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.

翻译：本文针对两种处理方案的比较问题，将协变量调整方法应用于Wilcoxon两样本统计量与Wilcoxon-Mann-Whitney检验。通过校准实现的协变量调整不仅提升了估计/推断的效率，而且拓宽了Wilcoxon两样本统计量与Wilcoxon-Mann-Whitney检验的应用范围，使其适用于采用协变量自适应随机化的研究场景。我们阐述了如何通过协变量调整降低方差，建立了调整后Wilcoxon两样本统计量的渐近分布，并明确给出了保证效率提升的理论结果。调整后Wilcoxon两样本统计量的渐近分布对所有常用协变量自适应随机化方案均保持不变，因此无论采用何种协变量自适应随机化方法，均可使用统一公式进行统计推断。