ABSTRACT
Chapter 6 introduces a method of analysis whose validity requires virtually no assumptions, randomization-based inference. Under the null hypothesis, treatment has no effect on outcome, so results ought to be just as plausible regardless of the treatment assignments. We construct a valid null distribution by repeatedly re-randomizing, the same way the original randomization labels were generated, and computing the treatment difference corresponding to the re-randomized labels. We show that with simple randomization and a binary endpoint, the re-randomization test is equivalent to Fisher's exact test in an unpaired setting and McNemar's test in a paired setting. When sample sizes are large, re-randomization tests are asymptotically equivalent to unstratified or stratified t-tests with conventional randomization. One of the advantages of re-randomization tests is that they can be used for any randomization method, including covariate- and response-adaptive randomization. Besides requiring almost no assumptions, the re-randomization test mitigates the effect of temporal trends. We also show how to use randomization-based methods to compute confidence intervals.
