Exact Semiparametric Inference About the Within-Subject Variability in 2 x 2 Crossover Trails.

The comparison of primary interest in a 2 x 2 crossover trial typically concerns the effect of the treatments, say A and B, on the mean response level. This article deals with another important aspect, namely the within-subject response variability under A and B. Differences in drug formulation and/or administration may lead to considerable differences in withinsubject variability, whatever is the difference in terms of mean level; and consideration of both these aspects may therefore be of considerable importance for the judgement of the treatments. It is shown that, although there are no within-subject treatment replications, it is possible to make various exact inferences about the AlB ratio of within-subject variances and about the (A - B)difference in mean level, simultaneously and marginally. These inferences are semiparametric in that no distributional assumption is made about the betweensubject variability, whereas a normality assumption is used for the within-subject variability. The inferences include tests, confidence regions, and a multiple test procedure. A power approximation is also given. The results are illustrated numerically