene Chloride
Diphenylhydrazine
EDB
Formaldehyde
Hexachlorobenzene
Hydrazine
Lead
Mustard Gas
2-Nophthylamine
NTA
TCDD
Tetracholorethylene
2,*», 6-Trichloro-
phenol
Toxaphene
-------
Table 2-3
AVERAGE LOSS AS DETERMINED BY THE SYMM£TRIC DISTANCE2
IOSS FUNCTION, BY ANALYSIS METHOD, PRECICTOR. AND SIEVE
0
1
3a
3b
4o
4b
4c
<»d
5
6
7
8a
80
8c
9
10
110
lid
12
13
14
15
16
17
18
19
20
21
22
23
24b
24c
24d
25
No Sieve
.650
.7rn
.7W
.779
.701
.684
.646
.767
.640
.240
.495
.514
.550
.367
.645
.541
.639
.659
.732
.490
.541
.352
.279
.368
.352
.289
.052
.090
.441
1 . 100
.530
1 . 181
.605
.580
.526
.630
.278
Predi
Sieve
.570
.630
.364
.620
.552
.599
.578
.516
.548
.159
577
.279
1.088
.246
.529
.412
.465
.488
.577
.256
.310
.459
.363
.430
234
.290
.064
.075
.752
.964
.574
1 . 170
.298
.318
.296
.276
.191
ctor
L20
No Sieve
.146
.261
.215
.266
.124
.166
.157
.134
.142
.001
.200
.430
.678
.189
. 141
.523
.272
.241
.253
.280
.541
.352
.279
.368
.289
.052
.090
.441
1 . 100
.530
1.181 1
.605
.580
.526
. 630
.232
Sieve
.298
.377
.310
. 113
.273
.316
.272
.267
.285
.001
.331
.224
.597
.243
.298
.268
.239
.274
.277
.228
.310
.459
.368
.430
.234
.290
.064
.075
.752
.962
.574
.170
.298
.319
.296
.277
.190
2-35
-------
1 \
Table 2-4
AVERAGE LGCS AS DETERMINED BY THE SYMMETRIC CAUCHY
LOSS FUNCTION, BY ANALYSIS METHOD, PREDICTOR, AND SltVE
Predictor
Analysis
0
1
3o
3b
4o
4b
4c
4d
5
6
7
8a
8b
8c
9
10
lla
11b
11C
11d
12
13
14
15
16
17
18
19
20
21
22
23
24a
24b
24C
24d
25
LM
L20
No No
Sieve Sieve Sieve Sieve
.566
.540
.547
.551
.597
.546
.546
.605
.560
.453
.496
.467.
.459
.511
.559
.530
.560
.477
.429
.528
.524
.490
.498
.500
.413
.375
.366
.344
.410
.242
.445
.460
.541
.522
.516
.550
.463
.509
.508
.464
.477
.492
.528
.493
.485
.511
.359
.523
441
.442
.533
.516
.482
.486
.447
.421
.490
.460
.519
.493
.489
.409
.333
.377
.322
.456
.452
.432
.445
.448
.477
.U51
,'*50
.494
.440
.478
.487
.453
.423
.420
.398
.428
.440
.270
.521
.430
.439
.432
.433
.499
.476
.381
.378
.488
.524
.490
.498
.500
.413
.375
.366
.344
.410
.424
.445
.460
.541
.•>i>2
.516
.550
.470
.457
.506
.467
.413
.437
.466
.440
.454
.455
.309
.491
.419
.447
.494
.643
.465
.448
.408
.390
.451
.460
.519
.493
.489
.409
.363
.377
.322
.456
.452
.432
. 443
. 448
.477
.451
.4r,0
.506
ML EM
NO
Sieve
.586
.569
.606
.558
.570
595
b84
.573
.591
.446
.559
.478
.604
.604
.589
.563
.575
.500
.445
.529
.566
.572
.564
.618
.437
.412
.366
.354
.614
.817
.66*
.665
.559
.571
.560
.570
.558
Sieve
.415
.513
.479
.483
.502
.536
.502
.492
.515
.360
.535
.463
.674
.578
.524
.495
.492
.466
.449
.458
.474
.567
.510
.579
.431
.399
.373
.327
.664
.766
.694
.680
.468
.491
.466
.468
.530
MLE2Q
NO
Sieve
.507
.619
.551
.520
.509
.492
.471
.508
.500
.261
.645
.453
.685
.711
.535
.538
.575
517
.527
.527
.566
.572
.564
.61ft
.437
.412
.366
.354
.614
.817
.664
.665
.559
.571
.560
.570
.494
Sieve
.482
.428
.492
.423
.463
.495
.467
.480
.476
.297
.510
.444
.651
.599
.490
.485
.488
.433
.428
.421
.474
.567
.579
.579
.431
.399
.573
.32.'
.664
.766
.694
.680
.468
.491
.466
.468
.561
•>-36
-------
Toble 2-5
AVERAGE LOSS AS DETERMINED BY THE SYMMETRIC TANH
LOSS FUNCTION, BY ANALYSIS METHOD, PREDICTOR. AND SIEVE
Predictor
LM
Analysis
0
1
3a
3(3
4a
4b
4c
4d
5
6
7
80
8b
8c
9
10
11a
11b
lie
I1d
12
13
14
15
16
17
18
19
20
21
22
23
2
-------
Table 2-S
COMPARISON OF ANALYSES; FIVE BEST ANALYSES.
BY PREDICTOR AND LOSS FUNCTION
a>
Loss Function
Predictor
LM
"-20
MLEM
MLE2Q
DISTANCE2
Analysis Avg.Loss
18
19
6
25
2
6
18
19
3b
4a
_.b
__b
.052 (ns)a
.075 (s)
.159 (S)
.191 (s)
.209 (ns)
.001 (s)
.052 (ns)
.075 (8)
.113 (S)
.124 (ns)
CAUCHY
Analysis Avg.Loss
19
6
17
18
16
6
19
17
11c
lib
19
6
18
17
16
6
19
18
17
lid
.322 (s)
.359 (s)
.363 (s)
.366 (ns)
.409 (s)
.270 (ns)
.302 (s)
.363 (s)
.378 (ns)
.381 (ns)
.327 (s)
.360 (s)
.366 (ns)
.399 (s)
.431 (s)
.261 fns)
.327 (s)
.366 (ns)
.399 (s)
.421 (s)
TANH
Analysis Avg.Loss
19
20
17
8b
6
6
19
20
17
8b
19
6
3b
24d
17
6
19
3b
11b
11c
.120 (s)
.121 (ns)
.121 (s)
.127 (ns)
.134 (8)
.:io (ns)
.120 (s)
.121 (ns)
.121 (s)
.125 (s)
.121 (s)
.134 (s)
.175 (s)
.203 (s)
.203 (s)
.111 (ns)
.121 (s)
.131 (s)
.199 (s)
.202 (s)
°The loss given is the smaller of the two losses (with and without the sieve)
for any analysis. The code in parentheses indicates whether it comes fro,T.
the analysis without the sieve (ns) or with the sieve (s).
bThe DISTANCE2 loss function is not used with MLE predictors.
-------
Toblo 2-7
COMPARISON OF ANALYSES; FIVE BEST ANALYSES, EXCLUDING
ANALYSES 6, 18, AND 19. BV PREDICTOR AND LOSS FUNCTION
Loss Function
DISTANCE2 CAUCHY TANH
i
m
10
Predictor
LM
1-20
MLfM
MLE20
Analysis
25
2
16
Be
lid
3b
4a
3a
4d
9
__b
_.b
Avg.Loss
.191 (s)a
.209 (ns)
.234 (s)
.254 (s)
.256 (s)
-113 (s)
.124 (ns)
.130 (s)
.134 (ns)
.141 (ns)
Analysis
17
16
20
11c
21
17
lie
lib
16
20
17
16
11c
11d
11b
17
11d
3b
11c
16
Avg.Loss
.363 (s)
.409 (s)
.41C (ns)
.421 (s)
.424 (ns)
.363 (s)
.3/3 (ns)
.381 (ns)
.409 (s)
.410 (ns)
.399 (s)
.431 (s)
.445 (ns)
.458 (s)
.466 (s)
.399 (s)
.421 (s)
.423 Is)
.428 (s)
.431 (s)
Analysis
20
17
8b
22
21
20
17
8b
22
3b
3b
24d
17a
24a
12
3b
lib
11c
24d
17
Avg.Loss
.121 (ns)
.121 (s)
.127 (ns)
.137 (s)
.141 (ns}
.121 (ns)
.121 (s)
.125 (s)
.137 (s)
.140 (s)
.175 (s)
.203 (s)
.203 (s)
.204 (s)
.204 (s)
.141 (s)
.199 (s)
.202 (s)
.203 (s)
.203 (s)
°The loss given is the smaller of the two losses (with and without the sieve)
for any analysis. The code in parentheses indicates whether it comes from
the analysis without the sieve (ns) or with the sieve (s).
hThe DISTANCE2 loss function is not used with MLE predictors.
-------
Table 2-8
TOTAL INCREMENTAL NORMALIZED LOSSES,
3Y ANALYSIS AND SIEVE0
Analysis
0
1
2
3a
3b
4a
4b
4c
4d
5
7
8a
8b
8c
9
10
11a
11b
11c
11d
12
13
14
15
16
17
20
21
22
23
24a
24b
24c
24d
25
Total Incremental
No Sieve
1.019
1.693
1.543
1 .719
1.079
0.920
0.900
0.698
0.853
1.015
1.825
1.534
0.996
0.758
0.961
1.944
1.1*50
0.746
0.741
1 .627
2.156
1.751
1.695
1.836
1.324
0.259
0.558
1.553
1.117
2.001*
2.398
2.242
2.084
2.484
1 .183
Normalized Loss
Sieve
1 .418
1.997
2.175
1.390
0.555
1.198
1.559
1.258
1.313
1.385
1.736
1.176
0.963
1.239
1.466
1 .M7
• 1 . 194
0.983
0.968
1.215
1.430
2.158
1.767
1.804
1 .133
0.166
1.231
1 .700
1.043
1 .888
1.325
1.591
1 .369
1 .301
1.292
°Calculated using L2Q as the predictor.
2-40
-------
Table 2-9
AVERAGE LOSS FOR RESTRICTED SETS OF CHEMICALS
FOR ANALYSES 3b, 17, and 20. BY LOSS FUNCTION0
Sets of
Chemicals
Analysis
Loss Function
DISTANCE2
CAUCHY
TANH
11 to which
Analysis 17
is applicable
17 to which
Analysis 20
is applicable
3b with sieve
17 with sieve
20 w/o sieve
3b with sieve
20 w/o sieve
0.053
0.290
0.161
0.082
0.441
0.414
0.363
0.409
0.360
0.410
0.131
0.121
0.133
0.100
0.121
°The L2Q predictor is used.
2-41
-------
Table 2-10
AVERAGE LOSS AS DETERMINED BY THE ASYMMETRIC TANH LOSS FUNCTION
FOR LM, BY ANALYSIS AND DEGREE OF ASYMMETRY
Asymmetry Constant (m)
Analysis01
0
1
2
3a
3b
4a
4b
4c
4d
5
6
7
8a
8b
8c
9
10
11a
lib
11e
11d
12
13
14
15
16
17
18
19
20
21
22
23
24a
24b
:>4c
i.4d
25
1 .5
.207
.220
.204
.200
.191
.201
.211
.205
.199
.207
.144
.213
.200
.157
.177
.208
.197
.200
.192
.191
.201
.192
.211
.199
.200
.189
. 140
.198
.134
. 154
.168
. 149
. 170
.188
.195
.189
.188
. 177
2
.224
.244
.222
.217
.205
.218
.228
.222
.218
.225
.149
.232
.218
.170
.186
.226
.214
.218
.209
.207
.220
.208
.224
.216
.219
.205
.157
.210
.146
.169
.177
.160
.187
.204
.211
.205
.204
.196
5
.279
.296
.264
.260
.247
.272
.282
.275
.270
.276
.161
.281
.282
.215
.211
.279
.266
.273
.264
.260
.271
.260
.256
.265
.263
.275
.218
.279
.215
.210
.225
.196
.257
.255
.259
.253
.254
.228
10
.312
.328
.284
.293
.283
.306
.312
.305
.305
.310
.173
.310
.290
.276
.232
.311
.294
.305
.296
.292
.291
.287
.267
.292
.276
.293
.23^
.335
.267
.270
.293
.225
.342
.283
.288
.281
.282
.253
50
.319
.332
.290
.321
.336
.312
.319
.312
.310
.316
.173
.313
.296
.352
.280
.314
.301
.309
.300
.297
.291
.288
.267
.301
.285
.312
.250
.363
.288
.340
.340
.230
.377
.287
.289
.282
.287
.305
100
.319
.332
.290
.321
.336
.312
.319
.312
.310
.316
.173
.313
.296
.352
.280
.314
.301
.309
.300
.297
.291
.288
.267
.301
.285
.312
.250
.363
.288
.340
.340
.230
.377
.287
.289
.282
.287
.305
°Analyses have been performed using the sieve.
2-42
-------
Table 2-11
AVERAGE LOSS AS DETERMINED BY THE ASYMMETRIC TANH LOSS FUNCTION
FOR L2Q. BY ANALYSIS AND DEGREE OF ASYMMETRY
Asymmetry Constant (m)
Analysis0
0
1
2
3a
3b
4a
4b
4c
4d
5
6
7
8a
8b
8c
9
10
lla
11b
lie
11d
12
13
14
15
16
17
18
19
20
21
22
23
24a
24b
24c
24d
25
1.5
.188
.208
.207
.195
.156
.184
.193
.185
.186
.188
.126
.199
.189
.148
.170
.189
.190
.184
.181
.182
.189
.192
.211
.199
.200
.189
.140
.198
.134
.154
.168
. 149
.170
.188
..195
.189
.188
.176
2
.203
.220
.223
.207
.169
.198
.205
.199
.200
.202
.130
.214
.204
.162
.179
.205
.207
.199
.197
.196
.207
.208
.224
.216
.219
.205
. 157
.210
.146
.169
.177
.160
.187
.204
.211
.205
.204
.189
5
.249
.267
.264
.237
.210
.240
.250
.243
.240
.247
. 144
.260
.269
.201
.205
.257
.251
.247
.246
.236
.258
.260
.256
.265
.263
.275
.218
.279
.215
.210
.225
.196
.257
.255
.259
.253
.254
.220
10
.283
.299
.279
.264
.235
.275
.281
.274
.275
.282
.149
.290
.277
.261
.227
.290
.279
.270
.272
.269
.279
.287
.267
.292
.276
.293
.234
.335
.267
.270
.293
.225
.342
.283
.288
.281
.282
.244
50
.290
.304
.287
.293
.283
.281
.288
.281
.281
.288
. 149
.293
.283
.339
.272
.292
.286
.284
275
.275
.279
.288
.267
.301
.285
.312
.250
.363
.288
.340
.340
.230
.377
.287
.289
.282
.287
.297
100
.290
.304
.287
.293
.285
.281
.288
.281
.281
.288
.149
.293
.283
.339
.272
.292
.286
.284
.275
.275
.279
.288
.267
.301
.285
.312
.250
.363
.283
.340
.340
.230
.377
.287
.289
.282
.287
.297
°Analyses have been performed using the sieve.
2-43
-------
Table 2-12
Y-INTERCEPT VALUES FOR BEST-FITTING LINES,
PREDICTOR, BY ANALYSIS, SIEVE, AND LOSS FUNCTION
No Sieve
Analysis
0
1
2
3o
3b
4a
4b
4c
4d
5
6
7
8a
8b
8c
9
10
110
11b
11c
1id
-2
13
14
15
16
17
18
19
20
21
22
23
24a
24b
24c
24d
25
DISTANCE
1.587
1 .450
0.927
1.683
1.528
0.890
1.352
1.309
2.563
1.546
2.453
1.151
1.120
0.869
0.860
1.565
1.162
1.370
1.322
1.235
1.301
0.939
0.319
0.482
0 . 298
0.905
0.7C9
1.274
1.188
0.450
0.106
0.233
-0.073
0.245
0.691
0.634
1 .812
1.033
CAUCHY
0.510
0.931
0.824
2.004
1.820
-0.462
0.308
0.344
1.230
0.440
1.519
1.723
1.135
0 . 071
1.732
0.493
0.665
0.340
0.359
0.361
0.228
0 . 664
0.709
1.003
0.693
0.613
0.443
0.518
0.374
-0.161
-0.159
-0 . 679
-0.564
0.113
0,182
0.328
1.943
1.758
TANH
1.714
1 .067
1.067
1.922
2.164
1.517
1.032
1.079
2.919
1.610
2.086
1.417
1.493
0.302
1.391
1.714
1.208
1.439
1.391
0.519
1.097
0.939
0.727
0.929
0.744
0.710
0.467
0.634
0.447
-0.110
0.233
-0.549
-0.058
0.361
0.498
0.545
2.179
1 .714
DISTANCE2
0.827
0.821
0.404
1.117
1.976
0.087
0.609
0.596
1.582
0 . 765
2.300
0.730
0.907
0.455
0.583
0.770
0.611
0.734
0.701
0.748
0.197
0.444
0.168
0.456
0.237
0.749
0 . 772
1.308
1 .254
0.159
0.053
0.286
-0.120
-0.305
0.226
0.209
1.201
0.722
Sieve
CAUCHY
1.066
1.357
0 . 537
1 «;84
O.S30
-0.095
0.546
0.599
1.621
1.084
1.488
0.960
1.045
-0.174
1.247
0.956
0.771
0.839
0.462
0.291
0.849
0.540
-0.045
0.360
0.291
0.679
0.451
0.616
0.450
0.038
-0.736
-0.657
-0.715
-0.372
0.249
0.261
1.296
1.381
TANH
1.067
1 .067
0.665
1 .374
1.260
0.072
0.742
0.725
1.617
1.071
2.086
1 .067
1.555
0.233
0.813
0.966
0.955
0.874
0.603
0.447
0.788
0.749
0.272
0.731
0.27J
0.631
0.447
0.988
0.'~',7
0.233
0.233
-0.549
-0.613
-0.212
0.470
0.471
1.364
0.955
2-44
-------
Table 2-13
Y-INTERCEPT VALUES FOR BEST-FITTING LINES.
