1
|
Ji J, Hou Z, He Y, Liu L, Xue F, Chen H, Yuan Z. Differential network knockoff filter with application to brain connectivity analysis. Stat Med 2024; 43:3830-3861. [PMID: 38922944 DOI: 10.1002/sim.10155] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2023] [Revised: 04/30/2024] [Accepted: 06/10/2024] [Indexed: 06/28/2024]
Abstract
The brain functional connectivity can typically be represented as a brain functional network, where nodes represent regions of interest (ROIs) and edges symbolize their connections. Studying group differences in brain functional connectivity can help identify brain regions and recover the brain functional network linked to neurodegenerative diseases. This process, known as differential network analysis focuses on the differences between estimated precision matrices for two groups. Current methods struggle with individual heterogeneity in measuring the brain connectivity, false discovery rate (FDR) control, and accounting for confounding factors, resulting in biased estimates and diminished power. To address these issues, we present a two-stage FDR-controlled feature selection method for differential network analysis using functional magnetic resonance imaging (fMRI) data. First, we create individual brain connectivity measures using a high-dimensional precision matrix estimation technique. Next, we devise a penalized logistic regression model that employs individual brain connectivity data and integrates a new knockoff filter for FDR control when detecting significant differential edges. Through extensive simulations, we showcase the superiority of our approach compared to other methods. Additionally, we apply our technique to fMRI data to identify differential edges between Alzheimer's disease and control groups. Our results are consistent with prior experimental studies, emphasizing the practical applicability of our method.
Collapse
Affiliation(s)
- Jiadong Ji
- Institute for Financial Studies, Shandong University, Jinan, Shandong, China
| | - Zhendong Hou
- Institute for Financial Studies, Shandong University, Jinan, Shandong, China
| | - Yong He
- Institute for Financial Studies, Shandong University, Jinan, Shandong, China
| | - Lei Liu
- Division of Biostatistics, Washington University in St. Louis, St. Louis, Missouri, USA
| | - Fuzhong Xue
- Department of Biostatistics, School of Public Health, Cheeloo College of Medicine, Shandong University, Jinan, Shandong, China
| | - Hao Chen
- Department of Biostatistics, School of Public Health, Cheeloo College of Medicine, Shandong University, Jinan, Shandong, China
| | - Zhongshang Yuan
- Department of Biostatistics, School of Public Health, Cheeloo College of Medicine, Shandong University, Jinan, Shandong, China
| |
Collapse
|
2
|
Liu D, Zhao C, He Y, Liu L, Guo Y, Zhang X. Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix-variate fMRI data. Biometrics 2023; 79:2246-2259. [PMID: 36017603 PMCID: PMC10309652 DOI: 10.1111/biom.13753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2021] [Accepted: 08/16/2022] [Indexed: 11/30/2022]
Abstract
Graphical models play an important role in neuroscience studies, particularly in brain connectivity analysis. Typically, observations/samples are from several heterogenous groups and the group membership of each observation/sample is unavailable, which poses a great challenge for graph structure learning. In this paper, we propose a method which can achieve Simultaneous Clustering and Estimation of Heterogeneous Graphs (briefly denoted as SCEHG) for matrix-variate functional magnetic resonance imaging (fMRI) data. Unlike the conventional clustering methods which rely on the mean differences of various groups, the proposed SCEHG method fully exploits the group differences of conditional dependence relationships among brain regions for learning cluster structure. In essence, by constructing individual-level between-region network measures, we formulate clustering as penalized regression with grouping and sparsity pursuit, which transforms the unsupervised learning into supervised learning. A modified difference of convex programming with the alternating direction method of multipliers (DC-ADMM) algorithm is proposed to solve the corresponding optimization problem. We also propose a generalized criterion to specify the number of clusters. Extensive simulation studies illustrate the superiority of the SCEHG method over some state-of-the-art methods in terms of both clustering and graph recovery accuracy. We also apply the SCEHG procedure to analyze fMRI data associated with attention-deficit hyperactivity disorder (ADHD), which illustrates its empirical usefulness.
