Bayesian inference on mixed-effects location scale models with skew-t distribution and mismeasured covariates for longitudinal data

In AIDS studies, heterogeneous between and within subject variations are often observed on longitudinal endpoints. To accommodate heteroscedasticity in the longitudinal data, statistical methods have been developed to model the mean and variance jointly. Most of these methods assume (conditional) normal distributions for random errors, which is not realistic in practice. In this article, we propose a Bayesian mixed-effects location scale model with skew-t distribution and mismeasured covariates for heterogeneous longitudinal data with skewness. The proposed model captures the between-subject and within-subject (WS) heterogeneity by modeling the between-subject and WS variations with covariates as well as a random effect at subject level in the WS variance. Further, the proposed model also takes into account the covariate measurement errors, and commonly assumed normal distributions for model errors are substituted by skew-t distribution to account for skewness. Parameter estimation is carried out in a Bayesian framework. The proposed method is illustrated with a Multicenter AIDS Cohort Study. Simulation studies are performed to assess the performance of the proposed method.