title: Multivariate-$t$ nonlinear mixed models with application to censored multi-outcome AIDS studies.
abstract: In multivariate longitudinal HIV/AIDS studies, multi-outcome repeated measures on each patient over time may contain outliers, and the viral loads are often subject to a upper or lower limit of detection depending on the quantification assays. In this article, we consider an extension of the multivariate nonlinear mixed-effects model by adopting a joint multivariate-$t$ distribution for random effects and within-subject errors and taking the censoring information of multiple responses into account. The proposed model is called the multivariate-$t$ nonlinear mixed-effects model with censored responses (MtNLMMC), allowing for analyzing multi-outcome longitudinal data exhibiting nonlinear growth patterns with censorship and fat-tailed behavior. Utilizing the Taylor-series linearization method, a pseudo-data version of expectation conditional maximization either (ECME) algorithm is developed for iteratively carrying out maximum likelihood estimation. We illustrate our techniques with two data examples from HIV/AIDS studies. Experimental results signify that the MtNLMMC performs favorably compared to its Gaussian analogue and some existing approaches.
authors.affiliation: Institute of Statistics, National Chung Hsing University, Taichung 402, Taiwan, Department of Public Health, China Medical University, Taichung 404, Taiwan.
authors.forename: Tsung-I
authors.initials: TI
authors.lastname: Lin
authors.affiliation: Department of Statistics, Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung 40724, Taiwan.
authors.forename: Wan-Lun
authors.initials: WL
authors.lastname: Wang
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000097:blood; D015658:HIV Infections / Q000097:blood*; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D017063:Outcome Assessment, Health Care / Q000379:methods*
keywords: CD4/CD8 ratio; ECME algorithm; HIV viral load; Multiple nonlinear profiles; Truncated multivariate-t distribution