A computationally efficient Bayesian Seemingly Unrelated Regressions model for high-dimensional Quantitative Trait Loci discovery

Abstract Motivation Our work is motivated by the search for metabolite Quantitative Trait Loci (QTL) in a cohort of more than 5,000 people. There are 158 metabolites measured by NMR spectroscopy measured in the 31-year follow-up of the Northern Finland Birth Cohort 1966 (NFBC66). These metabolites, as with many multivariate phenotypes produced by high-throughput biomarker technology, exhibit strong correlation structures. Existing approaches for combining such data with genetic variants for multivariate QTL analysis generally ignore phenotypic correlations or make restrictive assumptions about the associations between phenotypes and genetic loci. Results We present a computationally efficient Bayesian Seemingly Unrelated Regressions (SUR) model for high-dimensional data, with cell-sparse variable selection and sparse graphical structure for covariance selection. Cell-sparsity allows different phenotype responses to be associated with different genetic predictors and the graphical structure is used to represent the conditional dependencies between phenotype variables. To achieve feasible computation of the large model space, we exploit a factorisation of the covariance matrix. Applying the model to the NFBC66 data with 9,000 directly-genotyped Single Nucleotide Polymorphisms, we are able to simultaneously estimate genotype-phenotype associations and the residual dependence structure amongst the metabolites at the same time. Availability and implementation The R package BayesSUR with full documentation is available at https://cran.r-project.org/web/packages/BayesSUR/ Contact alex.lewin@lshtm.ac.uk