Armitage–Doll model is a statistical model of carcinogenesis proposed in 1954 by Peter Armitage and Richard Doll, in which cancer arises through a series of discrete heritable mutational events within a single cell lineage. The model was motivated by the observation that the age-specific incidence of many epithelial cancers increases with approximately the fifth or sixth power of age, a relationship that could be explained if carcinogenesis requires k sequential mutations, each occurring at a constant rate.

Under the Armitage-Doll framework, if each mutational step occurs at a constant rate independent of age, then cancer incidence should increase proportionally to age raised to the power of k−1, where k is the number of rate-limiting stages. This formulation provided the first quantitative explanation for the long latent periods characteristic of human carcinogenesis and the cumulative effect of carcinogen exposure over time. The original analysis of cancer mortality data suggested that 5–7 discrete events are typically required, a prediction that anticipated the modern understanding of multistep tumorigenesis involving sequential mutations in oncogenes and tumor suppressor genes.

Subsequent extensions by Moolgavkar, Venzon, and Knudson incorporated cell proliferation kinetics and the clonal expansion of intermediate cell populations, generalizing the Armitage-Doll framework into the two-mutation clonal expansion model that remains a foundation of cancer epidemiology.