Estimation of the competing probability for the van Elteren test

Abstract

The van Elteren (vE) test, a stratified Wilcoxon-Mann-Whitney test, is a widely used nonparametric method for comparing two treatments adjusting for stratum effects. Although the vE test produces a p-value for testing the null hypothesis of no treatment effect, additional heuristic methods need to be used to determine which treatment is better. Moreover, such heuristic methods may lead to inconclusive decisions in some situations. Furthermore, it is unclear on how to quantify treatment effect size when the van Elteren test is used. In this paper, we define a competing probability (CP) inherently related to the vE test and derive point and interval estimators for CP. The CP serves as an effect size measure and can be used to determine which treatment is better by comparing the CP with 0.5.