A regularized multivariate regression approach for eQTL analysis.

Expression quantitative trait loci (eQTLs) are genomic loci that regulate expression levels of mRNAs or proteins. Understanding these regulatory provides important clues to biological pathways that underlie diseases. In this paper, we propose a new statistical method, GroupRemMap, for identifying eQTLs. We model the relationship between gene expression and single nucleotide variants (SNVs) through multivariate linear regression models, in which gene expression levels are responses and SNV genotypes are predictors. To handle the high-dimensionality as well as to incorporate the intrinsic group structure of SNVs, we introduce a new regularization scheme to (1) control the overall sparsity of the model; (2) encourage the group selection of SNVs from the same gene; and (3) facilitate the detection of trans-hub-eQTLs. We apply the proposed method to the colorectal and breast cancer data sets from The Cancer Genome Atlas (TCGA), and identify several biologically interesting eQTLs. These findings may provide insight into biological processes associated with cancers and generate hypotheses for future studies.