Browsing by Author "Wang, Bingkai"

Now showing 1 - 5 of 5
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    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.