Fast and Accurate Bayesian Polygenic Risk Modeling with Variational Inference

The recent proliferation of large scale genome-wide association studies (GWASs) has motivated the development of statistical methods for phenotype prediction using single nucleotide polymorphism (SNP) array data. These polygenic risk score (PRS) methods formulate the task of polygenic prediction in terms of a multiple linear regression framework, where the goal is to infer the joint effect sizes of all genetic variants on the trait. Among the subset of PRS methods that operate on GWAS summary statistics, sparse Bayesian methods have shown competitive predictive ability. However, existing Bayesian approaches employ Markov Chain Monte Carlo (MCMC) algorithms for posterior inference, which are computationally inefficient and do not scale favorably with the number of SNPs included in the analysis. Here, we introduce Variational Inference of Polygenic Risk Scores (VIPRS), a Bayesian summary statistics-based PRS method that utilizes Variational Inference (VI) techniques to efficiently approximate the posterior distribution for the effect sizes. Our experiments with genome-wide simulations and real phenotypes from the UK Biobank (UKB) dataset demonstrated that variational approximations to the posterior are competitively accurate and highly efficient. When compared to state-of-the-art PRS methods, VIPRS consistently achieves the best or second best predictive accuracy in our analyses of 18 simulation configurations as well as 12 real phenotypes measured among the UKB participants of "White British" background. This performance advantage was higher among individuals from other ethnic groups, with an increase in R-squared of up to 1.7-fold among participants of Nigerian ancestry for Low-Density Lipoprotein (LDL) cholesterol. Furthermore, given its computational efficiency, we applied VIPRS to a dataset of up to 10 million genetic markers, an order of magnitude greater than the standard HapMap3 subset used to train existing PRS methods. Modeling this expanded set of variants conferred modest improvements in prediction accuracy for a number of highly polygenic traits, such as standing height. ### Competing Interest Statement The authors have declared no competing interest.