A Bayesian Adaptive Marker-Stratified Design for Phase II Clinical Trials Using Calibrated Spike-and-Slab priors.

The marker-stratified design (MSD) is useful for assessing subgroup-specific treatment effects of molecularly targeted agents (MTA). In MSD, patients are first classified into the marker-positive and marker-negative subgroups, and then randomized for MTA or control treatment within each subgroup. The clinical features of the biomarker and treatments used in MSD offer valuable information for treatment evaluation. Specifically, response rates for patients on the control treatment remain similar across different subgroups if the biomarker involved is not prognostic. Additionally, when the MTA is effective, the marker-positive patients generally exhibit significantly higher response rates compared to the marker-negative patients receiving the same MTA. This paper proposes a Bayesian adaptive design (SSS) that uses these clinical features to enhance the efficiency of MSD. The SSS design employs spike-and-slab priors to dynamically borrow information on response rates across different subgroups. The strength of this information borrowing is automatically determined by two posterior probabilities, which measure the similarities in response rates between different subgroups. Furthermore, an extension of the SSS design is proposed to accommodate patients with missing biomarker profiles, utilizing the Bayesian multiple imputation (BMI) method. Simulation studies confirm that the proposed SSS design demonstrates favorable operational characteristics and outperforms the conventional Bayesian designs.