Covariate Assisted Principal regression for covariance matrix outcomes

Longitudinal regression of covariance matrix outcomes

In this study, a longitudinal regression model for covariance matrix outcomes is introduced. The proposal considers a multilevel generalized linear model for regressing covariance matrices on (time-varying) predictors. This model simultaneously identifies covariate-associated components from covariance matrices, estimates regression coefficients, and captures the within-subject variation in the covariance matrices. Optimal estimators are proposed for both low-dimensional and high-dimensional cases by maximizing the (approximated) hierarchical-likelihood function. These estimators are proved to be asymptotically consistent, where the proposed covariance matrix estimator is the most efficient under the low-dimensional case and achieves the uniformly minimum quadratic loss among all linear combinations of the identity matrix and the sample covariance matrix under the high-dimensional case. Through extensive simulation studies, the proposed approach achieves good performance in identifying the covariate-related components and estimating the model parameters. Applying to a longitudinal resting-state functional magnetic resonance imaging data set from the Alzheimer's Disease (AD) Neuroimaging Initiative, the proposed approach identifies brain networks that demonstrate the difference between males and females at different disease stages. The findings are in line with existing knowledge of AD and the method improves the statistical power over the analysis of cross-sectional data.

Identifying covariate-related subnetworks for whole-brain connectome analysis

Whole-brain connectome data characterize the connections among distributed neural populations as a set of edges in a large network, and neuroscience research aims to systematically investigate associations between brain connectome and clinical or experimental conditions as covariates. A covariate is often related to a number of edges connecting multiple brain areas in an organized structure. However, in practice, neither the covariate-related edges nor the structure is known. Therefore, the understanding of underlying neural mechanisms relies on statistical methods that are capable of simultaneously identifying covariate-related connections and recognizing their network topological structures. The task can be challenging because of false-positive noise and almost infinite possibilities of edges combining into subnetworks. To address these challenges, we propose a new statistical approach to handle multivariate edge variables as outcomes and output covariate-related subnetworks. We first study the graph properties of covariate-related subnetworks from a graph and combinatorics perspective and accordingly bridge the inference for individual connectome edges and covariate-related subnetworks. Next, we develop efficient algorithms to exact covariate-related subnetworks from the whole-brain connectome data with an $\ell_0$ norm penalty. We validate the proposed methods based on an extensive simulation study, and we benchmark our performance against existing methods. Using our proposed method, we analyze two separate resting-state functional magnetic resonance imaging data sets for schizophrenia research and obtain highly replicable disease-related subnetworks.

Regression models for partially localized fMRI connectivity analyses

Background

Brain functional connectivity analysis of resting-state functional magnetic resonance imaging (fMRI) data is typically performed in a standardized template space assuming consistency of connections across subjects. Analysis methods can come in the form of one-edge-at-a-time analyses or dimension reduction/decomposition methods. Common to these approaches is an assumption that brain regions are functionally aligned across subjects; however, it is known that this functional alignment assumption is often violated.

Methods

In this paper, we use subject-level regression models to explain intra-subject variability in connectivity. Covariates can include factors such as geographic distance between two pairs of brain regions, whether the two regions are symmetrically opposite (homotopic), and whether the two regions are members of the same functional network. Additionally, a covariate for each brain region can be included, to account for the possibility that some regions have consistently higher or lower connectivity. This style of analysis allows us to characterize the fraction of variation explained by each type of covariate. Additionally, comparisons across subjects can then be made using the fitted connectivity regression models, offering a more parsimonious alternative to edge-at-a-time approaches.

Results

We apply our approach to Human Connectome Project data on 268 regions of interest (ROIs), grouped into eight functional networks. We find that a high proportion of variation is explained by region covariates and network membership covariates, while geographic distance and homotopy have high relative importance after adjusting for the number of predictors. We also find that the degree of data repeatability using our connectivity regression model-which uses only partial location information about pairs of ROI's-is comparably as high as the repeatability obtained using full location information.

