1
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Wang WL, Castro LM, Li HJ, Lin TI. Mixtures of t $$ t $$ factor analysers with censored responses and external covariates: An application to educational data from Peru. THE BRITISH JOURNAL OF MATHEMATICAL AND STATISTICAL PSYCHOLOGY 2024; 77:316-336. [PMID: 38095333 DOI: 10.1111/bmsp.12329] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2023] [Revised: 10/21/2023] [Accepted: 11/16/2023] [Indexed: 04/10/2024]
Abstract
Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures oft $$ t $$ factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.
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Affiliation(s)
- Wan-Lun Wang
- Department of Statistics and Institute of Data Science, National Cheng Kung University, Tainan, Taiwan
| | - Luis M Castro
- Department of Statistics, Pontificia Universidad Católica de Chile, Santiago, Chile
- Center for the Discovery of Structures in Complex Data, Santiago, Chile
| | - Huei-Jyun Li
- Institute of Statistics, National Chung Hsing University, Taichung, Taiwan
| | - Tsung-I Lin
- Institute of Statistics, National Chung Hsing University, Taichung, Taiwan
- Department of Public Health, China Medical University, Taichung, Taiwan
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2
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Tian YZ, Tang ML, Wong C, Tian MZ. Bayesian analysis of joint quantile regression for multi-response longitudinal data with application to primary biliary cirrhosis sequential cohort study. Stat Methods Med Res 2024:9622802241247725. [PMID: 38676359 DOI: 10.1177/09622802241247725] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/28/2024]
Abstract
This article proposes a Bayesian approach for jointly estimating marginal conditional quantiles of multi-response longitudinal data with multivariate mixed effects model. The multivariate asymmetric Laplace distribution is employed to construct the working likelihood of the considered model. Penalization priors on regression parameters are incorporated into the working likelihood to conduct Bayesian high-dimensional inference. Markov chain Monte Carlo algorithm is used to obtain the fully conditional posterior distributions of all parameters and latent variables. Monte Carlo simulations are conducted to evaluate the sample performance of the proposed joint quantile regression approach. Finally, we analyze a longitudinal medical dataset of the primary biliary cirrhosis sequential cohort study to illustrate the real application of the proposed modeling method.
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Affiliation(s)
- Yu-Zhu Tian
- School of Mathematics and Statistics, Northwest Normal University, LanZhou, China
- Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou, China
| | - Man-Lai Tang
- Department of Physics, Astronomy and Mathematics, University of Hertfordshire, UK
| | - Catherine Wong
- Digital Humanities Institut, University of Sheffield, UK
| | - Mao-Zai Tian
- Centre for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China
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3
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Lin TI, Wang WL. Flexible modeling of multiple nonlinear longitudinal trajectories with censored and non-ignorable missing outcomes. Stat Methods Med Res 2023; 32:593-608. [PMID: 36624626 DOI: 10.1177/09622802221146312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
Multivariate nonlinear mixed-effects models (MNLMMs) have become a promising tool for analyzing multi-outcome longitudinal data following nonlinear trajectory patterns. However, such a classical analysis can be challenging due to censorship induced by detection limits of the quantification assay or non-response occurring when participants missed scheduled visits intermittently or discontinued participation. This article proposes an extension of the MNLMM approach, called the MNLMM-CM, by taking the censored and non-ignorable missing responses into account simultaneously. The non-ignorable missingness is described by the selection-modeling factorization to tackle the missing not at random mechanism. A Monte Carlo expectation conditional maximization algorithm coupled with the first-order Taylor approximation is developed for parameter estimation. The techniques for the calculation of standard errors of fixed effects, estimation of unobservable random effects, imputation of censored and missing responses and prediction of future values are also provided. The proposed methodology is motivated and illustrated by the analysis of a clinical HIV/AIDS dataset with censored RNA viral loads and the presence of missing CD4 and CD8 cell counts. The superiority of our method on the provision of more adequate estimation is validated by a simulation study.
