A multiply robust Mann-Whitney test for non-randomised pretest-posttest studies with missing data

Pretest-posttest studies are a commonly used design by social scientists, medical and health researchers to examine the effect of a treatment or an intervention. We propose an empirical likelihood based Mann-Whitney test on the equality of the response distribution functions of the treatment and control arms for non-randomised pretest-posttest studies with missing responses. The proposed test is multiply robust in the sense that multiple working models can be postulated for the propensity score of treatment assignment, the missingness probability and the outcome regression, and the validity of the test only requires certain combinations of the working models to be correctly specified. Performances of the proposed test are examined through an application to the dataset from AIDS Clinical Trials Group Protocol 175 and simulation studies.