Number of Repetitions in Re-randomization Tests

In covariate-adaptive or response-adaptive randomization, the treatment assignment and outcome can be correlated. Under this situation, re-randomization tests are a straightforward and attractive method to provide valid statistical inference. In this paper, we investigate the number of repetitions in the re-randomization tests. This is motivated by the group sequential design in clinical trials, where the nominal significance bound can be very small at an interim analysis. Accordingly, re-randomization tests lead to a very large number of required repetitions, which may be computationally intractable. To reduce the number of repetitions, we propose an adaptive procedure and compare it with multiple approaches under pre-defined criteria. Monte Carlo simulations are conducted to show the performance of different approaches in a limited sample size. We also suggest strategies to reduce total computation time and provide practical guidance in preparing, executing and reporting before and after data are unblinded at an interim analysis, so one can complete the computation within a reasonable time frame.