Bayesian inference in a piecewise Weibull proportional hazards model with unknown change points

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Parametric survival models offer programming ease but limited flexibility for real-world data.
• Non-parametric models are flexible but can be complex to implement.
• Existing methods lack accuracy in determining change points for flexible parametric models.

Purpose of the Study:

• To develop a flexible parametric survival model by incorporating piecewise baseline hazard functions.
• To address the challenge of identifying the optimal number and location of change points in survival models.
• To enhance the adaptability of parametric models to diverse field data.

Main Methods:

• Developed a Weibull survival model with a piecewise baseline hazard function, treating change points as unknown parameters.
• Employed a Bayesian approach, specifically a Weibull log-normal animal frailty model.
• Utilized Metropolis-Hastings and Gibbs sampling for parameter estimation and model fitting.

Main Results:

• The developed methodology accurately estimated true parameter values in simulated datasets.
• The piecewise baseline hazard function effectively fitted survival data, comparable to smooth distributions.
• The model successfully identified appropriate fits using a reduced number of change points.

Conclusions:

• The proposed Bayesian piecewise Weibull model significantly enhances the flexibility of parametric survival analysis.
• This approach provides accurate estimation of change points, improving model performance on field data.
• The method offers a robust alternative for survival data analysis where standard parametric models fall short.