Armitage–Doll multistage model of carcinogenesis

The Armitage–Doll model is a statistical model of carcinogenesis, proposed in 1954 by Peter Armitage and Richard Doll, in which a series of discrete mutations result in cancer.^[1] The original paper has recently been reprinted with a set of commentary articles.

The rate of incidence and mortality from a wide variety of common cancers follows a power law: someone's risk of developing a cancer increases with a power of their age.^[2]

The model is very simple, and reads

${\displaystyle \mathrm {rate} ={\frac {Np_{1}p_{2}p_{3}\cdots p_{r}}{(r-1)!}}t^{r-1}}$

in Ashley's notation.^[3]

Their interpretation was that a series of ${\displaystyle r}$ mutations were required to initiate a tumour.^[1] This is now widely accepted, and part of the mainstream view of carcinogenesis. In their original paper, they found that ${\displaystyle r}$ was typically between 5 and 7. Other cancers were later discovered to require fewer mutations: retinoblastoma, typically emerging in early childhood, can emerge from as few as 1 or 2, depending on pre-existing genetic factors.

This was some of the earliest strong evidence that cancer was the result of an accumulation of mutations. With their 1954 paper, Armitage and Doll began a line of research that led to Knudson's two-hit hypothesis and thus the discovery of tumour suppressor genes.^[3][4]

• Steven A Frank (2004) "Commentary: Mathematical models of cancer progression and epidemiology in the age of high throughput genomics", Int. J. Epidemiol. 33(6): 1179-1181 doi:10.1093/ije/dyh222
• Suresh H Moolgavkar (2004) "Commentary: Fifty years of the multistage model: remarks on a landmark paper", Int. J. Epidemiol. 33(6): 1182-1183 doi:10.1093/ije/dyh288
• Richard Doll (2004) "Commentary: The age distribution of cancer and a multistage theory of carcinogenesis", Int. J. Epidemiol. 33(6): 1183-1184 doi:10.1093/ije/dyh359

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