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Affiliation(s)
- Tsung-I Lin
- Institute of Statistics, 34916National Chung Hsing University, Taichung, Taiwan.,Department of Public Health, China Medical University, Taichung, Taiwan
| | - Wan-Lun Wang
- Department of Statistics and Institute of Data Science, 34912National Cheng Kung University, Tainan, Taiwan
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4
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Model-based clustering via mixtures of unrestricted skew normal factor analyzers with complete and incomplete data. STAT METHOD APPL-GER 2022. [DOI: 10.1007/s10260-022-00674-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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5
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Lin TI, Wang WL. Multivariate linear mixed models with censored and nonignorable missing outcomes, with application to AIDS studies. Biom J 2022; 64:1325-1339. [PMID: 35723051 DOI: 10.1002/bimj.202100233] [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: 08/02/2021] [Revised: 04/16/2022] [Accepted: 04/22/2022] [Indexed: 11/08/2022]
Abstract
The analysis of multivariate longitudinal data could encounter some complications due to censorship induced by detection limits of the assay and nonresponse occurring when participants missed scheduled visits intermittently or discontinued participation. This paper establishes a generalization of the multivariate linear mixed model that can accommodate censored responses and nonignorable missing outcomes simultaneously. To account for the nonignorable missingness, the selection approach which decomposes the joint distribution as a marginal distribution for the primary outcome variables and a model describing the missing process conditional on the hypothetical complete data is used. A computationally feasible Monte Carlo expectation conditional maximization algorithm is developed for parameter estimation with the maximum likelihood (ML) method. Furthermore, a general information-based approach is presented to assess the variability of ML estimators. The techniques for the prediction of censored responses and imputation of missing outcomes are also discussed. The methodology is motivated and exemplified by a real dataset concerning HIV-AIDS clinical trials. A simulation study is conducted to examine the performance of the proposed method compared with other traditional approaches.
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Affiliation(s)
- Tsung-I Lin
- Institute of Statistics, National Chung Hsing University, Taichung, Taiwan.,Department of Public Health, China Medical University, Taichung, Taiwan
| | - Wan-Lun Wang
- Department of Statistics and Institute of Data Science, National Cheng Kung University, Tainan, Taiwan
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6
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Mattos TB, Lachos VH, Castro LM, Matos LA. Extending multivariate Student's- t $$ t $$ semiparametric mixed models for longitudinal data with censored responses and heavy tails. Stat Med 2022; 41:3696-3719. [PMID: 35596519 DOI: 10.1002/sim.9443] [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: 10/05/2020] [Revised: 04/25/2022] [Accepted: 05/10/2022] [Indexed: 11/08/2022]
Abstract
This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's t $$ t $$ -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.
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Affiliation(s)
- Thalita B Mattos
- Departamento de Estatística, Universidade Estadual de Campinas, São Paulo, Brazil
| | - Victor H Lachos
- Department of Statistics, University of Connecticut, Storrs, Connecticut, USA
| | - Luis M Castro
- Department of Statistics, Pontificia Universidad Católica de Chile, Santiago, Chile.,Millennium Nucleus Center for the Discovery of Structures in Complex Data, and Centro de Riesgos y Seguros UC, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Larissa A Matos
- Departamento de Estatística, Universidade Estadual de Campinas, São Paulo, Brazil
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7
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Wang WL, Yang YC, Lin TI. Extending finite mixtures of nonlinear mixed-effects models with covariate-dependent mixing weights. ADV DATA ANAL CLASSI 2022. [DOI: 10.1007/s11634-022-00502-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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8
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Robust clustering of multiply censored data via mixtures of t factor analyzers. TEST-SPAIN 2022. [DOI: 10.1007/s11749-021-00766-y] [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]
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9
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Taavoni M, Arashi M. Estimation in multivariate t linear mixed models for longitudinal data with multiple outputs: Application to PBCseq data analysis. Biom J 2021; 64:539-556. [PMID: 34821410 DOI: 10.1002/bimj.202000015] [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: 01/12/2020] [Revised: 04/17/2021] [Accepted: 05/01/2021] [Indexed: 01/10/2023]
Abstract
In many biomedical studies or clinical trials, we have data with more than one response variable on the same subject repeatedly measured over time. In analyzing such data, we adopt a multivariate linear mixed-effects longitudinal model. On the other hand, in longitudinal data, we often find features that do not impact modeling the response variable and are eliminated from the study. In this paper, we consider the problem of simultaneous variable selection and estimation in a multivariate t linear mixed-effects model (MtLMM) for analyzing longitudinally measured multioutcome data. This work's motivation comes from a cohort study of patients with primary biliary cirrhosis. The interest is eliminating insignificant variables using the smoothly clipped and absolute deviation penalty function in the MtLMM. The proposed penalized model offers robustness and flexibility to accommodate fat tails. An expectation conditional maximization algorithm is employed for the computation of maximum likelihood estimates of parameters. The calculation of standard errors is affected by an information-based method. The methodology is illustrated by analyzing Mayo Clinic Primary Biliary Cirrhosis sequential (PBCseq) data and a simulation study. We found drugs and sex can be eliminated from the PBCseq analysis, and over time the disease progresses.
