Selective randomization inference for subgroup effects with continuous biomarkers

Randomization tests are a popular method for testing causal effects in clinical trials with finite-sample validity. In the presence of heterogeneous treatment effects, it is often of interest to select a subgroup that benefits from the treatment, frequently by choosing a cutoff for a continuous biomarker. However, selecting the cutoff and testing the effect on the same data may fail to control the type I error. To address this, we propose using "self-contained" methods for selecting biomarker-based subgroups (cutoffs) and applying conditioning to construct valid randomization tests for the subgroup effect. Compared to sample-splitting-based randomization tests, our proposal is fully deterministic, uses the entire selected subgroup for inference, and is thus more powerful. Moreover, we demonstrate scenarios where our procedure achieves power comparable to a randomization test with oracle knowledge of the benefiting subgroup. In addition, our procedure is as computationally efficient as standard randomization tests. Empirically, we illustrate the effectiveness of our method on simulated datasets and the German Breast Cancer Study.