Mixed-Effects Tobit Joint Models for Longitudinal Data with Skewness, Detection Limits, and Measurement Errors

Complex longitudinal data are commonly analyzed using nonlinear mixed-effects (NLME) models with a normal distribution. However, a departure from normality may lead to invalid inference and unreasonable parameter estimates. Some covariates may be measured with substantial errors, and the response observations may also be subjected to left-censoring due to a detection limit. Inferential procedures can be complicated dramatically when such data with asymmetric characteristics, left censoring, and measurement errors are analyzed. There is relatively little work concerning all of the three features simultaneously. In this paper, we jointly investigate a skew- t NLME Tobit model for response (with left censoring) process and a skew- t nonparametric mixed-effects model for covariate (with measurement errors) process under a Bayesian framework. A real data example is used to illustrate the proposed methods.