Bayesian inference of networks across multiple sample groups and data types

Abstract

In this article, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to differing disease stage or subtype, is profiled across multiple platforms, such as metabolomics, proteomics, or transcriptomics data. Our proposed Bayesian hierarchical model first links the network structures within each platform using a Markov random field prior to relate edge selection across sample groups, and then links the network similarity parameters across platforms. This enables joint estimation in a flexible manner, as we make no assumptions on the directionality of influence across the data types or the extent of network similarity across the sample groups and platforms. In addition, our model formulation allows the number of variables and number of subjects to differ across the data types, and only requires that we have data for the same set of groups. We illustrate the proposed approach through both simulation studies and an application to gene expression levels and metabolite abundances on subjects with varying severity levels of chronic obstructive pulmonary disease. Bayesian inference; Chronic obstructive pulmonary disease (COPD); Data integration; Gaussian graphical model; Markov random field prior; Spike and slab prior.

Trial registration: ClinicalTrials.gov NCT00608764.

Keywords: Bayesian inference; Chronic obstructive pulmonary disease (COPD); Data integration; Gaussian graphical model; Markov random field prior; Spike and slab prior.

© The Author 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Figures

Fig. 1.

Left: Graphical model representation of the proposed model, illustrating variables, parameters, and hyper parameters for each of the groups and platforms.Right: A graphical illustration with subgroups and platforms.

Fig. 2.

RegAuto pathway, gene (top), and metabolite (bottom) platforms: estimated graphs for control (left), moderate (middle), and severe (right) subgroups, obtained by selecting edges with MPPs greater than 0.5. The size of the nodes is proportional to their degree.