Improving power in adaptive expansion of biomarker populations in phase 3 clinical trials

With the availability of unprecedented human genomic biomarker data, incorporating such biomarker data has received a lot of attention in phase 3 clinical trials. One particular enrichment design proposed recently in the literature is to recruit more biomarker positive patients in an all-comer study if the treatment effect in the biomarker negative group is less promising than expected. The intuition is to improve the chance of success of the trial since the success rate in the all-comer population may be low. We propose an enrichment design that unifies the existing biomarker adaptive designs for phase 3 clinical trials. In addition, we propose a new test accounting for the correlations among the test statistics based on different groups of patients, including all-comers, biomarker positive patients only, and biomarker negative patients only. We investigate the theoretical properties of the design and demonstrate the new test accurately controls the type I error rate and gains power over existing methods through extensive simulations. A computer program is developed for power calculations given a set of design parameters, including the proportion of biomarker positive patients, the distribution of the failure time in each treatment and biomarker group, and the number of patients in the first stage and the second stage (i.e. the enrichment stage), among others.