Covariate Adjustment for Wilcoxon Two Sample Statistic and Test

2026-02-17

AI Summary

This study addresses the efficiency loss of the conventional Wilcoxon two-sample test under covariate-adaptive randomization designs, where ignoring covariate adjustment leads to suboptimal inference. The authors propose the first covariate-adjusted framework for the Wilcoxon statistic, integrating nonparametric inference with asymptotic theory to derive a unified asymptotic distribution of the adjusted statistic across a broad class of randomization schemes. This approach substantially enhances estimation and inferential efficiency while providing explicit guarantees on the magnitude of efficiency gain. By formally incorporating covariate information into rank-based testing, the method significantly extends the applicability of nonparametric rank tests to complex experimental designs commonly encountered in modern clinical and observational studies.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• covariate adjustment
• Wilcoxon two sample statistic
• Wilcoxon-Mann-Whitney test
• covariate-adaptive randomization
• nonparametric inference

Innovation

• covariate adjustment
• Wilcoxon two-sample statistic
• covariate-adaptive randomization
• asymptotic distribution
• efficiency gain