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In this article, we develop an analytical approach for estimating brain connectivity networks that accounts for subject heterogeneity. More specifically, we consider a novel extension of a multi‐subject Bayesian vector autoregressive model that estimates group‐specific directed brain connectivity networks and accounts for the effects of covariates on the network edges. We adopt a flexible approach, allowing for (possibly) nonlinear effects of the covariates on edge strength via a novel Bayesian nonparametric prior that employs a weighted mixture of Gaussian processes. For posterior inference, we achieve computational scalability by implementing a variational Bayes scheme. Our approach enables simultaneous estimation of group‐specific networks and selection of relevant covariate effects. We show improved performance over competing two‐stage approaches on simulated data. We apply our method on resting‐state functional magnetic resonance imaging data from children with a history of traumatic brain injury (TBI) and healthy controls to estimate the effects of age and sex on the group‐level connectivities. Our results highlight differences in the distribution of parent nodes. They also suggest alteration in the relation of age, with peak edge strength in children with TBI, and differences in effective connectivity strength between males and females. 

Summary 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. 

Abstract Alzheimer's disease is the most common neurodegenerative disease. The aim of this study is to infer structural changes in brain connectivity resulting from disease progression using cortical thickness measurements from a cohort of participants who were either healthy control, or with mild cognitive impairment, or Alzheimer's disease patients. For this purpose, we develop a novel approach for inference of multiple networks with related edge values across groups. Specifically, we infer a Gaussian graphical model for each group within a joint framework, where we rely on Bayesian hierarchical priors to link the precision matrix entries across groups. Our proposal differs from existing approaches in that it flexibly learns which groups have the most similar edge values, and accounts for the strength of connection (rather than only edge presence or absence) when sharing information across groups. Our results identify key alterations in structural connectivity that may reflect disruptions to the healthy brain, such as decreased connectivity within the occipital lobe with increasing disease severity. We also illustrate the proposed method through simulations, where we demonstrate its performance in structure learning and precision matrix estimation with respect to alternative approaches.