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. The original paper has recently been reprinted with a set of commentary articles.
The model 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. The model is very simple, and reads
r a t e = N p 1 p 2 p 3 ⋯ p r ( r − 1 ) ! t r − 1 {\displaystyle \mathrm {rate} ={\frac {Np_{1}p_{2}p_{3}\cdots p_{r}}{(r-1)!}}t^{r-1}}
in Ashley's notation. Their interpretation was that a series of r {\displaystyle r} mutations were required to initiate a tumour. This is now widely accepted, and part of the mainstream view of carcinogenesis. In their original paper, they found that r {\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.
History 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.
References
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