Quantile regression-based Bayesian joint modeling analysis of longitudinal–survival data, with application to an AIDS cohort study

In longitudinal studies, it is of interest to investigate how repeatedly measured markers are associated with time to an event. Joint models have received increasing attention on analyzing such complex longitudinal–survival data with multiple data features, but most of them are mean regression-based models. This paper formulates a quantile regression (QR) based joint models in general forms that consider left-censoring due to the limit of detection, covariates with measurement errors and skewness. The joint models consist of three components: (i) QR-based nonlinear mixed-effects Tobit model using asymmetric Laplace distribution for response dynamic process; (ii) nonparametric linear mixed-effects model with skew-normal distribution for mismeasured covariate; and (iii) Cox proportional hazard model for event time. For the purpose of simultaneously estimating model parameters, we propose a Bayesian method to jointly model the three components which are linked through the random effects. We apply the proposed modeling procedure to analyze the Multicenter AIDS Cohort Study data, and assess the performance of the proposed models and method through simulation studies. The findings suggest that our QR-based joint models may provide comprehensive understanding of heterogeneous outcome trajectories at different quantiles, and more reliable and robust results if the data exhibits these features.