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On the Exact Hazard and Survival Functions of the MVK Stochastic Carcinogenesis Model
Author(s) -
Zheng Qi
Publication year - 1994
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/j.1539-6924.1994.tb00079.x
Subject(s) - hazard , carcinogenesis , mathematics , constant (computer programming) , function (biology) , stochastic modelling , homogeneous , statistical physics , statistics , physics , computer science , biology , cancer , ecology , genetics , programming language
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.