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A Numerical Solution to the Nonhomogeneous Two‐Stage MVK Model of Cancer
Author(s) -
Crump Kenny S.,
Subramaniam Ravi P.,
Van Landingham Cynthia B.
Publication year - 2005
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.1539-6924.2005.00651.x
Subject(s) - ordinary differential equation , stage (stratigraphy) , mathematics , hazard , process (computing) , function (biology) , differential equation , mathematical optimization , computer science , mathematical analysis , biology , ecology , paleontology , evolutionary biology , operating system
In this article, we describe a straightforward method for solving the probability of at least one malignant cell by time t , and the associated hazard function, in the general (i.e., nonhomogeneous) two‐stage Moolgavkar‐Venzon‐Knudson (MVK) model of cancer. The method consists of solving four coupled ordinary differential equations derived from the Kolmogorov backward equations for this process. The relationship of this method to previously proposed solutions is discussed.