Analysis of multivariate event times under informative censoring using vine copula

The study of times to nonterminal events of different types and their interrelation is a compelling area of interest. The primary challenge in analyzing such multivariate event times is the presence of informative censoring by the terminal event. While numerous statistical methods have been proposed for a single nonterminal event, i.e., semi-competing risks data, there remains a dearth of tools for analyzing times to multiple nonterminal events. This article introduces a novel analysis framework that leverages the vine copula to directly estimate the joint density of multivariate times to nonterminal and terminal events. Unlike the few existing methods based on multivariate or nested copulas, the developed approach excels in capturing the heterogeneous dependence between each pair of event times (nonterminal-terminal and between-nonterminal) in terms of strength and structure. We propose a likelihood-based estimation and inference procedure, which can be implemented efficiently in sequential stages. Through extensive simulation studies, we demonstrate the satisfactory finite-sample performance of our proposed stage-wise estimators and analytical variance estimators, as well as their advantages over existing methods. We apply the developed approach to data from a crowdfunding platform to investigate the relationship between various types of creator-backer interactions and a creator's lifetime on the platform.