Optimal designs for group sequential clinical trials

Group sequential tests have seen wide use in clinical trials. In this article a group sequential design is referred to an optimal one if the expected sample size under a specified alternative is minimized for a given choice of significance level and power among tests with a given sequence of groups of specific sizes. The optimal designs provide a standard for assessing the efficiency of many designs in the literature. This article concerns optimal two-sided tests with acceptance regions of the null hypothesis at early stages. We show that the backward induction method can be applied to compute optimal designs for group sequential tests. Subsequently we develop a numerical iterative procedure to compute the stopping boundaries of two-sided optimal sequential tests. Some numerical results are presented. The method can be generalized to one-sided tests and to two-sided tests without acceptance regions of the null hypothesis at early stages.