Bayesian Bivariate Cure Rate Models Using Copula Functions

Bivariate survival cure rate models extend the understanding of time-to-event data by allowing for a cured fraction of the population and dependence between paired units and make more accurate and informative conclusions. In this paper, we propose a Bayesian bivariate cure rate mode where a correlation coefficient is used for the association between bivariate cure rate fractions and a new generalized Farlie Gumbel Morgenstern (FGM) copula function is applied to model the dependence structure of bivariate survival times. For each marginal survival time, we apply a Weibull distribution, a log normal distribution, and a flexible three-parameter generalized extreme value (GEV) distribution to compare their performance. For the survival model fitting, DIC and LPML are used for model comparison. We perform a goodness-of-fit test for the new copula. Finally, we illustrate the performance of the proposed methods in simulated data and real data via Bayesian paradigm.