Keywords: Group Sequential Design, survival data, Constrained Optimal Designs
Optimized group sequential designs proposed in the literature have designs minimizing average sample size (ASN) with respect to a prior distribution of treatment effect with overall type I and type II error rates well-controlled. The optimized asymmetric group sequential designs that we present here additionally consider constrains on stopping probabilities at stage one: probability of stopping for futility at stage one when no drug effect exists as well as the probability of rejection when the maximum effect size is true at stage one so that accountability of group sequential design is ensured from the very first stage throughout. Besides, non-binding efficacy bounds are used to account for often-occurred overrunning in real trials, and the shape parameters for Wang-Tsiatis upper bounds and Kim-DeMets lower bounds are utilized to find optimized group sequential designs minimizing ASN while maintaining error and power requirements overall and at stage one. From examples illustrated, the maximum sample size determined through optimization turns out to be smaller than prior optimized designs using other ways of optimization.