The Mann-Whitney-Wilcoxon rank sum test (MWWRST) is a widely used method for comparing two treatment groups in randomized control trials, particularly when dealing with highly skewed data. However, when applied to observational study data, the MWWRST often yields invalid results for causal inference. To address this limitation, Wu et al. (2014) introduced an approach that incorporates inverse probability weighting (IPW) into this rank-based statistics to mitigate confounding effects. Subsequently, Mao (2018), Zhang et al. (2019), and Ai et al. (2020) extended this IPW estimator to develop doubly robust estimators. Nevertheless, each of these approaches has notable limitations. Mao's method imposes stringent assumptions that may not align with real-world study data. Zhang et al.'s (2019) estimators rely on bootstrap inference, which suffers from computational inefficiency and lacks known asymptotic properties. Meanwhile, Ai et al. (2020) primarily focus on testing the null hypothesis of equal distributions between two groups, which is a more stringent assumption that may not be well-suited to the primary practical application of MWWRST. In this paper, we aim to address these limitations by leveraging functional response models (FRM) to develop doubly robust estimators. We demonstrate the performance of our proposed approach using both simulated and real study data.

翻译：曼-惠特尼-威尔科克森秩和检验（MWWRST）是随机对照试验中比较两组治疗的常用方法，尤其在处理高度偏态数据时。然而，当应用于观察性研究数据时，MWWRST通常无法为因果推断提供有效结果。为克服这一局限性，Wu等人（2014）提出了一种方法，将逆概率加权（IPW）引入该秩统计量以减轻混杂效应。随后，Mao（2018）、Zhang等人（2019）以及Ai等人（2020）对该IPW估计量进行了扩展，开发了双重稳健估计量。然而，这些方法均存在显著缺陷：Mao的方法施加了严格假设，可能不符合实际研究数据；Zhang等人（2019）的估计量依赖自举推断，计算效率低且缺乏已知渐近性质；Ai等人（2020）主要关注检验两组分布相等的原假设，这一假设更为严格，可能不适用于MWWRST的主要实际应用。本文旨在通过利用函数响应模型（FRM）开发双重稳健估计量来解决上述局限性，并通过仿真和实际研究数据验证所提方法的性能。