Bayesian Inference for Bivariate Weibull Distributions Derived from Copulas Under Cure Fraction and Censoring

Abstract

This paper introduces bivariate Weibull distributions derived from copula functions to model survival data, incorporating cure fraction, censored observations, and covariates. The study explores two copula functions: the FGM (Farlie-Gumbel-Morgenstern) copula and the Gumbel copula. These copulas are used to describe the dependence structure between two survival times while accounting for the cure fraction, a scenario where a certain proportion of subjects are assumed to be immune or never experience the event of interest. The analysis also addresses the presence of censored data, which occurs when the event of interest is not observed for some subjects within the study period. To estimate the model parameters, we adopt a Bayesian inference approach using standard Markov Chain Monte Carlo (MCMC) methods. The proposed methodology is applied to a medical dataset, illustrating its practical applicability in real-world scenarios. The results highlight the advantages of using copula-based bivariate Weibull models for survival data analysis, especially when dealing with complex data structures, including censoring and cure fractions. This approach provides a robust framework for modelling dependencies between survival times and offers a comprehensive method for parameter estimation under Bayesian inference. The findings suggest that the incorporation of copula functions into the bivariate Weibull model enhances its flexibility and ability to capture the inherent dependence between survival times in various medical and reliability studies.