Multistage Risk Models and the Age Pattern in Familial Polyposis coli

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Abstract
Multistage risk models provide a close fit to most age patterns of adult-onset cancers. Such models posit that a number of events must occur before some cell in a tissue is transformed from normal to neoplastic. When an approximate version of the models has been fitted to data, this number has been estimated to be .apprx. 4-6. In fitting the same approximate model to the age pattern of onset of colon cancer in bearers of the familial polyposis coli (FPC) gene, several authors have found that the number of stages estimated was .apprx. 2-3 fewer than those for colon cancer in the general population. When an exact multistage model is used rather than an approximation to it, this is no longer the case; the number of stages estimated from the general population becomes too large to be compatible with what is known about carcinogenesis from laboratory experiments, and the number estimated from FPC victims is larger than that for the general population. Inherited-hit models of the nature of the FPC gene may be correct at the cellular level, but multistage models as commonly formulated cannot be used on data on the age-onset patterns in populations of individuals to infer such mechanisms or estimate their parameters.