Covariate Adjustment for Wilcoxon Two Sample Statistic and Test

Area of Science:

• Biostatistics
• Statistical Inference
• Clinical Trial Design

Background:

• The Wilcoxon two sample statistic and Wilcoxon-Mann-Whitney test are fundamental for comparing two treatments.
• Existing methods may lack efficiency or applicability in covariate-adaptive randomization settings.

Purpose of the Study:

• To develop and evaluate a covariate adjustment method for the Wilcoxon two sample statistic and Wilcoxon-Mann-Whitney test.
• To improve the efficiency and broaden the applicability of these tests, particularly in covariate-adaptive randomization.

Main Methods:

• Applying covariate adjustment through calibration to the Wilcoxon two sample statistic.
• Establishing the asymptotic distribution of the adjusted Wilcoxon two sample statistic.
• Analyzing efficiency gains and invariance properties of the adjusted statistic.

Main Results:

• Covariate adjustment demonstrably improves efficiency in estimation and inference.
• The adjusted Wilcoxon tests are applicable to situations employing covariate-adaptive randomization.
• A guaranteed efficiency gain is explicitly provided with the adjustment method.

Conclusions:

• Covariate adjustment offers a robust enhancement for the Wilcoxon two sample statistic and Wilcoxon-Mann-Whitney test.
• The proposed method increases statistical power and extends the utility of these tests in complex trial designs.
• The asymptotic distribution's invariance ensures unified inference across various covariate-adaptive randomization schemes.