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 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.

Multi-ancestry polygenic risk scores using phylogenetic regularization

“…We used a set of 100 randomly chosen HapMap3 SNPs [Consortium et al, 2010] located on chromosome 22 with minor allele frequency (MAF) > 0.05. We simulated effect sizes using the magenpy package developed by Zabad et al [2023]. Similar to the generative process outlined in the XPA method [Cai et al, 2021], effect sizes are drawn from a sparse mixture of multivariate Gaussian distributions, with covariance in effect sizes across populations scaled to be proportional to distance between the two corresponding nodes in the tree, while varying the minimum covariance in cross-population effect size (e.g.…”

“…We studied six phenotypes: height, body mass index (BMI), high-density lipoprotein cholesterol levels (HDL), hip circumference, waist circumference, and forced expiratory volume (FEV1), all of which are both commonly studied and known to exhibit generalization difficulties in non-European populations [Duncan et al, 2019, Zabad et al, 2023].…”

“…Approximately 80% of the individuals are denoted as having "White British" ancestry, but many other ancestries are represented at the scale of several thousand individuals each, permitting the training and testing of cross-ancestry PRS models. We studied six phenotypes: height, body mass index (BMI), high-density lipoprotein cholesterol levels (HDL), hip circumference, waist circumference, and forced expiratory volume (FEV1), all of which are both commonly studied and known to exhibit generalization difficulties in non-European populations [Duncan et al, 2019, Zabad et al, 2023.…”

GWASBrewer: An R Package for Simulating Realistic GWAS Summary Statistics

“…In recent years there has been a proliferation of statistical methods that use effect estimates and standard errors (summary statistics) from genome-wide association studies (GWAS) to infer interesting biological parameters. These include methods for estimating heritability [1,2,3,4], genetic correlation [5,6,7], causal effects via Mendelian randomization (MR) [8,9,10], and polygenic risk scores [11,12,13,14]. A common challenge in the development of all methods applied to genetic data is conducting simulation studies that adequately mimic properties of real data.…”

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

“…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].…”