Inference on subgroups identified based on a heterogeneous treatment effect in a post hoc analysis of a clinical trial

Due to the many benefits of understanding treatment effect heterogeneity in a clinical trial, an exploratory post hoc subgroup analysis is often performed to find subpopulations of patients with conditional average treatment effect that suggests better treatment efficacy than in the overall population. A naive re-substitution approach uses all available data to identify a subgroup and then proceeds with estimation and inference using the same data set. This approach generally leads to an overly optimistic estimate of conditional average treatment effect. In this article, in a post hoc analysis, we estimate the target optimal subgroup through maximizing a utility function, from candidates systematically identified with a penalized regression. We then compare two resampling-based bias-correction methods, cross-validation and debiasing bootstrap, for obtaining approximately unbiased estimates and valid inference of conditional average treatment effect in the identified subgroup, with either an empirical or an augmented estimator. Our results show that both the cross-validation and the debiasing bootstrap methods reduce the re-substitution bias effectively. The cross-validation method appears to have less biased point estimates, smaller standard error estimates, but poorer coverages than the debiasing bootstrap method when using the empirical estimator and the sample size is moderate. Using the augmented estimator in the debiasing bootstrap method leads to less biased point estimates but poorer coverages. We conclude that bias correction should be a part of every exploratory post hoc subgroup analysis to eliminate re-substitution bias and to obtain a proper confidence interval for the estimated conditional average treatment effect in the selected subgroup.