Simultaneous Bayesian Inference for Skew-Normal Semiparametric Nonlinear Mixed-Effects Models with Covariate Measurement Errors

Longitudinal data arise frequently in medical studies and it is a common practice to analyze such complex data with nonlinear mixed-effects (NLME) models which enable us to account for between-subject and within-subject variations. To partially explain the variations, covariates are usually introduced to these models. Some covariates, however, may be often measured with substantial errors. It is often the case that model random error is assumed to be distributed normally, but the normality assumption may not always give robust and reliable results, particularly if the data exhibit skewness. Although there has been considerable interest in accommodating either skewness or covariate measurement error in the literature, there is relatively little work that considers both features simultaneously. In this article, our objectives are to address simultaneous impact of skewness and covariate measurement error by jointly modeling the response and covariate processes under a general framework of Bayesian semiparametric nonlinear mixed-effects models. The method is illustrated in an AIDS data example to compare potential models which have different distributional specifications. The findings from this study suggest that the models with a skew-normal distribution may provide more reasonable results if the data exhibit skewness and/or have measurement errors in covariates.