Multivariate t nonlinear mixed-effects models for multi-outcome longitudinal data with missing values

• Published in: Statistics in medicine Vol. 33; no. 17; pp. 3029 - 3046
• Main Authors: Wang, Wan-Lun, Lin, Tsung-I
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 30.07.2014; Wiley Subscription Services, Inc
• Subjects: Abortion, Spontaneous - etiology; Adult; Algorithms; Chorionic Gonadotropin - blood; Clinical outcomes; Computer Simulation; Correlation analysis; damped exponential correlation; ECM algorithm; Estradiol - blood; Female; Humans; imputation; Likelihood Functions; Longitudinal Studies; Medical statistics; Multivariate Analysis; multivariate longitudinal data; Nonlinear Dynamics; Obstetrics; outlier detection; Pregnancy; Pregnancy Trimester, First - metabolism; Santiago Chile; multivariate longitudinal data; ECM algorithm; imputation; damped exponential correlation; outlier detection
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.6144

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. Copyright © 2014 John Wiley & Sons, Ltd.