Assessment of interaction between carcinogens in long-term factorially designed animal experiments

Two substances interact if the combined action results in an effect which is greater than, or less than, that of the sum of the effects produced separately by the substances. Finney (1971, Probit Analysis, 3rd ed. Cambridge: Cambridge University Press) proposed a probabilistic model for simple independent action of two substances for the case of dichotomous outcomes. Using Finney's underlying model, we examine tests for interaction between carcinogens or toxic substances for data from long-term 2 x 2 and 2 x 2 x 2 factorially designed animal experiments. The outcome of interest is the occurrence or not of a certain event (for example, the appearance of a tumor) and the time at which the event occurred. The proposed tests are based on the proportional hazards model. We discuss some simple methods for checking the appropriateness of the proportional hazards assumption. Applications of the tests are made to data from a 2 x 2 and a 2 x 2 x 2 experiment.