Multivariate-t nonlinear mixed models with application to censored multi-outcome AIDS studies

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 mixedeffects 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 fattailed 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.