Browsing by Author "Luo, Xi"

Now showing 1 - 9 of 9
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    Covariate Assisted Principal Regression for Covariance Matrix Outcomes
    (Oxford, 2019) Zhao, Yi; Wang, Bingkai; Mostofsky, Stewart H.; Ca, Brian S.; Luo, Xi; Biostatistics, School of Public Health
    In this study, we consider the problem of regressing covariance matrices on associated covariates. Our goal is to use covariates to explain variation in covariance matrices across units. As such, we introduce Covariate Assisted Principal (CAP) regression, an optimization-based method for identifying components associated with the covariates using a generalized linear model approach. We develop computationally efficient algorithms to jointly search for common linear projections of the covariance matrices, as well as the regression coefficients. Under the assumption that all the covariance matrices share identical eigencomponents, we establish the asymptotic properties. In simulation studies, our CAP method shows higher accuracy and robustness in coefficient estimation over competing methods. In an example resting-state functional magnetic resonance imaging study of healthy adults, CAP identifies human brain network changes associated with subject demographics.
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    Granger mediation analysis of multiple time series with an application to functional magnetic resonance imaging
    (Wiley, 2019-09) Zhao, Yi; Luo, Xi; Biostatistics, School of Public Health
    This paper presents Granger mediation analysis, a new framework for causal mediation analysis of multiple time series. This framework is motivated by a functional magnetic resonance imaging (fMRI) experiment where we are interested in estimating the mediation effects between a randomized stimulus time series and brain activity time series from two brain regions. The independent observation assumption is thus unrealistic for this type of time‐series data. To address this challenge, our framework integrates two types of models: causal mediation analysis across the mediation variables, and vector autoregressive (VAR) models across the temporal observations. We use “Granger” to refer to VAR correlations modeled in this paper. We further extend this framework to handle multilevel data, in order to model individual variability and correlated errors between the mediator and the outcome variables. Using Rubin's potential outcome framework, we show that the causal mediation effects are identifiable under our time‐series model. We further develop computationally efficient algorithms to maximize our likelihood‐based estimation criteria. Simulation studies show that our method reduces the estimation bias and improves statistical power, compared with existing approaches. On a real fMRI data set, our approach quantifies the causal effects through a brain pathway, while capturing the dynamic dependence between two brain regions.
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    Identifying brain hierarchical structures associated with Alzheimer’s disease using a regularized regression method with tree predictors
    (Oxford University Press, 2023) Zhao, Yi; Wang, Bingkai; Liu, Chin-Fu; Faria, Andreia V.; Miller, Michael I.; Caffo, Brian S.; Luo, Xi; Biostatistics and Health Data Science, School of Medicine
    Brain segmentation at different levels is generally represented as hierarchical trees. Brain regional atrophy at specific levels was found to be marginally associated with Alzheimer’s disease outcomes. In this study, we propose an ℓ1-type regularization for predictors that follow a hierarchical tree structure. Considering a tree as a directed acyclic graph, we interpret the model parameters from a path analysis perspective. Under this concept, the proposed penalty regulates the total effect of each predictor on the outcome. With regularity conditions, it is shown that under the proposed regularization, the estimator of the model coefficient is consistent in ℓ2-norm and the model selection is also consistent. When applied to a brain sMRI dataset acquired from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), the proposed approach identifies brain regions where atrophy in these regions demonstrates the declination in memory. With regularization on the total effects, the findings suggest that the impact of atrophy on memory deficits is localized from small brain regions, but at various levels of brain segmentation. Data used in preparation of this paper were obtained from the ADNI database.
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    Longitudinal regression of covariance matrix outcomes
    (Oxford, 2022-12-01) Zhao, Yi; Caffo, Brian S.; Luo, Xi; Alzheimer’s Disease Neuroimaging Initiative; Biostatistics and Health Data Science, School of Medicine
    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.
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    Pathway Lasso: Pathway Estimation and Selection with High-Dimensional Mediators
    (International Press, 2022) Zhao, Yi; Luo, Xi; Biostatistics, School of Public Health
    In many scientific studies, it becomes increasingly important to delineate the pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as the product of coefficients. However, it becomes unstable and computationally challenging to fit such models with high-dimensional mediators. This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity means that a small number of mediators have a nonzero mediation effect between a treatment and an outcome. To address the model selection challenge, we innovate by introducing a new penalty called Pathway Lasso. This penalty function is a convex relaxation of the non-convex product function for the mediation effects, and it enables a computationally tractable optimization criterion to estimate and select pathway effects simultaneously. We develop a fast ADMM-type algorithm to compute the model parameters, and we show that the iterative updates can be expressed in closed form. We also prove the asymptotic consistency of our Pathway Lasso estimator for the mediation effect. On both simulated data and an fMRI data set, the proposed approach yields higher pathway selection accuracy and lower estimation bias than competing methods.
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    Principal regression for high dimensional covariance matrices
    (Institute of Mathematical Statistics, 2021) Zhao, Yi; Caffo, Brian; Luo, Xi; Alzheimer’s Disease Neuroimaging Initiative; Biostatistics, School of Public Health
    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.
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    Regularized regression on compositional trees with application to MRI analysis
    (Oxford University Press, 2022) Wang, Bingkai; Caffo, Brian S.; Luo, Xi; Liu, Chin-Fu; Faria, Andreia V.; Miller, Michael I.; Zhao, Yi; Alzheimer’s Disease Neuroimaging Initiative; Biostatistics, School of Public Health
    A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees handle more complex relationships among random variables and appear in many disciplines, such as brain imaging, genomics and finance. We consider the problem of sparse regression on data that are associated with a compositional tree and propose a transformation-free tree-based regularized regression method for component selection. The regularization penalty is designed based on the tree structure and encourages a sparse tree representation. We prove that our proposed estimator for regression coefficients is both consistent and model selection consistent. In the simulation study, our method shows higher accuracy than competing methods under different scenarios. By analyzing a brain imaging data set from studies of Alzheimer's disease, our method identifies meaningful associations between memory decline and volume of brain regions that are consistent with current understanding.
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    Semiparametric partial common principal component analysis for covariance matrices
    (Wiley, 2021-12) Wang, Bingkai; Luo, Xi; Zhao, Yi; Caffo, Brian; Biostatistics, School of Public Health
    We consider the problem of jointly modeling multiple covariance matrices by partial common principal component analysis (PCPCA), which assumes a proportion of eigenvectors to be shared across covariance matrices and the rest to be individual-specific. This paper proposes consistent estimators of the shared eigenvectors in the PCPCA as the number of matrices or the number of samples to estimate each matrix goes to infinity. We prove such asymptotic results without making any assumptions on the ranks of eigenvalues that are associated with the shared eigenvectors. When the number of samples goes to infinity, our results do not require the data to be Gaussian distributed. Furthermore, this paper introduces a sequential testing procedure to identify the number of shared eigenvectors in the PCPCA. In simulation studies, our method shows higher accuracy in estimating the shared eigenvectors than competing methods. Applied to a motor-task functional magnetic resonance imaging data set, our estimator identifies meaningful brain networks that are consistent with current scientific understandings of motor networks during a motor paradigm.
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    A whole‐brain modeling approach to identify individual and group variations in functional connectivity
    (Wiley, 2021-01) Zhao, Yi; Caffo, Brian S.; Wang, Bingkai; Li, Chiang-Shan R.; Luo, Xi; Biostatistics, School of Public Health
    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.