An Independent Filter for Gene Set Testing Based on Spectral Enrichment

Abstract

Gene set testing has become an indispensable tool for the analysis of high-dimensional genomic data. An important motivation for testing gene sets, rather than individual genomic variables, is to improve statistical power by reducing the number of tested hypotheses. Given the dramatic growth in common gene set collections, however, testing is often performed with nearly as many gene sets as underlying genomic variables. To address the challenge to statistical power posed by large gene set collections, we have developed spectral gene set filtering (SGSF), a novel technique for independent filtering of gene set collections prior to gene set testing. The SGSF method uses as a filter statistic the p-value measuring the statistical significance of the association between each gene set and the sample principal components (PCs), taking into account the significance of the associated eigenvalues. Because this filter statistic is independent of standard gene set test statistics under the null hypothesis but dependent under the alternative, the proportion of enriched gene sets is increased without impacting the type I error rate. As shown using simulated and real gene expression data, the SGSF algorithm accurately filters gene sets unrelated to the experimental outcome resulting in significantly increased gene set testing power.

Unsupervised gene set testing based on random matrix theory

“…Although most gene set testing methods can only be used in a supervised context, i.e., assessing the association of gene set members with an outcome variable, a number of important unsupervised use cases exist. To address the lack of effective unsupervised gene set testing methods, we recently developed the SGSE method [15] and later demonstrated the effective use of this method for screening-testing [19] in the SGSF approach [24]. Although the SGSE method was shown to be superior to existing unsupervised techniques and was able to significantly improve gene set testing power when used in the SGSF screening-testing approach, the method only supports testing against a competitive null hypothesis and is not able to effectively identify biologically relevant gene sets for a number of important use cases.…”

“…For such large gene set collections, MHC can lower statistical power so substantially that it becomes impossible to identify true associations for many genomic data sets [24]. The link between p -value weighting and unsupervised gene set testing is based on the fact that an effective way to ensure the independence between data-driven weights and standard gene set test statistics under H 0 is to ignore the outcome variable when computing the weight, i.e., base the weight on an unsupervised gene set test.…”

“…The link between p -value weighting and unsupervised gene set testing is based on the fact that an effective way to ensure the independence between data-driven weights and standard gene set test statistics under H 0 is to ignore the outcome variable when computing the weight, i.e., base the weight on an unsupervised gene set test. In previously published research building on the SGSE method, we developed a screening-testing framework for gene set testing, called Spectral Gene Set Filtering (SGSF) [24], that computes binary weights using the p -values generated by the SGSE method.…”

“…Although it can be proven that weights based on an unsupervised gene set test (like the SGSE method) will be independent of common gene set test statistics under H 0 (see proof in the Supplemental Material for [24]), this independence only ensures type I error control. To actually improve statistical power, the weight must also be associated with the test statistic under H A .…”

“…For gene set testing, producing a data-driven weight therefore requires the use of an unsupervised test that can effectively identify the gene sets truly associated with the outcome of interest. As illustrated in the SGSF paper [24], statistics based on deviation from an identity population covariance structure represent a useful class of gene set weights that boost gene sets according to the empirical correlation among member genes. Although it is possible some biologically important gene sets exhibit little inter-gene correlation, it has been shown that groups of highly correlated genes are often associated with biological processes that play an important role in the measured experiment [11].…”