Copula and Its Application in Bivariate Survival Model

Abstract

In survival analysis, there exist various studies and applications that deal with a single event-time. On the other hand, although there are many potential needs to analyze multiple event-times simultaneously, there are not so many applications yet. We discuss copula modelling which is a useful approach to address multiple event-times in survival analysis. Focusing mainly on applications in biostatistics, we describe the main issues behind the copula, the fundamentals of copulas, and the history of their development. We discuss the usefulness of copula as an approach to solving problems in this area, such as addressing dependent censoring under semi-competing risk, in which we propose a new computational method on the estimation of survival function for a non-fatal event. As illustrative examples which deal with two event-times, we provide applications to bivariate Cox regression analysis and study design.