Fast and Accurate Bayesian Polygenic Risk Modeling with Variational Inference

Abstract

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 R2 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.

A flexible empirical Bayes approach to multivariate multiple regression, and its improved accuracy in predicting multi-tissue gene expression from genotypes

“…Clearly, applying mr.mash to much larger multi-trait data sets, and in particular for data sets with hundreds of thousands of individuals and millions of genetic variants (“biobank-scale” data sets), will require some additional innovation. One possible approach would be to adapt mr.mash to work with “summary data” [25, 60, 61].…”

“…To fit the mr.mash model we use variational inference methods [48, 49] which have been successfully applied to fit univariate multiple regressions [10, 20, 24, 25, 27, 50]. Variational inference recasts the posterior computation as an optimization problem.…”

“…The Elastic Net was used in the original PrediXcan method for gene expression prediction in TWAS [11], and therefore we view this approach as a baseline univariate regression method for comparison with the multivariate methods. (It is possible that more recent univariate regression approaches with more flexible priors could yield better predictions in this setting, e.g., [10, 25]. ) More recently, the Sparse Multi-task Lasso was used in UTMOST, a method for cross-tissue expression prediction in TWAS [39].…”

“…To fit the mr.mash model we use variational inference methods [48,49] which have been successfully applied to fit univariate multiple regressions [10,20,24,25,27,50].…”

“…However, Bayesian methods have received particular attention in genetic applications because they provide a natural way to incorporate prior information about and cope with different genetic architectures. This attractive feature has spurred the development and application of many Bayesian methods that differ in their prior distribution on the effect sizes and their approach to computing posterior distributions [6,10,[17][18][19][20][21][22][23][24][25][26][27].…”