Comparison of statistical tests for group differences in brain functional networks

The CBIT + TMS trial: study protocol for a two-phase randomized controlled trial testing neuromodulation to augment behavior therapy for youth with chronic tics

BACKGROUND

Comprehensive Behavioral Intervention for Tics (CBIT) is a first-line treatment for tic disorders that aims to improve controllability over tics that an individual finds distressing or impairing. However, it is only effective for approximately half of patients. Supplementary motor area (SMA)-directed neurocircuitry plays a strong role in motor inhibition, and activity in this region is thought to contribute to tic expression. Targeted modulation of SMA using transcranial magnetic stimulation (TMS) may increase CBIT efficacy by improving patients' ability to implement tic controllability behaviors.

METHODS

The CBIT + TMS trial is a two-phase, milestone-driven early-stage randomized controlled trial. The trial will test whether augmenting CBIT with inhibitory, non-invasive stimulation of SMA with TMS modifies activity in SMA-mediated circuits and enhances tic controllability in youth ages 12-21 years with chronic tics. Phase 1 will directly compare two rTMS augmentation strategies (1 Hz rTMS vs. cTBS) vs. sham in N = 60 participants. Quantifiable, a priori "Go/No Go Criteria" guide the decision to proceed to phase 2 and the selection of the optimal TMS regimen. Phase 2 will compare the optimal regimen vs. sham and test the link between neural target engagement and clinical outcomes in a new sample of N = 60 participants.

DISCUSSION

This clinical trial is one of few to date testing TMS augmentation of therapy in a pediatric sample. The results will provide insight into whether TMS is a potentially viable strategy for enhancing CBIT efficacy and reveal potential neural and behavioral mechanisms of change.

TRIAL REGISTRATION

ClinicalTrials.gov NCT04578912 . Registered on October 8, 2020.

Connectome-wide Functional Connectivity Abnormalities in Youth With Obsessive-Compulsive Symptoms

BACKGROUND

Obsessive-compulsive symptomatology (OCS) is common in adolescence but usually does not meet the diagnostic threshold for obsessive-compulsive disorder. Nevertheless, both obsessive-compulsive disorder and subthreshold OCS are associated with increased likelihood of experiencing other serious psychiatric conditions, including depression and suicidal ideation. Unfortunately, there is limited information on the neurobiology of OCS.

METHODS

Here, we undertook one of the first brain imaging studies of OCS in a large adolescent sample (analyzed n = 832) from the Philadelphia Neurodevelopmental Cohort. We investigated resting-state functional magnetic resonance imaging functional connectivity using complementary analytic approaches that focus on different neuroanatomical scales, from known functional systems to connectome-wide tests.

RESULTS

We found a robust pattern of connectome-wide, OCS-related differences, as well as evidence of specific abnormalities involving known functional systems, including dorsal and ventral attention, frontoparietal, and default mode systems. Analysis of cerebral perfusion imaging and high-resolution structural imaging did not show OCS-related differences, consistent with domain specificity to functional connectivity.

CONCLUSIONS

The brain connectomic associations with OCS reported here, together with early studies of its clinical relevance, support the potential for OCS as an early marker of psychiatric risk that may enhance our understanding of mechanisms underlying the onset of adolescent psychopathology.

Network analysis of neuroimaging in mice

Graph theory allows assessing changes of neuronal connectivity and interactions of brain regions in response to local lesions, e.g., after stroke, and global perturbations, e.g., due to psychiatric dysfunctions or neurodegenerative disorders. Consequently, network analysis based on constructing graphs from structural and functional MRI connectivity matrices is increasingly used in clinical studies. In contrast, in mouse neuroimaging, the focus is mainly on basic connectivity parameters, i.e., the correlation coefficient or fiber counts, whereas more advanced network analyses remain rarely used. This review summarizes graph theoretical measures and their interpretation to describe networks derived from recent in vivo mouse brain studies. To facilitate the entry into the topic, we explain the related mathematical definitions, provide a dedicated software toolkit, and discuss practical considerations for the application to rs-fMRI and DTI. This way, we aim to foster cross-species comparisons and the application of standardized measures to classify and interpret network changes in translational brain disease studies.

Hypothesis Testing for Network Data with Power Enhancement

Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Numerous existing network inference solutions focus on global testing of entire networks, without comparing individual network links. The observed data often take the form of vectors or matrices, and the problem is formulated as comparing two covariance or precision matrices under a normal or matrix normal distribution. Moreover, many tests suffer from a limited power under a small sample size. In this article, we tackle the problem of network comparison, both global and simultaneous inferences, when the data come in a different format, i.e., in the form of a collection of symmetric matrices, each of which encodes the network structure of an individual subject. Such data format commonly arises in applications such as brain connectivity analysis and clinical genomics. We no longer require the underlying data to follow a normal distribution, but instead impose some moment conditions that are easily satisfied for numerous types of network data. Furthermore, we propose a power enhancement procedure, and show that it can control the false discovery, while it has the potential to substantially enhance the power of the test. We investigate the efficacy of our testing procedure through both an asymptotic analysis and a simulation study under a finite sample size. We further illustrate our method with examples of brain connectivity analysis.

