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Cancer Dose-Response Models Incorporating Clonal Expansion

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Abstract

Under the assumption that a malignant tumor develops through a sequence of steps (normal cells → initiated cells/foci → nodules → tumors) two classes of mathematical models of carcinogenesis that have a potential to be used for cancer dose-response modeling are discussed. The two classes of models considered are (1) a general version of the two-stage model by Moolgavkar and colleagues [12, 13], henceforth called the MVK model, and (2) a clone process model derived from Tucker [21]. These two classes of models incorporate essentially the same biological information but in different ways and offer a conceptual contrast between the two differing approaches. The objectives of this paper are to (1) highlight issues and problems that arise in using biologically based dose-response models to predict cancer risk and (2) discuss how parameters in the models could be estimated using auxiliary information.

We have also demonstrated that use of an approximate form of the MVK model may lead to a biologically unrealistic implication of the model and an underestimation of risk at low doses when parameters are estimated from bioassay data.

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References

  1. Altman, P., Dittmer, D. Biology Data Book, 2nd edition, Vol. 1, Federation of American Societies for Experimental Biology, Bethesda, MD. (1972).

    Google Scholar 

  2. Burns, F., Albert, R. Mouse skin papillomas as early stage of carcinogenesis. J. Amer. College Toxicol. 1:29–45 (1982).

    Article  Google Scholar 

  3. Burns, F., Albert, R., Altshuler, B., and Morris, E. Approach to risk assessment for genotoxic carcinogens based on data from mouse skin initiation-promotion model. Environ. Health Perspect. 50:309–320 (1983).

    Article  Google Scholar 

  4. Chen, C, Blancato, J. Incorporation of biological information in cancer risk assessment. Example — vinyl chloride. To appear in Toxicology and Industrial Health (in press).

    Google Scholar 

  5. Chiang, C. Introduction to stochastic processes in biostatistics, John Wiley & Sons, Inc., NY. (1968).

    Google Scholar 

  6. Dewanji, A., Venzon, D., and Moolgavkar, S. A stochastic two-stage model for cancer risk assessment: II. The number and size of premalignant clones. Risk Analysis 9(2):179–189 (1989)

    Article  Google Scholar 

  7. Drew, R., Boorman, G., Haseman, J., McConnell, E., Busey, W., and Moore, J. The effect of age and exposure duration on cancer induction by a known carcinogen in rats, mice, and hamsters. Toxicol. Appl. Pharmacol. 58:120–130 (1983).

    Article  Google Scholar 

  8. Laib, R., Klein, K., and Bolt, H. The rat liver foci bioassay: I. Age-dependence of induction by vinyl chloride of the ATPase-deflcient foci. Carcinogenesis 6(1):65–68(1985).

    Article  Google Scholar 

  9. Laib, R., Pellio, T., Wunschel, U., Zimmermann, N., and Bolt, H. The rats liver foci bioassay: II. Investigation on the dose-dependent induction of ATPase-deficient foci by vinyl chloride at very low doses. Carcinogenesis 6(l):69–72 (1985).

    Article  Google Scholar 

  10. Laib, R., Stockle, G., Bolt, H., and Kunz, W. Vinyl chloride and trichloroethylene: Comparison of alkylating effects of metabolites and induction of preneoplastic enzyme deficiencies in rat liver. J. Cancer Res. Clin. Oncol. 94:139–147(1979).

    Google Scholar 

  11. Maltoni, C., Lefemine, G., Ciliberti, A., Cotti, G., and Carretti, D. Carcinogenicity bioassays of vinyl chloride monomer: A model of risk assessment on an experimental basis. Environ. Health Perspect. 41:3–29 (1981).

    Article  Google Scholar 

  12. Moolgavkar, S., Venzon, D. Two-event models for carcinogenesis: Incidence curves for childhood and adult tumors. Math. Biosciences 47:55–77 (1979).

    Article  Google Scholar 

  13. Moolgavkar, S., Knudson, A. Mutation and cancer: a model for human carcinogenesis. J. Natl. Cancer Inst. 66:1037–1052 (1981).

    Google Scholar 

  14. Moolgavkar, S., Dewanji, A., and Venzon, D. A stochastic two-stage model for cancer risk assessment: I. The hazard function and the probability of tumor. Risk Analysis 8:383–392 (1989).

    Article  Google Scholar 

  15. Pugh, T., King, J., Koen, H., Nychka, D., Chover, J., Wahba, G., He, Y., and Goldfarb, S. Reliable stereological method for estimating the number of microscopic hepatocellular foci from their transections. Cancer Research 43:1261–1268(1983).

    Google Scholar 

  16. Serio, G. Two-stage stochastic model for carcinogenesis with time-dependent parameters. Statist. Prob. Lett. 2:95–103 (1984).

    Article  Google Scholar 

  17. Tan, W. A stochastic Gompertz birth-death process. Statist. Prob. Lett. 4:25–28 (1986).

    Article  Google Scholar 

  18. Tan, W., Gastardo, M. On the assessment of effects of environmental agents on cancer tumor development by a two-stage model of carcinogenesis. Math. Biosciences 73:143–155 (1985).

    Article  Google Scholar 

  19. Tan, W., Brown, C. A nonhomogeneous two-stage model of carcinogenesis. Math. Model. 9(8):631–642 (1987).

    Article  Google Scholar 

  20. Thorslund, T., Brown, C, and Charnley, G. Biologically motivated cancer risk models. Risk Analysis 7:109–119 (1987).

    Article  Google Scholar 

  21. Tucker, H. A Stochastic model for a two-stage theory of carcinogenesis. Proceedings for the Fourth Berkeley Symposium, Berkeley, CA 4:387–403 (1961).

    Google Scholar 

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© 1990 Birkhäuser Boston

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Chen, C.W., Moini, A. (1990). Cancer Dose-Response Models Incorporating Clonal Expansion. In: Moolgavkar, S.H. (eds) Scientific Issues in Quantitative Cancer Risk Assessment. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-9218-7_9

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  • DOI: https://doi.org/10.1007/978-1-4684-9218-7_9

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-9220-0

  • Online ISBN: 978-1-4684-9218-7

  • eBook Packages: Springer Book Archive

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