Diagnostically distinct resting state fMRI energy distributions: A subject-specific maximum entropy modeling study.

Objective: Existing neuroimaging studies of psychotic and mood disorders have reported brain activation differences (first-order properties) and altered pairwise correlation-based functional connectivity (second-order properties). However, both approaches have certain limitations that can be overcome by integrating them in a pairwise maximum entropy model (MEM) that better represents a comprehensive picture of fMRI signal patterns and provides a system-wide summary measure called energy. This study examines the applicability of individual-level MEM for psychiatry and identifies image-derived model coefficients related to model parameters. Method: MEMs are fit to resting state fMRI data from each individual with schizophrenia/schizoaffective disorder, bipolar disorder, and major depression (n=132) and demographically matched healthy controls (n=132) from the UK Biobank to different subsets of the default mode network (DMN) regions. Results: The model satisfactorily explained observed brain energy state occurrence probabilities across all participants, and model parameters were significantly correlated with image-derived coefficients for all groups. Within clinical groups, averaged energy level distributions were higher in schizophrenia/schizoaffective disorder but lower in bipolar disorder compared to controls for both bilateral and unilateral DMN. Major depression energy distributions were higher compared to controls only in the right hemisphere DMN. Conclusions: Diagnostically distinct energy states suggest that probability distributions of temporal changes in synchronously active nodes may underlie each diagnostic entity. Subject-specific MEMs allow for factoring in the individual variations compared to traditional group-level inferences, offering an improved measure of biologically meaningful correlates of brain activity that may have potential clinical utility.

Threshold Selection for Brain Connectomes.

Introduction: Structural and functional brain connectomes represent macroscale data collected through techniques such as magnetic resonance imaging (MRI). Connectomes may contain noise that contributes to false-positive edges, thereby obscuring structure-function relationships and data interpretation. Thresholding procedures can be applied to reduce network density by removing low-signal edges, but there is limited consensus on appropriate selection of thresholds. This article compares existing thresholding methods and introduces a novel alternative "objective function" thresholding method. Methods: The performance of thresholding approaches, based on percolation and objective functions, is assessed by (1) computing the normalized mutual information (NMI) of community structure between a known network and a simulated, perturbed networks to which various forms of thresholding have been applied, and by (2) comparing the density and the clustering coefficient (CC) between the baseline and thresholded networks. An application to empirical data is provided. Results: Our proposed objective function-based threshold exhibits the best performance in terms of resulting in high similarity between the underlying networks and their perturbed, thresholded counterparts, as quantified by NMI and CC analysis on the simulated functional networks. Discussion: Existing network thresholding methods yield widely different results when graph metrics are subsequently computed. Thresholding based on the objective function maintains a set of edges such that the resulting network shares the community structure and clustering features present in the original network. This outcome provides a proof of principle that objective function thresholding could offer a useful approach to reducing the network density of functional connectivity data.

Structural covariance networks in schizophrenia: A systematic review Part I.

BACKGROUND: Schizophrenia is proposed as a disorder of dysconnectivity. However, examination of complexities of dysconnectivity has been challenging. Structural covariance networks (SCN) provide important insights into the nature of dysconnectivity. This systematic review examines the SCN studies that employed statistical approaches to elucidate covariation of regional morphometric variations. METHODS: A systematic search of literature was conducted for peer-reviewed publications using different keywords and keyword combinations for schizophrenia. Fifty-two studies met the criteria. RESULTS: Early SCN studies began using correlational structure of selected regions. Over the last 3 decades, methodological approaches have grown increasingly sophisticated from examining selected brain regions using correlation tests on small sample sizes to recent approaches that use advanced statistical methods to examine covariance structure of whole-brain parcellations on larger samples. Although the results are not fully consistent across all studies, a pattern of fronto-temporal, fronto-parietal and fronto-thalamic covariation is reported. Attempts to associate SCN alterations with functional connectivity, to differentiate between disease-related and neurodevelopment-related morphometric changes, and to develop "causality-based" models are being reported. Clinical correlation with outcome, psychotic symptoms, neurocognitive and social cognitive performance are also reported. CONCLUSIONS: Application of advanced statistical methods are beginning to provide insights into interesting patterns of regional covariance including correlations with clinical and cognitive data. Although these findings appear similar to morphometric studies, SCNs have the advantage of highlighting topology of these regions and their relationship to the disease and associated variables. Further studies are needed to investigate neurobiological underpinnings of shared covariance, and causal links to clinical domains.

Structural covariance networks in schizophrenia: A systematic review Part II.