L2Q PREDICTOR, BY ANALYSIS. SIEVE. AND LOSS FUMCTION
No Sieve
Analysis
0
1
2
'a
5b
Ha
4&
4c
4d
5
6
7
80
8b
8c
9
10
11 a
lib
1lc
1id
12
13
1i»
15
16
17
IS
19
20
21
22
23
24a
24b
24c
24d
25
DISTANCE2
0.?28
0.416
0.630
0.635
1 .314
-0.257
0.225
0.150
1.282
0.493
1 .667
0.370
1 .045
0.145
0.258
0.607
0.925
0.664
0.515
0 047
0.808
0.939
0.319
0.482
0.298
0.905
0.769
1.274
1.188
0.450
0.106
0.233
-0.073
0.245
0.691
0.634
1.817
0.516
CAUCHY
0.380
-0.270
0.258
1.454
0.612
-0.428
0.115
0.211
1.310
0.334
1 .670
0.872
0.686
-0.081
0.289
0.433
0 . 292
0.447
-0.064
-0.093
0.251
0.664
0.709
1.003
0.693
0.613
0.443
0.518
0.374
-0.161
-0. 159
-0.679
-0.564
0.113
0.182
0.328
1 .943
0.492
TANH
0.532
0.272
0.315
1.339
1.067
-0.143
0.226
0.338
1.598
0.434
1.873
0.977
0.742
0.233
0.413
0.532
1.065
0.841
0.173
0.267
1.067
0.939
0.727
0.929
C.744
0.710
0.447
0.634
0.447
-0.110
0.233
-0.549
-0.058
0.361
0.498
0.545
2.179
0.571
DISTANCE2
0.474
0.550
0.201
0.695
1.223
-0.358
0.236
0.186
1.183
0.435
1 .667
0.428
0.793
0.072
0.478
0.494
0.356
0.161
0.347
0.297
0.085
0.444
0.168
0.456
0.237
0.749
0 . 772
1.308
1.254
0.159
0.053
0.286
-0.120
-0.305
0.226
0.209
1 .201
0.651
Sieve
CAUCHY
0.199
0.135
-0.067
0.624
0.927
-0.566
-0.230
-0.079
1.017
0.154
1 .415
0.210
0.683
-0.036
-0.357
0.278
0.461
0.183
0.293
0.155
0.633
0.540
-0.045
0.360
0.291
0.679
0.451
0.616
0.450
0.038
-0.736
-0.657
-0.715
-0.372
0.249
0.261
1 .296
0.722
TANH
0.315
0.583
0.272
0.822
1.080
-0.401
0.069
0.024
1.222
0.315
1.873
0.555
0.742
0.233
0.654
0.449
0.459
0.283
0.447
0.283
0.571
0.749
0.272
0.731
0.272
0.631
0.447
0.988
0.447
0.233
0.233
-0.549
-0.613
-0.212
0.470
0.471
1 .364
0.813
2-45
-------
Table 2-14
Y-INTERCEPT VALUES FOR BEST-FITTING LINES,
MLEM PREDICTOR, BY ANALYSIS. SIEVE, AND LOSS FUNCTION
No oieve
Analysis
0
1
2
3o
3b
40
4b
'»c
4d
5
6
7
8a
8b
8c
9
10
11a
11b
11c
11d
12
13
14
15
16
17
18
19
20
21
22
23
24a
24b
24c
24d
25
DISTANCES
-1 .481
-1.617
-2.307
-1.68*
2.116
-2.192
-1.666
-1.685
-0.710
-1.528
2.129
-1.936
-2.600
-4.428
-4.192
-1.522
-1.903
-1.689
-1.713
-1.852
-2.861
-2. 150
-2.828
-2.520
-4.601
-2.932
-3.238
1.098
1.027
-4.892
-6.075
-7.516
-8,007
-2.874
-2.348
-2.381
-1 . 371
-2.502
CAUCHY
0.327
1.059
0.257
1.811
0.783
-0.496
-0.065
-0.011
1.238
0.278
1.470
1.113
1.026
0.444
1.231
0.292
0.338
0.519
0.294
0.162
0.663
0.132
-0.768
0.460
0.372
0.466
0.308
0.343
0.210
-0.352
-4.276
-0.969
-0.300
-0.670
-0.085
-0.015
0.980
1 .341
TANH
1.366
1.366
0.514
1.762
1.708
0.478
1.487
1.534
2.002
1.299
1.946
0.928
1.366
0.352
0.882
1.366
0.759
0.894
0.505
0.365
.0.908
0.430
-0.081
0.455
0.514
0.471
0.299
0.387
0.299
-0.378
0.023
-0.499
-0.294
-0.429
0.209
0.210
1.411
0.882
DISTANCE2
-1.814
-1.895
-4.060
-2.009
1.815
-2.556
-2.020
-2.014
-1.117
-1 .860
2.129
-2.154
-2.681
-6.527
-4.292
-1 .864
-2.079
-1.920
-1.958
-2.056
-3.358
-2.215
-4.380
-2.441
-4.502
-2.917
-3.222
1.176
1.094
-6.720
-8.220
-7.438
-8.063
02.961
-2.409
-2.416
-1 .519
-2.581
Sieve
CAUCHY
0.994
1.186
0.567
1.159
0.768
-0.081
0.624
0.487
1.557
0.994
1.319
0.846
0.917
0.633
1.261
0.783
0.680
0.784
0.374
0.177
0 . 75';
0.423
0.200
0.267
0.068
0.539
0.308
0.446
0.276
0.744
-1.706
-1.086
-0.902
-0.482
-0.183
0. 169
1 . 174
1.302
TANH
0.928
1.201
0.514
1.201
1.124
-0.069
0.610
0.592
1.476
0.933
1.946
0.882
1.008
0.449
0.882
0.752
0.859
0.737
0.505
0.299
0.908
0.555
0.299
0.528
0.031
0.733
0.299
0.739
0.299
0.306
0.549
-0.192
-0.255
-0.353
-0.279
0.281
1 . 178
0.882
2-46
-------
Table 2-15
Y-INTERCEPT VALUES FOR BEST-FITTING LINES. MLE2Q
PREDICTOR, BY ANALYSIS, SIEVE, AND LOSS FUNCTION
Analysis
0
1
2
3a
3b
4o
4b
bo
4d
5
6
7
8a
3b
8c
9
10
110
11b
11 C
I1d
12
13
14
15
16
17
18
19
20
21
22
23
240
24b
24c
24d
25
DISTANCE2
-4.168
-5 . 846
-5.944
-6.189
-1.873
-4.923
-4.358
-4.365
-3.482
-4.203
1.524
-8.983
-2.775
-8.556
-15.326
-5.517
-3.880
-4.041
-2.631
-4.437
-5.660
-2.150
-2.828
2.520
-4.601
-2.933
-3.238
1.098
1.027
-4 . 982
-6.075
-7.516
-8.007
-2.874
-2.349
-2 . 380
-1.371
-10.801
No Sieve
CAUCHY
0.010
-0.057
0.035
1.016
-0.045
-0.785
-0.303
-0.241
0.931
-0.027
1.310
0.537
0.563
1.231
-0.697
0.387
-0.046
0.240
-0.162
-0.986
0.451
0.132
-0.768
0.460
0.372
0.466
0.308
0.343
0.210
-0.352
-4.264
-0.969
-0.300
-0.679
-0.085
-0.015
0.980
-0.227
TANH
0.080
0.579
0.199
0.643
0.643
-0.594
-0.226
-0.179
1 .179
-0.029
1.454
0.574
0.604
0.145
-0.564
0.207
0.500
0.363
-0.095
-0.465
0.643
0.480
-0.087
0.455
0.514
0.471
0.299
0.387
0.299
-0.378
0.022
-0.499
-0.294
-0.429
0.209
0.021
1 .411
-0.047
DISTANCE2
-2.253
-2.302
-5.788
-2.417
1.075
-2.999
-2 . 484
-2.488
-1 .544
-2.303
1.524
-2.444
-2.845
-6.719
-4.436
-2.218
-2.294
-4.031
-2.327
-2.366
-3.491
-2.215
4.380
-2.440
-4.502
-2.917
-3.222
1.176
1 .094
-6.720
-8.220
-7.438
-8.063
-2.961
-2.<»03
-2.416
-1.518
-2.735
Sieve
CAUCHY TANH
0.074 0.372
0.154 5.793
0.041 0.199
0.596 0.064
0.744 0.946
-0.693 -0.543
-0.324 0.115
-0.204 -0.065
0.90S 1.179
0.034 0.273
1.180 1.454
0.114 0.372
0.561 0.603
1.166 0.248
0.463 0.574
0.147 0.372
0 310 0.520
0.156 0.251
0.168 0.299
0.009 0.131
0.535 0.643
0.423 0.555
0.200 0.299
0.267 0.528
0.068 0.031
0.539 0.733
0.308 0.299
0.446 0.739
0.276 0.299
0.744 0.306
-1.706 0.549
-1.086 -0.192
-0.902 -0.255
-0.482 -0.353
0.183 0.279
0.169 0.281
1.174 1.178
0.644 0.602
2-47
-------
Table 2-16
AVERAGE LOSS FOR SUPPLEMENTAL ANALYSES WITH THE LjQ
PRECICTOR, BY ANALYSIS, SIEVE, AND LOSS FUNCTION
Analysis
30
31
32
33
2k
35
36
37
38
41
42
43
44
45
46
<*7
48
49
50
No
Sieve
DISTANCE2 CAUCHY
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.224
.266
.263
.273
.288
.213
.370
195
.124
.330
.622
.185.
.229
.163
.220
.271
.367
.172
.496
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C
0
0
0
.441
.453
.434
.442
.458
.468
.457
.489
.434
.555
.462
.403
.461
.405
.454
.469
.486
.404
.538
TANH
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
149
151
152
154
150
176
173
181
156
183
174
110
146
142
154
163
166
149
168
Sieve
DISTANCE2 CAUCHY
0.
0.
0.
0.
C.
0.
0.
0.
0.
1 .
0.
0.
0.
0.
0.
0.
0.
0.
0.
107
113
124
141
131
738
549
129
273
303
567
253
887
072
234
084
792
953
711
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
390
413
420
437
400
511
502
445
437
535
461
435
577
376
411
378
509
509
448
TANH
0.137
0.140
0.142
0.149
0.138
0. 198
0.182
0. 174
0. 164
0.223
0.172
0.118
0. 18?
0.134
0. 145
0.133
0.180
0. 199
0.154
2-48
-------
Table 2-17
Y-INTERCEPT VALUES FOR BEST-FITTING LINES,
AMONG SUPPLEMENTAL ANALYSES,0
BY ANALYSIS, SIEVE, AND LOSS FUNCTION
No Sieve
Analysis
30
31
32
33
34
35
36
37
38
41
42
43
44
45
46
47
48
49
50
DISTANCE2
0.431
1.314
1.099
1.056
2.217
0.011
-0.177
-0.113
-0.257
-0.021
0.803
-0.238
-0.437
-0.561
0.799
0.531
0.321
-0. 105
0.446
CAUCHY
-0.147
0.612
0.250
0.157
1.606
-1.063
-0.578
0.673
-0.428
0.921
0.034
-0.747
-0.308
-0.014
0.161
-0.076
-0.363
-0.516
0.628
TANH
0.072
1.067
0.575
0.557
1.784
-0.226
-0.402
0.350
-0.143
0.072
0.476
-0.545
-0.217
0. 148
0.467
0.230
-0.007
-0.344
0.230
DISTANCE2
0.387
1.223
0.950
0.868
2.015
0.475
-0.597
-0.076
-0.358
0.549
0.689
-0.0^5
0.475
0.467
0.588
0.249
0.229
0.257
0.443
Sieve
CAUCHY
0.033
0.927
0.655
0.277
1.863
-0.362
-0.910
-0.308
-0.566
-0.529
0.005
-0.338
-0.030
3.063
-0.028
0.000
-0.120
-0.490
0. 184
TANH
0.230
1.080
0.774
0.820
1.901
-0.180
-0.650
-0.209
-0.401
-0.180
0.476
-0.295
0.106
0.230
0. 148
0.230
0.230
-0.238
0.117
°The
predictor is used.
2-49
-------
I
Ul
o
Table 2-18
AVERAGE LOSS. BY DOSE UNITS. SIEVE AND LOSS FUNCTION0
No Sieve
Units
mg/m^/day
mg/hg/day
ppm diet
ppm air
mg/kg/life
Analysis
0
12
31
4a
24a
30
4b
24b
32
4c
24c
33
4d
24d
34
DISTANCE2
0.146
0.541
0.266
0.124
0.605
0.224
0.166
0.580
0.263
0.157
0.526
0.273
0 134
0.630
0.288
CAUCHY
0.440
0.524
0.453
0.434
0.541
0.441
0.420
0.522
0.434
0.398
0.516
0.442
0.428
0.550
0.458
TANK
0.159
0.180
0.151
;56
v*.186
0.149
0.157
0.104
0.15?
0.152
0.179
0.154
0.153
0.187
0.150
DISTANCE2
0.298
0.310
0.113
0.273
0.298
0.107
0.316
0.319
0.124
0.272
0.296
0.141
0 . 2f, 7
0.277
0.131
Sieve
CAUCHY
0.457
0.460
0.413
0.437
0.448
0.390
0.466
0.477
0.420
0.440
0.451
0.437
0.454
0.450
0.400
TANH
0.170
0.169
0.140
0.164
0.167
0.137
0.175
0.173
0.142
0.167
0.169
0.149
0.166
0.166
0.138
°The l2Q predictor is used.
-------
Table 2-19
Y-INTERCEPTS BY DOSE UNITS. SIEVE. AND LOSS FUNCTION0
i
at
No Sieve
Units
mg/m^/day
mg/kg/day
ppm diet
ppm air
mg/kg/life
Analysis
0
12
31
i*a
24a
30
-------
Table 2-20
CONVERSION FACTORS0 FOR ALL DOSE UNITS.
BY METHOD OF ANALYSIS AND SIEVEb
Units
Analysis Method
No Sieve
mg/m2/day
mg/kg/doy
ppm diet
ppm air
Restricted routes.
unaveraged (0)
Restricted routes,
averaged0 (12)
Unrestricted routes,
unaveraged (31)
Restricted routes,
unaveraged (4a)
Restricted routes,
averaged0 (24a)
Unrestricted routes,
unaveraged (30)
Restricted routes,
unaveraged (4b)
Restricted routes,
averaged0 (24b)
Unrestricted routes,
unaveraged (32)
Restricted routes,
unaveraged (4c)
Restricted routes,
averaged0 (24c)
Unrestricted routes,
unaveraged (33)
2.40
4.61
4.09
0.37
1.30
0.72
1.30
1.52
3.76
1.62
2.13
1.1*3
-3.40
- 8.69
- 11.67
- 0.72
-2.30
- 1.18
-1.68
- 3.15
- 8.91
- 2.18
- 3.51
- 3.61
1.58 -
3.47 -
8.45 -
0.28 -
0.43 -
1.08 -
0.59 -
1.77 -
4.52 -
0.83 -
1.82 -
1.89 -
2.07
5.61
12.02
0.40
0.61
1.70
1.17
2.95
5.94
1.06
2.96
6.61
mg/kg/life
Restricted routes,
unaveraged (4d)
Restricted routes,
averaged0 (24d)
Unrestricted routes,
unaveraged (34)
20.42 - 39.63 10.40 - 16.67
87.70 - 151.01 19.63 - 23.12
40.36 - 60.81 72.95 - 79.62
°The factor by which a bioassay-based RRO estimate is multiplied to give
best fit, on average, to the human RRD estimates (RRDn/RRD^).
bThe range given is that suggested by the CAUCHY and TANH loss
functions, the two that use point estimates of human RRDs.
cAveraged analyses average over sex, study, and species, in that order.
