Multivariate Statistical Methods for Testing a Set of Variables Between Groups with Application to Genomics

Abstract

<p>The use of traditional univariate analyses for comparing groups in high-dimensional genomic studies, such as the ordinary t-test that is typically used to compare two independent groups, might be suboptimal because of methodological challenges including multiple testing problem and failure to incorporate correlation among genes. Hence, multivariate methods are preferred for the joint analysis of a group or set of variables. These methods aim to test for differences in average values of a set of variables across groups. The variables that make the set could be determined statistically (using exploratory methods such as cluster analysis) or biologically (based on membership to known pathways). In this thesis, the traditional One-Way Multivariate Analysis of Variance (MANOVA) method and a robustifed version of MANOVA (Robustifed MANOVA) are compared with respect to Type I error rates and power through a simulation study. We generated data from multivariate normal as well as multivariate gamma distributions with different parameter settings. The methods are illustrated using a real gene expression data. In addition, we investigated a popular method known as Gene Set Enrichment Analysis (GSEA), where sets of genes (variables) that belong to known biological pathways are considered jointly and assessed whether or not they are "enriched" with respect to their association with a disease or phenotype of interest. We applied this method to a real genotype data.</p>