ABSTRACT
This chapter explores some mathematical theories for various mixed models of carcinogenesis and indicate some possible applications. It presents some biological evidence supporting the mixed models of carcinogenesis in the population. The chapter proposes a general mixed model in the population involving four groups of subpopulations in each of which a different carcinogenesis model is entertained. It describes the age-specific incidence functions of tumors and provides some applications of mixed models in risk assessment of environmental agents. In cancers involving oncogenes and changing environments, it is expected that the population would consist of several subpopulations each of which involves a multiple pathway model of one-stage and two-stage carcinogenesis models. Much biological evidence exists indicating that for many cancers the process of carcinogenesis in the population is a mixture of different carcinogenesis models. For developing mathematical theories for the proposed mixed model, the chapter discusses the probability generating functions of the number of tumors for each population under some general conditions.
