ABSTRACT
This chapter aims to provide some mathematical theories of the multievent models and suggests some possible applications. It provides some biological evidence supporting the multievent models which may involve more than two stages. Much biological data suggest that in some cancers the process of carcinogenesis involves more than two stages. The chapter shows that the multievent model of carcinogenesis is in fact a filtered Poisson process under some general conditions. It explores the age-specific incidence functions of tumors and presents some approximations to these incidence functions by assuming that the mutation rates are very small and that the cell proliferation rates of intermediate cells are small. The chapter examines the expected numbers of tumors and the variances and covariances of the numbers of tumors by solving some ordinary differential equations. The special cases of multievent models include the homogeneous multievent models and the nonhomogeneous piece-wise multievent models which are analogs of the Tan-Gastardo two-stage models.
