Rank-Based Analyses of Stratified Experiments: Alternatives to the van Elteren Test

ABSTRACT The van Elteren test, a popular extension of the Wilcoxon rank sum test for comparing two treatments in a stratified experiment, uses within-stratum ranks and assigns larger weight to rank sums from smaller strata. It performs well if the treatment effect is constant across strata, but it can be grossly inefficient otherwise. Existing alternatives to the van Elteren test include tests that use overall ranks and/or equal stratum weights, and the aligned rank test of Hodges and Lehmann. We develop two new testing procedures. The first replaces the stratum weights in the van Elteren test with corresponding weights based on estimated treatment effects and sample sizes. The second uses the aligned rank test and a version of the van Elteren test with equal stratum weights in a sequential manner via an adaptive multiple testing strategy. The new and existing tests are compared to the van Elteren test via extensive simulations. The results show that the aligned rank test and the proposed adaptive testing procedure convincingly outperform the van Elteren test in terms of statistical power; the latter is recommended as a default based on overall performance. Data from two clinical trials are used for illustration.