2-52
-------
Tobl« 2-21
UNCERTAINTY FACTORS FOR ANALYSES WITHOUT THE SIEVE0
All Chemicals Chemiccls Below Lin«b
Analysis
0
1
2
3a
3b
4a
4b
4c
4d
5
6
7
8a
8b
8c
9
10
110
11b
11c
11d
12
13
14
15
16
17
18
19
20
21
22
23
24a
24b
24c
24d
25
30
31
32
33
34
35
nc
20
18
19
17
23
20
20
20
20
20
6
19
13
17
is
20
20
20
20
19
13
20
18
19
18
13
11
10
9
17
13
15
13
20
20
20
20
16
23
23
23
25
23
20
Factor
2.257
3.381
6.852
2.862
4.216
2.046
2.488
2.504
2.131
2.239
1.048
2.800
8.005
29.008
2.936
2.227
10.240
3.745
5.040
4.530
4.570
10.065
5.731
3.918
6.018
5.871
4.174
1.467
1.790
7. 113
62.713
8.561
89.156
11.292
9.954
10.541
10.455
3.032
3.275
4.216
4.328
4.408
4.728
2.858
nd
3
4
3
3
6
4
3
3
4
3
1
4
2
4
4
3
5
4
5
4
3
5
4
4
4
2
1
2
2
5
2
5
3
5
5
5
4
3
6
6
8
7
6
6
rottor
0.188
0.185
0.068
0.146
0.210
0.291
0.171
0.155
0.269
0.194
0.874
0.204
0.071
0.043
0.252
0.185
0.127
0.183
0.315
0.137
0.233
0.119
0.159
0.160
0.150
0.092
0.047
0.462
0.428
0.132
0.009
0.141
0.017
0.100
0.107
0.126
0.067
0.180
0.231
0.210
0.278
0.249
0.190
0.255
Chemicals Above Lineb
ne
5
5
4
6
4
4
6
6
5
6
1
6
2
4
5
5
3
3
2
3
1
3
5
5
5
2
2
1
1
4
3
5
4
3
3
3
4
3
4
4
4
4
4
4
Factor
3.292
5.194
8.248
3.242
8.251
3.752
3.228
2.735
3.336
2.950
1 . 14
-------
Table 2-21 (continued)
UNCERTAINTY FACTORS FOR ANALYSES WITHOUT THE SIEVE0
All Chemicals Chemicals Below Linab Chemicals Above Line6
Analysis
36
37
38
41
42
43
44
45
46
47
48
49
50
nc
19
17
20
20
16
17
19
23
23
23
23
21
18
Factor
5.954
2.662
2.046
4.604
17.063
2.817
3.164
2.557
3.104
3.856
4.623
2.657
6.807
nd
4
3
4
4
3
3
3
5
6
7
8
4
4
Factor
0.119
0.161
0.219
0.110
0.039
0.199
0.148
0.264
0.235
0.211
P. 190
0.239
0.073
ne
4
6
4
4
3
4
4
4
5
5
6
3
6
Factor
8.894
3.068
3.752
7.186
14.234
4.362
5.718
5.261
5.397
6.016
6.973
6.728
6.186
°The I-2Q predictor is used.
bThe line is the best-fitting line determined by the DISTANCE2 loss
function.
°Number of chemicals in analyses.
dNumber of chemicals with human RRO intervals completely below line.
eNjmber of chemicals with human RRO intervals completely above line.
2-54
-------
Table 2-22
UNCERTAINTY FACTORS FOR ANALYSES WITH THE SIEVE0
Analysis
0
1
2
3a
3b
4a
4b
4C
4d
5
6
7
8a
Bb
8c
9
10
110
11b
1lc
lid
12
13
1*
15
16
17
18
19
20
21
22
23
24a
2kb
24c
24d
25
30
31
32
33
34
35
All Chemicals Chemicals Below Lineb
nc Factor nd Factor
20
18
19
17
23
20
20
20
20
20
6
19
13
17
18
20
20
20
20
19
13
20
18
19
18
13
11
10
9
17
13
15
13
20
20
20
20
16
23
23
23
23
23
20
5.300
6.676
10.029
2.119
2.008
4.552
5.454
4.616
4.448
5.060
1.048
5.422
3.406
22.834
3.235
5.426
4.493
3.611
4.535
4.444
3.066
5.393
8.254
6.022
7.670
3.508
4.181
1.560
1.675
31.128
36.455
9.010
82 . 564
5.162
5.518
5.101
4.718
2.645
2.026
2.008
2.216
2.256
2.293
78.202
3
3
4
4
4
3
3
3
3
3
1
3
1
3
3
3
3
4
3
3
2
3
5
3
4
1
1
2
3
4
3
5
3
3
3
3
3
4
5
4
4
5
3
6
0.076
0.066
0.077
0.307
0.249
0.091
0.072
0.086
0.092
0.081
0.874
0.078
0.044
0.031
0.149
0.073
0.088
0.143
0.094
0.099
0.115
0.079
0.145
0.073
0.117
0.049
0.047
0.433
0.529
0.040
0.030
0.128
0.018
0.084
0.072
0.082
0.090
0.250
0.283
0.249
0.231
0.272
0.172
0.146
Chemicals Above Lineb
n»
5
4
4
3
4
4
5
5
4
5
1
5
2
4
4
6
7
5
4
4
3
4
4
3
4
2
2
1
1
4
4
4
4
4
5
5
4
3
4
4
4
4
4
4
Factor
4.623
6.407
15.975
4.190
3.342
5.534
4.968
4.327
5.322
4.462
1 .144
5.275
5.471
8.148
5.786
3.917
3.432
4.175
5.777
5.589
4.282
6.250
12.263
10.427
10.793
6.523
6.931
4.128
4.675
1 3 . 087
22.798
11 .914
17.378
6.150
5.054
4.869
5.639
5.322
.097
.432
.578
.362
.647
42.184
2-55
-------
Table 2-22 (continued)
UNCERTAINTY FACTORS FOR ANALYSES WITH THE SIEVE0
All Chemicals Chemicals Below Lineb Chemicals Above Lineb
Analysis nc Factor nd Factor ne Factor
36
37
38
41
42
43
44
45
46
47
48
49
50
19
17
20
20
16
17
19
23
23
23
23
21
18
10.196
2.076
4.552
96.444
14.512
4.200
84.246
1.670
3.594
1.770
67.502
129.229
23.545
c
3
3
5
3
4
5
5
7
4
5
6
4
0.111
0.247
0.091
0.034
0.048
0.219
0.089
0.363
0.256
0.298
0.059
0.074
0.062
4
4
4
4
3
3
3
4
4
3
4
4
4
16.301
3.319
5.584
91.020
13.458
8.401
87 . 708
2.608
7.166
3.354
42 . 975
57 . 072
20.743
°The 1.2Q predictor is used.
bThe line is the best-fitting line determined by the DISTANCE2 loss
function.
°Number of chemicals in analyses.
^Number of chemicals with human RRO intervals completely below line.
eNumber of chemicals with human RRO intervals completely above line.
2-56
-------
Table 2-23
COMPONENT-SPECIFIC UNCERTAINTY: MODES AND DISPERSION
FACTORS FOR RATIOS OF RRDSa, BY SUPPLEMENTAL ANALYSIS"
Analysis
31
32
33
34
35
36
37
38
41
42
43
44
45
46
47
48
49
50
Number of
Chemicals
44
44
44
44
40
34
24
40
39
29
31
37
44
44
44
43
39
36
Mode of
Histoqrom
.05
.2
.2
.02
.8
.8
.8
.8
.8
.8
.8
.8
.8
.8
.8
.8
.8
.8
- .1
- .5
- .5
- .05
- 1.2b
- 1.25
- 1.25
-1.25
- 1.25
-1.25
-1.25
-1.25
-1.25
-1.25
- 1.25
- 1.25
-1.25
-1.25
Dispersion
Factor0
2.3
1.7
1.8
1.3
28.5
86.0
5.3
33.7
290.6
75.6
39.6
54.1
1.2
1.7
2.2
23.2
39.6
335.6
Number of
Extremes^
0
0
0
3
1
4
0
2
3
1
1
4
0
0
0
2
3
3
°The ratios ara of the chemical-specific RRD estimates from the
indicated analysis to these of Analysis 30, the alternative standard.
bThe analyses were performed with the L2Q predictor and using the full
sieve.
°The dispersion factor i» the average factor by which the chemicals
differ from the mode.
dThe number of chemicols for which the ratios are greater than 100 or
less than J.01.
2-57
-------
2-1
Corr«l«ilon
SUnd*rd An«1y«l. (0)
CO
4
3
3 *
I uj ,
01 1
m Q
2
1 °
_i
-2
-3
_^
t
k*_ ^
-
^
_
r
tm
*-•
1 ^
-« -4
X
A
/
'
x^PS
B*
i '
-3
f
Jfc_
I
-2
i
CD
f
, 4
1
-
NC
~x*'-
> 4
Y
VC"
, u_
IT
x
X
^/
X
to
' *•
t 4
EC
»-
S3,
T
y
^
PC
i J
B?
i • i
-1 0 1
(
c.
/
.
"
" -
/
1?
*S
,
2
X
x
X
PH
1 JL-
3 4
J
!
sc .
*
Afi ,
f
ES >
-------
I *
I
Ol
(O
-2
-3
Qu*1Ity
Flgurw 2-2
Correlation Arwly«l«:
Standard Arwlycl* (0)
CO
NC
-B?
EO
EC
ISC
•HE
TC.
IS
PH
-4-3-2-1 0 1
Lag of AnlMl RRO E*tl*«t«e
IAB
ES
-------
j'
1,
c
-2
-3
Flgur* 2-3
Slgnlf lo*no« Sor««n
Corr*t«tlan
SUnctard AnalyvU (0)
*-E?
^CP
4E_ -89
v a; L
HC
^e«
sc
,&5
_L
->..
-4
-3
-2
Log
-1
F AnlMl
o i
E*tlMtM
-------
M
I
OB A
4 f
j°
-2
-3
—A
Figure 2-4
Correlation An«ly«l»:
SUnctard An*ly*U (0)
-3 -2-1 0 1
Log of AnlMl RRO E«tlMt««
-------
Figure 2-5
to
I
00
I
4*
•
'-1
-2
-4
Correlation An*ly*l»:
Long ExpwlMnt* Only (1)
to
-------
Flgur* 2-€
1 2
•
O>
tn
-2
-3
-4
Log of AnlMl RRO Estln
-------
4 *-
I
M
I
m
*•
-2
-3
Full Slovo
Flgur* 2-7
Correlation Analysis:
Long Dosing Only (21
/ *~~
tr f*
«^x
V-
!G-
/
y
\
KJ
Ei:
T
x
IS
AS
a_
-4 -3 -2 -t 0 1
Log of AnlMl RRO Estla*
l_.
3
-------
Klgur* 2-a
Corr*1*ilon
Rout* Th*i HUMWW Enoountar <3»)
IM
I
-------
Flgur* 2-9
4 4-
I
01
o>
I
-1
Correlation Arwlyolo!
Any Rout* of Expovur* Ob)
-3
Lag of AnlMl WO EotlM
-------
4 *•
M
I
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vj
,
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-2
-3
Quality
Flgur* 2-10
Correlation Analysis:
Any Rout* of Expoaur* (3b)
/
/-
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-------
i
Ol
a
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i
t
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-3
Figure 2-11
Cor•--'••• loo An*ly*l«:
of Expovur* Ob)
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I'
i,
i
i-
-2
-3
-4
\jtrj of AnlMl RRO ZafclM
-------
2-13
Corr«t«tlon
Avwaga Don ov«r 80X of EMpwlMnt (51
I*
M
X
o
ui
-2
-3
Log of AnlMl RRO E^I««
-------
Flgur« 2-14
Correlation An«ly«l»:
Itellgrwni Tu»or» Only (7)
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I
-2
-3
Fill! SI«V*
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[
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-2-1 0 1
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-------
I
vl
M
I *
i,
-2
-3
-------
Flgurti 2-16
Correlation An*ly«l«:
TiMor-fiMrlno AnlMl* (fib)
u
-2
-3
-4
Log of AnlMl ROD EvtlM
-------
Flgur* 2-17
4 *-
"1
-2
l-l
-------
I
*J
01
I
*>
bJ
-2
-3
-4
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Flour. 2-18
Correlation
over Sax (9)
CO
HC
X
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AS
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-4 -3-2 -1 0 1
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I 2
I,
-2
-3
-4
-3 -2-1 0 1
Log of AnlMl RRO E*tlMi««
-------
Flgur* 2-20
Correlation
Av«r*go over Study (101
CO A
4 r
|
i
u
t
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-2
-3
-4 L
No
Log of An I Ml RRO EailM
-------
M
CD
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u
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-2
-3
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Flgur* 2-21
Correction Amly*l«:
Av*r«g* ov«r Study (10)
^EC
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-H^
AS
-3 -2-1 0 1
Log of Anlcwl RRO E«tl*«
-------
•si
ID
4 V-
I'
i
I °
%
J-1
-2
-3
Flgur* 2-22
Correlation An«ly«l«:
Av«r*g» ovw All SpoolM C11«>
Log of An I Ml RRO E^lwi
-------
Flgur* 2-23
Correlation An«ty*l*:
QVM- All SfMOlM (11«)
!'
CD
o
-2
-3
Log of AnlMl RRO E^lMU*
-------
Flgur« 2-24
Correlation An«1y«l«:
Avw«g* ovw R»t* «nd Mlo« (lib)
4 <-
M
OD
5"
-2
-3
t
Lag of An I Ml MRO EvtlwtM
-------
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2,
-2
-3
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-------
Flgur* -» 28
a
o>
J *
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-3
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-9
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/
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lES
-3 -2-1 0 1
Log of An I M) RRO Eatl«*t««
-------
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3,
* i
1-
-2
-3
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Flgur* 2-27
Correlation An«1y«l»:
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-L.
-8-4-3
-2 -1 0
of AniMi ran
14
45C-
-Jp*
-------
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CO
4 f-
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U
1
'1
-2
-3
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Av«r«g* ov*r 8«x, Study, mnd Spool** (12)
-------
Flour* 2-2S
CorrcUtlon Amly»l«:
Av«r«o» owr S«M, Study, «nd
l«« (121
!'
00
o>
i
-2
-3
Log o^ AnlMl RRO E«tlM
-------
2-30
Corr*1«tlan
Avw«a» OVWP SOM, Study, *nd fpwlM (12)
OB
4 ?•
1
,
I"
-2
-a
Log of An I Ml NRO E^lM
-------
Figure 2-31
Correlation
Av«r«g* over $•*, Study, «ind Sp*ol*« (12)
4 <-
I
4)
W
8
-2
-3
Log of AnlMl RRD E^lM
-------
Flgur. 2-32
Correlation
(18)
4 f-
00
ID
-3
All; CtMblnttlon of
Log of AnlMl RRO EotlMUo
-------
Flgur* 2-33
Correlation Arw1y*l«:
AV«T*Q» ov«r All; Total Tuaor Bearing An I Ml* (20)
j
u>
o
-2
-3
Log of AnlMl RRD CuUm+
-------
Flour* 2-34
Correlation
Rout* and RMPOTIM LI tea HiuMn* (20)
K)
10
•>
4 ;
3
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i
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M
I
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-2
-3
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Prediction
Analyst* 17, M*dl«n Lo»«r Bound Predictor
1C
s
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18
TC
f
CO
-3 -2-1 0 1
Log of An I Ml RRO EotlM
-
-------
Flgur* 2-36
I
(O
o<
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il
-2
-3
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An«1y«l* 17, Itedlcn LOMT
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-3
-2
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-1 0
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re
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IO
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-3
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VC
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-4 -3
-2-1 0
Log °* AnlMl RHO
-------
Flgur* 2-38
Prediction An*1y«l«:
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IO
O>
j
1
-2
-3
Log of AnlMl RRD E^lMU*
-------
2-40
I
10
Amlywl* 20, Mwll*n
Prwllotlan An*1y»U:
•ound; iMt-f liilr^ LlnM with
I-
3,
-2
-f
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HI -4
4 •
-------
2-41
Arwly«lv 22. ttmdlmn
Prediction
BMt-f filing Ll
with Ir
4 f
l«
u
10
OB
-2
-3
-3 -2-1 0 1
Log of AnlMl RRD E*tlMiM
-------
.00 -
.01 •
.02 •
.05 •
.W -
.20 •
.50 •
.K •
1.25 •
2.00 •
5.00 •
10.00 •
20.00
50.00
100.00
oo
Figure 2-42
Component-Specific Uncertointy; Ratios of RRD« for
Analysis 31 (mg/n^/doy) to RROs for Analysis 30
M.ASBACDOE1.E5FOHCNCKPMISSCTC
ABACBZOIDBECEOISUIUICn)
.00 -
.01 -
.02 •
.05 •
.10 -
.20 •
.50 •
.10 •
1.25
2.00
5.00
10.00
20.00
50.00
100.00
Figure 2-43
Component-Specific Uncertainty; Ratios of RROs for
Analysis 32 Jppm diet) to RROs for Analysis 30
X TO
MMM-ASMBZCDCftOSOEOLECEOESFOISlEICMICPCPMISn)
2-99
-------
.00 -
.m -
.02 -
.as •
.10 -
.20 •
.50 •
.K •
1.25
2.00
S.QO
10.00 •
20.00
50.00
100.00
Figure 2-4*
Component-Specific Uncertainty; Ratio* of RRD« for
Analysis 33 (ppm air) to RRO* for Analysis 30
SC TO
AFMBMCaCOCSCTaSEDHCHVILNJirTTETrvC
MACM.BZCOaiDBOCDLECEOFOISL£ICMM:PCPN>STCTD
•A
AS E5
Figure 2-45
Component-Specific Uncertainty; Ratios of RRDs for
Analysis 34 (mg/kg/lifetime) to RROs for Analysis 30
.00 -
.01 -
.02 -
.05 -
.10 •
.20 -
.50 •
.W •
1.25
2.00
5.00
10.00
20.00
50.00
100.00
BZ E3 NJ
ci at H.
