Interaction between two carcinogens in the two-stage clonal expansion model of carcinogenesis

Exposure to two or more carcinogens may result in interactive effects in which the joint effect may be greater or less than that expected to arise as the sum of the effects of the two agents alone. In this article, we investigate the joint effects of exposure to two carcinogens within the context of the two-stage clonal expansion model of carcinogenesis.

Different measures of interaction are considered based on the notions of response and dose additivity, and an index of synergy S due to Thomas (1982) used to broadly characterise the effects of joint exposure.

Interactive effects based on the index S were found to be qualitatively similar, regardless of whether cancer risk was defined in terms of age-specific relative risk, or the cumulative probability of cancer occurrence at the same age. For joint exposure to two initiators or to two completers (affecting the first or second mutation rate in the two-mutation model, respectively), S assumed values near zero, reflecting an additive relative-risk relationship. For joint exposure to two promoters (which increase the rate of proliferation of initiated cells that have sustained the first mutation), the relative-risk relationship was found to range from supramultiplicative (S > 1) in younger age groups, to subadditive (S < 0) in older ages. Other combinations of carcinogens involving promotion also displayed a broad range of interaction effects.

These results differ markedly from those reported previously by Kodell et al. (1991) for an approximate form of the two-stage model, which predicts much higher values of the index of synergy S than the exact form of the model when promotion is involved.