Identifying quantitative trait loci via group-sparse multitask regression and feature selection: An imaging genetics study of the ADNI cohort

Motivation: Recent advances in high-throughput genotyping and brain imaging techniques enable new approaches to study the inuence of genetic variation on brain structures and functions. Traditional association studies typically employ independent and pairwise univariate analysis, which treats single nucleotide polymorphisms (SNPs) and quantitative traits (QTs) as isolated units and ignores important underlying interacting relationships between the units. New methods are proposed here to overcome this limitation. Results: Taking into account the interlinked structure within and between SNPs and imaging QTs, we propose a novel Group-Sparse Multi-task Regression and Feature Selection (G-SMuRFS) method to identify quantitative trait loci for multiple disease-relevant QTs and apply it to a study in mild cognitive impairment and Alzheimer's disease. Built upon regression analysis, our model uses a new form of regularization, group ℓ _2,1-norm (G _2,1-norm), to incorporate the biological group structures among SNPs induced from their genetic arrangement. The new G _2,1-norm considers the regression coefficients of all the SNPs in each group with respect to all the QTs together and enforces sparsity at the group level. In addition, an ℓ _2,1-norm regularization is utilized to couple feature selection across multiple tasks to make use of the shared underlying mechanism among different brain regions. The effectiveness of the proposed method is demonstrated by both clearly improved prediction performance in empirical evaluations and a compact set of selected SNP predictors relevant to the imaging QTs.