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

Abstract

Predicting phenotypes from genotypes is a fundamental task in quantitative genetics. With technological advances, it is now possible to measure multiple phenotypes in large samples. Multiple phenotypes can share their genetic component; therefore, modeling these phenotypes jointly may improve prediction accuracy by leveraging effects that are shared across phenotypes. However, effects can be shared across phenotypes in a variety of ways, so computationally efficient statistical methods are needed that can accurately and flexibly capture patterns of effect sharing. Here, we describe new Bayesian multivariate, multiple regression methods that, by using flexible priors, are able to model and adapt to different patterns of effect sharing and specificity across phenotypes. Simulation results show that these new methods are fast and improve prediction accuracy compared with existing methods in a wide range of settings where effects are shared. Further, in settings where effects are not shared our methods still perform competitively with state-of-the-art methods. In real data analyses of expression data in the Genotype Tissue Expression (GTEx) project our methods improve prediction performance on average for all tissues, with the greatest gains in tissues where effects are strongly shared, and in the tissues with smaller sample sizes. While we use gene expression prediction to illustrate our methods, the methods are generally applicable to any multi-phenotype applications, including prediction of polygenic scores and breeding values. Thus, our methods have the potential to provide improvements across fields and organisms.

Improving polygenic prediction from summary data by learning patterns of effect sharing across multiple phenotypes

“…Of note, mr.mash-rss outperformed competing methods in 14 out of 16 blood cell phenotypes, although the magnitude of the improvement varied across phenotypes, from modest to substantial. This highlights that the general mr.mash model can adapt to either more sparse (e.g., for gene expression [18]) or more dense (e.g., for complex traits) genetic architectures. We also showed that the improvement in prediction accuracy from using mr.mash-rss increased substantially with a smaller sample size.…”

“…This holds good promise for improving prediction accuracy for phenotypes that are difficult to measure and in samples of individuals of non-European descent, which are usually much smaller [33]. In addition, the performance of the mr.mash model depends on the accuracy of the "data-driven" covariance matrices [18]. Thus, advances in covariance matrix estimation can potentially lead to improvements in prediction accuracy.…”

“…Computational effiency is achieved by using Variational Inference (VI) as opposed to the more expensive Markov Chain Monte Carlo (MCMC) methods. Using multi-tissue gene expression prediction from cis-genotypes as an example, the authors showed that mr.mash is competitive in terms of both prediction accuracy and speed [18]. However, while powerful, mr.mash has some limitations.…”

“…The prior is determined by w 0 := ( w 0,1 , …, w 0, K ), the set of non-negative mixture weights, and ℐ 0 := { S 0,1 , …, S 0, K }, the set of r × r covariance matrices across responses. The elements of ℐ 0 are prespecified and are intended to capture plausible patterns of effect sharing across responses [18].…”

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

“…Note that the data sets used in this comparison were not the same as the ones used in the main full-data simulations; for this comparison, the data sets were simulated the exact same way except that synthetic genotypes were used instead of the genotypes from the GTEx Project. For more details on this comparison, see [64], in particular the file mrmash_vs_mtlasso_vs_utmost.html.…”