Bayesian inference for a nonlinear mixed-effects Tobit model with multivariate skew-t distributions: application to AIDS studies

Censored data are characteristics of many bioassays in HIV/AIDS studies where assays may not be sensitive enough to determine gradations in viral load determination among those below a detectable threshold. Not accounting for such left-censoring appropriately can lead to biased parameter estimates in most data analysis. To properly adjust for left-censoring, this paper presents an extension of the Tobit model for fitting nonlinear dynamic mixed-effects models with skew distributions. Such extensions allow one to specify the conditional distributions for viral load response to account for left-censoring, skewness and heaviness in the tails of the distributions of the response variable. A Bayesian modeling approach via Markov Chain Monte Carlo (MCMC) algorithm is used to estimate model parameters. The proposed methods are illustrated using real data from an HIV/AIDS study.