Power approximation for the van Elteren test based on location-scale family of distributions

The van Elteren test, as a type of stratified Wilcoxon-Mann-Whitney test for comparing two treatments accounting for stratum effects, has been used to replace the analysis of variance when the normality assumption was seriously violated. The sample size estimation methods for the van Elteren test have been proposed and evaluated previously. However, in designing an active-comparator trial where a sample of responses from the new treatment is available but the patient response data to the comparator are limited to summary statistics, the existing methods are either inapplicable or poorly behaved. In this paper we develop a new method for active-comparator trials assuming the responses from both treatments are from the same location-scale family. Theories and simulations have shown that the new method performs well when the location-scale assumption holds and works reasonably when the assumption does not hold. Thus, the new method is preferred when computing sample sizes for the van Elteren test in active-comparator trials.