Bayesian Hierarchical Model for Genetic Association with Multiple Correlated Phenotypes.

Title: Bayesian Hierarchical Model for Genetic Association with Multiple Correlated Phenotypes. Authors: Alex Lewin (1), Habib Saadi (1), Leonardo Bottolo (1), Sylvia Richardson (2) (1: Imperial College, London, 2: MRC Biostatistics Unit, Cambridge) Abstract: Genetic association studies are used to find regions of the genome associated with phenotypes of interest. Most association studies to date have been carried out for a single phenotype, or for small combination of phenotypes, with a single regression being performed for each marker. Here we study a data set in which the phenotypes are 137 metabolites measured by NMR in a birth cohort of 4000 people. The genetic associations with these phenotypes have been analysed previously one at a time, ie separate regressions have been done for each marker x phenotype combination (Tukiainen et al. 2012). Rather than carrying out thousands of separate univariate analyses, we model all the data simultaneously. We use the Bayesian model HESS (Hierarchical Evolutionary Stochastic Search) developed by Bottolo et al. 2011, for detecting genetic regulation of gene expression, in particular for finding genetic markers which are associated with multiple expression phenotypes. The hierarchical formulation incorporates a regression model for each phenotype against all the genetic markers, with a sparsity prior to induce variable selection amongst the markers. The Bayesian hierarchical model treats the multiple phenotypes in parallel, enabling information sharing across phenotypes, whilst allowing for different markers to be associated with different phenotypes. The data set used here exhibits a strong correlation structure between the phenotypes, linked to their related biological function. In this work we investigate the performance of the hierarchical model for analysing correlated outcomes, discuss a range of analysis strategy where the correlation of the phenotypes is exploited, and develop methods for assessing statistical importance of selected markers in the presence of correlated data. Bottolo L., Petretto E., Blankenberg S., Cambien F., Cook S., Tiret L. and Richardson S. 2011, Bayesian Detection of Expression Quantitative Trait Loci Hot Spots, Genetics, Vol. 189, 1449-1459. Tukiainen T, Kettunen J et al. 2012: Detailed metabolic and genetic characterization reveals new associations for 30 known lipid loci, Hum Mol Genet, 21(6), 1444 - 1455