Figure 1.

A. Three-stage CRC carcinogenesis model. The model agrees with the notion that adenoma initiation requires the biallelic inactivation of the APC gene. The parameters are: the number of susceptible stem cells, X, the mutation rate of the first hit at the APC gene, μ0, the mutation rate of the second copy of the APC gene, μ1, the adenoma cell division rate, α, the adenoma cell death or differentiation rate, β, and the malignant transformation rate, μ2.

B. The hazard (or incidence) function of the model (as a function of age t) exhibits three distinct phases that reveal the carcinogenic process in reverse. In particular, for older ages the hazard increases linearly reflecting the incidence of adenomas. The line approximating this (linear) phase has an intersect with the age axis that represents the mean time between adenoma initiation and its conversion into a clinical carcinoma (Ts). For mid-ages, the hazard rises exponentially, with a rate equal to the net growth rate of adenomas (α-β). For younger ages, the hazard increases as a power of age, consistent with the Armitage-Doll theory of multistage carcinogenesis