Permutation-based inference for spatially localized signals in longitudinal MRI data

Alzheimer's disease is a neurodegenerative disease in which the degree of cortical atrophy in specific structures of the brain serves as a useful imaging biomarker. Recent approaches using linear mixed effects (LME) models in longitudinal neuroimaging have been powerful and flexible in investigating the temporal trajectories of cortical thickness. However, massive-univariate analysis, a simplified approach that obtains a summary statistic (e.g., a p-value) for every vertex along the cortex, is insufficient to model cortical atrophy because it does not account for spatial similarities of the signals in neighboring locations. In this article, we develop a permutation-based inference procedure to detect spatial clusters of vertices showing statistically significant differences in the rates of cortical atrophy. The proposed method, called SpLoc, uses spatial information to combine the signals adaptively across neighboring vertices, yielding high statistical power while controlling family-wise error rate (FWER) accurately. When we reject the global null hypothesis, we use a cluster selection algorithm to detect the spatial clusters of significant vertices. We validate our method using simulation studies and apply it to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data to show its superior performance over existing methods. An R package for implementing SpLoc is publicly available.

Statistical and Machine Learning Link Selection Methods for Brain Functional Networks: Review and Comparison

Network-based representations have introduced a revolution in neuroscience, expanding the understanding of the brain from the activity of individual regions to the interactions between them. This augmented network view comes at the cost of high dimensionality, which hinders both our capacity of deciphering the main mechanisms behind pathologies, and the significance of any statistical and/or machine learning task used in processing this data. A link selection method, allowing to remove irrelevant connections in a given scenario, is an obvious solution that provides improved utilization of these network representations. In this contribution we review a large set of statistical and machine learning link selection methods and evaluate them on real brain functional networks. Results indicate that most methods perform in a qualitatively similar way, with NBS (Network Based Statistics) winning in terms of quantity of retained information, AnovaNet in terms of stability and ExT (Extra Trees) in terms of lower computational cost. While machine learning methods are conceptually more complex than statistical ones, they do not yield a clear advantage. At the same time, the high heterogeneity in the set of links retained by each method suggests that they are offering complementary views to the data. The implications of these results in neuroscience tasks are finally discussed.

Network Modeling in Biology: Statistical Methods for Gene and Brain Networks

The rise of network data in many different domains has offered researchers new insight into the problem of modeling complex systems and propelled the development of numerous innovative statistical methodologies and computational tools. In this paper, we primarily focus on two types of biological networks, gene networks and brain networks, where statistical network modeling has found both fruitful and challenging applications. Unlike other network examples such as social networks where network edges can be directly observed, both gene and brain networks require careful estimation of edges using covariates as a first step. We provide a discussion on existing statistical and computational methods for edge esitimation and subsequent statistical inference problems in these two types of biological networks.

Bayesian modeling of dependence in brain connectivity data

Brain connectivity studies often refer to brain areas as graph nodes and connections between nodes as edges, and aim to identify neuropsychiatric phenotype-related connectivity patterns. When performing group-level brain connectivity alternation analyses, it is critical to model the dependence structure between multivariate connectivity edges to achieve accurate and efficient estimates of model parameters. However, specifying and estimating dependencies between connectivity edges presents formidable challenges because (i) the dimensionality of parameters in the covariance matrix is high (of the order of the fourth power of the number of nodes); (ii) the covariance between a pair of edges involves four nodes with spatial location information; and (iii) the dependence structure between edges can be related to unknown network topological structures. Existing methods for large covariance/precision matrix regularization and spatial closeness-based dependence structure specification/estimation models may not fully address the complexity and challenges. We develop a new Bayesian nonparametric model that unifies information from brain network areas (nodes), connectivity (edges), and covariance between edges by constructing the function of covariance matrix based on the underlying network topological structure. We perform parameter estimation using an efficient Markov chain Monte Carlo algorithm. We apply our method to resting-state functional magnetic resonance imaging data from 60 subjects of a schizophrenia study and simulated data to demonstrate the performance of our method.

