Two-stage randomized trials: Outstanding issues

摘要

Tamura et al. [1] wrote a nice article describing a two-stage randomized design. Some collaborators and I described a rather similar design in the literature [2], but there were some issues with conducting an exact analysis of the data arising from such a design. Because the various stages are conducted to address similar, if not identical, questions, it makes sense to conduct a single comprehensive analysis, rather than separate analyses by stage. As is well known, exact analyses for randomized trials are conditional permutation tests [3]. Conducting permutation tests in the simplest case of a single 2 x 2 contingency table involves fixed margins, and the cell counts are permuted in all possible ways to keep the margins fixed. With a 2 x 2 table, there is but one degree of freedom which, for convenience, we may define as the number of placebo nonresponders. Call this quantity X. In the first stage, X is a random quantity that will vary across the permutations.