Armitage–Doll multistage model of carcinogenesis
The Armitage–Doll model is a statistical model of carcinogenesis, proposed in 1954 by Peter [Armitage (statistician)|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
in Ashley's notation.
Their interpretation was that a series of 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 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.