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Affiliation(s)
- Mozhgan Taavoni
- Department of Statistic, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
| | - Mohammad Arashi
- Department of Statistic, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
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10
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11
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de Alencar FHC, Galarza CE, Matos LA, Lachos VH. Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution. ADV DATA ANAL CLASSI 2021. [DOI: 10.1007/s11634-021-00448-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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12
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Galarza Morales CE, Lachos VH, Bourguignon M. A skew‐
t
quantile regression for censored and missing data. Stat (Int Stat Inst) 2021. [DOI: 10.1002/sta4.379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
| | - Victor H. Lachos
- Department of Statistics University of Connecticut CT Storrs CT 06269 USA
| | - Marcelo Bourguignon
- Departamento de Estatística Universidade do Rio Grande do Norte Natal Brazil
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13
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Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2021.107182] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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14
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Naderi M, Mirfarah E, Bernhardt M, Chen DG. Semiparametric inference for the scale-mixture of normal partial linear regression model with censored data. J Appl Stat 2021; 49:3022-3043. [DOI: 10.1080/02664763.2021.1931821] [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)
- Mehrdad Naderi
- Department of Statistics, Faculty of Natural & Agricultural Sciences, University of Pretoria, Pretoria, South Africa
| | - Elham Mirfarah
- Department of Statistics, Faculty of Natural & Agricultural Sciences, University of Pretoria, Pretoria, South Africa
| | - Matthew Bernhardt
- Department of Statistics, Faculty of Natural & Agricultural Sciences, University of Pretoria, Pretoria, South Africa
| | - Ding-Geng Chen
- Department of Statistics, Faculty of Natural & Agricultural Sciences, University of Pretoria, Pretoria, South Africa
- Department of Biostatistics, University of North Carolina, Chapel Hill, NC, USA
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15
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Bandyopadhyay D, Prates MO, Zhao X, Lachos VH. Spatial skew-normal/independent models for nonrandomly missing clustered data. Stat Med 2021; 40:3085-3105. [PMID: 33782991 DOI: 10.1002/sim.8960] [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: 04/06/2018] [Revised: 03/02/2021] [Accepted: 03/05/2021] [Indexed: 11/06/2022]
Abstract
Clinical studies on periodontal disease (PD) often lead to data collected which are clustered in nature (viz. clinical attachment level, or CAL, measured at tooth-sites and clustered within subjects) that are routinely analyzed under a linear mixed model framework, with underlying normality assumptions of the random effects and random errors. However, a careful look reveals that these data might exhibit skewness and tail behavior, and hence the usual normality assumptions might be questionable. Besides, PD progression is often hypothesized to be spatially associated, that is, a diseased tooth-site may influence the disease status of a set of neighboring sites. Also, the presence/absence of a tooth is informative, as the number and location of missing teeth informs about the periodontal health in that region. In this paper, we develop a (shared) random effects model for site-level CAL and binary presence/absence status of a tooth under a Bayesian paradigm. The random effects are modeled using a spatial skew-normal/independent (S-SNI) distribution, whose dependence structure is conditionally autoregressive (CAR). Our S-SNI density presents an attractive parametric tool to model spatially referenced asymmetric thick-tailed structures. Both simulation studies and application to a clinical dataset recording PD status reveal the advantages of our proposition in providing a significantly improved fit, over models that do not consider these features in a unified way.
