Covariate Adjustment for Wilcoxon Two Sample Statistic and Test

TL;DR

This paper introduces covariate adjustment methods for the Wilcoxon two sample statistic and Mann-Whitney test, enhancing efficiency and applicability in covariate-adaptive randomized experiments.

Contribution

It develops a covariate adjustment approach that improves inference efficiency and extends applicability to covariate-adaptive randomization schemes.

Findings

Covariate adjustment reduces variance in the Wilcoxon test.

Asymptotic distribution is invariant to randomization schemes.

Explicit efficiency gains are established.

Abstract

We apply covariate adjustment to the Wincoxon two sample statistic and Wincoxon-Mann-Whitney test in comparing two treatments. The covariate adjustment through calibration not only improves efficiency in estimation/inference but also widens the application scope of the Wilcoxon two sample statistic and Wincoxon-Mann-Whitney test to situations where covariate-adaptive randomization is used. We motivate how to adjust covariates to reduce variance, establish the asymptotic distribution of adjusted Wincoxon two sample statistic, and provide explicitly the guaranteed efficiency gain. The asymptotic distribution of adjusted Wincoxon two sample statistic is invariant to all commonly used covariate-adaptive randomization schemes so that a unified formula can be used in inference regardless of which covariate-adaptive randomization is applied.