Stratified Multivariate Mann–Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment

Abstract

Methodology for comparing two randomly assigned treatments for strictly ordinal response variables has been discussed throughout the literature on multivariate Mann–Whitney estimators with stratification adjustment. Although such estimators can be computed directly as weighted linear combinations of within-stratum Mann–Whitney estimators, consistent estimation of their covariance matrix is done using methods for multivariate U-statistics. The scope of these methods includes ways of managing randomly missing data and ways to invoke randomization-based covariance adjustment for no differences between treatments for background or baseline covariables. The assessment of treatment differences can be done using confidence intervals or statistical tests for the adjusted Mann–Whitney estimators. The methods in this article are illustrated using three examples. The first example is a randomized clinical trial with eight strata and a univariate ordinal response variable. The second example is a randomized clinical trial with four strata, two covariables, and four ordinal response variables. The third example is a randomized two-period crossover clinical trial with four strata, three covariables (as age, screening, first baseline), three response variables (as first period response, second baseline, second period response), and missing data. For these examples, the results are interpretable through the probability of better outcomes for one treatment over the other.