Nonparametric MANOVA Approaches for Non-Normal Multivariate Outcomes

Comparisons between groups play a central role in clinical research. As these comparisons often entail many potentially correlated response variables, the classical multivariate general linear model has been accepted as a standard tool. However, parametric methods require distributional assumptions such as multivariate normality while non-normal data often exist in clinical research. For example, a clinical trial investigating a treatment for depression is designed as a longitudinal study and the main outcome is survey scores of subjects on several time points, while the scores are ordinal. Although non-parametric multivariate methods are available in the statistical literature, they are not seen to be commonly used in clinical research. Moreover, automatic deletion of cases with missing values in response variables is a shortcoming of standard software when performing multivariate tests. This dissertation addresses the issues of violation of multivariate normality assumption and missing data, focusing on the non-parametric multivariate Kruskal-Wallis (MKW) test, likelihood-based and permutation-based methods. First, an R-based program is written to compute the p-value of MKW test for group comparison. Simulation studies show that the permutation-based MKW test provides better coverage and higher power level than likelihood-based MKW test and classical MANOVA. Second, an extension of MKW test is proposed for multivariate data with missingness. The proposed method retrieves information in partially observed cases and is permutation-based. A sensitivity analysis compares the performance of the proposed extension and the standard test utilizing only complete cases. Results show that the proposed extended method provides higher power level, encompassing a broad spectrum of multivariate effect sizes. An illustrative example using data from a psychiatric clinical trial is provided. The R program is ready to use for applied statistician. The public health relevance of this work lies in the development of a new powerful methodology with user-friendly computer software for group comparisons in non-normal multivariate data with or without missingness.