This study introduces a novel joint modeling framework integrating quantile regression for longitudinal continuous proportions data with Cox regression for time-to-event analysis, employing integrated nested Laplace approximation for Bayesian inference. Our approach facilitates an examination across the entire distribution of patient health metrics over time, including the occurrence of key health events and their impact on patient outcomes, particularly in the context of medication adherence and persistence. Integrated nested Laplace approximation's fast computational speed significantly enhances the efficiency of this process, making the model particularly suitable for applications requiring rapid data analysis and updates. Applying this model to a dataset of patients who underwent treatment with atorvastatin, we demonstrate the significant impact of targeted interventions on improving medication adherence and persistence across various patient subgroups. Furthermore, we have developed a dynamic prediction method within this framework that rapidly estimates persistence probabilities based on the latest medication adherence data, demonstrating integrated nested Laplace approximation's quick updates and prediction capability. The simulation study validates the reliability of our modeling approach, evidenced by minimal bias and appropriate credible interval coverage probabilities across different quantile levels.
Keywords: Joint modeling; integrated nested laplace approximation; longitudinal data analysis; medication adherence; quantile regression; time-to-event data.