1
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Green B, Lian H, Yu Y, Zu T. Semiparametric penalized quadratic inference functions for longitudinal data in ultra-high dimensions. J MULTIVARIATE ANAL 2023. [DOI: 10.1016/j.jmva.2023.105175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/07/2023]
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2
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Almohaimeed A, Einbeck J. Response transformations for random effect and variance component models. STAT MODEL 2020. [DOI: 10.1177/1471082x20966919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Random effect models have been popularly used as a mainstream statistical technique over several decades; and the same can be said for response transformation models such as the Box–Cox transformation. The latter aims at ensuring that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for inference based on a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. We develop such methodology, thereby not requiring parametric assumptions on the distribution of the random effects. This is achieved by extending the ‘Nonparametric Maximum Likelihood’ towards a ‘Nonparametric profile maximum likelihood’ technique, allowing to deal with overdispersion as well as two-level data scenarios.
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Affiliation(s)
- Amani Almohaimeed
- Department of Mathematics, College of Science and Arts, Qassim University, Oyoon Aljawa, Saudi Arabia
- Department of Mathematical Sciences, Durham University, Durham, UK
| | - Jochen Einbeck
- Department of Mathematical Sciences, Durham University, Durham, UK
- Durham Research Methods Centre, Durham University, Durham, UK
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3
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Chen T, Wang R. Inference for variance components in linear mixed-effect models with flexible random effect and error distributions. Stat Methods Med Res 2020; 29:3586-3604. [PMID: 32669048 DOI: 10.1177/0962280220933909] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In many biomedical investigations, parameters of interest, such as the intraclass correlation coefficient, are functions of higher-order moments reflecting finer distributional characteristics. One popular method to make inference for such parameters is through postulating a parametric random effects model. We relax the standard normality assumptions for both the random effects and errors through the use of the Fleishman distribution, a flexible four-parameter distribution which accounts for the third and fourth cumulants. We propose a Fleishman bootstrap method to construct confidence intervals for correlated data and develop a normality test for the random effect and error distributions. Recognizing that the intraclass correlation coefficient may be heavily influenced by a few extreme observations, we propose a modified, quantile-normalized intraclass correlation coefficient. We evaluate our methods in simulation studies and apply these methods to the Childhood Adenotonsillectomy Trial sleep electroencephalogram data in quantifying wave-frequency correlation among different channels.
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Affiliation(s)
- Tom Chen
- Department of Population Medicine, Harvard Medical School and Harvard Pilgrim Health Care Institute, Boston, MA, USA
| | - Rui Wang
- Department of Population Medicine, Harvard Medical School and Harvard Pilgrim Health Care Institute, Boston, MA, USA.,Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, USA
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4
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Zhang X, de Leon J, Crespo-Facorro B, Diaz FJ. Measuring individual benefits of psychiatric treatment using longitudinal binary outcomes: Application to antipsychotic benefits in non-cannabis and cannabis users. J Biopharm Stat 2020; 30:916-940. [DOI: 10.1080/10543406.2020.1765371] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Xuan Zhang
- Department of Biostatistics, The University of Kansas Medical Center, Kansas City, KS, United States
- Boston Strategic Partners, Inc, Boston, MA, United States
| | - Jose de Leon
- Mental Health Research Center at Eastern State Hospital, Lexington, KY, United States
| | - Benedicto Crespo-Facorro
- University Hospital Virgen Del Rocío, Seville, Spain
- CIBERSAM G26-IBiS, University of Seville, Seville, Spain
- Department of Psychiatry, Marqués De Valdecilla University Hospital, IDIVAL, Santander, Spain
- School of Medicine, University of Cantabria, Santander, Spain
| | - Francisco J. Diaz
- Department of Biostatistics, The University of Kansas Medical Center, Kansas City, KS, United States
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5
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Xing Y, Wenqing M, Liang C. A methodology for improving efficiency estimation based on conditional mix-GEE models in longitudinal studies. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2019.1649423] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Yanchun Xing
- School of Statistics, Jilin University of Finance and Economics, Changchun, Jilin, China
- School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
| | - Ma Wenqing
- School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
| | - Chunhui Liang
- School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
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6