Re-visiting Riemannian geometry of symmetric positive definite matrices for the analysis of functional connectivity

Common representations of functional networks of resting state fMRI time series, including covariance, precision, and cross-correlation matrices, belong to the family of symmetric positive definite (SPD) matrices forming a special mathematical structure called Riemannian manifold. Due to its geometric properties, the analysis and operation of functional connectivity matrices may well be performed on the Riemannian manifold of the SPD space. Analysis of functional networks on the SPD space takes account of all the pairwise interactions (edges) as a whole, which differs from the conventional rationale of considering edges as independent from each other. Despite its geometric characteristics, only a few studies have been conducted for functional network analysis on the SPD manifold and inference methods specialized for connectivity analysis on the SPD manifold are rarely found. The current study aims to show the significance of connectivity analysis on the SPD space and introduce inference algorithms on the SPD manifold, such as regression analysis of functional networks in association with behaviors, principal geodesic analysis, clustering, state transition analysis of dynamic functional networks and statistical tests for network equality on the SPD manifold. We applied the proposed methods to both simulated data and experimental resting state fMRI data from the human connectome project and argue the importance of analyzing functional networks under the SPD geometry. All the algorithms for numerical operations and inferences on the SPD manifold are implemented as a MATLAB library, called SPDtoolbox, for public use to expediate functional network analysis on the right geometry.

Combining the intersubject correlation analysis and the multivariate distance matrix regression to evaluate associations between fNIRS signals and behavioral data from ecological experiments

The development of methods to analyze data acquired using functional near-infrared spectroscopy (fNIRS) in experiments similar to real-life situations is of great value in modern applied neuroscience. One of the most used methods to analyze fNIRS signals consists of the application of the general linear model on the observed hemodynamic signals. However, it implies limitations on the experimental design that must be constrained by triggers related to the stimuli protocols (such as block design or event related). In this work, a novel methodology is proposed to overcome such restrictions and allow more flexible protocols. The method combines the intersubject correlation analysis and the multivariate distance matrix regression to evaluate the brain-behavior relationship of subjects submitted to experiments with no trigger-based protocols. Its applicability is demonstrated throughout a naturalistic experiment about emotions conveyed by music. Thirty-two participants freely listened to instrumental excerpts from the operatic repertoire and reported the valences of the emotions conveyed by the musical segments. The method was able to find a statistically significant correlation between the subjects' fNIRS signals and valences of their emotional responses, for the excerpt that evoked the most negative valence. This result illustrates the potential of this approach as an alternative method to analyze fNIRS signals from experiments in which block design or task-related paradigms might not be suitable.

Detecting and Testing Altered Brain Connectivity Networks with K-partite Network Topology

Emerging brain connectivity network studies suggest that interactions between various distributed neuronal populations may be characterized by an organized complex topological structure. Many neuropsychiatric disorders are associated with altered topological patterns of brain connectivity. Therefore, a key inquiry of connectivity analysis is to detect group-level differentially expressed connectome patterns from the massive neuroimaging data. Recently, statistical methods have been developed to detect differentially expressed connectivity features at a subnetwork level, extending more commonly applied edge level analysis. However, the graph topological structures in these methods are limited to community/cliques which may not effectively uncover the underlying complex and disease-related brain circuits/subnetworks. Building on these previous subnetwork detection methods, a new statistical approach is developed to automatically identify the latent differentially expressed brain connectivity subnetworks with k-partite graph topological structures from large brain connectivity matrices. In addition, statistical inferential techniques are provided to test the detected topological structure. The new methods are evaluated via extensive simulation studies and then applied to resting state fMRI data (24 cases and 18 controls) for Parkinson's disease research. A differentially expressed connectivity network with the k-partite graph topological structure is detected which reveals underlying neural features distinguishing Parkinson's disease patients from healthy control subjects.

A difference degree test for comparing brain networks

Recently, there has been a proliferation of methods investigating functional connectivity as a biomarker for mental disorders. Typical approaches include massive univariate testing at each edge or comparisons of network metrics to identify differing topological features. Limitations of these methods include low statistical power due to the large number of comparisons and difficulty attributing overall differences in networks to local variation. We propose a method to capture the difference degree, which is the number of edges incident to each region in the difference network. Our difference degree test (DDT) is a two-step procedure for identifying brain regions incident to a significant number of differentially weighted edges (DWEs). First, we select a data-adaptive threshold which identifies the DWEs followed by a statistical test for the number of DWEs incident to each brain region. We achieve this by generating an appropriate set of null networks which are matched on the first and second moments of the observed difference network using the Hirschberger-Qi-Steuer algorithm. This formulation permits separation of the network's true topology from the nuisance topology induced by the correlation measure that alters interregional connectivity in ways unrelated to brain function. In simulations, the proposed approach outperforms competing methods in detecting differentially connected regions of interest. Application of DDT to a major depressive disorder dataset leads to the identification of brain regions in the default mode network commonly implicated in this ruminative disorder.

