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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.