Bayesian graphical models for modern biological applications

A modeling framework for detecting and leveraging node-level information in Bayesian network inference

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

Learning Bayesian Networks: A Copula Approach for Mixed-Type Data

Estimating dependence relationships between variables is a crucial issue in many applied domains and in particular psychology. When several variables are entertained, these can be organized into a network which encodes their set of conditional dependence relations. Typically however, the underlying network structure is completely unknown or can be partially drawn only; accordingly it should be learned from the available data, a process known as structure learning. In addition, data arising from social and psychological studies are often of different types, as they can include categorical, discrete and continuous measurements. In this paper, we develop a novel Bayesian methodology for structure learning of directed networks which applies to mixed data, i.e., possibly containing continuous, discrete, ordinal and binary variables simultaneously. Whenever available, our method can easily incorporate known dependence structures among variables represented by paths or edge directions that can be postulated in advance based on the specific problem under consideration. We evaluate the proposed method through extensive simulation studies, with appreciable performances in comparison with current state-of-the-art alternative methods. Finally, we apply our methodology to well-being data from a social survey promoted by the United Nations, and mental health data collected from a cohort of medical students. R code implementing the proposed methodology is available at https://github.com/FedeCastelletti/bayes_networks_mixed_data .

Network Analysis of Behavioral Activation/Inhibition Systems and Brain Volume in Individuals With and Without Major Depressive Disorder or Social Anxiety Disorder

BACKGROUND

Social anxiety disorder (SAD) and major depressive disorder (MDD) are characterized by behavioral abnormalities in motivational systems, namely the behavioral inhibition system (BIS) and behavioral activation system (BAS). Limited studies indicate brain volume in regions that support emotion, learning/memory, reward, and cognitive functions relate to BIS/BAS. To increase understanding of BIS/BAS, the current study used a network approach.

METHODS

Patients with SAD (n = 59), patients with MDD (n = 64), and healthy control participants (n = 36) completed a BIS/BAS questionnaire and structural magnetic resonance imaging scans; volumetric regions of interest comprised cortical and limbic structures based on previous BIS/BAS studies. A Bayesian Gaussian graphical model was used for each diagnostic group, and groups were compared. Among network metrics, bridge centrality was of primary interest. Analysis of variance evaluated BIS/BAS behaviors between groups.

RESULTS

Bridge centrality showed hippocampus positively related to BAS, but not to BIS, in the MDD group; no findings were observed in the SAD or control groups. Yet, network density (i.e., overall strength of relationships between variables) and degree centrality (i.e., overall relationship between one variable to all other variables) showed that cortical (e.g., precuneus, medial orbitofrontal) and subcortical (e.g., amygdala, hippocampus) regions differed between diagnostic groups. Analysis of variance results showed BAS was lower in the MDD/SAD groups compared with the control group, while BIS was higher in the SAD group relative to the MDD group, which in turn was higher than the control group.

CONCLUSIONS

Preliminary findings indicate that network-level aberrations may underlie motivational abnormalities in MDD and SAD. Evidence of BIS/BAS differences builds on previous work that points to shared and distinct motivational differences in internalizing psychopathologies.

Causal association study of the dynamic development of the metabolic syndrome based on longitudinal data

The dynamic progression of metabolic syndrome (MetS) includes developmental deterioration and reverse recovery; however, the key factors in this bidirectional progression have not been identified. Our study aimed to use the data obtained from the China Health and Retirement Longitudinal Study (CHARLS) and construct a Bayesian network to explore the causal relationship between influential factor and the development and recovery of MetS. Followed up at 4 years, forward progression of MetS occurred in 1543 and reverse recovery of MetS occurred in 1319 of 5581 subjects. Bayesian Networks showed that hyperuricemia and body mass index (BMI) levels directly influenced progression of MetS, and gender, exercise and age play an indirect role through hyperuricemia and BMI levels; high hemoglobin A1c (HbA1c) and BMI levels directly influenced recovery of MetS, and gender and exercise play an indirect role through BMI levels. Bayesian Network inference found that the rate of progression of MetS in subjects with hyperuricemia increases from 36 to 60%, the rate of progression of MetS in subjects with overweight or obese increases from 36 to 41% and the rate of reverse recovery rate of MetS in subjects with high HbA1c decreased from 33 to 20%. Therefore, attention to individuals at high risk of hyperuricemia, high HbA1c levels, and overweight/obesity should be enhanced, with early detection and following healthy behavioral interventions to prevent, control and delay the progression of MetS and its components.

Sorption of four antibiotics onto pristine biochar derived from macadamia nutshell

In this study, the sorption properties of ciprofloxacin, ofloxacin, sulfamethoxazole, and trimethoprim on biochar derived from macadamia nut shells were investigated. The raw biomass was pyrolyzed at 600 °C to create a highly porous material with a surface area of 392 m2 g-1. The produced biochar was found to be a valuable material for both environmental remediation and carbon sequestration due to its high carbon and oxygen content. The sorption properties of four antibiotics on the produced biochar were compared using Bayesian nonlinear regression based on second-order kinetics and the Langmuir model. The Bayesian estimation successfully compared the adsorption coefficients of the antibiotics, which can be directly visualized through graphical grammar using the probability density distribution. The results demonstrated the ability of macadamia nut shell biochar to remove antibiotics from water at neutral pH, and this material has the potential to be used for treating other emerging contaminants.

Networks as mediating variables: a Bayesian latent space approach

The use of network analysis to investigate social structures has recently seen a rise due to the high availability of data and the numerous insights it can provide into different fields. Most analyses focus on the topological characteristics of networks and the estimation of relationships between the nodes. We adopt a different perspective by considering the whole network as a random variable conveying the effect of an exposure on a response. This point of view represents a classical mediation setting, where the interest lies in estimating the indirect effect, that is, the effect propagated through the mediating variable. We introduce a latent space model mapping the network into a space of smaller dimension by considering the hidden positions of the units in the network. The coordinates of each node are used as mediators in the relationship between the exposure and the response. We further extend mediation analysis in the latent space framework by using Generalised Linear Models instead of linear ones, as previously done in the literature, adopting an approach based on derivatives to obtain the effects of interest. A Bayesian approach allows us to get the entire distribution of the indirect effect, generally unknown, and compute the corresponding highest density interval, which gives accurate and interpretable bounds for the mediated effect. Finally, an application to social interactions among a group of adolescents and their attitude toward substance use is presented.