MWtfM.MA3BAMCDa>C3CTDBOEDLOSFCCDEOFOHC>*ISUH:
MNCKTPCPMBSCTtTOTfTOtrvC
2-100
-------
Figure 2-<»6
Component-Specific Uncertainty; Ratio* of RRDs for
.00 —r- Analysis 35 (Long Experiments Only) to RROs for Analysis 30
Q
.01
.02 -
.05 -
.10 -
.20 -
.50 -
.« -
1.25 -
2.00 •
5.00 •
10.00
20.00 •
50.00
100.00 •
vc
TC Tt
WM.ASMMCDCO'BOCa.eCEOFOHVISLEICMIICMTPCrHRSSCTOT?
AC Alt O>
CT
* OS
CR ES HC TQ
Figure 2-*7
Component-Specific Uncertainty; Ratios of RROs for
Analysis 36 (Long Dosing Only) to RROs for Analysis 30
.00 -
.01 -
.02 -
.05 -
.10 -
.20 -
.50 -
.10 -
1.25 •
2.00 •
5.00 •
10.00
20.00
50.00
100.00 —
KT
OL HA
« TO Tt
MOOaOBOSEDFOHC ISPCPMBSCTF
AC ED TC
HI U 1C
Af EC CS 1C
AB AS CD
2-101
-------
M«
.05 —
.20 —
1**
2fM
5.00 —
10.00 —
20.00 —
50.00 —
VMM MM
00 —
A
05
PC
TC Tt
W CD CS EC
ED
AC DE
--
AB Af ES PC
a
Figure 2-48
Component-Specific Uncertainty; Ratios of RRDs for
Analysis 37 (Route Like Humans) to RRDs for Analysis 30
.00
.01
.02
.05
.10
.20
BA
Figure 2-<»9
Component-Specific Uncertainty; Ratios of RRDs
for Analysis 38 (Inhalation, Oral, Gavage,
Route Like Humans) to RRDs for Analysis 30
.K •
1.25
2.00
5.00
10.00
20.00
50.00 --
100.00
AB Af E5 1C
-------
Figure 2-50
.00 •
.01
.02 •
.05
.10
.20
.SO
.80
1.25
2.00
5.00
10.00
20.00
50.00
KXJ.OO
oo
Component-Specific Uncertainty; Ratios of RRDs for
CSSC Analysi« 41 (Malignant Tumors Only) to RROs for Analysis 30
HC vc
CO TO
ABAFALAHWCDCHCTDBaEOSECEDEaFOHYISIIAICICTPCPHTCTCTOT?
AC U
US
01 K
SC
AS
.00 -
.01 -
.02 -
.05 -
.10 -
.20 -
.SO -
.M •
1.25 -
2.00 •
5.00 •
10.00 •
20.00
50.00
100.00
Figure 2-51
Component-Specific Uncertainty; Ratios of RRDs
for Analysis <»2 (Combination of Significant
Responses} to RROs for Analysis 30
AS
CB NC
OS VC
ED
M m OL ED IS HA
COECflCtfTrCRSTCTEn)
OE TP
L£
AF
MC t*
CS
vc ca
2-103
-------
.02 —
.20 —
1.25 —
W.OO —
Of
AS
08 NT
BA OS
BN PH
AB AC OE ED HC TO
CO DL ED TC TO
AF AL l£ BC US TE VC
PC
IS
ES
at cs
CD
Figure 2-52
Component-Specific Uncertointy; Ratios
of RRDs for Analysis U3 (Total Tumor-Bwaring
Animals) to RRDs for Analysis 30
Figure 2-53
Component-Specific Uncertainty; Ratios of RRDs for
Analysis kk (Response Like Humans) to RRDs for Analysis 30
.00 —
.02 —
1.25 —
5.00 —
oo —
BA
AS
OB
AL
UE
AB
AH
CO
IS
cs
NC
LE
CS ES
ID
PC TC
AC AF
EO FO
DL 1C
US
ES HV
-------
Figure 2-54
.00 -
.01 -
.02 -
.05 -
.10 -
.20 -
.50 •
.80 •
1.25 •
2.00 •
5.00 •
10.00 •
20.00
50.00
100.00
00
Component-Specific Uncertainty; Ratios of RRDs for
Analysis 45 (Average Over Sex) to RRDs for Analysis 30
ED FO
ACAfM.AflASBABZC8CDCaaiCSCTDEECEDE5HCHVISLEK:it.lUNANCirTPC<>CTCTDTET?
OS RS TO VC
.00 -
.01 -
.02 -
.OP -
.10 -
.20 -
.50 •
.« •
1.25 •
7.00
5.00 •
10.00 •
20.00 •
50.00
100.00
oe
Figure 2-55
Component-Specific Uncertainty; Ratios of RRDs for
Analysis
-------
Figure 2-56
.00 -
.01 •
.02 -
.05 •
.10 •
.20 •
.50 •
.80 •
1.25
2.00
5.00
10.00
20.00
50.00
100.00
Component-Specific Uncertointy; Ratios of
RRDs for Analysis <*7 (Average Over All
Species) to RRDs for Analysis 30
vc
ABACABBAWBZC8CDCHCTOBEOESISLEI1.HJHAKTPCPHSCTCTDTE
AFALASCOCSDEDLEDRJHCICTO
OS HV
HC RS
EC
m
MM
Bill II III
.10 —
.50 —
1 9^
2.00 —
5M»
WM
20.00 — •
50.00 —
100.00 —
cs
is vc
AB AC
AF N.
05 PC
NC
E5
AS
Figure 2-57
Component-Specific Uncertainty; Ratios of
RRDs for Analysis <»8 (Average Over Rats and Mice)
to RRDs for Analysis 30
AFALCOCTDEOlEDFOHCieiBTCTOTO
2-106
-------
Figure 2-58
.01 —
.10 —
.20 —
.10 —
1.25 —
2.00 —
5.00 —
«M M>
20.00 —
50.00 —
100. M —
aa __
CS OS *
vc
AB AC AL BN SZ
ED
CT
OS CO ES HY TO
AS
Component-Specific Uncertainty; Ratios of RRDfc for
Analysis 49 (Rat Data Only) to RRDs for Analysis 30
ABACM-eNSZCDCROeaEOLECEOFOHCISLEICMNCMTrCPHRSSCTClDTET?
Figure 2-59
Component-Specific Uncertainty; Ratios of RRDs for
Anal/sis 50 (Mouse Data Only) to RRDs for Analysis 30
.00 -
.01 -
.02 -
.35 -
.w -
.»-
.so -
.» •
1.25 -
2.00 •
5.00 •
10.00
20.00 •
M.OO
100.00
00
LE SC
IS M PC
NC
AFAHWCBCOCSCTDSEDHVNLIWKTrHTCTTTOrrvC
M. OE
NC ID
DL FO B
SC HC
a
2-107
-------
Section 3
DISCUSSION"
POSITIVE CORRELATION
The results presented in the previous section reveal that estimates of
risk-related doses from animal bioassay data are generally highly
correlated with the estimates derived directly from epidemiological
data. Of the thirty-eight initial analysis methods investigated, 35 hod
p-values less than 0.05, when the full sieve was applied, and with that
same sieve, 17 had p-volues of 0.0001 or smaller. Even with no sieve,
so that data from experiments of highly variable quality are included,
thirty-five analyses have p-values less than 0.05. Not only do most, of
the analyses yield correlation coefficients that are statistically
significantly positive, but the coefficients are large in on absolute
sense as well. Twenty-six of the analyses hove coefficients larger
than 0.7.
The strongly positive result of the correlation analysis was obtained
even though a number of uncertainties had to be accounted for. First,
the uncertainty of the human RRD estimates is explicitly incorporated
since the ranking that underlies the correlation analysis is based on
the lengths and positions of the intervals of RRD estimates derived from
the epidemiology. Those intervals reflect the uncertainty in the
exposure estimate* and statistical variability. Analysis of the
epidemiological data, including the exposure uncertainty derivation, was
conducted prior to the analysis of the animal data and, therefore,
without knowledge of its outcome. Moreover, since the criteria used to
determine the exposure uncertainty values were consistent across all
chemicals, the subjective aspect of their derivation should not affect
the correlations. That is, if the individual subfoctors corr3sponding
to sources of uncertainty in exposure estimation were to be altered, the
bounds on exposure estimates would change in a predictable and largely
consistent manner for all chemicals. The relative rankings of the
chemicals should be minimally affected. This is one advantage of using
3-1
-------
a nonparametric (rank-based) approach in the correlation analysis.
The second uncertainty accounted for in the correlation analysis
pertains to the bioassay data. The intervals defined for the animal
results also incorporate statistical variability; statistical lower
bound and upper bound estimates define the endpoints of the intervals.
In addition, the entire ensemble of data for a given chemical is
considered in the sense that that ensemble defines the median lower
bound and the median upper bound. So, while discounting extreme values,
the intervals defined take into consideration the RRD estimates that can
be obtained from each experiment in the data base.
These various uncertainties and the methods used to account for them
will tend to wash out any real correlations that may exist, in the sense
of producing small correlation coefficients that may not be
significantly different from zero (no correlation). Despite this,
strong correlations ore obtained. The positive correlations exist for
chemicals whose RRDs (and, therefore, potencies) span several orders of
magnitude. Indeed, the strong correlations obtained despite these
factors make it highly unlikely that the positive results are due to
chance or to othar factors not incorporated in the analysis.
The fact that these positive correlations exist is very important. The
assumption that risk estimates derived from bioassay data are relevant
to the estimation of human risk is crucial to all risk assessments for
which epidemiologicol data is limited. Heretofore, it has been a
largely untested assumption. The correlations determined in this
investigation strongly support that assumption and thereby strengthen th«
scientific suppprt for quantitative risk assessment.
The thirty-eight initial analysis methods represent a wide variety of
approaches to bioassay-based risk assessment. Although a few of them
appear to be less-well correlated with the epidemiological assessment
results, the fact that most are highly correlated makes it reasonable
to attempt to determine which methods ore best when point estimates of
risk ore desired. The variety of methods ensures that a variety of
point estimates will be available to discriminate between different
predictors and different acceptable analysis approaches. This is the
3-2
-------
subject of the prediction analysis, the interpretation of which will
follow a discussion of data quality and the data screenings.
DATA QUALITY AND DATA SCREENING
As discussed in the second volume of this report, the extent and quality
of the bioassay data varies greatly from chemical to chemical. Some
chemicals have few acceptable experiments (e.g., estrogen has two),
some have experiments testing only one species (e.g., chlorambucil with
mouse data only), and some only have experiments of short duration or
dosing (e.g., benzidine and chromium). Still other limitations exist
that affect the calculation of RROs, such as the number of animals on
test (which can greatly affect computation of the statistical confidence
limits) as well as the actual conduct of the experiment (animal
husbandry and care, adherence to protocol, etc., which we have not used
to rate experiments) and, most importantly, data reporting limitations.
Aside from reports like those produced by the National Toxicology
Program, rarely were full details of the bioassay results available.
Even though correlation coefficients were large and significant for many
of the unscreened (no sieve) analyses, as mentioned above, it was felt
that some attempt should be mode to use the "best" data that was
available. On the other hand, it would not be appropriate to eliminate
chemicals from the analyses on the basis of 'quality" consideration*.
First, the maximum number of chemicals is 23, so that elimination of
chemicals could lead to very small sample size. This is seen, for
instance, when very restrictive criteria on carcinogenic endpoint and/or
experimental protocol define an analysis method (e.g., Analysis 19 with
only nine chemicals) or when the doto requirements ore not satisfied by
the published bioossoy results available to us (e.g., Analysis 6 with
only six chemicals). Second, in any future risk assessment on a
particular chemical, the data will undoubtedly be limited in certain
respects. Port of our task is to try to determine how best to proceed
even with those limitations.
Consequently, the data screening (sieve) selects the better data
("better" being defined solely on the basis of the definition of the
3-3
-------
sieves) for use in the calculation of RRO estimates. In the present
investigation, two screenings have been defined: a screening based on
the significance of the dose-dependency of the carcinogenic responses
and a screening based on the number of dosed animals and length of
observation. The use of these two screenings yields three possible
sieve approaches. Of course many reasonable alternatives, whether
based on these criteria or others, are possible. No examination of
other sieves has been undertaken.
The goal of screening the data is to produce a data base that will
perform better when compared to the epidemiological estimates. The
sieves defined here appear generally to achieve that goal. The
significance screen, in particular, worked to increase the correlation
coefficients for 25 of the 38 initial analyses. Although the quality
screen does not provide substantial improvement over the significance
screen in most cases, certain analyses are much better correlated when
both screens (the full sieve) is applied. Rarely does the addition of
the quality screen to the significance screen decrease the correlation.
Thus, we have selected the full sieve to represent the action of data
screening in the prediction and uncertainty analyses.
However, in the prediction analysis, it is frequently the case that the
average loss for an analysis method is greater when the full sieve is
applied than when no sieve is applied (cf. Tables 2-3 through 2-5 and
Table 2-13), especially when the median lower bound estimate is the
predictor. One might be tempted to conclude that only those methods
yielding smaller loss when the sieve is applied should be considered as
good risk assessment procedures. Conversely, one might conclude that
either the sieve is not working correctly to select the better data or
thut it is working but the data it selucts are not. in actuality, better
for risk assessment purposes. We argue that any of these conclusions is
unwarranted.
First, the results of the correlation analysis strongly indicate that
the better data are being selected by the sieve and that these data are,
in actuality, better for risk assessment purposes. This in in
accordance with common sense: if too few animals ore tested or if the
period of observation is too short, then it is difficult to elicit an
3-*
-------
observable (dose-related) carcinogenic response. Similarly, those
responses that or* significantly related to doting tell us more about
the carcinogenicity of a chemical than the endpoints that lock a
significant relationship with dose (unless all responsec lack a
significant relationship, but then the significance screen does not
eliminate any of the responses from consideration). Had the results of
the correlation analysis been less consistent in indicating the benefit
of the sieve, then one might have reason to suspect that the "common
sense* reaction is not supported and may be in error.
Secondly, we prefer the correlation analysis results ov«»r the prediction
analysis results as indicators of the action of the sieve since the
former does not select a single estimate from each analysis method and
it is not dependent on the specification of loss. The correlation
analysis utilizes a range of estimates consistent with the ensemble of
data available for each chemical and employs a general measure of the
degree of similarity between the animal and human estimates. This
framework is less sensitive to variations in the data and results that
are due to unintentional changes (confounders) in the data base. It is
entirely possible that application of the sieve may tend to eliminate
certain routes of exposure, for example, although such a result is not
the intended result of the sieve. Unless the elimination entails
substantial change in the RRO estimates (as in the cose of arsenic or
estrogen, as discussed in Section 2) the generalized ranking scheme is
not unduly affect.d.
Indeed, we feel that such confounding changes in the data base and
random variation may largely explain the occurrence of overage losses
that are greater when thn sieve is applied than when it is not. For any
experiment, random factors affect the response rotes and, consequently,
the estimation of RRDs. For oil the bioassays of a particular chemical.
then, the changes seen when a sieve is applied depend on these random
variations. [Again, this is one reason for preferring the correlation
analysis over the prediction analysis as a test of the sieve: the
correlation analysis accounts for the random variation by using upper
and lower confidence limits instead of a single point.]
