Analysis of a stochastic model of cell survival

Abstract

A multiple-hit model used in the analysis of cell survival data is extended to include continuous parametric ranges of the gamma distribution. The justification of the extension involved is given a statistical interpretation. Furthermore, the model is placed in the context of a general stochastic theory of population and the relevant transition probability function is derived. An efficient numerical method for calculating the population curves as a function of time is shown. The general stochastic theory used in this paper is shown also to lead to a general survival equation, which clearly displays the important role played by the lifespan probability density function in survival studies. Several other survival models scattered throughout the biological literature are formulated in terms of the survival equation and thus these models, with different underlying biological processes, are shown to be related to a common mathematical structure.