MultiLink Analysis: Brain Network Comparison via Sparse Connectivity Analysis

The analysis of the brain from a connectivity perspective is revealing novel insights into brain structure and function. Discovery is, however, hindered by the lack of prior knowledge used to make hypotheses. Additionally, exploratory data analysis is made complex by the high dimensionality of data. Indeed, to assess the effect of pathological states on brain networks, neuroscientists are often required to evaluate experimental effects in case-control studies, with hundreds of thousands of connections. In this paper, we propose an approach to identify the multivariate relationships in brain connections that characterize two distinct groups, hence permitting the investigators to immediately discover the subnetworks that contain information about the differences between experimental groups. In particular, we are interested in data discovery related to connectomics, where the connections that characterize differences between two groups of subjects are found. Nevertheless, those connections do not necessarily maximize the accuracy in classification since this does not guarantee reliable interpretation of specific differences between groups. In practice, our method exploits recent machine learning techniques employing sparsity to deal with weighted networks describing the whole-brain macro connectivity. We evaluated our technique on functional and structural connectomes from human and murine brain data. In our experiments, we automatically identified disease-relevant connections in datasets with supervised and unsupervised anatomy-driven parcellation approaches and by using high-dimensional datasets.

A powerful and efficient multivariate approach for voxel-level connectome-wide association studies

We describe an approach to multivariate analysis, termed structured kernel principal component regression (sKPCR), to identify associations in voxel-level connectomes using resting-state functional magnetic resonance imaging (rsfMRI) data. This powerful and computationally efficient multivariate method can identify voxel-phenotype associations based on the whole-brain connectivity pattern of voxels, and it can detect linear and non-linear signals in both volume-based and surface-based rsfMRI data. For each voxel, sKPCR first extracts low-dimensional signals from the spatially smoothed connectivities by structured kernel principal component analysis, and then tests the voxel-phenotype associations by an adaptive regression model. The method's power is derived from appropriately modelling the spatial structure of the data when performing dimension reduction, and then adaptively choosing an optimal dimension for association testing using the adaptive regression strategy. Simulations based on real connectome data have shown that sKPCR can accurately control the false-positive rate and that it is more powerful than many state-of-the-art approaches, such as the connectivity-wise generalized linear model (GLM) approach, multivariate distance matrix regression (MDMR), adaptive sum of powered score (aSPU) test, and least-square kernel machine (LSKM). Moreover, since sKPCR can reduce the computational cost of non-parametric permutation tests, its computation speed is much faster. To demonstrate the utility of sKPCR for real data analysis, we have also compared sKPCR with the above methods based on the identification of voxel-wise differences between schizophrenic patients and healthy controls in four independent rsfMRI datasets. The results showed that sKPCR had better between-sites reproducibility and a larger proportion of overlap with existing schizophrenia meta-analysis findings. Code for our approach can be downloaded from https://github.com/weikanggong/sKPCR.

A linear mixed model framework for gene-based gene-environment interaction tests in twin studies

Interaction between genes and environments (G×E) can be well investigated in families due to the shared genes and environment among family members. However, the majority of the current tests of G×E interaction between a set of variants and an environment are only suitable for studies with unrelated subjects. In this paper, we extend several G×E interaction tests to a linear mixed model framework to study interaction between a set of correlated environments and a candidate gene in families. The correlated environments can either be modeled separately or jointly in one model. We demonstrate theoretically that the tests developed by modeling correlated environments separately are valid and present a computationally fast alternative to detect G×E interaction in families. For either strategy, we propose treating the genetic main effects as a random effect to reduce the number of main-effect parameters and thus improve the power to detect interactions. Additionally, we propose a generalization of a test of interaction that adaptively sums the interactions using a sequential algorithm. This generalized set of tests, referred to as the sequential algorithm for the sum of powered score (Seq-SPU) family of tests, can be expressed as a weighted version of the SPU. We find that the adaptive version of our test, Seq-aSPU, can outperform aSPU in cases where the interactions effects are in opposite directions. We applied these methods to the Minnesota Center for Twin and Family Research data set and found one significant gene in interaction with four psychosocial environmental factors affecting the alcohol consumption among the twins.

Interpretable High-Dimensional Inference Via Score Projection with an Application in Neuroimaging

In the fields of neuroimaging and genetics, a key goal is testing the association of a single outcome with a very high-dimensional imaging or genetic variable. Often, summary measures of the high-dimensional variable are created to sequentially test and localize the association with the outcome. In some cases, the associations between the outcome and summary measures are significant, but subsequent tests used to localize differences are underpowered and do not identify regions associated with the outcome. Here, we propose a generalization of Rao's score test based on projecting the score statistic onto a linear subspace of a high-dimensional parameter space. The approach provides a way to localize signal in the high-dimensional space by projecting the scores to the subspace where the score test was performed. This allows for inference in the high-dimensional space to be performed on the same degrees of freedom as the score test, effectively reducing the number of comparisons. Simulation results demonstrate the test has competitive power relative to others commonly used. We illustrate the method by analyzing a subset of the Alzheimer's Disease Neuroimaging Initiative dataset. Results suggest cortical thinning of the frontal and temporal lobes may be a useful biological marker of Alzheimer's disease risk.