Collapse
Affiliation(s)
- Dong Liu
- Shanghai University of Finance and Economics, Shanghai, China
| | - Changwei Zhao
- Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, China
| | - Yong He
- Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, China
| | - Lei Liu
- Division of Biostatistics, Washington University in St. Louis, St. Louis, Missouri, USA
| | - Ying Guo
- Rollins School of Public Health, Emory University, Atlanta, Georgia, USA
| | - Xinsheng Zhang
- Department of Statistics, School of Management, Fudan University, Shanghai, China
| |
Collapse
|
3
|
Smith J, Arashi M, Bekker A. Empowering differential networks using Bayesian analysis. PLoS One 2022; 17:e0261193. [PMID: 35077451 PMCID: PMC8789149 DOI: 10.1371/journal.pone.0261193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 11/24/2021] [Indexed: 11/19/2022] Open
Abstract
Differential networks (DN) are important tools for modeling the changes in conditional dependencies between multiple samples. A Bayesian approach for estimating DNs, from the classical viewpoint, is introduced with a computationally efficient threshold selection for graphical model determination. The algorithm separately estimates the precision matrices of the DN using the Bayesian adaptive graphical lasso procedure. Synthetic experiments illustrate that the Bayesian DN performs exceptionally well in numerical accuracy and graphical structure determination in comparison to state of the art methods. The proposed method is applied to South African COVID-19 data to investigate the change in DN structure between various phases of the pandemic.
Collapse
Affiliation(s)
- Jarod Smith
- Department of Statistics, University of Pretoria, Pretoria, South Africa
| | - Mohammad Arashi
- Department of Statistics, University of Pretoria, Pretoria, South Africa
- Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
| | - Andriëtte Bekker
- Department of Statistics, University of Pretoria, Pretoria, South Africa
| |
Collapse
|
4
|
Xia Y, Li L. Hypothesis Testing for Network Data with Power Enhancement. Stat Sin 2022; 32:293-321. [PMID: 35002179 PMCID: PMC8734582 DOI: 10.5705/ss.202019.0361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
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.
Collapse
Affiliation(s)
- Yin Xia
- Fudan University and University of California at Berkeley
| | - Lexin Li
- Fudan University and University of California at Berkeley
| |
Collapse
|
5
|
Chung J, Jackson BS, Mcdowell JE, Park C. Joint estimation and regularized aggregation of brain network in FMRI data. J Neurosci Methods 2021; 364:109374. [PMID: 34600917 DOI: 10.1016/j.jneumeth.2021.109374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Revised: 09/02/2021] [Accepted: 09/28/2021] [Indexed: 11/25/2022]
Abstract
BACKGROUND In the Gaussian graphical model framework, precision matrices reveal conditional dependence structure among random variables. In functional magnetic resonance imaging (fMRI) data, estimating such precision matrices of multi-subjects and aggregating them to a group-level is an essential step for constructing a group brain network. NEW METHOD In this article, we considered joint estimation of multiple precision matrices with regularized aggregation. Also, in the construction of a group precision matrix, we integrated robust aggregation to the estimation. In the estimation of individual precision matrices, we took a regularization approach to induce sparsity, which made brain network estimation more realistic. RESULTS We demonstrated the effectiveness of the proposed method through simulated examples, and analyses on real fMRI data acquired during eye movement tasks assessing cognitive control. For the fMRI data, the joint estimation of multiple precision matrices (JEMP) with regularized aggregation (RA) captured more robust associations between task-relevant neural regions of interest (ROIs), compared to the analyses using JEMP alone. The JEMP with RA also was sensitive to increased neural efficiency after task practice. COMPARISON WITH EXISTING METHOD(S) The simple average of individual precision matrices may be affected by outliers and provide inconsistent outcomes between subject-level and group-level networks. In contrast, the proposed method yielded a robust group graph that could identify and ease the effect of outliers. CONCLUSIONS The proposed method identified regions of practice-induced attenuation associated with reduced cognitive demand after repeat task exposure. Through simulated and real data, we demonstrated that this method does not require any distribution assumption, can identify outliers, and provides robust, representative group brain networks. This method can be applied to datasets that have extensive variability and/or multiple outliers, including applications to specific, and general, cognitive processes, as well as for studies that may require longitudinal data, such as pharmaceutical trials.
