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On the Exact Hazard and Survival Functions of the MVK Stochastic Carcinogenesis Model

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  • Qi Zheng

Abstract

The MVK two‐stage carcinogenesis model is one of the most widely accepted mechanistic models in carcinogenesis modeling. However, due to a perceived difficulty in obtaining analytic solutions for the hazard and survival functions, approximations and numerical methods have been used to calculate these two fundamental quantities. This paper focuses on a special case of the homogeneous MVK model where the number of normal cells is constant. The probability generating function (pgf) for the number of tumor cells is derived, and the exact analytic solutions to the hazard and survival functions are obtained from the pgf.

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  • Qi Zheng, 1994. "On the Exact Hazard and Survival Functions of the MVK Stochastic Carcinogenesis Model," Risk Analysis, John Wiley & Sons, vol. 14(6), pages 1081-1084, December.
    • Handle: RePEc:wly:riskan:v:14:y:1994:i:6:p:1081-1084
    DOI: 10.1111/j.1539-6924.1994.tb00079.x
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    References listed on IDEAS

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    1. Suresh Moolgavkar & Anup Dewanji, 1988. "Biologically Based Models for Cancer Risk Assessment: A Cautionary Note," Risk Analysis, John Wiley & Sons, vol. 8(1), pages 5-6, March.
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    Cited by:

    1. David W. Gaylor & Qi Zheng, 1996. "Risk Assessment of Nongenotoxic Carcinogens Based upon Cell Proliferation/Death Rates in Rodents," Risk Analysis, John Wiley & Sons, vol. 16(2), pages 221-225, April.
    2. David W. Gaylor & Qi Zheng, 1997. "A Note on the Relationship Between Lifetime Tumor Risk and Expected Time to Tumor," Risk Analysis, John Wiley & Sons, vol. 17(1), pages 5-7, February.
    3. Qi Zheng, 1997. "A Unified Approach to a Class of Stochastic Carcinogenesis Models," Risk Analysis, John Wiley & Sons, vol. 17(5), pages 617-624, October.
    4. Qi Zheng, 1995. "On the MVK Stochastic Carcinogenesis Model with Erlang Distributed Cell Life Lengths," Risk Analysis, John Wiley & Sons, vol. 15(4), pages 495-502, August.
    5. Harvey J. Clewell III & Dennis W. Quinn & Melvin E. Andersen & Rory B. Conolly, 1995. "An Improved Approximation to the Exact Solution of the Two‐Stage Clonal Growth Model of Cancer," Risk Analysis, John Wiley & Sons, vol. 15(4), pages 467-473, August.
    6. Leonid G. Hanin & Andrej Yu. Yakovlev, 1996. "A Nonidentifiability Aspect of the Two‐Stage Model of Carcinogenesis," Risk Analysis, John Wiley & Sons, vol. 16(5), pages 711-715, October.

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