Bayesian Nonparametric Modelling of Multiple Graphs with an Application to Ethnic Metabolic Differences

Abstract

We propose a novel approach to the estimation of multiple Gaussian graphical models (GGMs) to analyse patterns of association among a set of metabolites, under different conditions. Our motivating application is the SABRE (Southall And Brent REvisited) study, a triethnic cohort study conducted in the United Kingdom. Through joint modelling of pattern of association corresponding to different ethnic groups, we are able to identify potential ethnic differences in metabolite levels and associations, with the aim of gaining a better understanding of different risk of cardiometabolic disorders across ethnicities. We model the relationship between a set of metabolites and a set of covariates through a sparse seemingly unrelated regressions model and we use GGMs to represent the conditional dependence structure among metabolites. We specify a dependent generalised Dirichlet process prior on the edge inclusion probabilities to borrow strength across groups and we adopt the horseshoe prior to identify important biomarkers. Inference is performed via Markov chain Monte Carlo.