Random forests-based differential analysis of gene sets for gene expression data

In DNA microarray studies, gene-set analysis (GSA) has become the focus of gene expression data analysis. GSA utilizes the gene expression profiles of functionally related gene sets in Gene Ontology (GO) categories or priori-defined biological classes to assess the significance of gene sets associated with clinical outcomes or phenotypes. Many statistical approaches have been proposed to determine whether such functionally related gene sets express differentially (enrichment and/or deletion) in variations of phenotypes. However, little attention has been given to the discriminatory power of gene sets and classification of patients.In this study, we propose a method of gene set analysis, in which gene sets are used to develop classifications of patients based on the Random Forest (RF) algorithm. The corresponding empirical p-value of an observed out-of-bag (OOB) error rate of the classifier is introduced to identify differentially expressed gene sets using an adequate resampling method. In addition, we discuss the impacts and correlations of genes within each gene set based on the measures of variable importance in the RF algorithm. Significant classifications are reported and visualized together with the underlying gene sets and their contribution to the phenotypes of interest.Numerical studies using both synthesized data and a series of publicly available gene expression data sets are conducted to evaluate the performance of the proposed methods. Compared with other hypothesis testing approaches, our proposed methods are reliable and successful in identifying enriched gene sets and in discovering the contributions of genes within a gene set. The classification results of identified gene sets can provide an valuable alternative to gene set testing to reveal the unknown, biologically relevant classes of samples or patients.In summary, our proposed method allows one to simultaneously assess the discriminatory ability of gene sets and the importance of genes for interpretation of data in complex biological systems. The classifications of biologically defined gene sets can reveal the underlying interactions of gene sets associated with the phenotypes, and provide an insightful complement to conventional gene set analyses.