Cancer incidence and the biology of extreme old age

In this paper we explore the implications of two models of carcinogenesis on the incidence of cancer in extreme old age (80 years or older). Both models pose that cancer is the final stage of a multistage process and that the transition rates between stages slows with age. We find that in a 7-stage model, where all stages have monotonic transition rates, a decrease of as little as 60% in the transition rate of each stage could cause the observed decrease in cancer risk at extreme old age. If only the transition rate of a single stage slows, then a decrease of at least 90% is needed to explain the observed patterns of cancer incidence. Because of this, we conclude that it is likely that if a decrease in transition rates is indeed responsible for the decrease in cancer incidence risk at extreme old age then multiple stages are involved.