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OCR for page 258

CAPPENDIx- Estimates of the
Carcinogenicity of
Chiorobenzilate
EPA'S CAG derived its estimate of the pathological activity of chlorobenzi-
late from observations by Innes (Anderson 1978:19, Innes et al. 1969~.
The data employed are reproduced in Table C.1. Applying Abbott's
formula (see below) to these data, the excess probability of incurring a
hepatoma among the test animals is found to be 0.476. Since this
estimate was derived from a test group numbering only 17, it is subject to
a substantial sampling error. In this appendix the 90 percent confidence
interval for the excess probability of hepatomas will be derived and will
be used to compute the 90 percent confidence interval for the CAT for
chlorobenzilate.
TABLE C.1 Incidence of Hepatomas in Male Strain X
Mice Given Chlorobenzilate (after Innes et al. 1969)
Pooled
Test Group Control Group
With hepatomas 9 8
Without hepatomas 8 71
Group size 17 79
Source: Modified from Anderson (1978).
258

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Appendix C
259
Let pi and Pc be the proportions of test animals and control animals,
respectively, that contracted hepatomas. Then Abbott's (Abbott 1925)
formula for the excess probability of incidence among the test animals is:
1 - p,
1 - p
To a second-order approximation, the variance of Px is then
p = 1 -
(Px) ( ~ [, )
1 - EP,)2( ~ (P.') 2 +
-,c (1 - Up,)
° (Pc)
( 1 - EpC)
where O2 denotes variance and E is the expectation operator. The
maximum likelihood estimates of the two variances are
2 1 9 ~
s (p,) = ~7 17 17
= 0.01465,
52(pC' = 719 789 7l = 0.00115.
Since the contribution of O2 (DC) is relatively negligible, we neglect it, and
assume agog = 0. Then the variance formula reduces to
2 a (p,)
( 1 - Epc)
Now
a (p,)
( 1 - Pc)
a2(p) = ~ p (1 - P)
where Pi is the true, unknown, probability of hepatomas in a test animal.
Applying Abbott's formula again,
P. = Pc + (1 - Pc) Px,
where Px is the unknown excess probability of incidence in the test
animals. When pi and Pi are eliminated from these three equations,
a (Px) = n ~ _ p (Pc + (1 - Pc) Px)
The limits of the 90 percent confidence interval for Pa can now be
computed. The sample size of 17 is large enough that the normal

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260
Appendix C
distribution is a satisfactory approximation to the binomial for all
practical purposes. Then the upper limit of the confidence interval,
denoted pa, is the probability that satisfies
P - ~ ~ (Px) = Px
when Px is replaced by p in the formula for a2(oX) and ~ = 1.6945 is the
normal deviate corresponding to a 5 percent tail. This equation can be
written in the form
(P _ pX)2 = a2 a2 (Px) = n
a 1 P ~^ ~ i' - Pc)P).
1 _ p \Pc ' ~ ~
This is clearly a quadratic equation in p. Performing the, indicated
operations and rearranging produces the standard-form quadratic
(1 + a jp2 _ (2pX + 1 - p n ~ P
+ (PX - 1 -
a ~ = 0,
in which cat = 1.6945, n = 17, end pa is computed from Abbott's formula
with pi = 9/17 end pc = 8/79. Making the numerical substitutions and
solving the equation yields the two roots p = 0.683, 0.260. The larger
root is the upper confidence limit that we sought. The smaller root is
easily seen to be the lower confidence limit. Thus, the 90 percent
confidence interval for Px extends from 0.260 to 0.683.
The corresponding confidence interval for the CAT follows at once from
the formula
1 OOPx
Am -
aose ~
where dose equals lifetime intake in millimoles per kilogram of body
weight.
The calculation of the dose is as follows:
Daily ration
Concentration of chlorobenzilate
Daily intake of chlorobenzilate
Duration of test
Total intake of chlorobenzilate
Molecular weight of chlorobenzilate
Total intake in m moles
Weight of animal
Dose in m moles per kg per lifetime
5g
603 ppm
3.015 mg
575 days
1733 mg
325.2
5.33
0.030 kg
178

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Appendix C
The 90 percent confidence interval for the CAl therefore ranges from
0.146 to 0.384. The maximum likelihood estimate, which can be taken as
the most-probable value, is LOOM per dose = 0.267.
261
REFERENCES
Abbott, W.S. (1925) A method of computing the effectiveness of an insecticide. Journal of
Economic Entomology 18:265-267.
Anderson, E.L. (1978) CAG Final Risk Assessment for Chlorobenzilate. Memorandum to
Joe Boyd, Project Manager, Special Pesticide Review Division, Office of Pesticide
Programs, dated August 18, 1978. CAG, Office of Research and Development, U.S.
Environmental Protection Agency, Washington, D.C. (Unpublished)
Innes, J.R.M., B.M. Ulland, M.G. Valerio, L. Petrucelli, L. Fishbein, E.R. Hart, and A.J.
Pallotta (1969) Bioassay of pesticides and industrial chemicals for tumorigenicity in
mice: A preliminary note. Journal of the National Cancer Institute 42(6):1101-1114.