Discussion

While our analysis uses data that have been transformed into a common template-space, we also envision the method being useful in multi-atlas registration settings, where subject data remains in its own geometry and templates are warped instead. These results suggest the tantalizing possibility that fMRI connectivity analysis can be performed in subject-space, using less aggressive registration, such as simple affine transformations, multi-atlas subject-space registration, or perhaps even no registration whatsoever.

Covariance regression with random forests

Capturing the conditional covariances or correlations among the elements of a multivariate response vector based on covariates is important to various fields including neuroscience, epidemiology and biomedicine. We propose a new method called Covariance Regression with Random Forests (CovRegRF) to estimate the covariance matrix of a multivariate response given a set of covariates, using a random forest framework. Random forest trees are built with a splitting rule specially designed to maximize the difference between the sample covariance matrix estimates of the child nodes. We also propose a significance test for the partial effect of a subset of covariates. We evaluate the performance of the proposed method and significance test through a simulation study which shows that the proposed method provides accurate covariance matrix estimates and that the Type-1 error is well controlled. An application of the proposed method to thyroid disease data is also presented. CovRegRF is implemented in a freely available R package on CRAN.

Regression models for partially localized fMRI connectivity analyses

Brain functional connectivity analysis of resting-state functional magnetic resonance imaging (fMRI) data is typically performed in a standardized template space assuming consistency of connections across subjects. This can come in the form of one-edge-at-a-time analyses or dimension reduction/decomposition methods. Common to these approaches is the assumption of complete localization (or spatial alignment) of brain regions across subjects. Alternative approaches completely eschew localization assumptions by treating connections as statistically exchangeable (for example, using the density of connectivity between nodes). Yet other approaches, such as hyperalignment, attempt to align subjects on function as well as structure, thereby achieving a different sort of template-based localization. In this paper, we propose the use of simple regression models to characterize connectivity. To that end, we build regression models on subject-level Fisher transformed regional connection matrices using geographic distance, homotopic distance, network labels, and region indicators as covariates to explain variation in connections. While we perform our analysis in template-space in this paper, we envision the method being useful in multi-atlas registration settings, where subject data remains in its own geometry and templates are warped instead. A byproduct of this style of analysis is the ability to characterize the fraction of variation in subject-level connections explained by each type of covariate. Using Human Connectome Project data, we found that network labels and regional characteristics contribute far more than geographic or homotopic relationships (considered non-parametrically). In addition, visual regions had the highest explanatory power (i.e., largest regression coefficients). We also considered subject repeatability and found that the degree of repeatability seen in fully localized models is largely recovered using our proposed subject-level regression models. Further, even fully exchangeable models retain a sizeable amount of repeatability information, despite discarding all localization information. These results suggest the tantalizing possibility that fMRI connectivity analysis can be performed in subject-space, using less aggressive registration, such as simple affine transformations, multi-atlas subject-space registration, or perhaps even no registration whatsoever.

Genetic underpinnings of brain structural connectome for young adults

With distinct advantages in power over behavioral phenotypes, brain imaging traits have become emerging endophenotypes to dissect molecular contributions to behaviors and neuropsychiatric illnesses. Among different imaging features, brain structural connectivity (i.e., structural connectome) which summarizes the anatomical connections between different brain regions is one of the most cutting edge while under-investigated traits; and the genetic influence on the structural connectome variation remains highly elusive. Relying on a landmark imaging genetics study for young adults, we develop a biologically plausible brain network response shrinkage model to comprehensively characterize the relationship between high dimensional genetic variants and the structural connectome phenotype. Under a unified Bayesian framework, we accommodate the topology of brain network and biological architecture within the genome; and eventually establish a mechanistic mapping between genetic biomarkers and the associated brain sub-network units. An efficient expectation-maximization algorithm is developed to estimate the model and ensure computing feasibility. In the application to the Human Connectome Project Young Adult (HCP-YA) data, we establish the genetic underpinnings which are highly interpretable under functional annotation and brain tissue eQTL analysis, for the brain white matter tracts connecting the hippocampus and two cerebral hemispheres. We also show the superiority of our method in extensive simulations.