GraphVar 2.0: A user-friendly toolbox for machine learning on functional connectivity measures

BACKGROUND

We previously presented GraphVar as a user-friendly MATLAB toolbox for comprehensive graph analyses of functional brain connectivity. Here we introduce a comprehensive extension of the toolbox allowing users to seamlessly explore easily customizable decoding models across functional connectivity measures as well as additional features.

NEW METHOD

GraphVar 2.0 provides machine learning (ML) model construction, validation and exploration. Machine learning can be performed across any combination of graph measures and additional variables, allowing for a flexibility in neuroimaging applications.

RESULTS

In addition to previously integrated functionalities, such as network construction and graph-theoretical analyses of brain connectivity with a high-speed general linear model (GLM), users can now perform customizable ML across connectivity matrices, graph measures and additionally imported variables. The new extension also provides parametric and nonparametric testing of classifier and regressor performance, data export, figure generation and high quality export.

COMPARISON WITH EXISTING METHODS

Compared to other existing toolboxes, GraphVar 2.0 offers (1) comprehensive customization, (2) an all-in-one user friendly interface, (3) customizable model design and manual hyperparameter entry, (4) interactive results exploration and data export, (5) automated queue system for modelling multiple outcome variables within the same session, (6) an easy to follow introductory review.

CONCLUSIONS

GraphVar 2.0 allows comprehensive, user-friendly exploration of encoding (GLM) and decoding (ML) modelling approaches on functional connectivity measures making big data neuroscience readily accessible to a broader audience of neuroimaging investigators.

Aberrant Brain Connectivity in Schizophrenia Detected via a Fast Gaussian Graphical Model

Schizophrenia (SZ) is a chronic and severe mental disorder that affects how a person thinks, feels, and behaves. It has been proposed that this disorder is related to disrupted brain connectivity, which has been verified by many studies. With the development of functional magnetic resonance imaging (fMRI), further exploration of brain connectivity was made possible. Region-based networks are commonly used for mapping brain connectivity. However, they fail to illustrate the connectivity within regions of interest (ROIs) and lose precise location information. Voxel-based networks provide higher precision, but are difficult to construct and interpret due to the high dimensionality of the data. In this paper, we adopt a novel high-dimensional Gaussian graphical model - ψ-learning method, which can help ease computational burden and provide more accurate inference for the underlying networks. This method has been proven to be an equivalent measure of the partial correlation coefficient and, thus, is flexible for network comparison through statistical tests. The fMRI data we used were collected by the mind clinical imaging consortium using an auditory task in which there are 92 SZ patients and 116 healthy controls. We compared the networks at three different scales by using global measurements, community structure, and edge-wise comparisons within the networks. Our results reveal, at the highest voxel resolution, sets of distinct aberrant patterns for the SZ patients, and more precise local structures are provided within ROIs for further investigation.

A method to assess randomness of functional connectivity matrices

BACKGROUND

Functional magnetic resonance imaging (fMRI) allows for the measurement of functional connectivity of the brain. In this context, graph theory has revealed distinctive non-random connectivity patterns. However, the application of graph theory to fMRI often utilizes non-linear transformations (absolute value) to extract edge representations.

NEW METHOD

In contrast, this work proposes a mathematical framework for the analysis of randomness directly from functional connectivity assessments. The framework applies random matrix theory to the analysis of functional connectivity matrices (FCMs). The developed randomness measure includes its probability density function and statistical testing method.

RESULTS

The utilized data comes from a previous study including 603 healthy individuals. Results demonstrate the application of the proposed method, confirming that whole brain FCMs are not random matrices. On the other hand, several FCM submatrices did not significantly test out of randomness.

COMPARISON WITH EXISTING METHODS

The proposed method does not replace graph theory measures; instead, it assesses a different aspect of functional connectivity. Features not included in graph theory are small numbers of nodes, testing submatrices of an FCM and handling negative as well as positive edge values.

CONCLUSION

The random test not only determines randomness, but also serves as an indicator of smaller non-random patterns within a non-random FCM. Outcomes suggest that a lower order model may be sufficient as a broad description of the data, but it also indicates a loss of information. The developed randomness measure assesses a different aspect of randomness from that of graph theory.

Learning about learning: Mining human brain sub-network biomarkers from fMRI data

Modeling the brain as a functional network can reveal the relationship between distributed neurophysiological processes and functional interactions between brain structures. Existing literature on functional brain networks focuses mainly on a battery of network properties in "resting state" employing, for example, modularity, clustering, or path length among regions. In contrast, we seek to uncover functionally connected subnetworks that predict or correlate with cohort differences and are conserved within the subjects within a cohort. We focus on differences in both the rate of learning as well as overall performance in a sensorimotor task across subjects and develop a principled approach for the discovery of discriminative subgraphs of functional connectivity based on imaging acquired during practice. We discover two statistically significant subgraph regions: one involving multiple regions in the visual cortex and another involving the parietal operculum and planum temporale. High functional coherence in the former characterizes sessions in which subjects take longer to perform the task, while high coherence in the latter is associated with high learning rate (performance improvement across trials). Our proposed methodology is general, in that it can be applied to other cognitive tasks, to study learning or to differentiate between healthy patients and patients with neurological disorders, by revealing the salient interactions among brain regions associated with the observed global state. The discovery of such significant discriminative subgraphs promises a better data-driven understanding of the dynamic brain processes associated with high-level cognitive functions.

