A comparison of procedures for adaptive choice of location tests in flexible two-stage designs

Although linear rank statistics for the two-sample problem are distribution free tests, their power depends on the distribution of the data. In the planning phase of an experiment, researchers are often uncertain about the shape of this distribution and so the choice of test statistic for the analysis and the determination of the required sample size are based on vague information. Adaptive designs with interim analysis can potentially overcome both problems. And in particular, adaptive tests based on a selector statistic are a solution to the first. We investigate whether adaptive tests can be usefully implemented in flexible two-stage designs to gain power. In a simulation study, we compare several methods for choosing a test statistic for the second stage of an adaptive design based on interim data with the procedure that applies adaptive tests in both stages. We find that the latter is a sensible approach that leads to the best results in most situations considered here. The different methods are illustrated using a clinical trial example.