On the use of randomization tests following adaptive designs

Randomization tests (sometimes referred to as "re-randomization" tests) are used in clinical trials, either as an assumption-free confirmation of parametric analyses, or as an independent analysis based on the principle of randomization-based inference. In the context of adaptive randomization, either restricted or response-adaptive procedures, it is unclear how accurate such Monte Carlo approximations are, or how many Monte Carlo sequences to generate. In this paper, we describe several randomization procedures for which there is a known exact or asymptotic distribution of the randomization test. For a special class of procedures, called [Formula: see text], and binary responses, the exact test statistic has a simple closed form. For the limited subset of existing procedures with known exact and asymptotic distributions, we can use these as a benchmark for the accuracy of Monte Carlo randomization techniques. We conclude that Monte Carlo tests are very accurate, and require minimal computation time. For simple tests with binary response in the class of [Formula: see text] procedures, the exact distribution provides the best test, but Monte Carlo approximations can be used when the exact distribution is difficult to compute.