Semiparametric normal transformation joint model of multivariate longitudinal and bivariate time-to-event data

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Survival Analysis

Background:

• Joint models for longitudinal and survival data (JMLSs) are crucial for analyzing clinical trial data.
• Existing JMLSs often assume independent survival data, which is limiting.
• Bivariate correlation in survival data is frequently observed in clinical settings.

Purpose of the Study:

• To propose a novel JMLS that accommodates multivariate longitudinal and bivariate correlated time-to-event data.
• To develop a robust statistical framework for analyzing complex clinical trial data structures.
• To enhance predictor selection and parameter estimation in JMLSs with correlated survival outcomes.

Main Methods:

• Transformation of nonparametric marginal survival hazard functions into bivariate normal random variables.
• Utilizing Bayesian penalized splines for approximating unknown baseline hazard functions.
• Employing a Bayesian adaptive Lasso method, integrating Metropolis-Hastings within a Gibbs sampler, for simultaneous estimation, hazard function approximation, and predictor selection.

Main Results:

• The proposed JMLS effectively handles multivariate longitudinal and bivariate correlated time-to-event data.
• The Bayesian adaptive Lasso method demonstrates simultaneous parameter estimation, baseline hazard function estimation, and important predictor selection.
• Methodology validated through simulation studies and a real-world example from the International Breast Cancer Study Group.

Conclusions:

• The novel JMLS provides a powerful tool for analyzing complex longitudinal and correlated survival data in clinical trials.
• The developed Bayesian adaptive Lasso method offers a comprehensive approach for estimation and variable selection.
• This methodology advances the analysis of clinical trial data, particularly when dealing with correlated survival outcomes.