Generalized pairwise comparisons of prioritized outcomes in the two-sample problem

Abstract

This paper extends the idea behind the U-statistic of the Wilcoxon-Mann-Whitney test to perform generalized pairwise comparisons between two groups of observations. The observations are outcomes captured by a single variable, possibly repeatedly measured, or by several variables of any type (e.g. discrete, continuous, time to event). When several outcomes are considered, they must be prioritized. We show that generalized pairwise comparisons extend well-known non-parametric tests, and illustrate their interest using data from two randomized clinical trials. We also show that they lead to a general measure of the difference between the groups called the 'proportion in favor of treatment', denoted Δ, which is related to traditional measures of treatment effect for a single variable.