Bayesian estimation of covariate assisted principal regression for brain functional connectivity

This paper presents a Bayesian reformulation of covariate-assisted principal regression for covariance matrix outcomes to identify low-dimensional components in the covariance associated with covariates. By introducing a geometric approach to the covariance matrices and leveraging Euclidean geometry, we estimate dimension reduction parameters and model covariance heterogeneity based on covariates. This method enables joint estimation and uncertainty quantification of relevant model parameters associated with heteroscedasticity. We demonstrate our approach through simulation studies and apply it to analyze associations between covariates and brain functional connectivity using data from the Human Connectome Project.

Joint modeling of association networks and longitudinal biomarkers: An application to childhood obesity

The prevalence of chronic non-communicable diseases such as obesity has noticeably increased in the last decade. The study of these diseases in early life is of paramount importance in determining their course in adult life and in supporting clinical interventions. Recently, attention has been drawn to approaches that study the alteration of metabolic pathways in obese children. In this work, we propose a novel joint modeling approach for the analysis of growth biomarkers and metabolite associations, to unveil metabolic pathways related to childhood obesity. Within a Bayesian framework, we flexibly model the temporal evolution of growth trajectories and metabolic associations through the specification of a joint nonparametric random effect distribution, with the main goal of clustering subjects, thus identifying risk sub-groups. Growth profiles as well as patterns of metabolic associations determine the clustering structure. Inclusion of risk factors is straightforward through the specification of a regression term. We demonstrate the proposed approach on data from the Growing Up in Singapore Towards healthy Outcomes cohort study, based in Singapore. Posterior inference is obtained via a tailored MCMC algorithm, involving a nonparametric prior with mixed support. Our analysis has identified potential key pathways in obese children that allow for the exploration of possible molecular mechanisms associated with childhood obesity.

Bayesian dynamic network modelling: an application to metabolic associations in cardiovascular diseases

We propose a novel approach to the estimation of multiple Graphical Models to analyse temporal patterns of association among a set of metabolites over different groups of patients. Our motivating application is the Southall And Brent REvisited (SABRE) study, a tri-ethnic cohort study conducted in the UK. We are interested in identifying potential ethnic differences in metabolite levels and associations as well as their evolution over time, with the aim of gaining a better understanding of different risk of cardio-metabolic disorders across ethnicities. Within a Bayesian framework, we employ a nodewise regression approach to infer the structure of the graphs, borrowing information across time as well as across ethnicities. The response variables of interest are metabolite levels measured at two time points and for two ethnic groups, Europeans and South-Asians. We use nodewise regression to estimate the high-dimensional precision matrices of the metabolites, imposing sparsity on the regression coefficients through the dynamic horseshoe prior, thus favouring sparser graphs. We provide the code to fit the proposed model using the software Stan, which performs posterior inference using Hamiltonian Monte Carlo sampling, as well as a detailed description of a block Gibbs sampling scheme.

Bayesian Edge Regression in Undirected Graphical Models to Characterize Interpatient Heterogeneity in Cancer

It is well-established that interpatient heterogeneity in cancer may significantly affect genomic data analyses and in particular, network topologies. Most existing graphical model methods estimate a single population-level graph for genomic or proteomic network. In many investigations, these networks depend on patient-specific indicators that characterize the heterogeneity of individual networks across subjects with respect to subject-level covariates. Examples include assessments of how the network varies with patient-specific prognostic scores or comparisons of tumor and normal graphs while accounting for tumor purity as a continuous predictor. In this paper, we propose a novel edge regression model for undirected graphs, which estimates conditional dependencies as a function of subject-level covariates. We evaluate our model performance through simulation studies focused on comparing tumor and normal graphs while adjusting for tumor purity. In application to a dataset of proteomic measurements on plasma samples from patients with hepatocellular carcinoma (HCC), we ascertain how blood protein networks vary with disease severity, as measured by HepatoScore, a novel biomarker signature measuring disease severity. Our case study shows that the network connectivity increases with HepatoScore and a set of hub genes as well as important gene connections are identified under different HepatoScore, which may provide important biological insights to the development of precision therapies for HCC.

Bayesian learning of multiple directed networks from observational data

Graphical modeling represents an established methodology for identifying complex dependencies in biological networks, as exemplified in the study of co-expression, gene regulatory, and protein interaction networks. The available observations often exhibit an intrinsic heterogeneity, which impacts on the network structure through the modification of specific pathways for distinct groups, such as disease subtypes. We propose to infer the resulting multiple graphs jointly in order to benefit from potential similarities across groups; on the other hand our modeling framework is able to accommodate group idiosyncrasies. We consider directed acyclic graphs (DAGs) as network structures, and develop a Bayesian method for structural learning of multiple DAGs. We explicitly account for Markov equivalence of DAGs, and propose a suitable prior on the collection of graph spaces that induces selective borrowing strength across groups. The resulting inference allows in particular to compute the posterior probability of edge inclusion, a useful summary for representing flow directions within the network. Finally, we detail a simulation study addressing the comparative performance of our method, and present an analysis of two protein networks together with a substantive interpretation of our findings.

NExUS: Bayesian simultaneous network estimation across unequal sample sizes

MOTIVATION

Network-based analyses of high-throughput genomics data provide a holistic, systems-level understanding of various biological mechanisms for a common population. However, when estimating multiple networks across heterogeneous sub-populations, varying sample sizes pose a challenge in the estimation and inference, as network differences may be driven by differences in power. We are particularly interested in addressing this challenge in the context of proteomic networks for related cancers, as the number of subjects available for rare cancer (sub-)types is often limited.

RESULTS

We develop NExUS (Network Estimation across Unequal Sample sizes), a Bayesian method that enables joint learning of multiple networks while avoiding artefactual relationship between sample size and network sparsity. We demonstrate through simulations that NExUS outperforms existing network estimation methods in this context, and apply it to learn network similarity and shared pathway activity for groups of cancers with related origins represented in The Cancer Genome Atlas (TCGA) proteomic data.

AVAILABILITY AND IMPLEMENTATION

The NExUS source code is freely available for download at https://github.com/priyamdas2/NExUS.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.