Copula-based Cox Regression to Modelling Bivariate Time-to-Event Data

For assessing interventions in numerous disease areas, use of multiple time-to-event outcomes are common. In several natural phenomena in real world, an individual might experience two different events referred as bivariate time-to-event data, where the event are correlated. This association is due to both come from the same subject and are influenced by identical or similar individual characteristics. In medical studies, especially clinical trials regarding bilateral or chronic diseases the cases of bivariate time-to-event analyze by applying copula-based bivariate survival model, this study aims to get the information of the difference between survival bivariat model using the Clayton and Frank copula by using marginal model Cox proportional hazard to describe dependence structure of two events and also the covariates effect. We implemented these approaches to model blindness case on diabetic retinopathy patients considering the left and right eyes survival time until blindness as bivariate event times. By evaluating the AIC and BIC values, we concluded that Frank copula model is the best model to specify the study case. Predicted Kendall's τ = 0, 73 indicated that blindness in right and left eye has dependence by 73% and Xenon laser has significant effect to blindness.