Functional connectomics from a "big data" perspective

In the last decade, explosive growth regarding functional connectome studies has been observed. Accumulating knowledge has significantly contributed to our understanding of the brain's functional network architectures in health and disease. With the development of innovative neuroimaging techniques, the establishment of large brain datasets and the increasing accumulation of published findings, functional connectomic research has begun to move into the era of "big data", which generates unprecedented opportunities for discovery in brain science and simultaneously encounters various challenging issues, such as data acquisition, management and analyses. Big data on the functional connectome exhibits several critical features: high spatial and/or temporal precision, large sample sizes, long-term recording of brain activity, multidimensional biological variables (e.g., imaging, genetic, demographic, cognitive and clinic) and/or vast quantities of existing findings. We review studies regarding functional connectomics from a big data perspective, with a focus on recent methodological advances in state-of-the-art image acquisition (e.g., multiband imaging), analysis approaches and statistical strategies (e.g., graph theoretical analysis, dynamic network analysis, independent component analysis, multivariate pattern analysis and machine learning), as well as reliability and reproducibility validations. We highlight the novel findings in the application of functional connectomic big data to the exploration of the biological mechanisms of cognitive functions, normal development and aging and of neurological and psychiatric disorders. We advocate the urgent need to expand efforts directed at the methodological challenges and discuss the direction of applications in this field.

Adaptive testing for multiple traits in a proportional odds model with applications to detect SNP-brain network associations

There has been increasing interest in developing more powerful and flexible statistical tests to detect genetic associations with multiple traits, as arising from neuroimaging genetic studies. Most of existing methods treat a single trait or multiple traits as response while treating an SNP as a predictor coded under an additive inheritance mode. In this paper, we follow an earlier approach in treating an SNP as an ordinal response while treating traits as predictors in a proportional odds model (POM). In this way, it is not only easier to handle mixed types of traits, e.g., some quantitative and some binary, but it is also potentially more robust to the commonly adopted additive inheritance mode. More importantly, we develop an adaptive test in a POM so that it can maintain high power across many possible situations. Compared to the existing methods treating multiple traits as responses, e.g., in a generalized estimating equation (GEE) approach, the proposed method can be applied to a high dimensional setting where the number of phenotypes (p) can be larger than the sample size (n), in addition to a usual small P setting. The promising performance of the proposed method was demonstrated with applications to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, in which either structural MRI driven phenotypes or resting-state functional MRI (rs-fMRI) derived brain functional connectivity measures were used as phenotypes. The applications led to the identification of several top SNPs of biological interest. Furthermore, simulation studies showed competitive performance of the new method, especially for p>n.

Differential Effects of Brain Disorders on Structural and Functional Connectivity

Different measures of brain connectivity can be defined based on neuroimaging read-outs, including structural and functional connectivity. Neurological and psychiatric conditions are often associated with abnormal connectivity, but comparing the effects of the disease on different types of connectivity remains a challenge. In this paper, we address the problem of quantifying the relative effects of brain disease on structural and functional connectivity at a group level. Within the framework of a graph representation of connectivity, we introduce a kernel two-sample test as an effective method to assess the difference between the patients and control group. Moreover, we propose a common representation space for structural and functional connectivity networks, and a novel test statistics to quantitatively assess differential effects of the disease on different types of connectivity. We apply this approach to a dataset from BTBR mice, a murine model of Agenesis of the Corpus Callosum (ACC), a congenital disorder characterized by the absence of the main bundle of fibers connecting the two hemispheres. We used normo-callosal mice (B6) as a comparator. The application of the proposed methods to this data-set shows that the two types of connectivity can be successfully used to discriminate between BTBR and B6, meaning that both types of connectivity are affected by ACC. However, our novel test statistics shows that structural connectivity is significantly more affected than functional connectivity, consistent with the idea that functional connectivity has a robust topology that can tolerate substantial alterations in its structural connectivity substrate.

