Bayesian design and analysis of two x two factorial clinical trials

The 2 x 2 factorial design has been advocated for improving the efficiency of clinical trials. Most such trials are designed on the assumption that there is no interaction between the levels of the factors and outcome. This assumption is often problematic, however, because interactions are usually possible in clinical trials and the sample sizes often used provide little power in testing for interactions. We consider the use of Bayesian methods for the design and analysis of 2 x 2 factorial clinical trials. This approach avoids the need to dichotomize one's assumptions that interactions either do or do not exist and provides a flexible approach to the design and analysis of such clinical trials. Exact results are developed for balanced factorial designs with normal response. Approximations are then presented for factorial designs based on the logistic model for binary response or the proportional hazards model for time-to-event data. The resulting approximate posterior distributions are normal and hence no extensive computations are required. Suggestions for specification of prior distributions are presented.