More and more large-scale imaging genetic studies are being widely conducted to collect a rich set of imaging, genetic, and clinical data to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders. Several major big-data challenges arise from testing genome-wide (NC > 12 million known variants) associations with signals at millions of locations (NV ~ 106) in the brain from thousands of subjects (n ~ 103). The aim of this paper is to develop a Fast Voxelwise Genome Wide Association analysiS (FVGWAS) framework to e ciently carry out whole-genome analyses of whole-brain data. FVGWAS consists of three components including a heteroscedastic linear model, a global sure independence screening (G-SIS) procedure, and a detection procedure based on wild bootstrap methods. Specifically, for standard linear association, the computational complexity is O(nNV NC) for voxelwise genome wide association analysis (VGWAS) method compared with O((NC + NV)n2) for FVGWAS. Simulation studies show that FVGWAS is an effcient method of searching sparse signals in an extremely large search space, while controlling for the family-wise error rate. Finally, we have successfully applied FVGWAS to a large-scale imaging genetic data analysis of ADNI data with 708 subjects, 193,275 voxels in RAVENS maps, and 501,584 SNPs, and the total processing time was 203,645 seconds for a single CPU. Our FVG-WAS may be a valuable statistical toolbox for large-scale imaging genetic analysis as the field is rapidly advancing with ultra-high-resolution imaging and whole-genome sequencing