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At a consequence of this observation, it is appropriate to compare the
analysis methods in the prediction analysis both with and without the
sieve. An analysis that yie? s smell average loss under either of these
conditions should bs considered a -'table option in the sense o'
determining the best risk assessment procedures. Thus. for example.
Analysis 20 without the sieve is the best approach, as measured by the
TANH loss function, whei\ LJQ i» the predictor (cf. Table 2-7). Average
loss for that analysis is increased when the sieve is applied so that,
even among the analyses employing the sieve. Analysis 20 is no longer
the best. We wish to continue to consider Analysis 20 as a good
potential procedure since it is not Known whether the increaso in
average loss may be due to random variation or to data base changes
confounded with the application of the sieve, though we suspect that it
is. This procedire is followed throughout this discussion; those
analyses cited as being good are those with small average losses for at
least one of the pair (with sieve and without sieve). However, in the
suggested guidelines for presenting risk estimates, and in the examples
provided, screening of the data is always performed, no matter which
analysis method is applied.
APPLICATION OF ANALYSIS RESULTS IN EXTRAPOLATING FROM ANIMALS TO HUMANS
Heretofore, anjmol-to-human extrapolation has generally been conducted
by assuming that equal doses will produce the some lifetime risks in
animals and humans, when both animal and human doses are measi red in the
some particular units. Dose units that have been applied in the past
include mg/kg body weight/day, mg/m? surface area/day, ppm in diet or
air, and mg/kg body weight/lifetime. Because of differences between
animals and humans in body weights, life spans, etc.. use of different
units produce different estimates of human risk. There is limited
scientific support for use of any particular dose units (1.). Results
from the present study can be used empirically to determine appropriate
methods for animal-to-human extrapolation. Specifically, multiplication
of the animal RRO by the 10C. where c is the y-intercept from the best-
fitting line, provides an estimate of the human PRO in which the bias
due to systematic differences in unimal and human risk estimates found
in this study has been eliminated. With this approach, the dose units
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con be selected on the bo»is of those thot, olong with other focets of
on analysis, produced the best correlation* between animals and humans
(or smallest losses). The bios correction factor 10C corrects for any
overestimotion or underestimation by the analysis mevhod used.
IDENTIFICATION OF GOOD METHODS
Predictors
Each analysis method was run vIth the four predictors examined in
this investigation, the medlar, and the minimum of the lower bound RRDs
and of the maximum-likelihood RRDs. Three loss functions were defined
that determine the lines of unit slope that minimize the total loss for
the collection of chemicals being analyzed. Despite the fact that the
three loss functions calculate loss in different ways, all three are
consistent in indicating that the median lower bound RRD predictor, L.2Q.
yields the smallest average losses for most analysis methods. It should
be emphasized that this is a strong result not only because of the
consistency of the loss functions but primarily because it is not
dependent on the particular data that were available for analysis. For
any given analysis (with rare exceptions) the lots when L;Q is used is
smaller than losses with other predictors even though the very same data
are used to calculate the estimates and, hence, the losses for each
predictor.
It is important to note that the predictor, LjQ- which *• derived from
lower bound RRDs, yielded smaller losses than any of the predictors
based on maximum likelihood estimated RRDs. This is probably related to
the fact that small changes in the bioassay data can result in sizable
changes in MLE estimates of RROs, which suggests that the desirable
large-sample theoretical statistical properties possessed by MLE
estimates (such as consistency and asymptotic efficiency) are not
operative to any practical extent in this situation given the usual
sample sizes encountered in bioassays. This lack of stability of the
MLE estimates is a much more severe problem when extrapolating to low
doses Regulatory agencies hove in the past relied more on lower bound
RRDs vhan maximum likelihood estimates, mainly in the interest of being
protective of human health. This study shows that lower bound RRDs are,
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in fact, better predictors of the human data than are the MLE estimates,
and thus provides additional rationale f«y •mphasizing lower bound RRDs
in risk assessment. This study olso estimates the level of conservatism
(or anti-conservatism) that may be inherent in specific analyses that
use lower bound RRDs end estimates compensating or bias-removing
factor*, i.e. the conversion factors (10C). Thi» issue will be
discussed further later.
One potential problem with use of lower bound RRO» is that they are
always finite, ever when the data show no evidence of corcinogenicity
(consistent with infinite maximum likelihood RROs). To some this might
imply that use of lower bound RROs will lead a regulatory agency to
treat every chemical os a carcinogen, irrespective of bioassay results.
This need not be the cose. For most purposes, there must be reasonably
convincing evidence of carcinogenicity from bioassay results before an
agency will undertake the assessment of risk. Moreover, the problem may
be further mitigated if we recall that the correlation analysis
demonstrated the strong positive correlation between ranges of human and
ranges of animal RRDs. This result does not depend on tno position of
the best epidemiological or bioassay estimates, only on the bounds for
estimates. Consequently, we know that those chemicals that tend to have
larger RRD estimates (lower bounds) from epidemiological analyses also
tend to have larger bioassay-based estimates (lower bounds) so that
chemicals with large 1-20'* (in ° relative sense, compared to other
chemicals) ore those that may be of less concern when it comes to
regulation and/or control. One corollary of thi . line of reasoning is
that the degree of correlation, in addition to the average losses
calculated for specific predictors, is an important factor in comparing
the analysis methods and deciding which are better.
At any rate, there will always be the possibility that a noncarcinogen
may be regulated as a carcinogen on the Do»is of false-positive data.
Use of PILES would not remove this problem; MLE RROs from bioassoys of
noncorcinogans wpl be finite about 500 of the time. In this regard, it.
is of interest to note that in this study chemicals with infinite RRO
astimates based on the epidemiological analyses did not in general have
infinite maximum likelihood PRO estimates based on the animal data.
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However, this was to some extent prearranged because for a chemical to
be included in the analysis, positive evidence of corcinogenicity
(implying finite RRDs) hod to exist for either animals or humans.
Use of 1-20 °* the predictor is in a *ens« less conservative than us.e of
the minimum lower bound, L^. The y-intercepts for the analyses ans
almost always larger when LM is used in place of LJQ (compare Tables
7-12 and 2-13). This means that L^ is more conservative, in fact,
generally overconservative. Of course, if one applies the conversion
factors suggested by the y-intercepts, then no approach is more or less
conservative than another; estimates obtained by using the conversion
factors are those that come closes, to the epidemiologica.1. estimates.
In this sense, thv remaining error, expressed as average loss, is the
primary determinant of good or bad analyses or predictors. As
previously mentioned, LJQ i* preferable to LM in this regard. But it is
also the case that the conversion factors are less extreme with L^Q than
with LM.
Analysis Methods
Given the superiority of Lpo over the other predictors examined,
one can compare the analysis methods on the basis of how the/ perform
with l-2o- This has been done for each loss function separately (cf.
Table 2-7) and for the three functions combined (Table 2-8) for the
initial 38 analyses. The supplemental analyses (Table 2-16) si-ould also
be considered, especially since their template is Analysis 3b which is a
metnod producing excellent correlation and which is also identified as
resulting in small average loss.
Analyses 6, 18, and 19, which are applicable to limited numbers of
chemicals (six, ten, and nine, respectively), will not tie examined in
detail. Although both the correlation and prediction analyses suggest
that these methods may be beneficial, the data are not sufficient to
warrant detailed examination of these method*-. In order to use the
methods routinely, data availability would have to be improved. To
perform Ar.jlysis 6, one must have available the numoor of animals alive
in each dose group at the time of first occurrence of each tumor type.
For Analyses 18 and 19 (as well as ony other method that uses on
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endpoint that is a combination of individual carcinogen!: responses) one
must know which animals got which tumors in order to can.oir.s responses.
Detailed reporting procedures like these in many National Toxicology
Program reports are ideally suited for thes« purposes. Bioassoy results
published in peer-reviewed journals rarely contain such detail.
Nevertheless, torn* other means must be found to disseminate the full
results before analyses like 6. 18 or 19 can be more thoroughly
investigated. The incomplete bvt suggestive results of Analyses 6, 18,
and 19 indicate that this may be worthwhile.
Comparing the results in Table 2-16 to those i«* Table 2-7 reveals that
several analysis methods from the supplemental list are as good as or
better than the best of tie initial analyses. With the DISTANCE2 loss
function. Analyses 30, <»5, and k7 yield the smallest losses of any
analyses. Similarly, Analysis <»3 results in the smallest loss as
measured by the TANH lo&s function; Analy.es <»5 and
-------
<»3, 45, and ols is the single endpoint evaluated in the former
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cose. Similarly. Analyses 45 and 47 differ from Analysis 30 because
some averaging of RRDs does take place; for Analysis 45, estimates are
averaged over bioassay identical except for the sex of the test specie?
(i.e. over sex within study) and for Analysis 47. results obtained for
each species are averaged to yield the ultimate RRO estimates.
The Base Analysis (Analysis 0) employing the minimal lower bound
estimator, LM (second row of Table 3-1} has both the largest normalized
loss and the largest residual error. Moreover, RRDs derived from this
analysis underestimate the human PRDs on average by a factor of 12. By
all standards, this method is the poorest of those listed. However,
this method is perhaps most like that presently employed by EPA.
Modification of this i.iethod by using the median lower bound estimator,
LJQ. rather than l^, as represented in the first row of Table 3-1,
provides an improvement in terms of normalized loss, residual error, and
requiring a smaller conversion factor. These results illustrate further
the finding discussed earlier that analysis methods thot use median
lower bound RRDs as estimators provide smaller lov-.cs than use of
minimum estimates.
Although Analyse* 0, 7, 11c, and 11d were associated with generally good
correlation values, their normalized loss values do not compare with the
best of the remaining methods (e.g. Analyses 43, 45, and 47). Moreover,
the residual uncertainty factors associated with these analyses are
among the largest presented. Analyses 0. 7. 11d, and 11d therefore are
iiot considered to be among the better methods for predicting human risk
on the basis of bioassay results.
The case is somewhat more complex for Analyses 17 and 20. As previously
mentioned. Analysis 17 is the best method determined by the CAUCHY loss
function. In part because of that result, the total incremental
normalized loss for Analysis 17 is nearly the smallest. Nevertheless,
its correlation coefficient is also the smallest of thcte presented.
Even if one notes that Analysis 17 is applicable to only 11 chemicals
and that consequently the coefficient would be less stable, the
importance attached to the correlation results when using the L2Q
predictor (as described above) tends to make the use of method 17 less
desirable than use of the other methods. In addition, the residual
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uncertainty factor is relatively large, in the range of those associated
with Analyses 0, 7, lie, and 11d.
Analysis 20 also has a large uncertainty factor. That fact, plus the
large incremental loss value, makes Analysis 20 less appealing than the
remaining five analyses, 30, 31, 43, 45, and 47. Note also that
Analysis 43 is the only other method in Table 3-1 that uses the endpoint
used by Analysis 20, total tumor-Searing animals. Analysis 43 is
superior in all respects to Analysis 20. This is one other reason why
Analysis 20 should not be considered among the better methods for
extrapolating human risk.
There is another reason not to recommend Analyses 17 and 20 for use in
extrapolating between humans and animals. Aside from Analyses 0, 7,
11c, and 11d. which have already been deemed inappropriate, only
Analyses 17 and 20 are restricted to specific routes of exposure. It is
likely, given the pattern seen for other analysis methods, that methods
identical to 17 and 20 but without this restriction on route would do
even better. Th.s would seem to be the case because the supplemental
analyses generally yield smaller losses than those analyses in the
initial set that differ only with respect to allowable routes of
exposure and units of extrapolation, the latter having little effect on
average loss.
Analysis 20 and the other method using total tumor-bearing animals as
the endpoint. Analysis 43, are the only two that overestimate RRDs on
average. On the other hand, Analysis 31, a method extrapolating risk on
the basis of mg/m^/doy. underestimates RRDs by roughly an order of
magnitude. Analyses should not be compared on the basis of these
conversion factor*, however. When the estimates from any analysis
method are multiplied by the indicated conversion factors, a line fit to
the converted estimates (on the x-axis) and th« epidemiological results
(on the y-axis) would pass through the origin. The conversion factor
represents a degree r' freedom in the prediction analysis corresponding
to the estimation of the intercept. A conversion factor estimated here
for any method can be used to adjust the results obtained for a
particular risk assessment on a single chemical when the bioossay data
is analyzed by that method.
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One might be tempted to conclude that Analysis 45. which extrapolates
from animals to humans on a mg/kg/day basis, accepts all routes of
exposure, and averages results over pairs of experiments that differ
only with respect to the sex of the test aninvjls (i.e. the experi-
menters, protocol, and strain of the test animal are the same), is the
best of the analyse* presented in Table 3-1. Its correlation
coefficient is as good as any other, its incremental loss is smallest,
and its residual uncertainty factor is smallest (Figure 3-1). While
this analysis is certainly a good one by all these criteria, it is not
possible to conclude unequivocally that Analysis 45 is better than some
of the others listed. For one thing, the ranking of analyses differs
depending en vhe choice of loss function. Analysis 45 is best with the
DISTANCE2 loss function, Analysis 17 is best with CAUCHY and Analysis 43
with TANH. A minimax criteria would select Analysis 17. followed by
Analysis 43. Moreover, it is not clear which of the loss functions is
most appropriate for determining fits of RROs and no statistical
development that would allow us to test for lack of fit or to test
differences in values of average (or total) loss is available. Far
these reasons, the loss functions have been used in this investigation
as a method of ranking the analyses. Since no one loss function is
obviously more appropriate, an ove-oll measure such as total incremental
normalized loss has been employed to find analyses that are fairly
robust with respect to calculation of loss. The analyses in Table 3-1
remaining after elimination from consideration of Analysert 0, 7, lie,
11d, 17. and 20 (i.e. Analyses 30, 31, 43, 45, and *7) dr/monstrcte such
robustness.
Let us call these five analyses the set of recommended analyses. RRD
estimates derived using tliese analyses for each o' the chemicals
included in this investigation but lacking epidomiologicol data
sufficient for quantitative assessment are presented in Table 3-?. The
values in Table 3-2 have not been adjustej by the conversion factors.
When this is done ».he range of RRD estimates for each chemical appears
as in Table 3-3.
One final comment will conclude this discussion of recommended analysis
methods. Four of the five members of the recommended set make no
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restrictions on the carcinogenic endpoints considered, and data are
generally available for conducting these analyses. Analysis *»3 utilizes
total tumor-bearing animals as an endpoint. While, in theory, this
should pose no restrictions on the analysis of bioassay data, in
practice these endpoints often cannot be defined. Availability of
needed data is an important consideration when assessing human risk and
expressing the results as a range of RRDs consistent with the data but
quantitatively incorporating uncertainties.
COMPONENT-SPECIFIC UNCERTAINTY
The discussion to this point has not considered uncertainty associated
with any specific components of the risk assessment process. Rather, we
have emphasized the analysis methods as wholes and examined the
uncertainty remaining after the predictions have been obtained and
compared to the human RRDs (residual uncertainty). This course has been
followed because of the apparent interaction of the components. This
interaction takes two forms. First, certain components are not mutually
independent. A component that defines approaches to length of dosing
obviously also influences choices concerning length of observation; a
study cannot dose animals for 80 weeks without also observing the
animals for at least 80 weeks. Moreover, as discussed r>bove, altering
the approach to some components can also, unintentionally, affect the
make-up of the underlying base of data and, hence, changes attributed to
changing those components may be confounded by changes that may be
partially explicable by changes in other components. If, for example,
limiting experiments to those that last at least 90 percent of the
standard length also, unintentionally, excludes routet of exposure
besides inhalation, oral, or gavoge, then the change :.n RRDs attributed
to changing requirements on the length of observation is confounded by
changes due to restricting routes of exposure.
It is also the case that a component-specific investigation is not
sufficient to characterize the best approaches becauue of the second
type of interaction, the empirical interaction of th» components on the
results. Consider, for example, the components relating to choice of
dose units (specifically, the approaches specifying use of mg/m^/day and
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mg/kg/lifetime) and allowable routes of exposure (unrestricted v*rsu«
restriction to an oral rout*, gavage, inhalation, or the rout* that
human* encounter). These two components are not inherently
interrelated. Nevertheless, the effect on the RRD estimates and on the
estimation of loss (i.e. the adequacy of the predictions) resulting from
selection of approaches to the indicated components is not readily
attributable to one component or the other. Note that, when LJQ is the
predictor. Analysis 0 (mg/m2/doy, restricted routes) yields average loss
of 0.298 as measured by the DISTANCE2 function (sieve applied). If the
units are changed (Analysis <»d: mg/kg/lifetime, restricted routes) or if
the allowable routes are augmented (Analysis 31: mg/m^/day, unrestricted
routes) the loss decreases, to 0.267 or 0.113, respectively. When both
components are changed, howeve- (Analysis 34: mg/kg/lifetime,
unrestricted routes), the decrease is intermediate between the two;
average loss in that case is 0.131. Hence, the two components do rot
act independently on the estimates for some or all of the chemicals. In
this sense, it is pointless to debate whether mg/m^/day is an
appropriate dose measure for animal-to-human extrapolation without
taking into consideration the approaches taken for other components.