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Affiliation(s)
| | - Marcos O Prates
- Department of Statistics, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
| | | | - Victor H Lachos
- Departament of Statistics, University of Connecticut, Storrs, Connecticut, USA
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16
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Yaseen ASA, Gad AM. A stochastic variant of the EM algorithm to fit mixed (discrete and continuous) longitudinal data with nonignorable missingness. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2019.1601223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
| | - Ahmed M. Gad
- Statistics Department, Faculty of Economics and Political Science, Cairo University, Giza, Egypt
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17
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Taavoni M, Arashi M, Wang WL, Lin TI. Multivariate t semiparametric mixed-effects model for longitudinal data with multiple characteristics. J STAT COMPUT SIM 2020. [DOI: 10.1080/00949655.2020.1812608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- M. Taavoni
- Department of Statistic, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
| | - M. Arashi
- Department of Statistic, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
| | - Wan-Lun Wang
- Department of Statistics, Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung, Taiwan
| | - Tsung-I Lin
- Institute of Statistics, National Chung Hsing University, Taichung, Taiwan
- Department of Public Health, China Medical University, Taichung, Taiwan
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18
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Chen C, Shen B, Liu A, Wu R, Wang M. A multiple robust propensity score method for longitudinal analysis with intermittent missing data. Biometrics 2020; 77:519-532. [PMID: 32662124 DOI: 10.1111/biom.13330] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Revised: 04/15/2020] [Accepted: 06/16/2020] [Indexed: 01/05/2023]
Abstract
Longitudinal data are very popular in practice, but they are often missing in either outcomes or time-dependent risk factors, making them highly unbalanced and complex. Missing data may contain various missing patterns or mechanisms, and how to properly handle it for unbiased and valid inference still presents a significant challenge. Here, we propose a novel semiparametric framework for analyzing longitudinal data with both missing responses and covariates that are missing at random and intermittent, a general and widely encountered situation in observational studies. Within this framework, we consider multiple robust estimation procedures based on innovative calibrated propensity scores, which offers additional relaxation of the misspecification of missing data mechanisms and shows more satisfactory numerical performance. Also, the corresponding robust information criterion on consistent variable selection for our proposed model is developed based on empirical likelihood-based methods. These advocated methods are evaluated in both theory and extensive simulation studies in a variety of situations, showing competing properties and advantages compared to the existing approaches. We illustrate the utility of our approach by analyzing the data from the HIV Epidemiology Research Study.
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Affiliation(s)
- Chixiang Chen
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennsylvania
| | - Biyi Shen
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennsylvania
| | - Aiyi Liu
- Biostatistics and Bioinformatics Branch, National Institute of Child Health and Human Development, NIH, Bethesda, Maryland
| | - Rongling Wu
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennsylvania
| | - Ming Wang
- Division of Biostatistics and Bioinformatics, Department of Public Health Sciences, Penn State College of Medicine, Hershey, Pennsylvania
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19
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Mixtures of factor analyzers with covariates for modeling multiply censored dependent variables. Stat Pap (Berl) 2020. [DOI: 10.1007/s00362-020-01177-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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20
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Wang W. Bayesian analysis of multivariate linear mixed models with censored and intermittent missing responses. Stat Med 2020; 39:2518-2535. [DOI: 10.1002/sim.8554] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2019] [Revised: 02/01/2020] [Accepted: 03/31/2020] [Indexed: 11/05/2022]
Affiliation(s)
- Wan‐Lun Wang
- Department of Statistics, Graduate Institute of Statistics and Actuarial ScienceFeng Chia University Taichung Taiwan
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21
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Lin TI, Wang WL. Multivariate- t linear mixed models with censored responses, intermittent missing values and heavy tails. Stat Methods Med Res 2020; 29:1288-1304. [PMID: 31242813 DOI: 10.1177/0962280219857103] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Multivariate longitudinal data arisen in medical studies often exhibit complex features such as censored responses, intermittent missing values, and atypical or outlying observations. The multivariate-t linear mixed model (MtLMM) has been recognized as a powerful tool for robust modeling of multivariate longitudinal data in the presence of potential outliers or fat-tailed noises. This paper presents a generalization of MtLMM, called the MtLMM-CM, to properly adjust for censorship due to detection limits of the assay and missingness embodied within multiple outcome variables recorded at irregular occasions. An expectation conditional maximization either (ECME) algorithm is developed to compute parameter estimates using the maximum likelihood (ML) approach. The asymptotic standard errors of the ML estimators of fixed effects are obtained by inverting the empirical information matrix according to Louis' method. The techniques for the estimation of random effects and imputation of missing responses are also investigated. The proposed methodology is illustrated on two real-world examples from HIV-AIDS studies and a simulation study under a variety of scenarios.
