Multivariate analysis of variance test for gene set analysis

Motivation: Gene class testing (GCT) or gene set analysis (GSA) is a statistical approach to determine whether some functionally predefined sets of genes express differently under different experimental conditions. Shortcomings of the Fishers exact test for the overrepresentation analysis are illustrated by an example. Most alternative GSA methods are developed for data collected from two experimental conditions, and most is based on a univariate gene-by-gene test statistic or assume independence among genes in the gene set. A multivariate analysis of variance (MANOVA) approach is proposed for studies with two or more experimental conditions. Results: When the number of genes in the gene set is greater than the number of samples, the sample covariance matrix is singular and ill-condition. The use of standard multivariate methods can result in biases in the analysis. The proposed MANOVA test uses a shrinkage covariance matrix estimator for the sample covariance matrix. The MANOVA test and six other GSA published methods, principal component analysis, SAM-GS, analysis of covariance, Global, GSEA and MaxMean, are evaluated using simulation. The MANOVA test appears to perform the best in terms of control of type I error and power under the models considered in the simulation. Several publicly available microarray datasets under two and three experimental conditions are analyzed for illustrations of GSA. Most methods, except for GSEA and MaxMean, generally are comparable in terms of power of identification of significant gene sets.