Optimal interim decision rules based on a binary surrogate outcome for adaptive biomarker-based trials in oncology

Adaptive enrichment designs represent a promising approach to evaluate targeted therapies, e.g. in oncology. They allow selection of the most promising target population in an interim analysis and then combination of the data from the two trial stages for the final proof of efficacy. Application of these designs is motivated by the assumption that there might be a biomarker-defined subgroup of patients with an increased treatment benefit as compared to the total patient population. If the primary outcome is a time-to-event variable and the respective event takes a relatively long time to be observed, it could be beneficial to select the most promising patient population based on an earlier available binary surrogate, e.g. response, to save time and costs. We propose an adaptive enrichment design which allows to implement such a trial setting. For this design, optimal decision rules are derived minimizing the expected loss incurred due to a false interim decision. These rules are compared to <i>ad hoc</i> rules in terms of selection probability and power within a simulation study which is motivated by a clinical trial example. Furthermore, the impact of the correlation between surrogate and primary outcome on power is investigated.