Asymptotic Optimal Sample Sizes for Discovering a Promising Treatment in Phase II Group Sequential Clinical Trials

We propose an asymptotic optimal procedure for determining the per-study sample size of a series of Phase II clinical studies. The sequence of studies seeks to discover an active treatment among a sequence of treatments under evaluation. Each phase II study proceeds in r stages with r=1, 2, or 3. Our result serves two practical purposes. First, it yields asymptotic optimal sample sizes. Second, it reduces the dimension of the design space for finding the exact optimal sample sizes. The criterion of optimality is to minimize the total number of observations until one promising treatment is identified, while controlling the probabilities of false positive and false negative errors to desired levels. The asymptotic optimal sample sizes are given explicitly based on analytical results and their computation is straightforward. Numerical studies show that the asymptotic optimal sample sizes and true optimal sample sizes are quite close. The Bayesian formulation of the problem is used in the procedure and choice of prior distributions is discussed