Point and interval estimation in two-stage adaptive designs with time to event data and biomarker-driven subpopulation selection

In personalized medicine, it is often desired to determine if all patients or only a subset of them benefit from a treatment. We consider estimation in two-stage adaptive designs that in stage 1 recruit patients from the full population. In stage 2, patient recruitment is restricted to the part of the population, which, based on stage 1 data, benefits from the experimental treatment. Existing estimators, which adjust for using stage 1 data for selecting the part of the population from which stage 2 patients are recruited, as well as for the confirmatory analysis after stage 2, do not consider time to event patient outcomes. In this work, for time to event data, we have derived a new asymptotically unbiased estimator for the log hazard ratio and a new interval estimator with good coverage probabilities and probabilities that the upper bounds are below the true values. The estimators are appropriate for several selection rules that are based on a single or multiple biomarkers, which can be categorical or continuous.