Accelerating Heritability, Genetic Correlation, and Genome-Wide Association Imaging Genetic Analyses in Complex Pedigrees

National and international biobanking efforts led to the collection of large and inclusive imaging genetics datasets that enable examination of the contribution of genetic and environmental factors to human brains in illness and health. High-resolution neuroimaging (~10^4-6 voxels) and genetic (10^6-8 single nucleotide polymorphic [SNP] variants) data are available in statistically powerful (N = 10^3-5) epidemiological and disorder-focused samples. Performing imaging genetics analyses at full resolution afforded in these datasets is a formidable computational task even under the assumption of unrelatedness among the subjects. The computational complexity rises as ~N^2-3 (where N is the sample size), when accounting for relatedness among subjects. We describe fast, non-iterative simplifications to accelerate classical variance component (VC) methods including heritability, genetic correlation, and genome-wide association in dense and complex empirical pedigrees. These approaches linearize (from N^2-3 to N^~1) computational effort while maintaining fidelity (r ~ 0.95) with the VC results and take advantage of parallel computing provided by central and graphics processing units (CPU and GPU). We show that the new approaches lead to a 10⁴- to 10⁶-fold reduction in computational complexity-making voxel-wise heritability, genetic correlation, and genome-wide association studies (GWAS) analysis practical for large and complex samples such as those provided by the Amish and Human Connectome Projects (N = 406 and 1052 subjects, respectively) and UK Biobank (N = 31,681). These developments are shared in open-source, SOLAR-Eclipse software.