PMID: 8589544Jan 15, 1996Paper

An exact representation for the generating function for the Moolgavkar-Venzon-Knudson two-stage model of carcinogenesis with stochastic stem cell growth

Mathematical Biosciences
J Denes, D Krewski

Abstract

The two-stage clonal expansion model of carcinogenesis provides a convenient biologically based framework for the quantitative description of carcinogenesis data. Under this stochastic model, a cancer cell arises following the occurrence of two critical mutations in a normal stem cell. Both normal cells and initiated cells that have sustained the first mutation undergo birth-and-death processes responsible for tissue growth. In this article, a new expression for the probability generating function (pgf) for the two-stage model of carcinogenesis is derived. This characterization is obtained by solving a partial differential equation (pde) satisfied by the pgf derived from the corresponding Kolmogorov forward equation. This pde can be reduced to the hypergeometric differential equation of Gauss, which leads to a closed-form expression for the pgf requiring only the evaluation of hypergeometric functions. This result facilitates computation of the exact hazard function for the two-stage model. Several approximations that are simpler to compute are also given. Numerical examples are provided to illustrate the accuracy of these approximations.

References

Apr 15, 1992·Journal of the National Cancer Institute·S H Moolgavkar, E G Luebeck
Sep 1, 1991·Risk Analysis : an Official Publication of the Society for Risk Analysis·R L KodellJ M Zielinski
Jun 1, 1990·Risk Analysis : an Official Publication of the Society for Risk Analysis·S H Moolgavkar, G Luebeck
Sep 1, 1988·Risk Analysis : an Official Publication of the Society for Risk Analysis·S H MoolgavkarD J Venzon
Mar 1, 1988·Risk Analysis : an Official Publication of the Society for Risk Analysis·S Moolgavkar, A Dewanji

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Citations

Oct 24, 2001·Mutation Research·I M van Leeuwen, C Zonneveld
Aug 1, 1996·Risk Analysis : an Official Publication of the Society for Risk Analysis·B G LerouxE M Faustman
Oct 29, 2002·Journal of Radiological Protection : Official Journal of the Society for Radiological Protection·E Georg Luebeck, William D Hazelton
Dec 24, 1997·Risk Analysis : an Official Publication of the Society for Risk Analysis·Q Zheng
Apr 16, 2019·PLoS Computational Biology·Michael D Nicholson, Tibor Antal
Feb 3, 1998·Statistical Methods in Medical Research·A Kopp-Schneider

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