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

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.Author summary: Predicting phenotypes from genotypes is a fundamental problem in quantitative genetics. Thanks to recent advances, it is increasingly feasible to collect data on many phenotypes and genome-wide genotypes in large samples. Here, we tackle the problem of predicting multiple phenotypes from genotypes using a new method based on a multivariate, multiple linear regression model. Although the use of a multivariate, multiple linear regression model is not new, in this paper we introduce a flexible and computationally efficient empirical Bayes approach based on this model. This approach uses a prior that captures how the effects of genotypes on phenotypes are shared across the different phenotypes, and then the prior is adapted to the data in order to capture the most prominent sharing patterns present in the data. We assess the benefits of this flexible Bayesian approach in simulated genetic data sets, and we illustrate its application in predicting gene expression measured in multiple human tissues. We show that our methods can outperform competing methods in terms of prediction accuracy, and the computations involved in fitting the model and making the predictions scale well to large data sets.