Collapse
Affiliation(s)
- Jongik Chung
- Department of Statistics and Data Science, University of Central Florida, Orlando, FL 32816, USA
| | - Brooke S Jackson
- Department of Psychology, University of Georgia, Athens, GA 30602, USA
| | | | - Cheolwoo Park
- Department of Mathematical Sciences, KAIST, Daejeon 34141, South Korea.
| |
Collapse
|
6
|
Ji J, He Y, Liu L, Xie L. Brain connectivity alteration detection via matrix-variate differential network model. Biometrics 2021; 77:1409-1421. [PMID: 32829503 PMCID: PMC7900256 DOI: 10.1111/biom.13359] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Revised: 08/10/2020] [Accepted: 08/14/2020] [Indexed: 10/23/2022]
Abstract
Brain functional connectivity reveals the synchronization of brain systems through correlations in neurophysiological measures of brain activities. Growing evidence now suggests that the brain connectivity network experiences alterations with the presence of numerous neurological disorders, thus differential brain network analysis may provide new insights into disease pathologies. The data from neurophysiological measurement are often multidimensional and in a matrix form, posing a challenge in brain connectivity analysis. Existing graphical model estimation methods either assume a vector normal distribution that in essence requires the columns of the matrix data to be independent or fail to address the estimation of differential networks across different populations. To tackle these issues, we propose an innovative matrix-variate differential network (MVDN) model. We exploit the D-trace loss function and a Lasso-type penalty to directly estimate the spatial differential partial correlation matrix and use an alternating direction method of multipliers algorithm for the optimization problem. Theoretical and simulation studies demonstrate that MVDN significantly outperforms other state-of-the-art methods in dynamic differential network analysis. We illustrate with a functional connectivity analysis of an attention deficit hyperactivity disorder dataset. The hub nodes and differential interaction patterns identified are consistent with existing experimental studies.
Collapse
Affiliation(s)
- Jiadong Ji
- School of Statistics, Shandong University of Finance and Economics, Jinan, China
| | - Yong He
- Institute for Financial Studies, Shandong University, Jinan, China
| | - Lei Liu
- Division of Biostatistics, Washington University in St. Louis, U.S.A
| | - Lei Xie
- The Graduate Center, The City University of New York, New York, 10016, U.S.A
- Department of Computer Science, Hunter College, The City University of New York, New York, 10065, U.S.A
| |
Collapse
|
7
|
Affiliation(s)
- Mathias Drton
- Department of Mathematics, Technical University of Munich
| | | | - Peter Hoff
- Department of Statistical Science, Duke University
| |
Collapse
|
8
|
Min K, Mai Q, Zhang X. Fast and Separable Estimation in High-Dimensional Tensor Gaussian Graphical Models. J Comput Graph Stat 2021. [DOI: 10.1080/10618600.2021.1938086] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Keqian Min
- Department of Statistics, Florida State University, Tallahassee, FL
| | - Qing Mai
- Department of Statistics, Florida State University, Tallahassee, FL
| | - Xin Zhang
- Department of Statistics, Florida State University, Tallahassee, FL
| |
Collapse
|
9
|
Lee KY, Ji D, Li L, Constable T, Zhao H. Conditional Functional Graphical Models. J Am Stat Assoc 2021; 118:257-271. [PMID: 37193511 PMCID: PMC10181795 DOI: 10.1080/01621459.2021.1924178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2019] [Revised: 03/01/2021] [Accepted: 04/22/2021] [Indexed: 10/21/2022]
Abstract
Graphical modeling of multivariate functional data is becoming increasingly important in a wide variety of applications. The changes of graph structure can often be attributed to external variables, such as the diagnosis status or time, the latter of which gives rise to the problem of dynamic graphical modeling. Most existing methods focus on estimating the graph by aggregating samples, but largely ignore the subject-level heterogeneity due to the external variables. In this article, we introduce a conditional graphical model for multivariate random functions, where we treat the external variables as conditioning set, and allow the graph structure to vary with the external variables. Our method is built on two new linear operators, the conditional precision operator and the conditional partial correlation operator, which extend the precision matrix and the partial correlation matrix to both the conditional and functional settings. We show that their nonzero elements can be used to characterize the conditional graphs, and develop the corresponding estimators. We establish the uniform convergence of the proposed estimators and the consistency of the estimated graph, while allowing the graph size to grow with the sample size, and accommodating both completely and partially observed data. We demonstrate the efficacy of the method through both simulations and a study of brain functional connectivity network.
