Modeling times to multiple events under informative censoring with C-vine copula

2025-02-28

AI Summary

Joint modeling of multivariate non-terminal event times under informative censoring—particularly due to terminal events—remains challenging, as existing methods are restricted to univariate non-terminal events and fail to capture complex dependence structures between non-terminal and terminal events. Method: We propose the first flexible joint model based on C-vine copulas, enabling heterogeneous pairwise dependence modeling and covariate regression for all marginal distributions—thus balancing dependence flexibility with parameter interpretability. Estimation employs a two-stage likelihood approach with analytic variance estimation. Results: Simulation studies demonstrate excellent finite-sample properties. Empirical analysis of crowdfunding platform data uncovers fine-grained dynamic associations between multi-type creator-backer interactions and project lifecycle trajectories, illustrating the model’s capacity to reveal nuanced interdependencies under informative censoring.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Multi-modal Vision
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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. These events involve more complex dependence structures between nonterminal and terminal events and between nonterminal events themselves. This paper introduces a novel modeling framework leveraging the vine copula to directly estimate the joint distribution of the multivariate times to nonterminal and terminal events. Unlike the few existing methods based on multivariate or nested copulas, our model excels in capturing the heterogeneous dependence between each pair of event times in terms of strength and structure. Furthermore, our model allows regression modeling for all the marginal distributions of times to nonterminal and terminal events, a feature lacking in existing methods. We propose a likelihood-based estimation and inference procedure, which can be implemented efficiently in sequential stages. Through simulation studies, we demonstrate the satisfactory finite-sample performance of our proposed stage-wise estimators and analytical variance estimators, as well as their superiority over existing methods. We apply our approach to data from a crowdfunding platform to investigate the relationship between creator-backer interactions of various types and a creator's lifetime on the platform.

Problem

• Analyzing multivariate event times with informative censoring
• Modeling heterogeneous dependence between nonterminal and terminal events
• Developing efficient likelihood-based estimation for multiple event types

Innovation

• Uses vine copula for joint density estimation
• Captures heterogeneous dependence between event times
• Implements likelihood-based sequential estimation