BACKGROUND: Examination of structural covariance network (SCN) is gaining prominence among the strategies to delineate dysconnectivity that case-control morphometric comparisons cannot address. Part II of this review extends on the part I of the review that included SCN studies using statistical approaches by examining SCN studies applying graph theoretic approaches to elucidate network properties in schizophrenia. This review also includes SCN studies using graph theoretic or statistical approaches on persons at-risk for schizophrenia. METHODS: A systematic literature search was conducted for peer-reviewed publications using different keywords and keyword combinations for schizophrenia and risk for schizophrenia. Thirteen studies on schizophrenia and five on persons at risk for schizophrenia met the criteria. RESULTS: A variety of findings from over the last 1½ decades showing qualitative and quantitative differences in the global and local structural connectome in schizophrenia are described. These observations include altered hub patterns, disrupted network topology and hierarchical organization of the brain, and impaired connections that may be localized to default mode, executive control, and dorsal attention networks. Some of these connectomic alterations were observed in persons at-risk for schizophrenia before the onset of the illness. CONCLUSIONS: Observed disruptions may reduce network efficiency and capacity to integrate information. Further, global connectomic changes were not schizophrenia-specific but local network changes were. Existing studies have used different atlases for brain parcellation, examined different morphometric features, and patients at different stages of illness making it difficult to conduct meta-analysis. Future studies should harmonize such methodological differences to facilitate meta-analysis and also elucidate causal underpinnings of dysconnectivity.

Inference for Multiple Heterogeneous Networks with a Common Invariant Subspace.

The development of models and methodology for the analysis of data from multiple heterogeneous networks is of importance both in statistical network theory and across a wide spectrum of application domains. Although single-graph analysis is well-studied, multiple graph inference is largely unexplored, in part because of the challenges inherent in appropriately modeling graph differences and yet retaining sufficient model simplicity to render estimation feasible. This paper addresses exactly this gap, by introducing a new model, the common subspace independent-edge multiple random graph model, which describes a heterogeneous collection of networks with a shared latent structure on the vertices but potentially different connectivity patterns for each graph. The model encompasses many popular network representations, including the stochastic blockmodel. The model is both flexible enough to meaningfully account for important graph differences, and tractable enough to allow for accurate inference in multiple networks. In particular, a joint spectral embedding of adjacency matrices-the multiple adjacency spectral embedding-leads to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, the estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation. In both simulated and real data, the model and the embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing, and community detection. Specifically, when the embedding is applied to a data set of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by human subject and a meaningful determination of heterogeneity across scans of different individuals.

On a two-truths phenomenon in spectral graph clustering.

Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering-clustering the vertices of a graph based on their spectral embedding-is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian spectral embedding (LSE) or adjacency spectral embedding (ASE). Recent theoretical results provide deeper understanding of the problem and solutions and lead us to a "two-truths" LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome dataset: The different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core-periphery structure.

Comparing machine learning and logistic regression methods for predicting hypertension using a combination of gene expression and next-generation sequencing data.

Machine learning methods continue to show promise in the analysis of data from genetic association studies because of the high number of variables relative to the number of observations. However, few best practices exist for the application of these methods. We extend a recently proposed supervised machine learning approach for predicting disease risk by genotypes to be able to incorporate gene expression data and rare variants. We then apply 2 different versions of the approach (radial and linear support vector machines) to simulated data from Genetic Analysis Workshop 19 and compare performance to logistic regression. Method performance was not radically different across the 3 methods, although the linear support vector machine tended to show small gains in predictive ability relative to a radial support vector machine and logistic regression. Importantly, as the number of genes in the models was increased, even when those genes contained causal rare variants, model predictive ability showed a statistically significant decrease in performance for both the radial support vector machine and logistic regression. The linear support vector machine showed more robust performance to the inclusion of additional genes. Further work is needed to evaluate machine learning approaches on larger samples and to evaluate the relative improvement in model prediction from the incorporation of gene expression data.

A Bayesian Framework for the Classification of Microbial Gene Activity States.

Numerous methods for classifying gene activity states based on gene expression data have been proposed for use in downstream applications, such as incorporating transcriptomics data into metabolic models in order to improve resulting flux predictions. These methods often attempt to classify gene activity for each gene in each experimental condition as belonging to one of two states: active (the gene product is part of an active cellular mechanism) or inactive (the cellular mechanism is not active). These existing methods of classifying gene activity states suffer from multiple limitations, including enforcing unrealistic constraints on the overall proportions of active and inactive genes, failing to leverage a priori knowledge of gene co-regulation, failing to account for differences between genes, and failing to provide statistically meaningful confidence estimates. We propose a flexible Bayesian approach to classifying gene activity states based on a Gaussian mixture model. The model integrates genome-wide transcriptomics data from multiple conditions and information about gene co-regulation to provide activity state confidence estimates for each gene in each condition. We compare the performance of our novel method to existing methods on both simulated data and real data from 907 E. coli gene expression arrays, as well as a comparison with experimentally measured flux values in 29 conditions, demonstrating that our method provides more consistent and accurate results than existing methods across a variety of metrics.