We investigate the use of permutation tests for the analysis of parallel and stepped-wedge cluster randomized trials. Permutation tests for parallel designs with exponential family endpoints have been extensively studied. The optimal permutation tests developed for exponential family alternatives require information on intraclass correlation, a quantity not yet defined for time-to-event endpoints. Therefore, it is unclear how efficient permutation tests can be constructed for cluster-randomized trials with such endpoints. We consider a class of test statistics formed by a weighted average of pair-specific treatment effect estimates and offer practical guidance on the choice of weights to improve efficiency. We apply the permutation tests to a cluster-randomized trial evaluating the effect of an intervention to reduce the incidence of hospital-acquired infection. In some settings, outcomes from different clusters may be correlated, and we evaluate the validity and efficiency of permutation test in such settings. Lastly, we propose a permutation test for stepped-wedge designs and compare its performance to mixed effect modeling, and illustrate its superiority when sample sizes are small, the underlying distribution is skewed, or there is correlation across clusters.



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