Beyond Massive Univariate Tests: Covariance Regression Reveals Complex Patterns of Functional Connectivity Related to Attention-Deficit/Hyperactivity Disorder, Age, Sex, and Response Control

Background

Studies of brain functional connectivity (FC) typically involve massive univariate tests, performing statistical analysis on each individual connection. In this study, we apply a novel whole-matrix regression approach referred to as covariate assisted principal regression to identify resting-state FC brain networks associated with attention-deficit/hyperactivity disorder (ADHD) and response control.

Methods

Participants included 8- to 12-year-old children with ADHD (n = 115; 29 girls) and typically developing control children (n = 102; 35 girls) who completed a resting-state functional magnetic resonance imaging scan and a Go/NoGo task. We modeled three sets of covariates to identify resting-state networks associated with an ADHD diagnosis, sex, and response inhibition (commission errors) and variability (ex-Gaussian parameter tau).

Results

The first network includes FC between striatal-cognitive control (CC) network subregions and thalamic-default mode network (DMN) subregions and is positively related to age. The second consists of FC between CC-visual-somatomotor regions and between CC-DMN subregions and is positively associated with response variability in boys with ADHD. The third consists of FC within the DMN and between DMN-CC-visual regions and differs between boys with and without ADHD. The fourth consists of FC between visual-somatomotor regions and between visual-DMN regions and differs between girls and boys with ADHD and is associated with response inhibition and variability in boys with ADHD. Unique networks were also identified in each of the three models, suggesting some specificity to the covariates of interest.

Conclusions

These findings demonstrate the utility of our novel covariance regression approach to studying functional brain networks relevant for development, behavior, and psychopathology.

Global Brain Functional Network Connectivity in Infants With Prenatal Opioid Exposure

BACKGROUND

Infants with prenatal opioid and substance exposure are at higher risk of poor neurobehavioral outcomes in later childhood. Early brain imaging in infancy has the potential to identify early brain developmental alterations that may help predict behavioral outcomes in these children. In this study, using resting-state functional MRI in early infancy, we aim to identify differences in global brain network connectivity in infants with prenatal opioid and substance exposure compared to healthy control infants.

METHODS AND MATERIALS

In this prospective study, we recruited 23 infants with prenatal opioid exposure and 29 healthy opioid naïve infants. All subjects underwent brain resting-state functional MRI before 3 months postmenstrual age. Covariate Assisted Principal (CAP) regression was performed to identify brain networks within which functional connectivity was associated with opioid exposure after adjusting for sex and gestational age. Associations of these significant networks with maternal comorbidities were also evaluated. Additionally, graph network metrics were assessed in these CAP networks.

RESULTS

There were four CAP network components that were significantly different between the opioid exposed and healthy control infants. Two of these four networks were associated with maternal psychological factors. Intra-network graph metrics, namely average flow coefficient, clustering coefficient and transitivity were also significantly different in opioid exposed infants compared to healthy controls.

CONCLUSION

Prenatal opioid exposure is associated with alterations in global brain functional networks compared to non-opioid exposed infants, with intra-network alterations in graph network modeling. These network alterations were also associated with maternal comorbidity, especially mental health. Large-scale longitudinal studies can help in understanding the clinical implications of these early brain functional network alterations in infants with prenatal opioid exposure.

