Bayesian bivariate generalized Lindley model for survival data with a cure fraction

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Cure fraction models are essential for survival data where some individuals are immune to the event.
• Analyzing correlated survival times requires advanced statistical approaches.

Purpose of the Study:

• To propose a novel bivariate survival model incorporating a cure fraction.
• To utilize the three-parameter generalized Lindley distribution and copula functions for modeling joint survival times.
• To apply the developed model to real-world invasive cervical cancer data.

Main Methods:

• Development of a bivariate survival model based on the generalized Lindley distribution.
• Integration of Farlie-Gumbel-Morgenstern (FGM), Clayton, and Gumbel-Barnett copulas to model the joint distribution of survival times.
• Implementation within a Bayesian framework using Markov Chain Monte Carlo (MCMC) for parameter estimation.

Main Results:

• The proposed bivariate cure fraction model provides a flexible framework for analyzing dependent survival data.
• Successful application of the model to invasive cervical cancer data demonstrates its practical utility.
• The Bayesian approach with MCMC enables robust parameter estimation for the complex model.

Conclusions:

• The bivariate generalized Lindley distribution with copulas offers a powerful tool for survival analysis with cure fractions.
• This methodology enhances the understanding of survival data in medical research, particularly for diseases with a potentially cured segment of the population.
• The study validates the model's effectiveness through a real-world application in oncology.