Simultaneous Bayesian Inference for Longitudinal Data with Asymmetry, Left-censoring and Covariates Measured with Errors

Abstract

It is a common practice to analyze complex longitudinal data using flexible nonlinear mixed-effects (NLME) models with normality assumption. However, a serious departure of normality may cause lack of robustness and subsequently lead to invalid inference and unreasonable estimates. Covariates are usually introduced in such models to partially explain inter-subject variations, but some covariates may be often measured with substantial errors. Moreover, the response observations may be subject to left-censoring due to a detection limit. Inferential procedures can be complicated dramatically when data with asymmetric (skewed) characteristics, leftcensoring and measurement errors are observed. In the literature, there has been considerable interest in accommodating either skewness, censoring or covariate measurement errors in such models, but there is relatively little work concerning all of the three features simultaneously. In this article, we jointly investigate a skew-t NLME model for response (with left-censoring) process and a skew-t nonparametric mixedeffects model for covariate (with measurement errors) process. We propose a robust skew-t Bayesian modeling approach in a general form to analyze data in capturing the effects of skewness, censoring and measurement errors in covariates simultaneously. A real data example is offered to illustrate the methodologies. The proposed modeling alternative offers important advantages in the sense that the model can be easily fitted in freely available software and the computational effort for the model with a skew-t distribution is almost equivalent to that of the model with a standard normal distribution.