Abstract
In many randomized placebo-controlled trials with a biomarker defined subgroup, it is believed that this subgroup has the same or higher treatment effect compared with its complement. These subgroups are often referred to as the biomarker positive and negative subgroups. Most biomarker-stratified pivotal trials are aimed at demonstrating a significant treatment effect either in the biomarker positive subgroup or in the overall population. A major shortcoming of this approach is that the treatment can be declared effective in the overall population even though it has no effect in the biomarker negative subgroup. We use the isotonic assumption about the treatment effects in the two subgroups to construct an efficient way to test for a treatment effect in both the biomarker positive and negative subgroups. A substantial reduction in the required sample size for such a trial compared with existing methods makes evaluating the treatment effect in both the biomarker positive and negative subgroups feasible in pivotal trials especially when the prevalence of the biomarker positive subgroup is less than 0.5.