Flexible parametric joint modelling of longitudinal and survival data

Area of Science:

• Biostatistics
• Survival Analysis
• Longitudinal Data Analysis

Background:

• Joint modeling of longitudinal and survival data is crucial in biostatistics.
• Standard parametric models for survival submodels can lack flexibility.
• Linear mixed-effects models are common for longitudinal biomarker submodels.

Purpose of the Study:

• To propose a flexible parametric approach for the survival submodel in joint modeling.
• To overcome limitations of standard parametric survival models.
• To provide computational benefits and improve model stability.

Main Methods:

• Utilized restricted cubic splines to model the log baseline cumulative hazard.
• Employed an analytically tractable form for the cumulative hazard, avoiding complex numerical integration.
• Conducted extensive simulations to compare the proposed model with B-spline formulations.
• Evaluated non-adaptive versus fully adaptive quadrature for joint likelihood computation.

Main Results:

• The proposed flexible parametric model demonstrated greater flexibility and improved stability.
• Parameter estimates showed insensitivity to baseline cumulative hazard function specification.
• Adaptive quadrature proved superior for evaluating the joint likelihood.
• The model was illustrated using liver cirrhosis patient data, showing advantages over B-spline approaches.

Conclusions:

• The flexible parametric joint model offers significant advantages in terms of flexibility, stability, and computational efficiency.
• The approach provides a robust alternative for analyzing longitudinal and survival data.
• User-friendly Stata software is available for implementing the proposed methods.