Isotonic design for single-arm biomarker stratified trials

In single-arm trials with a predefined subgroup based on baseline biomarkers, it is often assumed that a biomarker defined subgroup, the biomarker positive subgroup, has the same or higher response to treatment compared to its complement, the biomarker negative subgroup. The goal is to determine if the treatment is effective in each of the subgroups or in the biomarker positive subgroup only or not effective at all. We propose the isotonic stratified design for this problem. The design has a joint set of decision rules for biomarker positive and negative subjects and utilizes joint estimation of response probabilities using assumed monotonicity of response between the biomarker negative and positive subgroups. The new design reduces the sample size requirement when compared to running two Simon's designs in each biomarker positive and negative. For example, the new design requires 23%-35% fewer patients than running two Simon's designs for scenarios we considered. Alternatively, the new design allows evaluating the response probability in both biomarker negative and biomarker positive subgroups using only 40% more patients needed for running Simon's design in the biomarker positive subgroup only.