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

Wan Lun Wang, Tsung I. Lin

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)3029-3046
Number of pages18
JournalStatistics in Medicine
Issue number17
Publication statusPublished - 2014 Jul 30

All Science Journal Classification (ASJC) codes

  • Epidemiology
  • Statistics and Probability


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