Bayesian-frequentist hybrid approach for skew-normal nonlinear mixed-effects joint models in the presence of covariates measured with errors

It is a common practice to analyze complex longitudinal data using nonlinear mixed-effects (NLME) models. Existing methods often assume a normal model for the errors, which is not realistic. To explain between-and within-subject variations, covariates are usually introduced in such models to partially explain inter-subject variations, but some covariates may often be measured with substantial errors. Moreover, although statistical methods for analyzing longitudinal data have been evolving substantially, existing methods are either frequentist or full Bayesian, not taking into account scenarios where only part of the parameters have sound prior information available. In an attempt to take full advantage of both approaches, we adopt a Bayesian-frequentist hybrid (BFH) approach to NLME models with a skew-normal distribution in the presence of covariate measurement errors and jointly model the response and covariate processes. We illustrate the proposed method in a real example from an AIDS clinical trial by modeling the viral dynamics to compare potential models with different inference methods. Simulation studies are conducted to assess the performance of the proposed model and method.