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Affiliation(s)
- Tsung-I Lin
- Institute of Statistics, National Chung Hsing University, Taichung, Taiwan.,Department of Public Health, China Medical University, Taichung, Taiwan
| | - Wan-Lun Wang
- Department of Statistics, Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung, Taiwan
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22
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Naderi M, Bekker A, Arashi M, Jamalizadeh A. A theoretical framework for Landsat data modeling based on the matrix variate mean-mixture of normal model. PLoS One 2020; 15:e0230773. [PMID: 32271785 PMCID: PMC7144982 DOI: 10.1371/journal.pone.0230773] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 02/11/2020] [Indexed: 11/19/2022] Open
Abstract
This paper introduces a new family of matrix variate distributions based on the mean-mixture of normal (MMN) models. The properties of the new matrix variate family, namely stochastic representation, moments and characteristic function, linear and quadratic forms as well as marginal and conditional distributions are investigated. Three special cases including the restricted skew-normal, exponentiated MMN and the mixed-Weibull MMN matrix variate distributions are presented and studied. Based on the specific presentation of the proposed model, an EM-type algorithm can be directly implemented for obtaining maximum likelihood estimate of the parameters. The usefulness and practical utility of the proposed methodology are illustrated through two conducted simulation studies and through the Landsat satellite dataset analysis.
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Affiliation(s)
- Mehrdad Naderi
- Department of Statistics, Faculty of Natural & Agricultural Sciences, University of Pretoria, Pretoria, South Africa
- * E-mail:
| | - Andriette Bekker
- Department of Statistics, Faculty of Natural & Agricultural Sciences, University of Pretoria, Pretoria, South Africa
| | - Mohammad Arashi
- Department of Statistics, Faculty of Natural & Agricultural Sciences, University of Pretoria, Pretoria, South Africa
- Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
| | - Ahad Jamalizadeh
- Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
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23
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Wu J, Chen MH, Schifano ED, Ibrahim JG, Fisher JD. A new Bayesian joint model for longitudinal count data with many zeros, intermittent missingness, and dropout with applications to HIV prevention trials. Stat Med 2019; 38:5565-5586. [PMID: 31691322 DOI: 10.1002/sim.8379] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2018] [Revised: 09/02/2019] [Accepted: 09/05/2019] [Indexed: 11/08/2022]
Abstract
In longitudinal clinical trials, it is common that subjects may permanently withdraw from the study (dropout), or return to the study after missing one or more visits (intermittent missingness). It is also routinely encountered in HIV prevention clinical trials that there is a large proportion of zeros in count response data. In this paper, a sequential multinomial model is adopted for dropout and subsequently a conditional model is constructed for intermittent missingness. The new model captures the complex structure of missingness and incorporates dropout and intermittent missingness simultaneously. The model also allows us to easily compute the predictive probabilities of different missing data patterns. A zero-inflated Poisson mixed-effects regression model is assumed for the longitudinal count response data. We also propose an approach to assess the overall treatment effects under the zero-inflated Poisson model. We further show that the joint posterior distribution is improper if uniform priors are specified for the regression coefficients under the proposed model. Variations of the g-prior, Jeffreys prior, and maximally dispersed normal prior are thus established as remedies for the improper posterior distribution. An efficient Gibbs sampling algorithm is developed using a hierarchical centering technique. A modified logarithm of the pseudomarginal likelihood and a concordance based area under the curve criterion are used to compare the models under different missing data mechanisms. We then conduct an extensive simulation study to investigate the empirical performance of the proposed methods and further illustrate the methods using real data from an HIV prevention clinical trial.
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Affiliation(s)
- Jing Wu
- Department of Computer Science and Statistics, University of Rhode Island, Kingston, Rhode Island
| | - Ming-Hui Chen
- Department of Statistics, University of Connecticut, Storrs, Connecticut
| | | | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
| | - Jeffrey D Fisher
- Department of Psychology and Institute for Collaboration on Health, Intervention, and Policy (InCHIP), University of Connecticut, Storrs, Connecticut
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24
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Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values. TEST-SPAIN 2018. [DOI: 10.1007/s11749-018-0612-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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