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Kinson C, Tang X, Zuo Z, Qu A. Longitudinal Principal Component Analysis With an Application to Marketing Data. J Comput Graph Stat 2019. [DOI: 10.1080/10618600.2019.1677244] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Christopher Kinson
- Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL
| | - Xiwei Tang
- Department of Statistics, University of Virginia, Charlottesville, VA
| | - Zhen Zuo
- Department of Quantitative and Computational Biosciences, Baylor College of Medicine, Houston, TX
| | - Annie Qu
- Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL
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7
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Liu L, Xiang L. Missing covariate data in generalized linear mixed models with distribution-free random effects. Comput Stat Data Anal 2019. [DOI: 10.1016/j.csda.2018.10.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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8
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Bi X, Qu A, Shen X. Multilayer tensor factorization with applications to recommender systems. Ann Stat 2018. [DOI: 10.1214/17-aos1659] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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9
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Tang N, Wu Y, Chen D. Semiparametric Bayesian analysis of transformation linear mixed models. J MULTIVARIATE ANAL 2018. [DOI: 10.1016/j.jmva.2018.03.007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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10
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Yu D, Zhang X, Yau KKW. Asymptotic properties and information criteria for misspecified generalized linear mixed models. J R Stat Soc Series B Stat Methodol 2018. [DOI: 10.1111/rssb.12270] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Dalei Yu
- Yunnan University of Finance and Economics; Kunming People's Republic of China
| | - Xinyu Zhang
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Beijing People's Republic of China
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11
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Xing Y, Xu L, Ma W, Zhu Z. Conditional mix-GEE models for longitudinal data with unspecified random-effects distributions. COMMUN STAT-THEOR M 2018. [DOI: 10.1080/03610926.2016.1267763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Yanchun Xing
- School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
- School of Statistics, Jilin University of Finance and Economics, Changchun, Jilin, China
| | - Lili Xu
- School of Education and Science, Northeast Normal University, Changchun, Jilin, China
| | - Wenqing Ma
- School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
| | - Zhichuan Zhu
- School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
- School of Statistics, Jilin University of Finance and Economics, Changchun, Jilin, China
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12
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Affiliation(s)
- Jiming Jiang
- Department of Statistics, University of California, Davis, CA
| | - J. Sunil Rao
- Division of Biostatistics, Department of Public Health Sciences, University of Miami, Coral Gables, FL
| | - Jie Fan
- Division of Biostatistics, Department of Public Health Sciences, University of Miami, Coral Gables, FL
| | - Thuan Nguyen
- Department of Public Health and Preventive Medicine, Oregon Health and Sciences University, Portland, OR
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13
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Zhang X, Yu D, Zou G, Liang H. Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models. J Am Stat Assoc 2017. [DOI: 10.1080/01621459.2015.1115762] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Xinyu Zhang
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and School of Mathematical Science, Beijing, China
| | - Dalei Yu
- Statistics and Mathematics College, Yunnan University of Finance and Economics, Kunming, China
| | - Guohua Zou
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and School of Mathematical Science, Beijing, China
| | - Hua Liang
- Department of Statistics, Geoge Washington University, Washington, DC, USA
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14
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Efficient estimation for marginal generalized partially linear single-index models with longitudinal data. TEST-SPAIN 2016. [DOI: 10.1007/s11749-015-0462-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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15
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Diaz FJ. Measuring the individual benefit of a medical or behavioral treatment using generalized linear mixed-effects models. Stat Med 2016; 35:4077-92. [PMID: 27323698 DOI: 10.1002/sim.7005] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2015] [Revised: 05/07/2016] [Accepted: 05/11/2016] [Indexed: 11/06/2022]
Abstract
