title: Calculating tumor incidence rates in stochastic models of carcinogenesis.
abstract: Multistage models of carcinogenesis are increasingly used in the estimation of risks from exposure to environmental agents. The two-stage model of carcinogenesis is routinely used because it agrees with much of the existing tumor incidence data, parallels the biological two-stage model, and has much of its mathematical details derived. However, recent findings on the mechanisms of carcinogenesis has led researchers to believe that there are a greater number of stages and a more complex structure to these models than a single pathway. In this paper, a method for readily computing tumor incidence rates for arbitrarily complex multistage models is derived. The formulas for the two-stage model with time-varying rates are given explicitly. Simple rules for more complicated models are given, and computer code able to implement these formulas are provided.
authors.affiliation: National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina, USA.
authors.forename: C J
authors.initials: CJ
authors.lastname: Portier
authors.forename: A
authors.initials: A
authors.lastname: Kopp-Schneider
authors.forename: C D
authors.initials: CD
authors.lastname: Sherman
mesh_terms: D000818:Animals; D003043:Cocarcinogenesis; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D009369:Neoplasms / Q000453:epidemiology* / Q000209:etiology*; D013269:Stochastic Processes