Mitigating site effects in covariance for machine learning in neuroimaging data

To acquire larger samples for answering complex questions in neuroscience, researchers have increasingly turned to multi‐site neuroimaging studies. However, these studies are hindered by differences in images acquired across multiple sites. These effects have been shown to bias comparison between sites, mask biologically meaningful associations, and even introduce spurious associations. To address this, the field has focused on harmonizing data by removing site‐related effects in the mean and variance of measurements. Contemporaneously with the increase in popularity of multi‐center imaging, the use of machine learning (ML) in neuroimaging has also become commonplace. These approaches have been shown to provide improved sensitivity, specificity, and power due to their modeling the joint relationship across measurements in the brain. In this work, we demonstrate that methods for removing site effects in mean and variance may not be sufficient for ML. This stems from the fact that such methods fail to address how correlations between measurements can vary across sites. Data from the Alzheimer's Disease Neuroimaging Initiative is used to show that considerable differences in covariance exist across sites and that popular harmonization techniques do not address this issue. We then propose a novel harmonization method called Correcting Covariance Batch Effects (CovBat) that removes site effects in mean, variance, and covariance. We apply CovBat and show that within‐site correlation matrices are successfully harmonized. Furthermore, we find that ML methods are unable to distinguish scanner manufacturer after our proposed harmonization is applied, and that the CovBat‐harmonized data retain accurate prediction of disease group.

Principal regression for high dimensional covariance matrices

This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. In many areas of study, such as resting-state functional magnetic resonance imaging (fMRI) studies, this type of regression can be utilized to characterize variation in the covariance matrices across units. Model parameters are estimated by maximizing a likelihood formulation of a generalized linear model, conditioning on a well-conditioned linear shrinkage estimator for multiple covariance matrices, where the shrinkage coefficients are proposed to be shared across matrices. Theoretical studies demonstrate that the proposed covariance matrix estimator is optimal achieving the uniformly minimum quadratic loss asymptotically among all linear combinations of the identity matrix and the sample covariance matrix. Under certain regularity conditions, the proposed estimator of the model parameters is consistent. The superior performance of the proposed approach over existing methods is illustrated through simulation studies. Implemented to a resting-state fMRI study acquired from the Alzheimer's Disease Neuroimaging Initiative, the proposed approach identified a brain network within which functional connectivity is significantly associated with Apolipoprotein E ε4, a strong genetic marker for Alzheimer's disease.

A whole-brain modeling approach to identify individual and group variations in functional connectivity

Resting-state functional connectivity is an important and widely used measure of individual and group differences. Yet, extant statistical methods are limited to linking covariates with variations in functional connectivity across subjects, especially at the voxel-wise level of the whole brain. This paper introduces a modeling approach that regresses whole-brain functional connectivity on covariates. Our approach is a mesoscale approach that enables identification of brain subnetworks. These subnetworks are composite of spatially independent components discovered by a dimension reduction approach (such as whole-brain group ICA) and covariate-related projections determined by the covariate-assisted principal regression, a recently introduced covariance matrix regression method. We demonstrate the efficacy of this approach using a resting-state fMRI dataset of a medium-sized cohort of subjects obtained from the Human Connectome Project. The results suggest that the approach may improve statistical power in detecting interaction effects of gender and alcohol on whole-brain functional connectivity, and in identifying the brain areas contributing significantly to the covariate-related differences in functional connectivity.

Multimodal neuroimaging data integration and pathway analysis

With advancements in technology, the collection of multiple types of measurements on a common set of subjects is becoming routine in science. Some notable examples include multimodal neuroimaging studies for the simultaneous investigation of brain structure and function and multi-omics studies for combining genetic and genomic information. Integrative analysis of multimodal data allows scientists to interrogate new mechanistic questions. However, the data collection and generation of integrative hypotheses is outpacing available methodology for joint analysis of multimodal measurements. In this article, we study high-dimensional multimodal data integration in the context of mediation analysis. We aim to understand the roles that different data modalities play as possible mediators in the pathway between an exposure variable and an outcome. We propose a mediation model framework with two data types serving as separate sets of mediators and develop a penalized optimization approach for parameter estimation. We study both the theoretical properties of the estimator through an asymptotic analysis and its finite-sample performance through simulations. We illustrate our method with a multimodal brain pathway analysis having both structural and functional connectivity as mediators in the association between sex and language processing.