OFGSD: Optimal Futility Stopping Rules for Group Sequential Design

Group sequential design (GSD) has been widely used in pharmaceutical industry for drug development, especially in phase III pivotal studies. Efficacy boundaries in a GSD usually can be determined by an alpha-spending function. To determine the futility boundaries, a classical approach is to use a beta-spending function under the efficacious treatment effect assumption, ensuring target power. However, this method does not explicitly control the probability of stopping a trial before the final analysis under the null hypothesis. We propose an Optimal Futility stopping GSD (OFGSD) framework that selects futility boundaries to minimize total sample size while guaranteeing a prespecified probability of early stopping under the null hypothesis. An R Shiny App has been developed to implement this method. With the proposed OFGSD, one can also save total sample size by more than 8% in some cases to achieve the same study power and futility stopping probability (FSP) compared with using the traditional GSD with futility boundaries determined by a beta-spending function. This gain comes at a trade-off though: under the null hypothesis OFGSD in general leads to larger average sample sizes – in some cases OFGSD can cost 18% more on average sample size compared with the traditional GSD.