Pair-switching rerandomization

Rerandomization discards assignments with covariates unbalanced in the treatment and control groups to improve estimation and inference efficiency. However, the acceptance-rejection sampling method used in rerandomization is computationally inefficient. As a result, it is time-consuming for rerandomization to draw numerous independent assignments, which are necessary for performing Fisher randomization tests and constructing randomization-based confidence intervals. To address this problem, we propose a pair-switching rerandomization (PSRR) method to draw balanced assignments efficiently. We obtain the unbiasedness and variance reduction of the difference-in-means estimator and show that the Fisher randomization tests are valid under PSRR. Moreover, we propose an exact approach to invert Fisher randomization tests to confidence intervals, which is faster than the existing methods. In addition, our method is applicable to both nonsequentially and sequentially randomized experiments. We conduct comprehensive simulation studies to compare the finite-sample performance of the proposed method with that of classical rerandomization. Simulation results indicate that PSRR leads to comparable power of Fisher randomization tests and is 3-23 times faster than classical rerandomization. Finally, we apply the PSRR method to analyze two clinical trial datasets, both of which demonstrate the advantages of our method.