Evaluation of risk assessment methods should focus on the complete
process rather than on individual components.
Consequently, one must be cautious in interpreting results of component-
specific changes in analysis methods and should not evaluate analysis
methods solely on the basis of component-specific changes. Neverthe-
less, such an examination may be useful in determining sources of
uncertainty in risk assessment and in suggesting means of improving risk
estimation through additional research or data acquisition. The results
of our component-specific ur.certainty investigation may also be useful
for presenting a range of human risk estimates and so can be
incorporated into the guidelines for determining that range.
The components can be divided into two sets. First ore those that
do not change the data base underlying the assessment. Included in this
group ore the components dictating the dose units used for extrapolation
and those specifying the manner in which results ore averaged. Such
components are not susceptible to confounding due to unintentional
changes in the data base. These are the components that show very
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consistent changes when approaches to them ore altered (cf. Table 2-23).
The components relctad to averaging results have relatively little
effect on the RRO estimates; the modes are in the interval 0.8 to 1.25
and the dispersion factors are between 1.2 and 2.2. Interestingly, two
of the analyses included in the recommended set (45 and 47) differ from
the standard. Analysis 30 (also in the recommended set), only in the
way they average results. It appears that Analysis 30 is a satisfactory
method of bioassay analysis and RRD prediction; the analyses that ciffer
from it only in the approach to a component that produces consistent
changes in RRDs also tend to be satisfactory. Changing dose units also
produces consistent changes in RRD estimates (dispersion factors between
1.3 and 2.3) although the modes of the distributions are shifted, often
substantially. Again, the analyses that differ from 30 only with
respect to dose units yield relatively good prediction; Analysis 31 is
included in the recommended set.
The second category of components includes those that change the data
base on which a risk assessment is based. These display the least
amount of consistency with respect to RRO changes and so are the most
uncertain aspects of quantitative risk assessment. This conclusion is
not diminished by the fact that these components are subject to
confounding due to unintentional data changes. In any assessment of a
particular chemical, which may have more limited data than many of the
chemicals in our data base, such confounding remains a potential
problem.
With one exception (Analysis 43), the analyses that incorporate
alternative approaches to these components are -elotively poor methods
of human risk prediction; the predictive power ind good correlation
noted for Analysis 30 are diminished by altering one component. It
seems likely that the high degree of chemical-specific change (lack of
consistency) is responsible. That is not to soy that some degree of
chemical-specificity is not desired. One would li'
-------
large dispersion factor, 39.6, associated with the change in choice of
endpoint.
A corollary of these observations is that these highly uncertain
components — related to length of observation and dosing, route of
exposure, carcinogenic responses to use, and species to use — deserve
much more investigation (certainly more than choice of dose units for
extrapolation). The goals of such an investigation include elucidation
of the reasons behind the observed changes in RROs and identification of
new approaches x!*nt would produce the desired changes in RRDs, that is,
ones that improve the predictiveness of the bioassay analyses.
Potentially useful studies of the high degree of chemical-specific
changes may start with identification of groups of chemicals (e.g.
aromatic hydrocarbons, epigenetic carcinogens, early-stage carcinogens,
etc.) and examination of patterns within the groups. Tor some
components, notably the one associated with choice of species, other
considerations, such as pharmocokinetic or genetic differences, may need
to be e; ominsd. The empirical approach adopted for the present
investigation may not be sufficient to explicate oil of the changes
seen. But ooove all else, availability of good data sets presenting
information sufficient for studying these components with a minimum of
con'ounding is essential.
OPTIONS FOR PRESENTING A RANGE OF RISK ESTIMATES
In this section we discuss three options for presenting a range of risk
estimates suggested by the data. These options are derived from the
five recommended analyses discussed in the previous section. Option 1
requires selection of a single analysis method from among the five,
while Options 2 and 3 involve combining results from more than one
analysis.
Regardless of the option selected, it seems reasonable to screen the
data that ore going to be used. The correlation analysis indicates that
data screening improves the correlations in general. Consequently, a
process akin to the sieve that has been defined here, one that selects
the best of the available bioatsays. is recommended. In applications to
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a single chemical, a less automated, more customized procedure could be
applied. On the other hand, if a consistent and uniform approach is
desired for many chemicals, some automated sieve may be preferable.
Option 1
This option involve* selecting one froa> among the five analyses
discussed in the previous section. The selected analysis method is
applied to each of the eligible data sett. th>> median of the resulting
lower bound estimates is used as the predictor, and the conversion
factor, 10C (cf. Table 3-1), is applied to the predictor to correct for
bias. The resulting estimate is multiplied and divided by the residue!
uncertainty factor (cf. Table 3-1) and the resulting range of RRDs is
the ciesired range. Analysis-specific results are shovn in Table 3-4 for
the twenty-one chemicals in the data base for which human data are not
available. Any one of the five intervals displayed for each chemical
can be used to represent the range of risk estimates. Note that for
several chemicals, it was not possible to apply Analysis 43.
Options 2 and 5
For these options, all five analyses must be performed, using the
appropriate endpoints and dose units for extrapolation. For each
analysis, select as the predictor the median of the lower bounds
resulting from the analysis and apply the corresponding conversion
factors. The values obtained in this manner represent the results of
the methods of bioassay analysis that appear to ".e most appropriate for
estimating human risk and form the basis for determining the range of
those human estimates consistent with the data.
It is always possible to determine estimates via Analyses 30, 31, 45,
and 47. It may, nowever, be the case that Analysis 43 cannot be
completed given the data available (cf. Table 3-2 in which several
chemicals lack estimates associated with this analysis). When this
occurs, additional uncertainty is associated with the risk estimates-
the full characterization of the range of estimates consistent with tlie
recommended analyses is not possible. To account for this, on? may wish
to impute values for the missing estimates. The component-specific
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uncertainty analysis, with its dispersion factor, provides the means to
do so.
Analysis 43 is a single-component variant of Analysis 30. The histogram
associated with this variation (Figure 2-52) indicates the mode lies
between 0.8 and 1.25 (the geometric mean of the*-', values being 1.0).
Th9 RROs for Analysis <»3 are imputed by taking the RRDs from Analysis 30
and multiplying them by a factor indicating the average ratio of the RRO
pairs. We have used the geometric moan of the interval wttich contains
the mode, i.e. 1.0. (Another reasonable factor could be based on the
median ratio.) In doing this, the uncertainty is increased (reflecting
the uncertainty due to lack of the complete ensemble of results) which
is estimated by the dispersion factor. The imputed Analysis *3 results
are multiplied and divided by the dispersion factor (39.6) since that
factor is the average amount by which the ratios differ from the mode.
The imputation of predictions for Analysis 43 is completed by applying
the conversion factors for Analysis 43 just as if the estimate* were not
imputed.
At this stage, the assessment (i.e. prediction) of risk is completed.
One has derived the best predictions of human RROs that are possible
from the data available: for an analysis that could be performed, a
short interval (derived from the range of conversion factors pertinent
to that method) of predictions is available, whwreos for an analysis
whose results have had to be imputed a generally much wider interval of
predictions is the best that can be obtained. However, because of the
variability characterized by the residual uncertainty factor, these
intervals are not sufficient indicators of the range of risk estimates
consistent with the data. The converted predictions must be multiplied
and divided by the residual uncertainty factors to derive upper and
lower uncertainty bounds for the risk estimates from each analysis
method.
Since the recommended set of analyses contains methods that are good
with respect to prediction of human risk, the ranges of estimates
associated with those analyses characterize the human RROs for the
chemical in question. The ranges extending from the lower to the upper
uncertainty bounds for each individual method con be considered as self-
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contained results (this is Option 1) or they may be considered as a
whole to present overall ranges of risks. Two lines of reasoning
dictJte how this might be accomplished. First (Option 2). one may
reason as follows: to be most certain of including the true RRD in the
overall range, one must consider each analysis (since the best one for
any given chemical is not known) and characterize the range of estimates
by the interval from the smallest lower bound to the largest upper bound
(the "full range"). On the other hand (Option 3). one might argue that
any of these methods is adequate and that the range of human estimates
is suitably represented by the estimates from the method(s) that are
most consistent with the entire ensemble of results. In this context,
consistency can only be determined modulo the degree of uncertainty.
[This is analogous to a statistical argument concerning the difference
between point estimates, for example, which can only be resolved to the
extent that the statistical variability allows.] Consequently, the
Option 3 characterization of the range of risk estimates is defined as
the union of the intervals from the lower to the upper bounds associated
with some subset of the analyses such that the union contains the
predictions from all the analyses (i.e. the values, like those in Table
3-3, that have been adjusted by tho conversion factors but have not had
the reeidual uncertainty factors applied) and is the smallest union
satisfying that condition. This is a reasonable representation of the
range of estimates consistent with the results from all recommended
analyses, given our present degree of uncertainty. Wo will call it the
smallest consistent range.
Comparison of Options
All three options present*d define ranges of estimates by utilizing one
or more of the methods that hove been shown empirically in this
investigation to do well with respect to prediction of human risk.
Moreover, they all incorporate quantitatively those aspects of
uncertainty that are summarized by the re*idual uncertainty factor.
Several of the advantages and disadvantages of the options are discussed
below.
Option \ requires analysis of the bioaisay data by a single method only.
The selection of the single method may be somewhat problematical,
3-21
-------
however. It hos been orgued that the ability of the analyse* in the
recommended set to predict human risk is not clearly distinguishable by
the empirical approach adopted for the present investigation. Neverthe-
less, other factors, based on toxicological consideration* for example,
may dictate the choice of one of the analyses methods. In that case,
there is no question about the method that should underlie Option 1.
It is hard to conceive of other factors that could clearly dictate the
choice of a single analysis method, however. Aside from Analysis 43,
all the analyses in the recommended set use exactly the same experiments
and carcinogenic responses to estimate risk. If Analysis <*3 is deemed
inappropriate because it uses total tumor-bearing animals, for instance,
cne is left with four other methods one of which must, a priori, supply
the range of risk estimates, if or.e follows the procedure of Option 1.
A priori selection of a method may suit regulatory purposes very well.
Options 2 and 3, however, consider the intervals of estimates derived
from all of the methods. No a priori, decision is made about the
particular method to use. Rather, the results of all the methods are
examined for consistency and the summary i jnge of estimates reflects
that consistency as well os the analysis-specific uncertainty. (In this
sense, these options reflect ocross-method uncertainty in addition to
within-metnod uncertainties.) Greater consistency across analysis
methods yields smaller ranges. Of Course, the overall range is no
smaller than the smallest range associated with any given method (which,
given the conversion arid residual uncertainty factors, must be from
Analysis <»5); an overall range can reflect no more certainty than the
method with least uncertainty.
It may be the case tnat the full range estimated via Optior 2 over-
estimates uncertainty. It is true that inclusion of more analysis
methods in the preferred set can never diminish the Option 2 range. So,
for example, should further investigation reveal other analysis methods
worranting inclusion in the recommended set, their inclusion could not
shrink the range determined by Option 2 and the current s»t of analyses
Furthermore, no particular u*e is made of the analysts with least
residual uncertainty. If all analyse* predicted the some RPDs. the
method with the largest uncertainty factor, not the one with the
3-22
-------
smallest factor, determines the full range.
Option 3 doe* rot share these disadvantages with Option 2. Because the
third option selects the smallest range that is consistent with all tne
predictions, priority is given to the methods with least uncertainty.
Moreover, it it entirely possible that additional methods could reduce
the smallest consistent range, even if they hove larger uncertainty
factors, if the added methods "cover" more of th» original predictions.
In this manner, additional information of comparable quality (i.e. as
good in terms of predicting human risk) can refine our estimates of
human health effects.
At first glance, it appears that the necessity cf imputing values when
particular analyses cannot be performed is a major disadvartage of
Options 2 and 3. Indeed, the need to imputo adds greatly to the
uncertainty and may provi.de some justification for dropping from the
recommended set those analyses for which imputation may be required.
(Note that Options 2 and 3 are equally applicable no matter how many
analysis methods are considered.) It must be emphasized, however, that
the problem with imputation is not a methodological one, i.e. there is
nothing inherent ir Options 2 or 3 that makes them suff*.' from this
difficulty. (In fact. Option 1 would have the same difficulty if the
• ingle method selected by that option was *»3.) The i .creased
uncertainty that results from imputation is caused by inadequacies in
r.ata reporting or data dissemination. If complete results, especially
those allowing definition of the responses need, total tumor-bearing
oniirols or the combination uf significant responses, were available,
then no imputation would be required and uncertainty caused by lack of
data considerably reduced. The need to impute values is not a
legitimate criticism of Option 2 or Option 3.
In closing this comparison, it should be noted that the uncertainties
dis«.us»etf in connection with oil three of the options may not completely
characterize uncertainty. In particular, there is uncertainty about the
shape of the dose-recponte curve that is not quantitatively estimated.
Moreover, the residual uncertainty factors represent only that uort of
t*« ufcertaiitty thot is not explainahle by uncertainty in the human
estimates. The uncertainties not quantified fall outside tl.e definition
3-23
-------
of those that ore particularly associated with any given analysis
method, but they should be borne in mind when considering the ranges of
estimates of human risk derived from any option.
The chemicals included in this investigation but lacking epidemiological
data sufficient for quantitative risk assessment (Table 2-2} can serve
as examples of the application of the three options. Tables 3-2 through
3-<» present the median lower bound RRDs, the converted predictions, and
intervals of estimates derived by appiicatitn of the analysis-specific
residual uncertainty factors, respectively, that underlie the
application of these options. As mentioned earlier, any one column of
Table 3-<* represents the output from Option 1. Table 3-5 contains the
two overall ranges from Option* 2 and 3.
Several interesting features are illustrated by the ranges in Table 7-5.
First, as an example of the procedure for determining the smallest
consistent range (Option 3), consider ocrylonitrlie. The interval
(Table 3-%) associated with Analysis
-------
of those that art particularly associated with any given analysis
method, but they should be borne in mind when considering the ranges of
estimates of human risk derived from any option.
Examples
The chemicals included in this investigation but lacking epidemiological
data sufficient for quantitative risk assessment (Table 2-2) can serve
as examples of the application of the three options. Tables 3-2 through
5-
-------
involve* other features of the data a« well. In particular, note in
Table 3-2 that the median lower bound estimates from Analysis 43 are
generally smaller than those front the other analyses. Moreover, the
conversion factors for Analysis 43 are 0.18 and 0.29; i.e. the converted
values are even smaller than the raw values, whereas the factors for
other analyses in the restricted recommended set are greater than or
equal to one. (This also explains why, even when no imputation is
necessary. Analysis 43 uncertainty bounds always determine the lower end
of the smallest consistent range.) The difference in conversion factors
and the reason why they tend to separate the predictions of Analysis 43
from those of the other analyses can be explained by reference to Figure
2-52. This histogram depicts the chemical-specific ratios of RRD
estimates derived from Analysis 43 to those derived from Analysis 30.
The six chemicals whose ratios are greater than 1.25 are only from the
set that nav« epidemiological data suitable for estimating the
conversion factors. Given that the conversion factor for Analysis 30 it
roughly unity, these six chemicals, especially, have shifted the best
fitting line to the right, decreasing the y-intercept, and entailing
conversion factors substantially less thnn one. But, as already notod,
the chemicals represented in Tadle 3-2 generally have ratios in Fig-jre
2-52 that are less than 0.80. Hence the divergence of the RRD
predictions. The dichotomy displayed in Figure 2-52 between those
chemicals with suitable epidemiological data and those without is
undoubtedly fortuitous. Nevertheless, it does show that a dispersion
factor as large as 39.6 used in the context of the imputation of values
is necessary to cover such occurrences. It is important to note that
this added uncertainty is unnecessary: imputation is dictated solely by
data availability (having the ability to define the total tumor-bearing
animal response). Better data reporting procedures can substantially
reduce the ranges of risk estimates.
For purposes of comparison. Table 3-6 presents the ranges of estimates
..hot are obtained from Options 2 and 3 when Analysis 43 is not
considered. This eliminates the wide ranges produced as a results of
imputation. However, by simply ignoring a method of extropolot.ion that
ham been deemed to be of a value comparable to those of the other
rriethods in the recommended set, these ranges may be too narrow to the
extent tnat ocr-oss-method uncertainty is underestimated. Certainly, the
3-25
-------
range* presented in Table 3-5 ore to be preferred ovsr those in Table
3-6 wnen no imputation is necessary. When Analysis i»3 cannot be
performed and imputation is necessary, it is not clear which range is
more appropriate; those based on fewer analyses (Table 3-6) may be too
narrow while those hoseo ?•* an ad hoc imputation procedure may be too
wide. It bears repeating thav this dilemma csuld be avoided entirely if
some better meant of data dissemination were to be found.
