A comparison of estimation methods adjusting for selection bias in adaptive enrichment designs with time-to-event endpoints

Adaptive enrichment designs in clinical trials have been developed to enhance drug developments. They permit, at interim analyses during the trial, to select the sub-populations that benefits the most from the treatment. Because of this selection, the naive maximum likelihood estimation of the treatment effect, commonly used in classical randomized controlled trials, is biased. In the literature, several methods have been proposed to obtain a better estimation of the treatments' effects in such contexts. To date, most of the works have focused on normally distributed endpoints, and some estimators have been proposed for time-to-event endpoints but they have not all been compared side-by-side. In this work, we conduct an extensive simulation study, inspired by a real case-study in heart failure, to compare the maximum-likelihood estimator (MLE) with an unbiased estimator, shrinkage estimators, and bias-adjusted estimators for the estimation of the treatment effect with time-to-event data. The performances of the estimators are evaluated in terms of bias, variance, and mean squared error. Based on the results, along with the MLE, we recommend to provide the unbiased estimator and the single-iteration bias-adjusted estimator: the former completely eradicates the selection bias, but is highly variable with respect to a naive estimator; the latter is less biased than the MLE estimator and only slightly more variable.