Bayesian joint modeling of longitudinal measurements and time-to-event data using robust distributions

Area of Science:

• Biostatistics
• Statistical Modeling
• Longitudinal Data Analysis

Background:

• Existing joint models for longitudinal and time-to-event data often lack robustness to outliers.
• Outliers can significantly distort results in standard statistical analyses.
• There is a need for flexible modeling approaches that accommodate data imperfections.

Purpose of the Study:

• To develop and implement a robust joint modeling framework for longitudinal and time-to-event data.
• To incorporate outlier robustness using normal/independent distributions.
• To apply the proposed methods to real-world data from an AIDS clinical trial.

Main Methods:

• Utilized normal/independent distributions (Student's t, slash, contaminated normal) for outlier robustness.
• Employed a linear mixed-effects model for the longitudinal process and a Weibull proportional hazards model for the time-to-event process.
• Adopted a Bayesian approach with Markov-chain Monte Carlo (MCMC) for parameter estimation.

Main Results:

• Simulation studies demonstrated the proposed method's effectiveness in both the presence and absence of outliers.
• The model was successfully applied to AIDS clinical trial data, analyzing CD4 counts and time to death/dropout.
• Model selection was performed using Deviance Information Criterion (DIC), Expected Akaike Information Criterion (EAIC), and Expected Bayesian Information Criterion (EBIC).

Conclusions:

• The proposed joint modeling approach provides a robust alternative for analyzing longitudinal and time-to-event data.
• The method effectively handles outliers, leading to more reliable statistical inferences.
• This framework offers improved tools for analyzing complex biomedical data, such as that from clinical trials.