Edgewise and subgraph-level tests for brain networks

Resting-state functional magnetic resonance image is a useful technique for investigating brain functional connectivity at rest. In this work, we develop flexible regression models and methods for determining differences in resting-state functional connectivity as a function of age, gender, drug intervention, or neuropsychiatric disorders. We propose two complementary methods for identifying changes of edges and subgraphs. (i) For detecting changes of edges, we select the optimal model at each edge and then conduct contrast tests to identify the effects of the important variables while controlling the familywise error rate. (ii) We adopt the network-based statistics method to improve power by incorporating the graph topological structure. Both methods have wide applications for low signal-to-noise ratio data. We propose stability criteria for the choice of threshold in the network-based statistics procedure and utilize efficient massive parallel procedure to speed up the estimation and inference procedure. Results from our simulation studies show that the thresholds chosen by the proposed stability criteria outperform the Bonferroni threshold. To demonstrate applicability, we use both methods in the context of the Oxytocin and Aging Study to determine effects of age, gender, and drug treatment on resting-state functional connectivity, as well as in the context of the Autism Brain Imaging Data Exchange Study to determine effects of autism spectrum disorder on functional connectivity at rest. Copyright © 2016 John Wiley & Sons, Ltd.

Statistical Approaches for the Study of Cognitive and Brain Aging

Neuroimaging studies of cognitive and brain aging often yield massive datasets that create many analytic and statistical challenges. In this paper, we discuss and address several limitations in the existing work. (1) Linear models are often used to model the age effects on neuroimaging markers, which may be inadequate in capturing the potential nonlinear age effects. (2) Marginal correlations are often used in brain network analysis, which are not efficient in characterizing a complex brain network. (3) Due to the challenge of high-dimensionality, only a small subset of the regional neuroimaging markers is considered in a prediction model, which could miss important regional markers. To overcome those obstacles, we introduce several advanced statistical methods for analyzing data from cognitive and brain aging studies. Specifically, we introduce semiparametric models for modeling age effects, graphical models for brain network analysis, and penalized regression methods for selecting the most important markers in predicting cognitive outcomes. We illustrate these methods using the healthy aging data from the Active Brain Study.

Mixed Effects Models for Resampled Network Statistics Improves Statistical Power to Find Differences in Multi-Subject Functional Connectivity

Many complex brain disorders, such as autism spectrum disorders, exhibit a wide range of symptoms and disability. To understand how brain communication is impaired in such conditions, functional connectivity studies seek to understand individual differences in brain network structure in terms of covariates that measure symptom severity. In practice, however, functional connectivity is not observed but estimated from complex and noisy neural activity measurements. Imperfect subject network estimates can compromise subsequent efforts to detect covariate effects on network structure. We address this problem in the case of Gaussian graphical models of functional connectivity, by proposing novel two-level models that treat both subject level networks and population level covariate effects as unknown parameters. To account for imperfectly estimated subject level networks when fitting these models, we propose two related approaches-R (2) based on resampling and random effects test statistics, and R (3) that additionally employs random adaptive penalization. Simulation studies using realistic graph structures reveal that R (2) and R (3) have superior statistical power to detect covariate effects compared to existing approaches, particularly when the number of within subject observations is comparable to the size of subject networks. Using our novel models and methods to study parts of the ABIDE dataset, we find evidence of hypoconnectivity associated with symptom severity in autism spectrum disorders, in frontoparietal and limbic systems as well as in anterior and posterior cingulate cortices.

A powerful score-based statistical test for group difference in weighted biological networks

BACKGROUND

Complex disease is largely determined by a number of biomolecules interwoven into networks, rather than a single biomolecule. A key but inadequately addressed issue is how to test possible differences of the networks between two groups. Group-level comparison of network properties may shed light on underlying disease mechanisms and benefit the design of drug targets for complex diseases. We therefore proposed a powerful score-based statistic to detect group difference in weighted networks, which simultaneously capture the vertex changes and edge changes.

RESULTS

Simulation studies indicated that the proposed network difference measure (NetDifM) was stable and outperformed other methods existed, under various sample sizes and network topology structure. One application to real data about GWAS of leprosy successfully identified the specific gene interaction network contributing to leprosy. For additional gene expression data of ovarian cancer, two candidate subnetworks, PI3K-AKT and Notch signaling pathways, were considered and identified respectively.

CONCLUSIONS

The proposed method, accounting for the vertex changes and edge changes simultaneously, is valid and powerful to capture the group difference of biological networks.

An Adaptive Association Test for Multiple Phenotypes with GWAS Summary Statistics

We study the problem of testing for single marker-multiple phenotype associations based on genome-wide association study (GWAS) summary statistics without access to individual-level genotype and phenotype data. For most published GWASs, because obtaining summary data is substantially easier than accessing individual-level phenotype and genotype data, while often multiple correlated traits have been collected, the problem studied here has become increasingly important. We propose a powerful adaptive test and compare its performance with some existing tests. We illustrate its applications to analyses of a meta-analyzed GWAS dataset with three blood lipid traits and another with sex-stratified anthropometric traits, and further demonstrate its potential power gain over some existing methods through realistic simulation studies. We start from the situation with only one set of (possibly meta-analyzed) genome-wide summary statistics, then extend the method to meta-analysis of multiple sets of genome-wide summary statistics, each from one GWAS. We expect the proposed test to be useful in practice as more powerful than or complementary to existing methods.

