Bayesian joint modeling for partially linear mixed-effects quantile regression of longitudinal and time-to-event data with limit of detection, covariate measurement errors and skewness.

Joint modeling analysis of longitudinal and time-to-event data has been an active area of statistical methodological study and biomedical research, but the majority of them are based on mean-regression. Quantile regression (QR) can characterize the entire conditional distribution of the outcome variable, and may be more robust to outliers/heavy tails and misspecification of error distribution. Additionally, a parametric specification may be insufficient and inflexible to capture the complicated longitudinal pattern of biomarkers. Thus, this study proposes novel QR-based partially linear mixed-effects joint models with three components (QR-based longitudinal response, longitudinal covariate, and time-to-event processes), and applies to Multicenter AIDS Cohort Study (MACS). Many common data features, including left-censoring due to a limit of detection, covariate measurement error, and asymmetric distribution, are considered to obtain reliable parameter estimates. Many interesting findings are discovered by the complicated joint models under Bayesian inference framework. Simulation studies are also implemented to assess the performance of the proposed joint models under different scenarios.