Cancer models and statistical analysis of age distribution of cancers

Abstract

In this paper, mathematical mutational models of the age distribution of cancers are obtained. These are two models - a simple model and a complex model, which takes into account the growth of the cell population and the transmission of mutations to daughter cells. Using the resulting formulas, we approximated real age-specific cancer incidence datasets in women (colon, lung, mammary, stomach) and men (colon, lung, prostate, stomach). We estimated parameters such as the average number of mutations (per cell per unit of time) and number of mutations required for cancer to occur. The number of mutations averaged (over four types of cancer) required for cancer to occur is 5.5 (mutations per cell for women) and 6.25 (mutations per cell for men) for the complex mutational model. As an alternative to mutational models, we also consider the model of delayed carcinogenic event.