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An exact representation for the generating function for the Moolgavkar-Venzon-Knudson two-stage model of carcinogenesis with stochastic stem cell growth.
Authors
- Denes, J, Denes J, Health Canada, Ottawa, Ontario, Canada.
- Krewski, D, Krewski D,
YEAR OF PUBLICATION: 1996
SOURCE: Math Biosci. 1996 Jan 15;131(2):185-204. doi: 10.1016/0025-5564(95)00046-1.
JOURNAL TITLE ABBREVIATION: Math Biosci
JOURNAL TITLE: Mathematical biosciences
ISSN: 0025-5564 (Print) 0025-5564 (Linking)
VOLUME: 131
ISSUE: 2
PAGES: 185-204
PLACE OF PUBLICATION: United States
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.
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.
LANGUAGE: eng
DATE OF PUBLICATION: 1996 Jan 15
DATE COMPLETED: 19960327
DATE REVISED: 20191024
MESH DATE: 1996/01/15 00:01
EDAT: 1996/01/15 00:00
STATUS: MEDLINE
PUBLICATION STATUS: ppublish
OWNER: NLM
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Chief Risk Scientist
Dr. Daniel Krewski is Chief Risk Scientist and co-founder of Risk Sciences International (RSI), a firm established in 2006 to bring evidence-based, multidisciplinary expertise to the challenge of understanding, managing, and communicating risk. As RSI’s inaugural CEO and long-time scientific...