Ultra-Fast Implementation of Multivariate GWAS in Genomic SEM Using Flexible Analytic Estimation

Many medical, physiological, and psychiatric traits and disorders are highly polygenic and exhibit complex patterns of genetic sharing and differentiation. In 2018, we introduced Genomic Structural Equation Modelling (Genomic SEM) as a formal framework and free, open source, R-based software for modelling the multivariate genetic architecture of both continuous and binary Genome-Wide Association Study (GWAS) phenotypes, interrogating their joint and distinct functional genomic pathways, and leveraging empirical models of the genetic relations among phenotypes to guide multivariate GWAS discovery. Here we introduce a closed-form analytic solution for estimating SNP effects within multivariate GWAS in Genomic SEM. This estimator is over 800 times faster than the existing iterative estimator, drastically decreasing reliance on high performance computing (HPC). On a MacBook pro laptop with M4 Max chip, a multivariate GWAS (~1M SNPs) of 5 common factors underlying 13 phenotypes takes approximately 2 minutes. Concurrent with the release of this preprint, we are adding an analytic estimation option to the userGWAS function in the GenomicSEM package for alpha testing along with a tutorial on our GitHub wiki.