Abstract
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-tNLME Tobit model for response (with left censoring) process and a skew-tnonparametric mixed-effects model for covariate (with measurement errors) process under a Bayesian framework. A real data example is used to illustrate the proposed methods.
Highlights
Modeling of longitudinal data is an active area of biostatistics and statistics research that has received a lot of attention in the recent years
Attempts to jointly fit the viral load data and CD4 cell counts with measurement errors are compromised by left censoring in viral load response due to detection limits
We addressed this problem using Bayesian nonlinear mixed-effects Tobit models with skew distributions
Summary
Modeling of longitudinal data is an active area of biostatistics and statistics research that has received a lot of attention in the recent years. Various statistical modeling and analysis methods have been suggested in the literature for analyzing such data with complex features Higgins et al 1 , Liu and Wu 2 , Wulfsohn and Tsiatis 3 , and Wu 4. There is a relatively little work done on simultaneously accounting for skewness, left censoring due to a detection limit for example, a threshold below which viral loads are not quantifiable and covariate measurement errors, which are inherent features of longitudinal data. This paper proposes a joint skew-t NLME Tobit model for a response and measurement errors in covariate by simultaneously accounting for left-censoring and skewness. The proposed model addresses three important features of longitudinal data such as viral load in an AIDS study.
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