Resumen de Recent advances in copula-based methods for dependent censoring

Gilles Crommen, Negera Wakgari Deresa, Myrthe D'Haen, Jie Ding, Ilias Willems, Ingrid Van Keilegom

• When modeling time-to-event data that are subject to right censoring, it is commonly as- sumed that the survival time T and the censoring time C are independent. However, this assumption frequently fails in practice, leading to biased estimators and testing proce- dures having invalid type 1 error rates. To overcome this issue, several models relaxing the independent censoring assumption have been proposed in the literature. Among these, copula-based approaches have become popular due to their ability to separately model the marginal distributions of T and C and their dependence structure. This review paper gives a comprehensive overview of recent advances in copula-based methods for dependent censoring, along with a discussion of the most important historical papers on this topic. As it is well known that the distribution of (T,C) (and hence of T ) is not identifed in a fully nonparametric way, we examine different strategies to achieve model identifability. These strategies consist of imposing assumptions on either the copula or the marginal distributions of T and C. Both of these approaches will be discussed, with and without covariates. We also consider the case where a dependent censoring time is accompanied by an additional latent independent censoring time. Lastly, we briefy explain alternative approaches that are not based on copulas.