A multivariate to multivariate approach for voxel-wise genome-wide association analysis.

The joint analysis of imaging-genetics data facilitates the systematic investigation of genetic effects on brain structures and functions with spatial specificity. We focus on voxel-wise genome-wide association analysis, which may involve trillions of single nucleotide polymorphism (SNP)-voxel pairs. We attempt to identify underlying organized association patterns of SNP-voxel pairs and understand the polygenic and pleiotropic networks on brain imaging traits. We propose a bi-clique graph structure (ie, a set of SNPs highly correlated with a cluster of voxels) for the systematic association pattern. Next, we develop computational strategies to detect latent SNP-voxel bi-cliques and an inference model for statistical testing. We further provide theoretical results to guarantee the accuracy of our computational algorithms and statistical inference. We validate our method by extensive simulation studies, and then apply it to the whole genome genetic and voxel-level white matter integrity data collected from 1052 participants of the human connectome project. The results demonstrate multiple genetic loci influencing white matter integrity measures on splenium and genu of the corpus callosum.