Primary Submission Category: Randomized Designs and Analyses
Optimal randomization-based FWER control
Authors: Andy Chen,
Presenting Author: Andy Chen*
Randomization tests are finite-sample valid, model-lean, and well suited to moderate-sample analysis. In randomized trials, researchers are often presented with several potentially related hypotheses arising from multiple subgroups or multiple treatment levels. In this paper, we investigate family-wise error rate (FWER) control using individual randomization-test p-values.
Noting that sharp nulls are closed under intersection, we apply the closure principle for FWER control, constructing randomization tests directly for the induced intersection nulls, thereby avoiding the inefficiency of generic p-value aggregation. Combined with recent optimality results for a single randomization test, we show that the proposed procedure, when paired with most powerful single-test statistics, is optimal within the class of randomization-based FWER-control methods. Computationally, we develop branch-and-bound–type shortcuts and reduce the number of randomizations by sharing treatment reassignments across hypotheses.