Mathematical models for human cancer incidence rates

The overall cancer incidence rate declines at old ages. Possible causes of this decline include the effects of cross-sectional data that transform cohort dynamics into age patterns, population heterogeneity that selects individuals susceptible to cancer, a decline in some carcinogenic exposures in older individuals, underdiagnostics, and the effects of individual aging that slow down major physiological processes in an organism. We discuss several mathematical models contributing to the explanation of this phenomenon. We extend the Strehler and Mildvan model of aging and mortality and apply it to the analysis of data on cancer incidence at old ages (data source: International Agency for Research on Cancer). The model explains the observed time trends and age patterns of cancer incidence rates.