Document O1Yqa0db59g66j4x3aM4Bzv1j

2 2) Metabolic processes or mechanisms which counteract the effects of the chemical carcinogen after it reaches the target area, 3) Delays in development of cancer resulting in a latency period sufficiently long to insure inter vention of an independent cause of death. Some of the evidence for each of these types of threshold is summarized below. It is now generally accepted that chemical carcin ogenesis is initiated when electrophilic molecules (alkylating agents) are covalently bound to nucleophilic groups in certain cellular macromolecules (e.g., DMA and RNA) . Moreover, most chemical carcinogens are not themselves chemically reactive but must be converted or "activated" by metabolic processes to 3/ form the necessary electrophilic species. Thus, if the physiological mechanisms invoked in absorption, distribution, metabolization, and excretion of small amounts of a carcinogenic substance can operate either to prevent metabolic activation or block access to reactive sites on vulnerable macromolecules, 4/ an exposure threshold exists for that carcinogen. The crucial Heidelberger, C., Chemical Carcinogenesis, in Annual Review of Biochemistry, Volume 44, Eds. Snell, Boyer, Meister, and Richardson, at 79-121 (1975); Hiller, J.A. and Miller, E.C. , Chemical Carcinogenesis: Mechanisms and Approaches.to Its Control, 47 J. Hat' 1 Cancer Inst. V-XIV (1971)-; Neumann, H. G.-,-Ultimate--electroohilic carcinogens and cellular nucleophilic reactants, 32 Arch*. Toxicol. 27 (1974). Brown, C. C., Mathematical aspects of dose-response studies in carcinogenesis--The concept of threshold, 33 Oncology 62 (1976); Freese, E., Thresholds in toxic, teratogenic, mutagenic, and carcinogenic effects. Environmental Health Perspectives, December 1973, at 171. CB* 2302569 RSV0030355 > 3 parameter in cancer initiation is consequently not the ambient exposure, but the "effective dose" eventually delivered to the target area, which is likely to be "some complex function of the actual exposure along with the biochemical and physiological 5/ parameters of the host." A metabolic threshold for chemical carcinogenesis could result whenever non-carcinogenic metabolic and excretary pathways are saturable and are supplanted by carcinogenic alternative pathways at higher dosages. As summarized below, several recent experiments have confirmed the existence of exactly this type of dose-dependent differential metabolism. Reviewing some of this recent evidence, P. J. Gehring and his colleagues concluded. Detoxification of many chemicals is a dose-dependent process which can be overwhelmed, leading to dis proportionate increases in their toxicity, including carcinogenicity. When detoxification mechanisms are overwhelmed, there is a disproportionate retention of chemicals per se and/or their degradation products in the body, and reactions of reactive electrophilic metabolities of the chemicals with macromolecules are often enhanced greatly.^/ In some instances, a chemical may combine with other 7/ reactive substances or be rapidly excreted before it can be 17 Brown, C. C., note 4 supra, at 63. / Gehring, P. J., Watanabe, P. G., Young, J. D., and Le Beau, J.E., Metabolic thresholds in assessing carcinogenic hazard. Toxicology 56 (1976), at 56. V Kolbye, C., Jr., Cancer in humans: Exposure and responses in a real world, 33 Oncology 90 (1976), at 94. CBY 23025 70 RSV0030356  4 converted to an electrophilic metabolite. For example, furosemide is excreted primarily via the kidney at low dosages. However, at higher dosages, renal elimination is overwhelmed and the formation of toxic metabolites which 8/ react with macromolecules increases disproportionately. Once electrophilic metabolites have been formed, they can be detoxified before reacting with macromolecules by various saturable enzymatic and non-enzymatic pathways, including conjugation with glutathione, sulfate, or glu9/ curonide. For example, bromobenzene is detoxified by conversion to the glutathione conjugate. However, when glutathione stores are depleted by higher bromobenzene dosages, alkylation of macromolecules by the reactive electro- 10/ philic metabolite increases dramatically. Recent studies of the metabolization in rats of vinyl chloride monomer (VCM), a known human carcinogen, confirm that low doses of VCM are detoxified by conjugation with nonprotein sulfhydryl groups in glutathione. However, administration of higher doses results in depletion of F Gillette, J.R., A perspective on the role of chemically reactive metabolites of foreign compounds in toxicity--I. Correlation of changes in covalent binding of reactivity metabolites with changes in the incidence and severity of toxicity, 23 Biochem. Pharm. 