title: Multivariate t nonlinear mixed-effects models for multi-outcome longitudinal data with missing values.
abstract: The multivariate nonlinear mixed-effects model (MNLMM) has emerged as an effective tool for modeling multi-outcome longitudinal data following nonlinear growth patterns. In the framework of MNLMM, the random effects and within-subject errors are assumed to be normally distributed for mathematical tractability and computational simplicity. However, a serious departure from normality may cause lack of robustness and subsequently make invalid inference. This paper presents a robust extension of the MNLMM by considering a joint multivariate t distribution for the random effects and within-subject errors, called the multivariate t nonlinear mixed-effects model. Moreover, a damped exponential correlation structure is employed to capture the extra serial correlation among irregularly observed multiple repeated measures. An efficient expectation conditional maximization algorithm coupled with the first-order Taylor approximation is developed for maximizing the complete pseudo-data likelihood function. The techniques for the estimation of random effects, imputation of missing responses and identification of potential outliers are also investigated. The methodology is motivated by a real data example on 161 pregnant women coming from a study in a private fertilization obstetrics clinic in Santiago, Chile and used to analyze these data.
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
authors.forename: Tsung-I
authors.initials: TI
authors.lastname: Lin
mesh_terms: D000022:Abortion, Spontaneous / Q000209:etiology; D000328:Adult; D000465:Algorithms; D006063:Chorionic Gonadotropin / Q000097:blood; D003198:Computer Simulation; D004958:Estradiol / Q000097:blood; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D015999:Multivariate Analysis; D017711:Nonlinear Dynamics; D011247:Pregnancy; D011261:Pregnancy Trimester, First / Q000378:metabolism
chemical_list: D006063:Chorionic Gonadotropin; D004958:Estradiol
keywords: ECM algorithm; damped exponential correlation; imputation; multivariate longitudinal data; outlier detection