Stochastic modeling of carcinogenesis: Some new insights

By surveying recent studies by molecular biologists and cancer geneticists, in this paper we have proposed some stochastic models of carcinogenesis and provided some biological evidences for these models. Because most of these models are quite complicated far beyond the scope of the MVK two-stage model, the traditional Markov theory approach becomes too complicated to be of much use. In this paper, we thus propose an alternative approach through stochastic differential equations. For validating the model and for estimating unknown parameters, we further use these stochastic differential equations to develop state space models (Kalman filter models) for carcinogenesis. In this paper, we have used the multievent model as an example to illustrate our modeling approach and some basic theories. These theories will be used by these authors to analyze data from experiments by scientists at BPNNL (Battelle Pacific Northwest National Laboratory) in Richland, WA.