2785 (1974), and II. Alter ations in the kinetics of covalent binding, 23 Biochem. Pharm. 2927 (1974). 9/ 10/ Gehring, et al., note 6 supra. Gillette, note 8 supra. I CBY 2302571 RSV0030357 hepatic nonprotein sulfhydryl content, freeing the electrophilic metabolites of VCM to react with cellular macromolecules such as 11/ DNA and RNA. These studies indicate that "there is -a threshold of exposure in rats at which the ability to replace sulfhydryl groups is not overwhelmed and physiologic defense 12/ mechanisms remain fully operative." According to H. E. Stockinger, these findings "must be accepted as indisputable biological evidence for a threshold for vinyl chloride carcin ogenesis in rats."--^ The identification of similar thresholds for other, chemical carcinogens,also derivative of dose-dependent variation in metabolism, is likely and may "prove to be the rule rather 14/ than the exception." In fact, the eminent cancer researchers Miller and Miller have observed, tI]nhibition of carcinogenesis via trapping of the ultimate carcinogen(s) with noncritical nucleophiles probably occurs to some extent with all chemical carcinogens and may provide a natural protective mechanism .... The removal of ultimate carcin ogenic forms through noncarcinogenic reactions may be an important factor in the determination of threshold doses of carcinogens ... .15/ w------------------------------------Hefner, R.E., Jr., Watanabe, P.G., and Gehring, P.J., Preliminary studies of the fate of inhaled vinyl chloride monomer in rats, 246 Ann. N.Y. Acad. Sci. 135 (1975); Watanabe, P.G., Hefner, R.E., Jr., and Gehring, P.J., Vinyl chloride incuded depression of hepatic non-protein sulfhydryl content and effects on bromsulfalein clearance in rats, 6 Toxicology 1 (1976), Gehring, et al., note 6 supra. 12/ Gehrinq; et al., note 6 supra, at 69. 13/ Stockinger, H.E., Presentation before the National Drinking Water Advisory Council, August 25, 1976, at 6. w Gehring, et al., note 6 supra, at 70. 15/ Miller and Miller, note 3 supra, at XII. ----c---- cay 2302572 RSV0030358 * 6 Dose-dependent variation in metabolism is not the only argument for the existence of thresholds for chemical carcinogenesis. Several reputable authorities have argued that cancer induction should not be expected unless the num ber of carcinogen molecules in a given target cell exceeds a stochastic threshold.--^ According to these theorists, any substance must be present in a minimum number of mole cules or particles in order to exert a deleterious effect on the host organism. It is appropriate to note that some of the most often cited evidence for the notion that there is no thresh old for chemical carcinogenesis is derived from studies of radiation induced cancer which suggest a linear dose-response relationship. However, only the briefest consideration is necessary to conclude that such evidence is basically inap posite to the problem of chemical carcinogenesis. While a chemical carcinogen may be metabolically deactivated or 27 Claus, G., Environmental carcinogens: Is there a thresh old of exposure? 7 Clin. Toxicology 497 (1974); Claus, G., Krisko, G., and Bolander, K., Chemical carcinogens in the en vironment and in the human diet: Can a threshold be established? 12 Food Cosmet Toxicology 737 (1974); Dinman, B.D., "Non-concept" of "no-threshold"i Chemicals in the environment - Stochastic determinants impose a lower limit on the dose-response relation ship between cells and chemicals, 125 Science 405 (1972); Stockinger, H.E., Concepts of thresholds in standards setting, 25 Arch. Env. Health 153 (1972). I 1 , CBY 2302573 RSV0030359 7 encounter physiological barriers such as impermeable mem branes before it achieves the necessary proximity to crucial macromolecules/ the likelihood that a particle of radiation will penetrate and damage the nucleus of a given cell is determined only by the mass of the intervening tissue.--^ In any event, "it is not yet feasible to define the kinetics ... or to prove the existence or absence of a threshold dose" for radiation carcinogenesis.--18'/ Even if metabolic mechanisms are not sufficient to prevent the carcinogen or its metabolites from reacting with critical receptor sites, other metabolic mechanisms may still be sufficient at low doses to prevent induction of cancer. In particular, DNA repair mechanisms can prevent point mutations caused by alkylation of DNA from resulting in permanent genetic alterations, and immunological surveillance can prevent pro liferation of cancerous cells. Though a number of different types of DNA repair ap19/ pear to be operable in mammalian tissue,-- "dark repair" or iZ/ Kolbye, C., Jr,, note 7 supra, at 96; Gehring, P. J. and Blau, G. E., Mechanisms of carcinogenesis; Dose reponse. Pre sented at the Environmental Carcinogenesis Conference in Houston, Texas, January 12-13, 1977, Toxicol. Appl. Pharmacol. , at 9-10. --------- 18/ Upton, A.C., The dose-response relation in radiation-induced cancer, 21 Cancer Research 717 (1961), at 726. 