Two stage model for carcinogenesis: number and size distributions of premalignant clones in longitudinal studies

The two stage clonal expansion model of carcinogenesis provides a convenient biologically based framework for the description of toxicologic and epidemiologic data on carcinogenesis. Under this model, a cancer cell is generated following the occurrence of two critical mutations in a single stem cell. Initiated cells that have sustained the first mutation undergo a stochastic birth-death process resulting in clonal expansion of the initiated cell population. In this article, we consider the analysis of longitudinal data on the number and size of premalignant clones, formed by clonal expansion of initiated cells. In particular, the joint distribution of the number of premalignant clones observed at different points in time in the same subject is derived. The application of these results in the statistical analysis of longitudinal data on the number and size of premalignant clones observed in initiation-promotion experiments is indicated.