At present, there are no quantitative estimates of RRDs derived from the
epidemiologicol literature to which these predictions can be compared.
It might be possible to qualitatively compare the predictions to the
epidemiology in a couple of ways. The predictions could be used to rank
the chemicals in order of their RRDs (reverse order of their
carcinogrnic potencies). Another ordering could be based on a
comparative examination of the epidemiology. The degree of
correspondence of the two orders might provide information about the
predictions. Of course, without quantitative estimates, the
epidemiologically based ordering would be subject to considerable
uncertainty in and of itself. A chemical-specific examination of the
epidemiology might be useful in uncovering predictions that are way off
the mark. Such a comparison would probably be quite crude and may be
limited to identifying those chemicals for which the predictions (being
finite) indicate carcinogenicity but v.he epidemiology indicates no
carcinogenicity. Neither type of comparison has been undertaken for
this project.
GENERAL CONSIDERATIONS AND MAJOR CONCLUSIONS
It is apparent that the animal data base and the methods used in this
study provide a useful basis for evaluating quantitative risk
assessment. Their use in the present context has demonstrated the
relevance of animul carcinogenicity experiment..- to human risk
estimation. Moreover, it has been possible to identify methods of
analysis of the bioassay data, including the choice of the median lower
bound predictor, that satisfactorily predict risk-related doses in
humans. Application of these methods has led to suggested guidelines
concerning the prediction of human risks and the presentation of ranges
3-20
-------
of estimates incorporating the relevant uncertainties.
Certain features of this investigation must be borne in mind. Primary
among these is the fact that the level of risk for which RRDs have tien
determined is 0.25. This value is a compromise between the need to use
a value high enough to be fairly independent of the choice of dose-
response model in the bioassay analyses and the desire not to greatly
exceed the risk found in most epidemiologically studied cohorts. A risk
level of 0.25 is higher than that which exists in most human exposure
situations. While we would not expect some of the results to be altered
if the investigation had utilized a different risk level (e.g. 10~6), it
is not certain that all the conclusions would remain the same. In
particular, the evaluation of uncertainty in this report does not encom-
pass that related to the shape of the dose-response curve. It may be
worthwhile to check some of the results at lower levels of risk,
although it mus. be noted that the increased uncertainty associated with
the shape of the dose-response curve at low doses may moke interpreta-
tion of results concerning other components of risk assessment
difficult.
Also recall that the bioassay data, though extensive, is rather crude in
many respect*. We hove already noted the problems associated with data
deficiencies, mostly caused by incomplete reporting of results. Over
and above that, however, the analyses performed did not use time-to-
tumor data, i.e. a quantal model has been used to estimate RRDs. Time
and data constraints dictated that choice, but it is of interest to
determine if time-to-tumor analyses, which utilize more of the
information obtained from o bioassay, could refine our results and
conclusions.
It must be recoiled that when several forms of a suspected carcinogen
have been tested in animal bioassays, the results for all forms have
been grouped together. This primarily influences the data and resjlts
for the metals. Since all forms are individually identified, it is
possible to perform the analyses on each form separately. Of course,
the number of experiments for the affected chemicals would be reduced
Moreover, it is often not known, even for substantiated human carcino-
gens, which particular moieties cause cancer or which are most potent.
3-27
-------
Other reasonable approaches to the components of risk assessment could
have been defined. Thus, for example, the component related to length
of dosing did not have to include only two approaches, one including all
experiments and the other including only those experiments lasting at
least 90 percent of the standard length. Short experiments by
themselves could have been studied. This may have led to an examination
of thfc correction factor that has been used to adjust for short
observation periods.
As discussed in Volume 1 of this report, the epidemiological data used
in this study are jf variable quality. The bounds determining ranges of
exposure are somewhat arbitrary and, for each chemical, one cancer
endpoint from a single study was selected to reprecent the range of RRD
estimates and to be the target of the bioas«ay analyses. It would be
interest to determine how robust our findings are with respect to these
choices. Moreover, the pattern of exposure for which RROs hove been
estimated ("»5 years of constant exposure storting at age 20) is not
realistic for some of the study chemicals (suc.fi as DCS ' • estrogen).
This choice, too, it a compromise between the usual lifetime exposure
administered in bioassays (that is, lifetime after start of exposure
which may be several weeks after the birth of the test animals) and the
less consistent exposures which humans encounter.
In the prediction analysis, three loss functions have been defined.
None of thorn is the standard squared-error loss routinely applied, since
the latter is clearly not appropriate for the estimates derived here.
No statistical development of these loss function* exists to inform us
about lack of fit, significance of differences in loss, etc. If a
statistical underpinning did exist, it would be possible to use the loss
functions in som* capacity besides as ranking procedures and. thereby,
to be able to better differentiate between t.ie analysis methods an-j
refine the conclusions.
Finally, only 55 distinct bioassay analysis methods have been defined.
This is only a small fraction of those that could be considered, even
fixing the approaches to the components at those defined here.
3-28
-------
Despite the caveats just presented, the following major conclusions have
emerged from the present investigation.
• Animal and human RRDs are strongly correlated. The knowledge
that this correlation exists should strengthen the scientific
basis for cancer risk assessment and cause increased confidence
to be placed in estimates of human concur risk made from animal
data.
• In the majority of cases considered, analysis methods for
bioassay data that utilize lower statistical confif- :e limits
as predictors yield better predictions of human risX than do the
some methods using maximum likelihood estimates.
• Analysis methods for i-^oassoy data that utilize median lower
bound RROs determined from che ensemble of data for a chemical
generally yield better predictions of human results than
analyses that utilize minimum lower bound RRDe (assuming
approaches to other risk assessment components are chosen
appropriately.
• Use of the "ing intake/kg body weight/day" (body weight) method
for atiimal-to-humon extrapolation generally cause* RROs
estimated from animal and human data to correspond more closely
than the other methods evaluated, including the "mg intake/m^
surface area/day* (surface area) method.
• The risk assessment approach for animal data that was intended
lo mimic that used by the EPA underestimates the RROs
(equivalent to overestimating human risk) obtained from the
human data in this study by about on order of magnitude, on
average. However, it should be understood that the risk
assessment approaches implemented in this study ore computer
automated and do not always utilize the some data or provide the
•ar,
-------
the overage multiplicative factor by which the RRD predictors
obtained from the animal data are inconsistent with the ranges
of hunvju RROs consistent with the human data) to 1.7. This is
not the same as saying that the predictors are accurate to
within a factor-of 1.7, because the estimated ranges of human
RROs that are consistent with the human data cover an order of
magnitude or more for most chemicals.
• It has been possible to identify a set of analysis methods using
the median lower bound estimates that ore most appropriate for
extrapolating risk front u.-.imols to humans, given the current
state of knowledge and data analysis. It is possible to use the
information and results presented in this investigation to
calculate ranges of risk estimates that are consistent with the
data and also incorporate many uncertainties associated with the
extrapolation procedure.
• Evaluation of risk assessment methods should focus on the
complete risk assessment process rather than on individual
components.
• The data base and methods used in this study can provide a
useful basis for the evaluation of various risk assessment
methods.
DIRECTIONS FOR FUTURE RESEARCH
In the course of the previous discussion, several proposed extensions of
(• . s project have been mentioned. Several fall under the heading of
.-u.nsitivity analyses of the results already obtained. fhese include
investigation of the robustness of the results to reasonable alternative
choices for the «plJ
-------
The data that is available from this project could provide an
interesting and pertinent example to which that development could apply.
Also discussed in connection with component-specific uncertainty are
efforts directed at reducing or explaining that uncertainty. The
greatest uncertaintins are related to the components specifying how to
handle experiments of different lengths of dosing, routes of exposure.
or test species and specifying the carcinogenic responses to use. Many
aspects of these components and their uncertainties can be addressed in
an investigation of pharmacokinetics. The data base contains detailed
data on the timing and intensity of exposure for each bioassay, so a
pharmacokinetic study, which requires such information, is entirely
feasible with the currently collected data. Two specific proposals are
discussed here.
Risk estimates incorporating pharmacokinetic data could be used to
determine appropriate surrogate doses. It is sometimes assumed that a
given dcse measured as average concentration of the active metabolite at
the target tissue will produce the saite risk in animals and humans.
However, given the many differences between animals and humo.is (size, '
life span, and metabolic rotes, to mention a few), it is ncc clear
which, if any, surrogate dose is the most appropriate. This issue is
similar to that of choice of the most appropriate surrogate dose measure
for animal to human extrapolation (e.g. mg/kg/day versus mg/i>2/dov)
considered in this study and can be studied in a similar manner. Risk
estimates using phormocokinetic data could be used to determine
empirically the most appropriate surrogate dose. Even though the range
of RROs consistent with the human data generally cover a range of an
order of magnitude or greater, the potential surrogate doses cover on
even wider range. Just us the present study indicates that certain dose
measures appear to predict human results well in conjunction with
appropriate choices for ether risk assessment components, a study using
pharmacokinetic data should allow similar conclusions regarding the
surrogate dose. A preliminary investigation indicates that possibly 16
of the 23 chemicals with suitable human data used in this study might
also have data that would support a risk assessment that incorporates
pharmacokinetic data.
3-31
-------
A second potentially useful investigation incorporating pharmacokinetic
data involves using the data in the data base on different routes of
exposure to study the best means of extrapolating from route to route in
animal studies. RisK assessment methods, including the ones examined in
this study, often assume a given dose rate involves the same risk,
regardless of route. This clearly is a gross oversimplification. The
animal data collected for this study contains numerous examples of
carcinogenicity studies on the same chemical and animal species, but for
which exposure is through different routes. Those studies could be used
to determine how pharmacokinetic data could best be applied to perform
route-to-route extrapolation. Since human data would not be essential
in these investigations, our total data base that encompasses k<*
chemicals could be used.
The question of different cnemical classes and the consistency that may
be apparent within any 'jf the classes is deserving of further study. It
would be reasonable to couple this work with pharmacokinetic methods.
In the present data base, several classes ore represented. However, the
number within any particular class is somewhat limited. An expanded
data base may be recessary for a thorough investigation.
In fact, one desirable goal in and of itself, but one that would enhance
the prospects for successful, completion of these other proposals, is the
maintenance and updating of the bioassay data base. All aspects of
this, including accumulation of more data sets for the chemicals already
included and addition of more substances, may be necessary. Some
revamping o'' the data coding format may also make future analyses eaeie-
and more accurate. Especially for phormacokinetic studies, for
instance, dose patterns could be recorded on a daily rather than weekly
basis.
As a counterpart to th* bicastoy data base enhancement, updating and
augmenting tha epidemiologicol doto is essential. Since the
epidemiological data (in particular, data on exposure) is the single
most limiting factor preventing use of hjman data, any hope of
increasing the size of the sample of chemicals uteful in estimating
conversion factors and residual uncertainty must be based on an effort
to acquire such data. For those chemicals already analyzed, more
3-32
-------
•pacific exposure doto would reduce the uncertainty bounds surrounding
epidemiological RRD estimates and refine our estimates. At it the case
with the bioassay data, much of the limitation or uncertainty i» solely
a matter of inadequate reporting of data.
It should be noted in passing that th« methods and portions of the
computer programs developed and applied in this project may be useful in
other contexts. Of particular interest is a study of other types of
health effects, e.g. reproductive effects. The investigation of these
issues could include determinations of uncertainty at well as
identification of the most appropriate methods. Other projects,
including investigation of other types of extrapolations, e.g. from one
temporal dosing pattern to another or from rot* to mice, could also be
facilitated by use of the data base, met,.ods, and programs developed in
the present work.
Finally, one would like to investigate cancer risk assessment methods
appropriate when data available to a particular assessment are limited.
We have mentioned this problem in connection with component specific
uncertainty (i.e. noting that confounding like that affecting those
uncertainty calculations will often be present in any given risk
analysis setting) and in connection with the set of recommended bioassay
analysis methods. In the latter instance, it was pointed out that each
analysis in the recommended set, save for Analysis 17, is capable of
being applied to any data base but that data limitations due to
incomplete data presentation may entail that Analyses 20 and *3 are not
possible. The remaining analyses (30, 31, <»5, and *7) can be performed
no matter what the data set contains, but they may be seriously affected
by the extent and nature of the contents.
Consequently, the following investigation is proposed as o means of
studying the effects of the limitations on the data for any chemical of
Interest and of determining how best to extrapolate risks to humans.
Pick the doto in the data base that most nearly matches the data for the
chemical in question. The matching may be based on specie?. routes of
exposure, and quality of '.he data. Moreover, one may wish to restrict
attention to chemicals that are in the same class of the substance of
interest. Suppose, for example, a volatile organic chemical is under
3-33
-------
investigation and that the only data available are from rat inhalation
studies. Then, the proposed procedure would first select rat inhalation
bioassoys conducted using appropriate chemicals (i.e., perhaps limited
to volatile organics). The components of risk assessing,t not fixed by
the selection could be varied and the method that works best with the
selected data would be the basis for extrapolating to humans risks due
to the chemical in question. Since we olso have a recommended set
consisting of methods that appear to perform well for the data and
chemicala considered as a whole, the risks estimated on that basis (i.e.
using the recommended *et) would be available for comparison. These
estimates reveal what would happen if other species, other routes, and
other chemicals are included. The relationship between the estimates
obtained by the two approaches would suggest a general type of
uncertainty attributable to use of a limited data base (in this example,
rat inhalation studies). A pilot study could investigate the
feasibility of such c chemical-specific approach to risk assessment.
REFERENCE
1. Crump, K., Silvers. A., Ricci. P., nnd Wyzga, R. (1985). Inter-
species Comparison for Carcinogenic Potency to Humans. Princ tples
of Health Ri«x Assessment. Ricci. P. (ed.). Prentice Holl.
S-5<»
-------
Table 3-1
COMPARISON OF RESULTS FOR SELECTED ANALYSES0
Bias-
Analysis
0
0«
7
lie
110
17
20
SO
31
43
45
47
Number of
Chemicals
20
20
19
19
13
11
17
23
23
17
23
23
Correlation
Coefficient
0.
0.
0.
0.
0.
0,
0
0,
0
0
0
0
78
78
76
77
78
.58
.67
.91
.90
.74
.91
.89
Correcting Residual
Total Incremental Conversion Uncertainty
Normalized Lossb Fac*.orsc Factor^
1 .
1 .
1 .
0.
1 .
0
0
0.
0
0
0
0
15
71
40
62
O'l
.27
,62
.39
.53
.28
.27
.28
1
12
1
0
3
2
0
1
8
0
1
1
.6 -
-
.6 -
.81 -
.7 -
.8 -
.69 -
. 1 -
.5 -
.18 -
.2 -
.0 -
2
12
3
1
4
7.
0
1
12
0
1
1
. 1
.6
.9
.3
.8
.78
.7
.29
.7
.7
5.
16.
5.
4.
3.
4
7
2.
2
2
1 .
1
3
2
4
5
1
.2
. 1
.0
.0
.8
.7
.8
°TI-,e results correspond to trie member of the pair (with sieve, without
sieve) that gives best results. For Analyses 11c, 20, and 43 this is
without the sieve; for other analyses this is with the sieve. The
median lower bound predictor, LJQ. is used in all analyses except for
the exception noted.
t>This value is not the sama as that in Table 2-8 because th>> inclusion
of the supplemental analysss reduced the minimum average loss for two
of the three loss functions and increased the maximum loss for all
three of the functions.
°These values ore the factors, 10C. based on the y-intercepts from the
CAUCHY and TAriH loss functions (cf. Tables 2-13 and 2-17) and represent
the average ratio of human RROs to animal RRDs.
^Residual uncertainty is frcwn Table 2-21 or 2-22. It is the factor
computed for all chemicals and represents the average factor by which n
prediction must be multiplied or divided in order to eliminate
uncertainty not due to uncertainty in the humor estimates.
•Using minimal lower bound estimator \.n.
3-35
-------
Toble 3-2
MEDIAN COWER BOUND RRO ESTIMATES, BY CHEMICAL AND ANALYSIS METHOD0
Analysis
Cheffliccl
Acrylonitrile
Ally! Chloride
4-Aminobiphenyl
Benzo(a)pyrene
Carbon tetrachloride
Chlordane
3, 3-Dichlorobenzidine
1 , 2-Oichloroethane
EDB
Formaldehyde
Hexachlorobenzene
Hydrazine
Mustard Cos
Lead
2-Napthylomine
NTA
2,4, 8-Trichlorophenol
TCDO
Tetrochloroethylene
Toxaphene
Vinylidene chloride
4.
