Stochastic modeling of carcinogenesis by state space models: a new approach

In this paper, we have developed some state space models for carcinogenesis involving multievent models and multiple pathways models. In these state space models, the stochastic system models are stochastic models of carcinogenesis expressed in terms of stochastic differential equations, whereas the observation models are statistical models based on the observed number of detectable preneoplastic lesions per individual over time and the observed number of detectable cancer tumors per individual over time. In this paper, we have applied some of the theories to some animal papillomas data from some initiation-promotion experiments on skin cancer in mice to estimate some unknown parameters. For this data set we have obtained excellent fit by a model with three piece-wise intervals.