Pairwise non-parametric non-inferiority tests in 3 x 3 cross-over trials: should we adjust for period?

Before an active compound can be registered as a drug, it needs to be demonstrated that it does not cause particular unwanted compound specific side effects. Demonstrating non-inferiority of an active drug with placebo with respect to an unwanted side effect is often based on pharmacodynamic 3 x 3 cross-over trials, with the third treatment arm consisting of a positive control. The main comparison then is the pairwise comparison between active drug and placebo. In this paper, two different non-parametric methods with adjustment for period effect are compared with the non-parametric non-adjusted test and the parametric period-adjusted test with respect to size and power. The non-parametric test with period adjustment based on rank alignment has generally the largest power, but its size exceeds the nominal significance level. The non-parametric test with period adjustment based on stratification has low power for trials with a small number of subjects. The non-parametric test without period adjustment is a valid alternative in such cases, but its power decreases substantially in the presence of period effects. In the case of unbalanced designs, however, only the non-parametric test with period adjustment based on stratification can be used.