19/ Trosko, J.E. and Chu, H.Y., The role of DNA repair and somatic mutation in carcinogenesis, 21 Adv. Cancer Research 391 (1975). CBV 2302574 RSV0030360 8 "unscheduled DNA synthesis," which involves excision of damaged DNA segments by-special enzyme-systems, is thought to be' of greatest importance in man.--/ Recent research has demonstrated a clear correlation between the capability of various tissues to enzymatically excise alkylated lesions and the susceptibility of such tissues to carcinogenesis.^/ The existence of DNA re pair mechanisms is of great significance to the threshold issue because they "may be able to handle only a limited number of DNA alterations and be overwhelmed by too high concentrations of a mutagen,"--22'/ resulting in an exposure threshold. There is considerable evidence that immunological sur veillance against clones of malignant cells is very important in prevention of cancer. For example, the incidence of cancer in kidney transplant patients who have taken immunosuppressive drugs is eighty times higher than in the general population.--23 / Toy Mitchell, A.D., The potential utility of DNA repair for pre dicting the effects of human exposure to hazardous agents. Pre sented at the NIEHS Conference on the Problems of Extrapolating the Results of Laboratory Animal Data to Man and of Extrapolating the Results from High Dose Level Experiments to Low Dose Exposures, in Pinehurst, North Carolina, March 10-12, 1976. 21/ Kleibues, P. and Cooper, H.K., Repair excision of alkylated bases from DNA in vivo, 33 Oncology 86 (1976). 22/ Freese, note 4 supra, at 174. 23/ Penn, A., Starzl, T.E., 14 Transplantation 407 (1972). CBY 2302575 RSV0030361 * 9 Since many chemical carcinogens have been shown to induce immunological depression_in laboratory animals,--24/ it is likely that immunological surveillance is substantially more effective at low exposure levels, indicating a possible ex posure threshold. One particularly persuasive and lucid argument for exposure thresholds for chemical carcinogenesis is provided by recent research which demonstrates the existence of a quantitative inverse relationship between dosage of a car cinogen and the latency period for cancer development, i.e., as a dosage is decreased, the latency period is increased. Ihisrelationship was first identified by H. Druckery of West Germany, who used the results of an ingenious series of ex periments relating dose and latency period to derive the formula dtn - k where d equals dosage, t equals time elapsed to tumor ap pearance, n is a number between two and four, usually about three, and k is a constant.--25 / In another more recent study. 247 Laroye, G.J., How efficient is immunological surveillance against cancer and why does it fail? 1 Lancet 1097 (1974). 25/ ------------- Druckrey, H., Quantitative aspects in chemical carcino genesis, in Potential Carcinogenic Hazards for Drugs-Evaluation of Risks, Ed. R. Truhaut, UICC Monograph Series, vol. 7, SpringerVerlag (1967), at 60-78. CBY 2302576 RSV0030362 Jones and Grendon used both laboratory and epidemiological data to derive essentially the same formula, and proposed a corresponding hypothesis regarding the mechanism of cancer induction.-- The inverse relationship between dosage and latency period necessarily implies the existence of a real exposure threshold, in that at sufficiently low exposure levels the time required for tumor development will exceed the expected lifespan of the exposed population. Moreover, since the Druckrey formula has been found to be consistent with data from many different epidemiological and laboratory studies, it should be of con siderable utility in calculating actual exposure thresholds.--^ When the inverse relationship between dosage and latency'period is considered in combination with the evidence for various meta bolic thresholds, the case for an exposure threshold for chemi cal carcinogenesis is compelling indeed. II. Many Apparent Carcinogens are in Fact Cocarcinogens or Secondary Carcinogens Which Affect the Incidence of Cancer Only When the Cumulative Dose is Sufficient to Disturb Metabolic Equilibria. -26/ -~ ' ---------Jones, H.B. and Grendon, A., Environmental factors in the origin of cancer and estimation of the possible harard to man, 13 Food Cosmet. Toxicol. 