Causal inference for Mann-Whitney-Wilcoxon rank sum and other nonparametric statistics

• Published in: Statistics in medicine Vol. 33; no. 8; pp. 1261 - 1271
• Main Authors: Wu, P., Han, Y., Chen, T., Tu, X.M.
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 15.04.2014; Wiley Subscription Services, Inc
• Subjects: Adolescent; Computer Simulation; counterfactual outcome; Female; functional response models; Humans; Kendall's τ; Mathematical models; Models, Statistical; outliers; Random variables; Ratings & rankings; Regression analysis; Sexual Behavior; Simulation; Statistics; Statistics, Nonparametric; Test methods; Treatment Outcome; U-statistics-based generalized estimating equations (UGEE); Young Adult; U-statistics-based generalized estimating equations (UGEE); outliers; functional response models; Kendall's τ; counterfactual outcome
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.6026

The nonparametric Mann–Whitney–Wilcoxon (MWW) rank sum test is widely used to test treatment effect by comparing the outcome distributions between two groups, especially when there are outliers in the data. However, such statistics generally yield invalid conclusions when applied to nonrandomized studies, particularly those in epidemiologic research. Although one may control for selection bias by using available approaches of covariates adjustment such as matching, regression analysis, propensity score matching, and marginal structural models, such analyses yield results that are not only subjective based on how the outliers are handled but also often difficult to interpret. A popular alternative is a conditional permutation test based on randomization inference [Rosenbaum PR. Covariance adjustment in randomized experiments and observational studies. Statistical Science 2002; 17(3):286–327]. Because it requires strong and implausible assumptions that may not be met in most applications, this approach has limited applications in practice. In this paper, we address this gap in the literature by extending MWW and other nonparametric statistics to provide causal inference for nonrandomized study data by integrating the potential outcome paradigm with the functional response models (FRM). FRM is uniquely positioned to model dynamic relationships between subjects, rather than attributes of a single subject as in most regression models, such as the MWW test within our context. The proposed approach is illustrated with data from both real and simulated studies. Copyright © 2013 John Wiley & Sons, Ltd.