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

By Songxi Chen, Jing Qin and Chengyong Tang

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.

Topics: C0 - General, C1 - Econometric and Statistical Methods and Methodology: General, C2 - Single Equation Models; Single Variables, C3 - Multiple or Simultaneous Equation Models; Multiple Variables, C4 - Econometric and Statistical Methods: Special Topics, C5 - Econometric Modeling, C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling, C7 - Game Theory and Bargaining Theory, C8 - Data Collection and Data Estimation Methodology; Computer Programs, C9 - Design of Experiments, G0 - General
Year: 2013
DOI identifier: 10.1111/j.1467-9868.2012.01036.x
OAI identifier: oai:mpra.ub.uni-muenchen.de:46275

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