Mann-Whitney Test with Adjustments to Pre-treatment Variables for Missing Values and Observational Study

Chen, Songxi and Qin, Jing and Tang, Chengyong (2013): Mann-Whitney Test with Adjustments to Pre-treatment Variables for Missing Values and Observational Study. Published in:

Abstract

The conventional Wilcoxon/Mann-Whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies. This is because the missingness of the outcomes or the participation in the treatments may depend on certain pre-treatment variables. We propose an approach to adjust the Mann-Whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pre-treatment variables. We also propose semiparametric extensions of the adjusted Mann-Whitney test which leads to dimension reduction for high dimensional covariate. A novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations. Results from simulation studies and an economic observational study data analysis are presented to demonstrate the performance of the proposed approach.

• Item Type: MPRA Paper
• Language: English
• Keywords: Dimension reduction; Kernel smoothing; Mann-Whitney statistic; Missing outcomes;Observational studies;Selection bias.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs; C - Mathematical and Quantitative Methods > C9 - Design of Experiments; G - Financial Economics > G0 - General

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