Multivariate-t nonlinear mixed models for censored multi-outcome longitudinal data

Abstract

In complex longitudinal data, multi-outcome repeated measures on each subject over time may contain outliers, and the measurements are often subject to an upper or lower limit of detection depending on the quantification assays. In this talk, I will present the extension of the multivariate nonlinear mixed 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 model with censored responses (MtNLMMC). The MtNLMMC approach, which contains the multivariate t linear mixed model with censored responses (MtLMMC) as a special case, allows 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 of model parameters. The effectiveness of our proposed methodology and its practical use are illustrated with simulated datasets and real data examples from HIV/AIDS studies. Experimental results signify that the MtNLMMC performs favorably compared to its Gaussian analogue and some existing approaches. Keywords: CD4/CD8 ratio; ECME algorithm; HIV viral load; Multiple nonlinear profiles; Truncated multivariate-t distribution.