Additive and multiplicative models and multistage carcinogenesis theory.

In light of the Armitage-Doll multistage carcinogenesis theory, this paper examines the assumption that an additive relative risk relationship is indicative of two carcinogens that affect the same stage in the cancer process. We present formulas to compute excess cancer risks for a variety of patterns for limited exposure durations to two carcinogens that affect the first and penultimate stages; and using an index of synergy proposed by Thomas (1982), we find a number of these patterns to produce additive, or nearly additive, relative risk relationships. The consistent feature of these patterns is that the two exposure periods are of short duration and occur close together.