Bayesian inference on mixed-effects varying-coefficient joint models with skew-t distribution for longitudinal data with multiple features

In AIDS clinical study, two biomarkers, HIV viral load and CD4 cell counts, play important roles. It is well known that there is inverse relationship between the two. Nevertheless, the relationship is not constant but time varying. The mixed-effects varying-coefficient model is capable of capturing the time varying nature of such relationship from both population and individual perspective. In practice, the nucleic acid sequence-based amplification assay is used to measure plasma HIV-1 RNA with a limit of detection (LOD) and the CD4 cell counts are usually measured with much noise and missing data often occur during the treatment. Furthermore, most of the statistical models assume symmetric distribution, such as normal, for the response variables. Often time, normality assumption does not hold in practice. Therefore, it is important to explore all these factors when modeling the real data. In this article, we establish a joint model that accounts for asymmetric and LOD data for the response variable, and covariate measurement error and missingness simultaneously in the mixed-effects varying-coefficient modeling framework. A Bayesian inference procedure is developed to estimate the parameters in the joint model. The proposed model and method are applied to a real AIDS clinical study and various comparisons of a few models are performed.