A New Overall-Subgroup Simultaneous Test for Optimal Inference in Biomarker-Targeted Confirmatory Trials

We propose a joint hypothesis test for simultaneous confirmatory inference in the overall population and a pre-defined marker-positive subgroup under the assumption that the treatment effect in the marker-positive subgroup is larger than that in the overall population. The proposed confirmatory overall-subgroup simultaneous test (COSST) is based on partitioning the sample space of the test statistics in the marker-positive and marker-negative subgroups. We define two rejection regions in the joint sample space of the two test statistics: (1) efficacy in the marker-positive subgroup only; (2) efficacy in the overall population. COSST achieves higher statistical power to detect the overall and subgroup efficacy than most sequential procedures while controlling the family-wise type I error rate. COSST also takes into account the potentially harmful effect in the subgroups in the decision. The optimal rejection regions depend on the specific alternative hypothesis and the sample size. COSST can be useful for Phase III clinical trials with tailoring objectives.