251 (1975). 27/ See, e.q. , Albert, R.E. and Altshuler, B., Considerations relating to the formulation of limits of unavoidable population exposures to environmental carcinogens, in Radionuclide Carcino genesis , Proceedings of the Twelfth Annual Hanford Biology Symposium at Richland, Washington, May 10-12, 1972, Atomic Energy Commission Office of Information Services (1973), at 234-253; Salst D.S., Mantel-Bryan - Its faults and alternatives available after thirteen more years of experimentation, 30 Food, Drug and Cosmetic L.J- 116 (1975). . ( CBY 2302577 RSV0030363 j/ - 11 Because a variety of chemical carcinogens commonly occur both in the food supply and in the environment, evidence of a correlation between exposure to a given substance and increased incidence of cancer is often insufficient to establish the actual role of the substance in cancer induction. Indeed, the National Cancer Advisory Board recently observed, "[I]n most of the current human epidemiologic approaches and certain animal bioassays it is not possible to differentiate clearly between initiating agents, promoting agents, and certain modifying factors."--' This observation is crucial, because the existence of thresholds for promoting agents and modifying factors is not questioned. Chemicals which facilitate expression of the carcino genic potential of an independent agent or agents are referred to variously as cocarcinogens or secondary carcinogens. They may operate either by increasing the susceptibility of given cells to malignant transformation or by facilitating metabolic activation of a primary carcinogen.^/ The distinction between H7 ] National Cancer Advisory Board, General Criteria for Assessing the Evidence for Carcinogenicity of Chemical Substances: Report of the Subcommittee on Environmental Carcinogenesis, 58 J. National Cancer Inst. 461 (1977) ~ 29/ See, generally, Bingham, E. and Falk, H.L., Environmental carcinogens - The modifying effect of cocarcinogens on the thresh old response, 19 Arch. Env. Health 779 (1969); Falk, H.L., Possible mechanisms of combination effects in chemical carcinogenesis, 33 Oncology 77 (1976); Kolbye, note 7 supra. CBY 2302578 RSV0030364 12 cocarcinogens and secondary carcinogens is somewhat vague. It would appear that a chemical is usually referred to as a co carcinogen when it has been observed to potentiate the effects of specific chemical initiating agents and as a secondary car cinogen when the postulated mechanism involves a more general metabolic disturbance or toxic insult. In any event, there is general agreement that these substances must be present in substantial amounts in order to facilitate induction of cancer. 2^2/ A. C. Kolbye, an Associate Director of FDA, observed in a recent article: Many so-called "carcinogens" are poorly de fined as to their toxicological effects which in some instances may decrease resistance to an independently caused cancer. Some "car cinogens" are probably not carcinogenic per se, but though, their toxicity effects can de crease resistance to other causative factors present in control animals or in heir environ ment or diet. The detection of a positive carcinogenic result should serve as a warning that a critical convergence of events can take place resulting m an increased incidence of cancer .... The expression of toxicity is generally a doserelated phenomenon that behaves much as do pharma cologically active agents in `that there are relatively clear gradations of qualitative re sponse of cells, tissues, or organs to different levels of toxic insult .... When a threshold is crossed, the cell, tissue, organ, or organism incurs a functional shift in physiological per- 30/ Falk, note 29 supra; Kolbye, note 7 supra; Weisburger, J.H., Environmental cancer, 18 J. Occupational Medicine 245 (1976); World Health Organization, Assessment of the Carcinogenicity and Mutagenicity of Chemicals, Technical Report No. 546 (1974). CBY 2302579 RSV0030365 13 formance in response to a cumulated dose . . . . If certain functional capabili ties are important to maintaining normality in a cell, or serve to protect against in duction of malignant changes, then altera tions of these functions are likely to be important factors in the critical' convergence ... of events that precede the induction of cancer.--' Thus, whenever a chemical "carcinogen" actually operates by inducing functional changes or disturbing metabolic equilibria, the chemical in question will be "carcinogenic" only above a given exposure threshold. It is not surprising that chemical exposures suffi cient to cause a toxic or pathological response sometimes cause cancer. Cancers often develop in chronically inflamed or scarred tissue.