Collapse
Affiliation(s)
- Kuang-Yao Lee
- Department of Statistical Science, Temple University, Philadelphia, PA
| | - Dingjue Ji
- Department of Biostatistics, Yale University, New Haven, CT
| | - Lexin Li
- Division of Biostatistics, University of California, Berkeley, CA
| | - Todd Constable
- Department of Biostatistics, Yale University, New Haven, CT
- Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT
| | - Hongyu Zhao
- Department of Biostatistics, Yale University, New Haven, CT
| |
Collapse
|
10
|
Chen H, Guo Y, He Y, Ji J, Liu L, Shi Y, Wang Y, Yu L, Zhang X. Simultaneous differential network analysis and classification for matrix-variate data with application to brain connectivity. Biostatistics 2021; 23:967-989. [PMID: 33769450 DOI: 10.1093/biostatistics/kxab007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Revised: 02/20/2021] [Accepted: 02/22/2021] [Indexed: 01/03/2023] Open
Abstract
Growing evidence has shown that the brain connectivity network experiences alterations for complex diseases such as Alzheimer's disease (AD). Network comparison, also known as differential network analysis, is thus particularly powerful to reveal the disease pathologies and identify clinical biomarkers for medical diagnoses (classification). Data from neurophysiological measurements are multidimensional and in matrix-form. Naive vectorization method is not sufficient as it ignores the structural information within the matrix. In the article, we adopt the Kronecker product covariance matrices framework to capture both spatial and temporal correlations of the matrix-variate data while the temporal covariance matrix is treated as a nuisance parameter. By recognizing that the strengths of network connections may vary across subjects, we develop an ensemble-learning procedure, which identifies the differential interaction patterns of brain regions between the case group and the control group and conducts medical diagnosis (classification) of the disease simultaneously. Simulation studies are conducted to assess the performance of the proposed method. We apply the proposed procedure to the functional connectivity analysis of an functional magnetic resonance imaging study on AD. The hub nodes and differential interaction patterns identified are consistent with existing experimental studies, and satisfactory out-of-sample classification performance is achieved for medical diagnosis of AD.
Collapse
Affiliation(s)
- Hao Chen
- School of Statistics, Shandong University of Finance and Economics, Jinan, 250014, China
| | - Ying Guo
- Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, GA 30322, USA
| | - Yong He
- Institute for Financial Studies, Shandong University, Jinan, 250100, China
| | - Jiadong Ji
- Institute for Financial Studies, Shandong University, Jinan, 250100, China
| | - Lei Liu
- Division of Biostatistics, Washington University in St.Louis, St. Louis, MO 63110, USA
| | - Yufeng Shi
- Institute for Financial Studies, Shandong University, Jinan, 250100, China
| | - Yikai Wang
- Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, GA 30322, USA
| | - Long Yu
- Department of Statistics, School of Management, Fudan University, Shanghai, 200433, China
| | - Xinsheng Zhang
- Department of Statistics, School of Management, Fudan University, Shanghai, 200433, China
| | | |
Collapse
|
11
|
Wang YXR, Li L, Li JJ, Huang H. Network Modeling in Biology: Statistical Methods for Gene and Brain Networks. Stat Sci 2021; 36:89-108. [PMID: 34305304 DOI: 10.1214/20-sts792] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
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.
Collapse
Affiliation(s)
- Y X Rachel Wang
- School of Mathematics and Statistics, University of Sydney, Australia
| | - Lexin Li
- Department of Biostatistics and Epidemiology, School of Public Health, University of California, Berkeley
| | | | - Haiyan Huang
- Department of Statistics, University of California, Berkeley
| |
Collapse
|
12
|
Tang Z, Yu Z, Wang C. A fast iterative algorithm for high-dimensional differential network. Comput Stat 2019. [DOI: 10.1007/s00180-019-00915-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|