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Given the complex relationship between gene expression and phenotypic outcomes, computationally efficient approaches are needed to sift through large high-dimensional datasets in order to identify biologically relevant biomarkers. In this report, we describe a method of identifying the most salient biomarker genes in a dataset, which we call "candidate genes", by evaluating the ability of gene combinations to classify samples from a dataset, which we call "classification potential". Our algorithm, Gene Oracle, uses a neural network to test user defined gene sets for polygenic classification potential and then uses a combinatorial approach to further decompose selected gene sets into candidate and non-candidate biomarker genes. We tested this algorithm on curated gene sets from the Molecular Signatures Database (MSigDB) quantified in RNAseq gene expression matrices obtained from The Cancer Genome Atlas (TCGA) and Genotype-Tissue Expression (GTEx) data repositories. First, we identified which MSigDB Hallmark subsets have significant classification potential for both the TCGA and GTEx datasets. Then, we identified the most discriminatory candidate biomarker genes in each Hallmark gene set and provide evidence that the improved biomarker potential of these genes may be due to reduced functional complexity.