A doubly robust estimator for the Mann Whitney Wilcoxon rank sum test when applied for causal inference in observational studies

Ruohui Chen, Tuo Lin, Lin Liu, Jinyuan Liu, Ruifeng Chen, Jingjing Zou, Chenyu Liu, Loki Natarajan, Wan Tang, Xinlian Zhang and Xin Tu

Journal of Applied Statistics, 2024, vol. 51, issue 16, 3267-3291

Abstract: 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. (Causal inference for Mann–Whitney–Wilcoxon rank sum and other nonparametric statistics, Stat. Med. 33 (2014), pp. 1261–1271) introduced an approach that incorporates inverse probability weighting (IPW) into this rank-based statistic to mitigate confounding effects. Subsequently, Mao (On causal estimation using U-statistics, Biometrika 105 (2018), pp. 215–220), Zhang et al. (Estimating Mann Whitney-type causal effects, J. Causal Inference 7 (2019), ARTICLE ID 20180010), and Ai et al. (A Mann–Whitney test of distributional effects in a multivalued treatment, J. Stat. Plan. Inference 209 (2020), pp. 85–100) 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 (Estimating Mann Whitney-type causal effects, J. Causal Inference 7 (2019), ARTICLE ID 20180010) estimators rely on bootstrap inference, which suffers from computational inefficiency and lacks known asymptotic properties. Meanwhile, Ai et al. (A Mann–Whitney test of distributional effects in a multivalued treatment, J. Stat. Plan. Inference 209 (2020), pp. 85–100) 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.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/02664763.2024.2346357 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:japsta:v:51:y:2024:i:16:p:3267-3291

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/CJAS20

DOI: 10.1080/02664763.2024.2346357

Access Statistics for this article

Journal of Applied Statistics is currently edited by Robert Aykroyd

More articles in Journal of Applied Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().