Carcinogenesis is commonly described as a multistage process. In a first step, a stem cell is transformed via a series of mutations into an intermediate cell having a growth advantage. Under favorable conditions, such a cell will give rise to a clone of initiated cells. Eventually, further alterations may transform a cell out of this clone into a malignant tumor cell. A mechanistic model of this process is given by the widely used two-stage clonal expansion model (TSCE). In this thesis, we take up a generalization of the TSCE, and study, how to introduce the concept of population heterogeneity into the model. We use mixture modeling, which allows to describe frailty in a biologically meaningful way. In a first part, we focus on theoretical properties of the extended model. Especially identifiability is discussed extensively. In a second part, we fit the model to human cancer incidence data. We analyze a situation, in which maximum likelihood estimation fails, and describe alternatives for statistical inference. The applications show that good fits are achieved only when the mixing distribution separates the population clearly into a large, virtually immune group, and into a small, high risk group.