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

Group-level comparison of brain connectivity networks

BACKGROUND

Functional connectivity (FC) studies are often performed to discern different patterns of brain connectivity networks between healthy and patient groups. Since many neuropsychiatric disorders are related to the change in these patterns, accurate modelling of FC data can provide useful information about disease pathologies. However, analysing functional connectivity data faces several challenges, including the correlations of the connectivity edges associated with network topological characteristics, the large number of parameters in the covariance matrix, and taking into account the heterogeneity across subjects.

METHODS

This study provides a new statistical approach to compare the FC networks between subgroups that consider the network topological structure of brain regions and subject heterogeneity.

RESULTS

The power based on the heterogeneity structure of identity scaled in a sample size of 25 exhibited values greater than 0.90 without influencing the degree of correlation, heterogeneity, and the number of regions. This index had values above 0.80 in the small sample size and high correlation. In most scenarios, the type I error was close to 0.05. Moreover, the application of this model on real data related to autism was also investigated, which indicated no significant difference in FC networks between healthy and patient individuals.

CONCLUSIONS

The results from simulation data indicated that the proposed model has high power and near-nominal type I error rates in most scenarios.

Riemannian Geometry of Functional Connectivity Matrices for Multi-Site Attention-Deficit/Hyperactivity Disorder Data Harmonization

The use of multi-site datasets in neuroimaging provides neuroscientists with more statistical power to perform their analyses. However, it has been shown that the imaging-site introduces variability in the data that cannot be attributed to biological sources. In this work, we show that functional connectivity matrices derived from resting-state multi-site data contain a significant imaging-site bias. To this aim, we exploited the fact that functional connectivity matrices belong to the manifold of symmetric positive-definite (SPD) matrices, making it possible to operate on them with Riemannian geometry. We hereby propose a geometry-aware harmonization approach, Rigid Log-Euclidean Translation, that accounts for this site bias. Moreover, we adapted other Riemannian-geometric methods designed for other domain adaptation tasks and compared them to our proposal. Based on our results, Rigid Log-Euclidean Translation of multi-site functional connectivity matrices seems to be among the studied methods the most suitable in a clinical setting. This represents an advance with respect to previous functional connectivity data harmonization approaches, which do not respect the geometric constraints imposed by the underlying structure of the manifold. In particular, when applying our proposed method to data from the ADHD-200 dataset, a multi-site dataset built for the study of attention-deficit/hyperactivity disorder, we obtained results that display a remarkable correlation with established pathophysiological findings and, therefore, represent a substantial improvement when compared to the non-harmonization analysis. Thus, we present evidence supporting that harmonization should be extended to other functional neuroimaging datasets and provide a simple geometric method to address it.

Low-Rank Plus Sparse Decomposition of fMRI Data With Application to Alzheimer's Disease

Studying functional brain connectivity plays an important role in understanding how human brain functions and neuropsychological diseases such as autism, attention-deficit hyperactivity disorder, and Alzheimer's disease (AD). Functional magnetic resonance imaging (fMRI) is one of the most popularly used tool to construct functional brain connectivity. However, the presence of noises and outliers in fMRI blood oxygen level dependent (BOLD) signals might lead to unreliable and unstable results in the construction of connectivity matrix. In this paper, we propose a pipeline that enables us to estimate robust and stable connectivity matrix, which increases the detectability of group differences. In particular, a low-rank plus sparse (L + S) matrix decomposition technique is adopted to decompose the original signals, where the low-rank matrix L recovers the essential common features from regions of interest, and the sparse matrix S catches the sparse individual variability and potential outliers. On the basis of decomposed signals, we construct connectivity matrix using the proposed novel concentration inequality-based sparse estimator. In order to facilitate the comparisons, we also consider correlation, partial correlation, and graphical Lasso-based methods. Hypothesis testing is then conducted to detect group differences. The proposed pipeline is applied to rs-fMRI data in Alzheimer's disease neuroimaging initiative to detect AD-related biomarkers, and we show that the proposed pipeline provides accurate yet more stable results than using the original BOLD signals.

Multitask fMRI and machine learning approach improve prediction of differential brain activity pattern in patients with insomnia disorder

We investigated the differential spatial covariance pattern of blood oxygen level-dependent (BOLD) responses to single-task and multitask functional magnetic resonance imaging (fMRI) between patients with psychophysiological insomnia (PI) and healthy controls (HCs), and evaluated features generated by principal component analysis (PCA) for discrimination of PI from HC, compared to features generated from BOLD responses to single-task fMRI using machine learning methods. In 19 patients with PI and 21 HCs, the mean beta value for each region of interest (ROIbval) was calculated with three contrast images (i.e., sleep-related picture, sleep-related sound, and Stroop stimuli). We performed discrimination analysis and compared with features generated from BOLD responses to single-task fMRI. We applied support vector machine analysis with a least absolute shrinkage and selection operator to evaluate five performance metrics: accuracy, recall, precision, specificity, and F2. Principal component features showed the best classification performance in all aspects of metrics compared to BOLD response to single-task fMRI. Bilateral inferior frontal gyrus (orbital), right calcarine cortex, right lingual gyrus, left inferior occipital gyrus, and left inferior temporal gyrus were identified as the most salient areas by feature selection. Our approach showed better performance in discriminating patients with PI from HCs, compared to single-task fMRI.

