İki değişkenli yaşam verilerinin kopulaya dayalı modellemesi ve analizi

Modelling dependence structure of a bivariate survival data is one of the main issues in biomedical studies. Copulas are key tools to analyze the dependence structures. A bivariate survival function can be expressed as the composition of marginal survival functions and a bivariate copula. Since a survival copula is a great deal of flexibility in modelling bivariate survival data, it provides an effective approach for understanding and modelling the dependent random variables and so the dependence structure. Survival copula deals with a lifetime data and is used for modelling and understanding the distributional structure. In survival studies, the researcher can come across censored survival data. In this study, we consider modelling and analyzing the bivariate survival data in the presence of right censoring using Archimedean copula functions. We use Emura et al. (2010) goodness-of-fit testing procedure for the model selection. Throughout the model selection procedure, we obtain the goodness-of-fit statistics for Gumbel, Frank and Clayton copula models. First, we examine the heart transplant data and model the dependence structure between waiting time for transplant and post-transplant survival time to see the co-movements of these variables. Second, we examine the diabetic retinopathy data and model the dependence between the survival times of the two eyes of the same patient in case of laser photocoagulation treatment. Finally, we use the survival hazard scenario approach to evaluate the probability of exceeding some critical layers. We develop R code to implement the study.