We propose statistical definitions of the individual benefit of a medical or behavioral treatment and of the severity of a chronic illness. These definitions are used to develop a graphical method that can be used by statisticians and clinicians in the data analysis of clinical trials from the perspective of personalized medicine. The method focuses on assessing and comparing individual effects of treatments rather than average effects and can be used with continuous and discrete responses, including dichotomous and count responses. The method is based on new developments in generalized linear mixed-effects models, which are introduced in this article. To illustrate, analyses of data from the Sequenced Treatment Alternatives to Relieve Depression clinical trial of sequences of treatments for depression and data from a clinical trial of respiratory treatments are presented. The estimation of individual benefits is also explained. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Francisco J Diaz
- Department of Biostatistics, The University of Kansas Medical Center, Mail Stop 1026, 3901 Rainbow Blvd., Kansas City, 66160, KS, U.S.A
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16
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Zhu X, Qu A. Individualizing drug dosage with longitudinal data. Stat Med 2016; 35:4474-4488. [DOI: 10.1002/sim.7016] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2016] [Revised: 04/30/2016] [Accepted: 05/16/2016] [Indexed: 11/06/2022]
Affiliation(s)
- Xiaolu Zhu
- Department of StatisticsUniversity of Illinois at Urbana‐Champaign Champaign 61820 IL U.S.A
| | - Annie Qu
- Department of StatisticsUniversity of Illinois at Urbana‐Champaign Champaign 61820 IL U.S.A
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17
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Qiu J, Wu L. A moving blocks empirical likelihood method for longitudinal data. Biometrics 2015; 71:616-24. [PMID: 25967250 DOI: 10.1111/biom.12317] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2013] [Revised: 02/01/2015] [Accepted: 03/01/2015] [Indexed: 11/30/2022]
Abstract
In the analysis of longitudinal or panel data, neglecting the serial correlations among the repeated measurements within subjects may lead to inefficient inference. In particular, when the number of repeated measurements is large, it may be desirable to model the serial correlations more generally. An appealing approach is to accommodate the serial correlations nonparametrically. In this article, we propose a moving blocks empirical likelihood method for general estimating equations. Asymptotic results are derived under sequential limits. Simulation studies are conducted to investigate the finite sample performances of the proposed methods and compare them with the elementwise and subject-wise empirical likelihood methods of Wang et al. (2010, Biometrika 97, 79-93) and the block empirical likelihood method of You et al. (2006, Can. J. Statist. 34, 79-96). An application to an AIDS longitudinal study is presented.
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Affiliation(s)
- Jin Qiu
- School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang, 310018, P. R. China
| | - Lang Wu
- Department of Statistics, University of British Columbia, 2207 Main Mall, Vancouver, BC, Canada V6T 1Z4
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18
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Hu J, Wang P, Qu A. Estimating and Identifying Unspecified Correlation Structure for Longitudinal Data. J Comput Graph Stat 2015; 24:455-476. [PMID: 26361433 PMCID: PMC4562694 DOI: 10.1080/10618600.2014.909733] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Identifying correlation structure is important to achieving estimation efficiency in analyzing longitudinal data, and is also crucial for drawing valid statistical inference for large size clustered data. In this paper, we propose a nonparametric method to estimate the correlation structure, which is applicable for discrete longitudinal data. We utilize eigenvector-based basis matrices to approximate the inverse of the empirical correlation matrix and determine the number of basis matrices via model selection. A penalized objective function based on the difference between the empirical and model approximation of the correlation matrices is adopted to select an informative structure for the correlation matrix. The eigenvector representation of the correlation estimation is capable of reducing the risk of model misspecification, and also provides useful information on the specific within-cluster correlation pattern of the data. We show that the proposed method possesses the oracle property and selects the true correlation structure consistently. The proposed method is illustrated through simulations and two data examples on air pollution and sonar signal studies.
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Affiliation(s)
- Jianhua Hu
- University of Texas MD Anderson Cancer Center, Houston, TX 77030 ()
| | - Peng Wang
- Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403 ()
| | - Annie Qu
- Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL 61820
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19
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Choudhary PK, Sengupta D, Cassey P. A general skew-t mixed model that allows different degrees of freedom for random effects and error distributions. J Stat Plan Inference 2014. [DOI: 10.1016/j.jspi.2013.11.015] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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20
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Jiang J. The subset argument and consistency of MLE in GLMM: Answer to an open problem and beyond. Ann Stat 2013. [DOI: 10.1214/13-aos1084] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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