Sample size determination for phase II clinical trials based on Bayesian decision theory

This paper describes an application of Bayesian decision theory to the determination of sample size for phase II clinical studies. The approach uses the method of backward induction to obtain group sequential designs that are optimal with respect to some specified gain function. A gain function is proposed focussing on the financial costs of, and potential profits from, the drug development programme. On the basis of this gain function, the optimal procedure is also compared with an alternative Bayesian procedure proposed by Thall and Simon. The latter method, which tightly controls type I error rate, is shown to lead to an expected gain considerably smaller than that from the optimal test. Gain functions with respect to which Thall and Simon's boundary is optimal are sought and it is shown that these can only be of the form considered, that is, with constant cost for phase III study and cost of the phase II study proportional to the sample size, if potential profit increases over time.