Confidence intervals and point estimates for treatment effects in adaptive enrichment designs

Adaptive enrichment designs allow subgroup selection of the patient population within a confirmatory trial via an interim analysis. However, this design complicates treatment effect estimation and uncertainty quantification. This paper introduces a $p$-value inversion method using various sample space orderings to construct confidence intervals either unconditionally or conditional on the subgroup selected for a general class of two-stage two-group designs. In addition, the $p$-value functions can be used to derive median-unbiased estimators and conditional moment estimators. Through simulation it is shown that the proposed intervals have close to nominal coverage, in contrast to naive confidence intervals based on the maximum likelihood estimator. Moreover, the median-unbiased estimators and conditional moment estimators have good performance with respect to median and mean bias, respectively. The method is illustrated by a re-analysis of a trial investigating treatment interactions with KRAS mutation type in patients with metastatic colorectal cancer.