Abstract
BackgroundGene set testing, or pathway analysis, is a bioinformatics technique that performs statistical testing on biologically meaningful sets of genomic variables. Although originally developed for supervised analyses, i.e., to test the association between gene sets and an outcome variable, gene set testing also has important unsupervised applications, e.g., p-value weighting. For unsupervised testing, however, few effective gene set testing methods are available with support especially poor for several biologically relevant use cases.ResultsIn this paper, we describe two new unsupervised gene set testing methods based on random matrix theory, the Marc̆enko-Pastur Distribution Test (MPDT) and the Tracy-Widom Test (TWT), that support both self-contained and competitive null hypotheses. For the self-contained case, we contrast our proposed tests with the classic multivariate test based on a modified likelihood ratio criterion. For the competitive case, we compare the new tests against a competitive version of the classic test and our recently developed Spectral Gene Set Enrichment (SGSE) method. Evaluation of the TWT and MPDT methods is based on both simulation studies and a weighted p-value analysis of two real gene expression data sets using gene sets drawn from MSigDB collections.ConclusionsThe MPDT and TWT methods are novel and effective tools for unsupervised gene set analysis with superior statistical performance relative to existing techniques and the ability to generate biologically important results on real genomic data sets.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1299-8) contains supplementary material, which is available to authorized users.
Highlights
Gene set testing, or pathway analysis, is a bioinformatics technique that performs statistical testing on biologically meaningful sets of genomic variables
To address the shortcomings of existing unsupervised tests and to support both self-contained and competitive tests across a wider range of biologically relevant data models, we have developed two novel unsupervised gene set tests, the Marcenko-Pastur Distribution Test (MPDT) and the Tracy-Widom Test (TWT) that are based on the covariance structure of the measured genomic variables
The supervised nature of these tests means they cannot be used to support p-value weighting, case-only analyses or other unsupervised use cases. Both the MPDT and TWT methods are based on random matrix theory (RMT) findings regarding the distribution of the eigenvalues of matrices with a white Wishart distribution [32, 33], i.e., the distribution of the sample covariance matrix for multivariate normal data with an identity population covariance matrix
Summary
Pathway analysis, is a bioinformatics technique that performs statistical testing on biologically meaningful sets of genomic variables. By focusing the analysis on the association between a smaller number of functional gene sets and a specific clinical outcome, gene set testing can substantially improve statistical power, biological interpretation and replication relative to an analysis based on individual genomic variables [1, 3,4,5] Given these advantages, researchers have invested significant effort in the last 10 to 15 years creating large gene set collections [6,7,8] and developing effective gene set testing methods [4, 9,10,11,12]. Tests based on a competitive null hypothesis are viewed as more biologically relevant, and
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