6.
2.
5.
3.
2.
1 .
2.
3.
1 .
1 .
1
1
6
1
6
1
7
9
2
1
30
39
92E+1
17E+1
21E-1
10E+1
36
24E+1
79E + 1
77
88
30
8.'
.40E-7
.14
.20E»1
.24E+2
. 73E+2
. 32E-5
.22E+1
.58
.34
9.
1 .
2.
7.
2
1 .
2
4.
2.
3.
2
1
1
1
A
*>
1
1
8
1
2
31
29E-1
02E+1
03
02E-2
89
96E-1
62
62
94E-1
09E-1
OOE-1
. 74E-1
.31E-8
.30
.54
.66E»1
.61E+1
. 55C-5
.25
.89E-1
.45E-1
1 .
6.
4.
1.
5.
1 .
2.
2
6
2
2
8
1
7
43
01
71E*1
_-b
80E-2
—
56
59E-1
28E+1
96
--
8"»E-1
—
--
.09
--
. 23E+1
--
.56E-5
.06E»1
.37
-26E-1
3.
7.
2.
5.
3.
1 .
1 .
3.
3.
1 .
1 ,
1
1
6
1
R
2
6
8
4
5
45
57
27E»1
42E+1
87E-1
57E+1
99
91E + 1
34E + 1
29
15
.30
87
.40E-7
. 14
.20E+1
. 24E+2
.11E+2
.87E-5
.70E+1
23
.56E-1
„
1 .
2.
5.
3.
4.
1 .
4.
4.
3.
2
9
1
6
1
6
1
9
1
4
2
47
39
11E-
17E-
>2
^1
21E-1
10E + 1
43
24E+1
31E
82
16
48
15
.40E
. 14
. 20E
. 97E
. 90E
fl
-7
+ 1
+ 2
+ 2
.05E-5
.13E+2
.74
.34
°Th« full «i«v« wot uted to «cr»an th« data; th* •stimatcc have not be«n
odju*t«d by th« oppropriat* conversion factors.
bA •--" indicates that tn» data w«r» not available to apply the m«thod
to the chemical.
3-36
-------
Table 3-3
RRO PREDICTIONS0. BY CHfMICAL AND ANALYSIS METHOD
Oemcal
Acrylonitrlie
Allyl Chloride
4-A/»inobipfieny 1
B«>i2o(o Jpyrene
Carbon Tetrochlorirte
Chlorco.ie
3 3-Dichlerobenjridine
1 .2-DicMoroet'iane
EOB
f ortna] Oehyde
Analysis
30
[4 74.
[7 «7E
[2 34E
[5 63E
[i 35E
[2 55.
[1 3*-E
[3 DIE
(4 07.
[2 03.
[1 40.
[2 02.
[1 51E
[6 63.
[1 JOE
[6 7/.E
[1 87E
1 7 91E
(9 96E
|2 79.
[1 45.
7
•1 .
»1.
-1.
«1 .
4
*1.
«1 .
6
3
p
i
-7.
1
«1.
t2.
.2.
-5.
»1.
4
2
46]'
1 18t+2]
3.69E»1]
8 86E-1]
5 27E.1]
01]
2 11E.1]
4. 74E* 1 j
41]
20]
21]
'8J
2 3HC-7J
04E»1]
2 04E.1]
1 06Et3]
2 94E«2]
t .24E-4J
1 57E»2]
39]
JBJ
[7 85. 1
[8 62E*1
[1 72E»1
[5.93E-1
[2 44E»1
[1 66. 2
[2 1]
3.97E-1]
2.11E-1]
[4.14, 6.
[8.43E + 1 .
[2.81E+1,
[6.81E-1.
[4. 14E*1 .
[2.31. 3.
[2.22E+1.
[3.87E+1.
[3.82. 5.
[1.J.. 1.
[1 .51. 2.
[2.17. 3.
[1.62E-7.
[7.12. 1.
[1 . 39E+1.
[7.24E»2.
[2.45E+2.
[7.97E-5.
[1.01E+2.
[4.91, 7.
[6.45E-1.
07]
1 .24£ + 2]
4. 11E + 1]
9.98E-1 ]
6.0/Etl]
58]
3.25E+1]
5.68E*1 J
59]
96]
21]
18]
2.38E-7]
04E+1]
2.04E*1 J
1 .06E+3]
3.59E+2]
1.18E-4]
1 .48E + 2J
19]
9.45E-1]
[4.39. 7
[1 . 11E*2
[2.17E*1
[5.21E-1
[3.10EO
[4.43. 7
[1 .24E»1
l4.31E»1
[4.82, 8
[3.16, 5
[2.48, 4
[9.15, 1
[1 .40E-7,
[6.14. 1.
[1 .20E+1.
[6.97E+2.
[ 1 .90E»2.
[9.05E-5.
[1 . 13E+2.
[4.74, 8.
[2.34. 3.
47
.46]
. 1.89E+2]
. 3.69E»1]
. 8.86E-1]
. 5.2/tt-l]
.53]
. 2. 11F»1 J
, 7.33E 1]
.19]
37]
22]
56Et1]
2.38E-7]
04E»1]
2.04E+1 J
1. 18t*3]
3.23E»2]
1.54E-4]
1.92E+2J
06]
98]
^iQr^Zjne
W^jitor{J COS
lead
2-Nocthy Icwnine
NT*
24.6-Trichlorophenol
TCOO
Tetrochloroethylene
To*ophene
Vinylidene Cr,
°i^e predictions are derived frofli the voli_«t. in Table 3-2 oy cpplicoticr of the appropriate conversion factors.
''The interval* o-e the 'eiclt of oi/plying the t«*o conv».rsion factors giver in Table 3-1 for each analysis method.
CA •--• indicates that tic Co!.o were no' available to apply '.he nwthod to the chemical.
-------
Table 3-4
UNCERTAINTY INTERVALS FOR RRO PREDICTIONS0. BY CHEMICAL AND ANALYSIS METHOD
Analysis
Cheirical
Acrylonitrile
Allyl Chloride
4-Aminobiphenyl
Benzo(a)pyrene
Carbon Tetrachloride
Chi or done
3,3-Dichlorobenzidine
j, 1,2-Dichloroethane
* EDB
30 Formaldehyde
Hexach lor obenzene
Hydrazine
Mustard Gas
Lead
2-Nap thy lamina
NTA
2 , 4, 6-Tr ichlorophenol
TCDO
Tetrochloroethylene
Toxophene
Vinylidene Chloride
30
[2.37, 1.49E+1]
[3.74E+1. 2.36E+2]
[1.17E+1. 7.38E+1]
[2.82E-1. 1.77]
[1.68E+1. 1.05E+2]
[1.28. 8.'02]
[6.70. 4.22E+1]
[1.51E+1. 9.48E+1]
[2.04, 1.28E+1]
[1.02. 6.40]
[7.00E-1, 4.42]
[1.01. 6.36]
[7.55E-8. 4.76E-7]
[3.32. 2.08E+1]
[6.50, 4.08E+1]
[3.37E+2, 2.12E+3]
[9.35E+1. 5.88E+2]
[3.96E-5, 2.48E-4]
[4.98E+1, 3.14E+2]
[1-40. 8.78]
[7.25E-1. 2.56]
[3.93, 2
[4.31E+1
[8.60. 4
[2.96E-1
[1.22E+1
[8.30E-1
[1.10E+1
[1.95E+1
[1.24. 7
[1.30. 7
[8.45E-1
[7.35E-1
[5.55E-8
[5.50. 3
[1.08E+1
[2.39E+2
[6.80E+1
[6.55E-5
[3.48€+1
[8.00E-1
[1.04. 5
31
.24E+1]
. 2.46E+2]
.88E+1]
. 1.69]
! 4.72]
, 6.30E+1]
. 1.11E+2]
.06]
.42]
. 4.80]
. 4.18]
. 3.14E-7]
.12E+1]
. 6.10E+1]
, 1.36E+3]
. 3.88E+2]
. 3.72E-4]
. 1.98E+2]
. 4 54]
.88]
43
[6
[4
[3
[1
[3
[8
[1
[1
[3
[1
[1
[5
[8
[4
.50E-2.
.32. 5.
.09E-3.
-OOE-1.
.61E-2.
-21E-1.
.90E-1.
.82E-2.
.93E-1.
.43. 1.
.65E-6.
.18. 6.
.82E-2.
.68E-2.
8.20E-1]
46E+1]
3.89E-2]
1.27]
4.54E-1]
1.04E+1]
2.40]
2.31]
4.96]
81E+1]
2.08E-5]
55E+1]
1.11]
5.91E-1]
[2.44. 1
[4.96E+1
[1.65E+1
[4.01E-1
[2.44E+1
[1.36. 5
[1.31E+1
[2.28E+1
[2.25. 9
[7.82E-1
[8.88E-1
[1.28. 5
[9.53E-8
[4.19. 1
[8.18. 3
[4.26E+2
[1.44E+2
[4.69E-5
[5.94E+1
[2.89. 1
[3.79E-1
45
.03E+1]
, 2.11E+2]
. 6.99E+1]
. 1.70]
. 1.03E+2]
.75]
. 5.53E+1]
, 9.66E+1]
.50]
. 3.33]
. 3.76]
.41]
. 4.05E-7]
.77E+1]
.47E+1]
. 1.80E+3]
. 6.10E+2]
. 2.01E-4]
. 2.52E+2]
.22E+1]
. 1.61]
[2.44. 1
[6.17E+1
[1.21E+1
[2.89E-1
[1.72E+1
[2.46. 1
[6.89. 3
[2.39E+1
[2.68. 1
[1.76. 9
[1.38. 7
[5.08, 2
[7.78E-8
[3.41. 1
[6.67. 3
[3.87E+2
[1.06E+2
[5.03E-5
[6.28E+1
[2.63, 1
[1-30. 7
47
.34E+1]
, 3.40E+2]
, 6.64E+1]
. 1.59]
. 9.49E+1]
.36E+1]
.80E+1]
. 1.32E+2]
.47E+1]
.67]
.60]
.81E+1]
. 4.28E-7]
.87E+1]
.67E+1]
. 2.12E+3]
. 5.81E+2]
. 2.77E-4]]
, 3.46E+2]
.45E+1]
.16]
°The intervals are derived from the values in Table 3-3 by application of the residual uncertainty factors (cf.
Table 3-1).
bA "—" indicates that the data were not available to apply the method to the chemical.
-------
I
U
to
Table 3-5
RANGES OF HUMAN RROS DERIVED FROM THE RECOMMENDED SET OF ANALYSES0
Chemical
Acrylonitrile
Allyl Chloride
4-Aminobiphenyl
Benzo(a)pyrene
Carbon Tetrachloride
Chlordane
3. 3-Dichlorobenzidine
1 , 2-Dichloroethane
EDB
Formaldehyde
Hexachlorobenzene
Hydrazine
Mustard Gas
Lead
2-Napthylamine
NTA
2,4,6-Trichlorophenol
TCDD
Tetrach loroethylene
Toxaphene
^inylidene Chloride
Option 2 =
Fu'll Ranaeb
[6.50E-2. 2.24E+1]
[4.32, 3.40E+2]
[3.52E-2. 6.98E+2]*
[3.09E-3. 1.77]
[5.03E-2. 9.97E+2]"
[1.00E-1. 1.S6E+1]
[3.61E-2. 6.30E+1]
[8.21E-1. 1.32E+2]
[1.90E-1. 1.47E+1]"
[3.05E-3. 6.05E+1]"
[1.B2E-2. 7.60]
[3.04E-3. 6.01E+1]"
[2.27E-10. 4.50E-6]"
[3.93E-1. 3.12E+1]
[1.95E-2. 3.86E+2]"
[1.43. 2.12E+3]
[2.81E-1. 5.56E+3J"
[1.65E-6. 3.72E-4]
[5.18. 3.46E+2]
[8.82E-2. 1.45E+1]
[4.68E-2, 7.16]
Option 3:
Smallest Consistent Range0
[6.50E-2, 8.20E-1] U [2.44. 1.34E+1] (43,
[4.32. 2.11E+2] (43. 45)
[3.52E-2, 6.98E+2] (%3)
[3.09E-3. 3.89E-2] U [4.01E-1. 1.70] (43,
[5.03E-2. 9.97E+2] (43)
[1.00E-1, 1.27] U [1.28. 8.02] (43. 30)
[3.61E-2. 4.54E-1] U [6.89. 3 80E+1] (43.
47 )<
45)
47)
[8.21E-1, 1.04E+1] U [2.28E+'lt 9.66E+1] (43. 45)
[1.90E-1. 9.50] (43. 45)
[3.05E-3. 6.05E+1] (43)
[1.82E-2, 4.42] (43. 30)
[3.04E-3. 6.01E+1] (43)
[2.27E-10. 4.50E-6] (43)
[3.93E-1. 1.77E+1] (43. 45)
[1.95E-2, 3.86E+2] (43)
[1.43. 1.81E+1] U [4.26E+2. 1.80E+3] (43.
[2.81E-1, 5.56E+3] (43)
*5)
[1.65E-6, 2.08E-5] U [4.69E-5. 2.01E-4] (43. 45)
[5.18. 1.98E+2] (43. 31)
[8.82E-2, 1.11] U [1.40. 8.78] (43. 30)
[4.68E-2, 5.88] (43. 45. 31)
°Values of RRDs are in mg/kg/day.
bThe full range extends from the smallest lower bound to the largest upper bound among
analyses in the recommended set.
cThe smallest consistent range is the union of intervals from analyses in the recommended
set such that the union includes all predictions (from Table 3-3) and is the smallest union
that does so.
''When the union is of disjoint parts, both parts are shown, connected by the union symbol,
"U". In parentheses are the analyses whose union defines the smallest consistent range.
"An asterisk marks those intervals that are the result of imputing values for Analysis 43.
-------
Table 3-6
RANGES OF HUMAN RRDS DERIVED FROM THE RECOMMENDED
SET OF ANALYSES IGNORING ANALYSIS 43°
Chemical
Acrylonitrile
Allyl Chloride
4-Aminobiphenyl
Benzo(a)pyrene
Carbon Tetrachloride
Chlordane
3, 3-Dichlorobenzidine
1 ,2-Dichloroethane
EDB
Formaldehyde
Hexachlorobenzene
Hydrazine
Mustard Gar.
Lead
2-Napthylamine
NTA
2,4, 6-~- ichlorophenol
TCDD
Tetrachloroethylene
Yoxaphene
Vinylidene Chloride
Option 2:
Full Ranqeb
[2.37. 2.24E+1]
[3.74E+1. 3.40E+2]
[8.60. 7.38E+1]
[2.82E-1. 1.77]
[1.22E+1, V.05E+2]
[8.30E-1. 1.36E+1]
[6.70, 6.30E+1]
[1.51E+1, 1.32E+2]
[1.2*. 1.47E+1]
[7.82E-1. 9.67]
[7.00E-1. 7.60]
[7.35E-1. 2.81E+1]
[5.55E-8. 4.76E-7]
[3.32. 3.12E+1]
[6.50, 6.10E+1]
[2.39E+2, 2.12E+5]
[6.80E+1, 6.10E+2]
[3.96E-5, 3.72E-4]
[3.WE-H. 3.i»6E-i-2]
[8.00E-1, 1.WE+1]
[3.79E-1. 7.16]
Option S:
Smallest Consistent Range0
[2.44. 1.34E+1] (47)
[4.96E+1, 2.11E+2] (45)
[1.65E+1, 6.99E+1] (45)
[4.01E-1, 1.70] (45)
[2.44E+1. 1.03E+2] (45)
[1.28. 8.02] (30)
[6.89, 3.80E+1] (47)
[2.28E+1, 9.66E-H] (45)
[2.25, 9.50] (45)
[1.30, 7.42] (31)
[1.38, 7.60] (47)
[1.28, 2.81E-H] (45, 47)
[9.53E-8, 4.05E-7] (45)
[4.19. 1.77E+1] (45)
[8.18. 3.47E+1] (45)
[4.26E+2, 1.80E+3] (45)
[1.06E+2. 5.81E+2] (47)
[4.69E-S, 2.01E-4] (45)
[5.94E+1, 2.52E-t-2] (45)
[1.40, 8.78] (30)
[3.79E-1. 5.88] (31, 45)
°Values of RRDs are in mg/kg/day.
bThe full range extends from the smallest lower bound to the largest
upper bound among analyses in the recommended set.
cThe smallest consistent range is the union of intervals from analyses
in the recommended set such that the union includes all predictions
(from Table 3-3) and is the smallest union that does so.
3-40
-------
Flgur* 3-1
Plot For Araly*I* 45 (All RoutM, A
ovw Sm)
8C
-2
-3
-« -4
------- |