MULTISTAGE MODELS OF CARCINOGENESIS - AN APPROXIMATION FOR THE SIZE AND NUMBER-DISTRIBUTION OF LATE-STAGE CLONES

Multistage models have become the basic paradigm for modeling carcinog enesis. One model, the two-stage model of carcinogenesis, is now routi nely used in the analysis of cancer risks from exposure to environment al chemicals. In its most general form, this model has two states, an initiated state and a neoplastic state, which allow for growth of cell s via a simple linear birth-death process. In all analyses done with t his model, researchers have assumed that tumor incidence is equivalent to the formation of a single neoplastic cell and the growth kinetics in the neoplastic state have been ignored. Some researchers have discu ssed the impact of this assumption on their analyses, but no formal me thods were available for a more rigorous application of the birth-deat h process. In this paper, an approximation is introduced which allows for the application of growth kinetics in the neoplastic state. The ad equacy of the approximation against simulated data is evaluated and me thods are developed for implementing the approximation using data on t he number and size of neoplastic clones.