Hypothesis Testing in a Confirmatory Phase III Trial With a Possible Subset Effect

Many new drugs under development in oncology may have greater benefit in, or provide benefit to, a subset of the overall population. The subpopulation of interest may be characterized with a gene expression signature or other biomarker. The evidence for the subpopulation effect is generally not conclusive prior to Phase III, leading to risk inherent in studying only the subpopulation in Phase III. However, studying the overall population in Phase III is also risky in that one may miss activity that is present in the subset only. To mitigate the risk, researchers have proposed a method that assigns different but fixed Type I error rates to the overall hypothesis and the subset hypothesis based on mid-trial data. This method also allows discovery of the subpopulation in the first half of the trial, if the subpopulation has not previously been identified. Post-study adaptation methods have also been proposed. In this article, we propose a method that provides optimal alpha-split (as opposed to fixed alpha-split) by explicitly maximizing an objective function that properly incorporates all prior information on treatment effect available at the decision point. The method is introduced in the simpler setting where the decision is made up front based on external Phase II data. It is applied to an optimal futility boundary search for interim analyses and is extended to optimize resource allocation between Phase II and Phase III, alpha-split for multiple subpopulations, and alpha-split when mid-trial data are used. Although the work is motivated by oncology trials, the method is equally applicable to drug development programs in other disease areas.