Both Stationary and Dynamic Functional Interhemispheric Connectivity Are Strongly Associated With Performance on Cognitive Tests in Multiple Sclerosis

Although functional connectivity has been extensively studied in MS, robust estimates of both stationary (static connectivity at the time) and dynamic (connectivity variation across time) functional connectivity has not been commonly evaluated and neither has its association to cognition. In this study, we focused on interhemispheric connections as previous research has shown links between anatomical homologous connections and cognition. We examined functional interhemispheric connectivity (IC) in MS during resting-state functional MRI using both stationary and dynamic strategies and related connectivity measures to processing speed performance. Twenty-five patients with relapsing-remitting MS and 41 controls were recruited. Stationary functional IC was assessed between homologous Regions of Interest (ROIs) using correlation. For dynamic IC, a sliding window approach was used to quantify changes between homologous ROIs across time. We related IC measures to cognitive performance with correlation and regression. Compared to control subjects, MS demonstrated increased IC across homologous regions, which accurately predicted performance on the symbol digit modalities test (SDMT) (R ² = 0.96) and paced auditory serial addition test (PASAT) (R ² = 0.59). Dynamic measures were not different between the 2 groups, but dynamic IC was related to PASAT scores. The associations between stationary/dynamic connectivity and cognitive tests demonstrated that different aspects of functional IC were associated with cognitive processes. Processing speed measured in SDMT was associated with static interhemispheric connections and better PASAT performance, which requires working memory, sustain attention, and processing speed, was more related to rigid IC, underlining the neurophysiological mechanism of cognition in MS.

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.

A comparison of functional and tractography based networks in cerebral small vessel disease

Objective

MRI measures of network integrity may be useful disease markers in cerebral small vessel disease (SVD). We compared the sensitivity and reproducibility of MRI derived structural and functional network measures in healthy controls and SVD subjects.

Methods

Diffusion tractography and resting state fMRI were used to create connectivity matrices from 26 subjects with symptomatic MRI confirmed lacunar stroke and 19 controls. Matrices were constructed at multiple scales based on a multi-resolution cortical atlas and at multiple thresholds for the matrix density. Network parameters were calculated over the multiple resolutions and thresholds. In addition the reproducibility of structural and functional network parameters was determined in a subset of the subjects (15 SVD, 10 controls) who were scanned twice.

Results

Structural networks showed a highly significant loss of network integrity in SVD cases compared to controls, for all network measures. In contrast functional networks showed no difference between SVD and controls. Structural network measures were highly reproducible in both cases and controls, with ICC values consistently over 0.8. In contrast functional network measures showed much poorer reproducibility with ICC values in the range 0.4-0.6 overall, and even lower in SVD cases.

Conclusions

Structural networks identify impaired network integrity, and are highly reproducible, in SVD, supporting their use as markers of SVD disease severity. In contrast, functional networks showed low reproducibility, particularly in SVD cases, and were unable to detect differences between SVD cases and controls with this sample size.

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.

A variance components model for statistical inference on functional connectivity networks

We propose a variance components linear modeling framework to conduct statistical inference on functional connectivity networks that directly accounts for the temporal autocorrelation inherent in functional magnetic resonance imaging (fMRI) time series data and for the heterogeneity across subjects in the study. The novel method estimates the autocorrelation structure in a nonparametric and subject-specific manner, and estimates the variance due to the heterogeneity using iterative least squares. We apply the new model to a resting-state fMRI study to compare the functional connectivity networks in both typical and reading impaired young adults in order to characterize the resting state networks that are related to reading processes. We also compare the performance of our model to other methods of statistical inference on functional connectivity networks that do not account for the temporal autocorrelation or heterogeneity across the subjects using simulated data, and show that by accounting for these sources of variation and covariation results in more powerful tests for statistical inference.

Semiparametric Bayes conditional graphical models for imaging genetics applications

Motivated by the need for understanding neurological disorders, large-scale imaging genetic studies are being increasingly conducted. A salient objective in such studies is to identify important neuroimaging biomarkers such as the brain functional connectivity, as well as genetic biomarkers, which are predictive of disorders. However, typical approaches for estimating the group level brain functional connectivity do not account for potential variation, resulting from demographic and genetic factors, while usual methods for discovering genetic biomarkers do not factor in the influence of the brain network on the imaging phenotype. We propose a novel semiparametric Bayesian conditional graphical model for joint variable selection and graph estimation, which simultaneously estimates the brain network after accounting for heterogeneity, and infers significant genetic biomarkers. The proposed approach specifies priors on the regression coefficients, which clusters brain regions having similar activation patterns depending on covariates, leading to dimension reduction. A novel graphical prior is proposed, which encourages modularity in brain organization by specifying denser and sparse connections within and across clusters, respectively. The posterior computation proceeds via a Markov chain Monte Carlo. We apply the approach to data obtained from the Alzheimer's disease neuroimaging initiative and demonstrate numerical advantages via simulation studies.

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.

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.