Mathematical Models for Carcinogenesis Based on the Evidence of Molecular Biology and Its Application to Data Analysis

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We developed multistage models of carcinogenesis and cell death with taking account the effect of genomic instability. As for Armitage-Doll type of multistage models for carcinogenesis, some Monte Carlo simulations on the relationship between the number of stages and mutation rate were done. Using the follow-up data among atomic-bomb survivors and offspring, we examined the property of the models.The classical multi-target models have been also considered for use in analyzing data of the dose-response relationship. We tried to make some extended models. The target sizes we are concerned with are heterogeneous as simplified using geometric progression. We apply two models for establishing the multi-target models: a Poisson regression model constructed by assuming that the response variable follows Poisson distribution, and a gamma-frailty model as a Poisson mixture model derived by adding random common risks having a gamma distribution.Based on the theoretical results of our study, we developed several computer programs for analyzing dose-response data, and applied them to many sort of real data sets related to animal experiments, clinical researches and epidemiological studies including atomic bomb survivor's cohort data.