Optimal designs for the analysis of interactive effects of two carcinogens or other toxicants

In this paper we consider the design of animal experiments conducted to test for interaction between two carcinogens or other toxicants. We examine 2 x 2 designs which contain an untreated control group, two groups treated with a single dose of each toxic agent alone, and one group treated with both agents together. Optimal rules for allocating animals to the experimental groups are derived on the basis of expected response rates for acute toxicity studies and these rules are then extended to long-term carcinogenesis studies by considering times-to-tumor under an assumption of proportional hazards. Unbalanced designs with more animals in the combination group than in the control group are shown to provide a gain in efficacy of about 20% over balanced designs.