Highly adaptive tests for group differences in brain functional connectivity

Resting-state functional magnetic resonance imaging (rs-fMRI) and other technologies have been offering evidence and insights showing that altered brain functional networks are associated with neurological illnesses such as Alzheimer's disease. Exploring brain networks of clinical populations compared to those of controls would be a key inquiry to reveal underlying neurological processes related to such illnesses. For such a purpose, group-level inference is a necessary first step in order to establish whether there are any genuinely disrupted brain subnetworks. Such an analysis is also challenging due to the high dimensionality of the parameters in a network model and high noise levels in neuroimaging data. We are still in the early stage of method development as highlighted by Varoquaux and Craddock (2013) that “there is currently no unique solution, but a spectrum of related methods and analytical strategies” to learn and compare brain connectivity. In practice the important issue of how to choose several critical parameters in estimating a network, such as what association measure to use and what is the sparsity of the estimated network, has not been carefully addressed, largely because the answers are unknown yet. For example, even though the choice of tuning parameters in model estimation has been extensively discussed in the literature, as to be shown here, an optimal choice of a parameter for network estimation may not be optimal in the current context of hypothesis testing. Arbitrarily choosing or mis-specifying such parameters may lead to extremely low-powered tests. Here we develop highly adaptive tests to detect group differences in brain connectivity while accounting for unknown optimal choices of some tuning parameters.

The proposed tests combine statistical evidence against a null hypothesis from multiple sources across a range of plausible tuning parameter values reflecting uncertainty with the unknown truth. These highly adaptive tests are not only easy to use, but also high-powered robustly across various scenarios. The usage and advantages of these novel tests are demonstrated on an Alzheimer's disease dataset and simulated data.

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Rigorous testing for genuinely altered functional networks between two groups

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The proposed tests are high powered and general across a wide range of scenarios.

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Data-driven penalized network estimation

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Data-driven choice between correlations and partial correlations to describe association

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Some key differences between network estimation and testing are highlighted.

A parsimonious statistical method to detect groupwise differentially expressed functional connectivity networks

Group-level functional connectivity analyses often aim to detect the altered connectivity patterns between subgroups with different clinical or psychological experimental conditions, for example, comparing cases and healthy controls. We present a new statistical method to detect differentially expressed connectivity networks with significantly improved power and lower false-positive rates. The goal of our method was to capture most differentially expressed connections within networks of constrained numbers of brain regions (by the rule of parsimony). By virtue of parsimony, the false-positive individual connectivity edges within a network are effectively reduced, whereas the informative (differentially expressed) edges are allowed to borrow strength from each other to increase the overall power of the network. We develop a test statistic for each network in light of combinatorics graph theory, and provide p-values for the networks (in the weak sense) by using permutation test with multiple-testing adjustment. We validate and compare this new approach with existing methods, including false discovery rate and network-based statistic, via simulation studies and a resting-state functional magnetic resonance imaging case-control study. The results indicate that our method can identify differentially expressed connectivity networks, whereas existing methods are limited.

Testing group differences in brain functional connectivity: using correlations or partial correlations?

Resting-state functional magnetic resonance imaging allows one to study brain functional connectivity, partly motivated by evidence that patients with complex disorders, such as Alzheimer's disease, may have altered functional brain connectivity patterns as compared with healthy subjects. A functional connectivity network describes statistical associations of the neural activities among distinct and distant brain regions. Recently, there is a major interest in group-level functional network analysis; however, there is a relative lack of studies on statistical inference, such as significance testing for group comparisons. In particular, it is still debatable which statistic should be used to measure pairwise associations as the connectivity weights. Many functional connectivity studies have used either (full or marginal) correlations or partial correlations for pairwise associations. This article investigates the performance of using either correlations or partial correlations for testing group differences in brain connectivity, and how sparsity levels and topological structures of the connectivity would influence statistical power to detect group differences. Our results suggest that, in general, testing group differences in networks deviates from estimating networks. For example, high regularization in both covariance matrices and precision matrices may lead to higher statistical power; in particular, optimally selected regularization (e.g., by cross-validation or even at the true sparsity level) on the precision matrices with small estimation errors may have low power. Most importantly, and perhaps surprisingly, using either correlations or partial correlations may give very different testing results, depending on which of the covariance matrices and the precision matrices are sparse. Specifically, if the precision matrices are sparse, presumably and arguably a reasonable assumption, then using correlations often yields much higher powered and more stable testing results than using partial correlations; the conclusion is reversed if the covariance matrices, not the precision matrices, are sparse. These results may have useful implications to future studies on testing functional connectivity differences.