Bias correction based on weighted likelihood for conditional estimation of subgroup effects in randomized clinical trials

Currently, many confirmatory randomized clinical trials (RCTs) with predictive markers have taken the all‐comers approach because of the difficulty in developing predictive markers that are biologically compelling enough to apply the enrichment approach to restrict the patient population to a marker‐defined subgroup. However, such a RCT with weak marker credentials can conclude that the new treatment is efficacious only in the subgroup, especially when the primary analysis demonstrates some treatment efficacy in the subgroup, but the overall treatment efficacy is not significant under a control of study‐wise alpha rate. In this article, we consider conditional estimation of subgroup treatment effects, given the negative result in testing the overall treatment efficacy in the trial. To address the problem of unstable estimation due to the truncation in the distribution of the test statistic on overall treatment efficacy, we propose a new approach based on a weighted likelihood for the truncated distribution. The weighted likelihood can be derived by invoking a randomized test with a smooth critical function for the overall test. Our approach allows for point and interval estimations of the conditional effects consistently based on the standard maximum likelihood inference. Numerical evaluations, including simulations and application to real clinical trials, and guidelines for implementing our methods with R‐codes, are provided.