title: Extending multivariate- t linear mixed models for multiple longitudinal data with censored responses and heavy tails.
abstract: The analysis of complex longitudinal data is challenging due to several inherent features: (i) more than one series of responses are repeatedly collected on each subject at irregularly occasions over a period of time; (ii) censorship due to limits of quantification of responses arises left- and/or right- censoring effects; (iii) outliers or heavy-tailed noises are possibly embodied within multiple response variables. This article formulates the multivariate- t linear mixed model with censored responses (MtLMMC), which allows the analysts to model such data in the presence of the above described features simultaneously. An efficient expectation conditional maximization either (ECME) algorithm is developed to carry out maximum likelihood estimation of model parameters. The implementation of the E-step relies on the mean and covariance matrix of truncated multivariate- t distributions. To enhance the computational efficiency, two auxiliary permutation matrices are incorporated into the procedure to determine the observed and censored parts of each subject. The proposed methodology is demonstrated via a simulation study and a real application on HIV/AIDS data.
authors.affiliation: 1 Department of Statistics, Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung, Taiwan.
authors.forename: Wan-Lun
authors.initials: WL
authors.lastname: Wang
authors.affiliation: 2 Institute of Statistics, National Chung Hsing University, Taichung, Taiwan.|3 Department of Public Health, China Medical University, Taichung, Taiwan.
authors.forename: Tsung-I
authors.initials: TI
authors.lastname: Lin
authors.affiliation: 4 Departamento de Estatística, Universidade Estadual de Campinas, Brazil.
authors.forename: Victor H
authors.initials: VH
authors.lastname: Lachos
mesh_terms: D015982:Bias; D000068597:Censorship, Research; D002986:Clinical Trials as Topic; D003198:Computer Simulation; D015658:HIV Infections; D016013:Likelihood Functions; D016014:Linear Models; D008137:Longitudinal Studies; D015999:Multivariate Analysis
keywords: AIDS clinical trials; ECME algorithm; censored data; multivariate longitudinal data; outliers