--^ Subcutaneous injections of such common substances as water and glucose have been observed to cause cancer, presumably as a result of local irritation.--/ Recent studies of 1, 4-dioxane, a chemical which in duces hepatomas and nasal carcinomas in rats, indicate that it is carcinogenic only when administered at doses sufficient to cause death and severe pathology of the liver and kidney. Intermediate dosages, which are still sufficient to cause morphological damage of liver and kidney tissues, are apparently not carcino- H7 Kolbye, note 7 supra, at 94, 96. 32/ Laroye, note 24 supra, at 1098. 33/ Grasso, P. and Golberg, L., Subcutaneous sarcoma as an index of carcinogenic potency, 4 Pood Cosmet. Toxicol. 297 (1966). ---------------- l CBY 2302580 RSV0030366 14 * genic.--^ On the basis of this evidence/ it appears likely that 1/ 4-dioxane is a secondary carcinogen and induces cancer only when exposure levels exceed a threshold of toxicity. Administration of Myrj 45 (polyoxyethylene mono stearate) in rats provides another example of secondary car cinogenesis. Resulting cancers of the urinary bladder are thought to result from the presence of bladder calculi in duced by the chemical rather than from its direct action. It is often difficult to demonstrate conclusively that a given chemical carcinogen induces cancer directly rather than by disturbing metabolic equilibria. Carcinogens which operate by facilitating the expression of other causative factors are likely to be inactive below a critical exposure threshold. Consequently, attempts should be made to identify the mechanism of carcinogenesis for each individual carcinogen as precisely as possible before setting regulatory standards based on the hypothetical effects of low exposures. 347 Kociba, R.J., McCollister, G.B., Park, C., Torkelson, J.R., and Gehring, P.J., 1, 4-Dioxane. 1. Results of a two- year ingestion study in rats, 30 Toxicol. Appl. Pharm. 275 (1974); Argus, M. T., Sohal, R.S., Bryant, G.M., Hoch-Ligeti, C-, andArcos, J.C., Dose-response and ultrastructural altera tions in dioxane carcinogenesis, 9 Eur. J. Cancer 237 (1973). 35/ ~ World Health Organization, note 30 supra, at 11. CBY 2302581 RSV0030367 15 III. Even if Variability in Individual Susceptibility to a Given Chemical Precludes Identification of an' Absolute Threshold for Carcinogenicity, There is a "Practical" Threshold Which Represents an Infinitesimal Risk to the Exposed Population. As summarized above, the evidence for existence of threshold effects in chemical carcinogenesis is con siderable. However, demonstration that a particular carcinogen exhibits threshold behavior may not enable determination of a single exposure threshold which is applicable to every individual in the exposed population. This potential lack of uniformity is a consequence of genetic variability in some of the parameters most likely to contribute to threshold phenomena, such as microsomal 36/ 37/ enzyme inducibilitv, DNA repair capability, and 38/ immunological competence. Variability in individual susceptibility should not diminish the significance of threshold evidence to the enlightened policy maker. On the contrary, identifica tion of hypersusceptible individuals with genetically H7-------------------- Kellermar., G. , Shaw, C.R. , Luyten-Xellerman, M. , Aryl hydrocarbon hydroxylase inducibilitv and bronchogenic carcinoma, 239 h'. Engl. J. Med. 934 (1973) . 11/ Robbins, J.H., Xraemer, K.H., and Lutzner, M.A., Xeroderma pigmentosum. An inherited disease with sun sensitivity, multiple cutaneous neoplasma, and abnormal DNA repair, 80 Ann. Intern. Med. 221 (1974). 38/ Laroye, note 24 supra. ! CBV 2302582 RSV0030368 16 lower thresholds could be a very important component of cancer 39/ prevention policy. However, if hereditary variation in thresholds is significant, this suggests that the analyst should be interested in identification of a "practical" threshold which represents an acceptable risk to the exposed population. The most well known method for estimation of a "practical" threshold is the procedure introduced by Mantel and Bryan, who recommended use of linear regression, with an arbitrarily assigned slope of one probit per tenfold increase in dose, to extrapolate from observed dose-response data to the dose corresoonding to a hypothetical cancer risk 40/ of one in 100,000,000. This procedure has considerable advantages in that it is relatively straitforward and easily applicable to a wide variety of experimental data. However, extrapolation methodologies based on statistical functions have no real basis in any hypothesis as to the mechanism of T57--------------------------- See Stockinger, H.E., Pharmacogenetics in the detection of the hypersusceptible worker, 151 Ann. N.Y. Acad. Sci. 968 (1968); Stockinger, note 16 supra, at 157; Stockinger, note 13 supra, at 9-10.---............... 40/ Mantel, N. and Bryan, M.R., "Safery" testing of carcin ogenic agents, 27 J. Nat. Cancer Inst. 455 (1961); Mantel, N. Bohidar, N.R., Brown, C.C., Ciminera, J.L., and Tukey, J.W., An improved Mantel-3ryan procedure for "safety" testing of carcinogens, 35 Cancer Research 865 (1975); Mantel, N. and Schneiderman, 14.A., Estimating "safe" levels, a hazardous undertaking, 35 Cancer Research 1379 (1975). CBY 2802583 RSV0030369 17 41/ cancer induction. Moreover, they fail to incorporate the reductions in toxic stress and changes in metabolic and excretory pathways which can be associated with decreasing 42/ dosage. Consequently, they are little more than con venient fictions. The completely arbitrary nature of statistical extrapolation techniques when applied to prediction of dose-response relationships at low dosages can best be illustrated by an example. Though several different statistical dose-response functions (the probit, logit, and one-particle curves) are all very similar within the observable range, the predicted practical threshold or "virtually" safe dose of Mantel and Bryan varies from one-hundredth to one-one-millionth of the TD1 (the dose which causes a maximum tumor incidence of one per cent), 43/ depending on which statistical function is selected. Little wonder that the Panel on Carcinogenesis of the PDA Advisory Committee on Protocols for Safety Evaluation H7--------------------------Hoel, D.G., Statistical extrapolation methods for estimating risks from animal data, 271 Ann. N.Y. Acad. Sci. 418 (1976); Salsbury, note 27 supra, at 116-8; Weil, C.S., Statistics vs. safety factors and scientific judgment in the 'evaluation'of s'kfety for*'man", 21 Toxicol" ~~Appl. Pharm. 454 (1972) . 42/ Gehring and Blau, note 17 supra. 43/ FDA Advisory Committee on Protocols for Safety Evalua tion, Panel on Carcinogenesis Report on Cancer Testing in the Safety Evaluation of Food Additives and Pesticides, 20 Toxicol. AddI. Pharm. 418 (1971), at 430-3. 1 C6Y 2302584 RSV0030370 * 13 concluded, "[I]t would be imprudent to place excessive reliance on mathematical sleight of hand, particularly when the dose- response curves used are largely empirical descriptions, lack44/ ing any theoretical physical or chemical basis." An additional problem with statistical extrapolation methodologies is that they entail an a priori assumption that the viability of physiological defense mechanisms and the metabolic fate of the carcinogen are not dose dependent. Mantel has acknowledged that the Mantel-Bryan Procedure is 45/ "essentially a conservative one." In a recent study, Gehring and Blau utilized dose-dependent or nonlinear pharmacokinetics to demonstrate that statistical extrapolation technicues are 46/ likely to substantially overestimate risk at low dosages. Consequently, setting exposure standards on the basis of statistical extrapolations can be "highly misleading, resulting 47/ in unnecessarily conservative 'permissible exposures'. ..." T?------------------------------ Id. at 433. 45/ Mantel, N., Conservation and "safe" dose estimates by the Mantel-Bryan procedure. 46/ Gehring and Blau, note 17 supra. 47/ Claus, et al., note 16 supra, at 745. CBY 2302585 RSV0030371 > 19 T The chief defects of ell statistical extrapolation methodologies are: (1) they have no theoretical basis, and (2) they involve a false a priori assumption that the propor tion of the carcinogen actually delivered in an activated form to the target area (the "effective dose") is not-doseHZ^ dependent. Consequently, calculations of "practical" exposure thresholds which represent an acceptable quantum of risk are more likely to be meaningful and realistic if they are based on Dlausible stochastic models of carcinogene- 48/ sis such as those proposed by Amitage and Doll and 49/ Neyman and Scott and non-linear pharmacokinetic models 50/ such as that proposed by Gehring and Blau. i!/ Amitage, P. and Doll, R., Stochastic models for carcin ogenesis, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. IV, Ed. Neyman, J. Untv. Cal. Press (1961), at 19-38. 49/ Neyman, J. and Scott, E. L., Statistical aspects of the problem of carcinogenesis, in Proceedings of the Fifth Berkeley Svnoosium on Mathematical Statistics and Probability, vol. IV~, Ed. LeCam, L.M. and Neyman, J. , Univ. Cal. Press (1967), at 745-776; see also Salsbury, note 27 supra, at 120-1. 50/ Gehring and Blau, note 17 supra. CBY 2302586 RSV0030372