A bivariate cure copula model with zero-inflated gamma frailty: dependence in both cure fractions and survival times

2026-04-25

AI Summary

Existing methods struggle to simultaneously model the cure fraction and complex dependence structures in paired survival data. This work proposes a bivariate cure frailty-copula model that incorporates a zero-inflated gamma frailty term to jointly capture the cure proportion and continuous heterogeneity among uncured individuals. Dependence between cure status and survival time is modeled through a unified framework combining an odds-ratio parameter with a copula function. The proposed approach is the first to address both types of dependence within a single model, subsuming existing bivariate cure models as special cases, and yields a population-level corrected rank correlation coefficient. Under certain specifications, the joint survival function admits a closed-form expression, enabling maximum likelihood estimation and likelihood ratio testing. Simulations and real-data analyses demonstrate the method’s effectiveness, and an accompanying open-source R package, curecopula, has been released.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Cooperative Game Theory

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In biomedical studies, paired survival data arise naturally when two event times are observed within the same subject. Existing statistical models seldom accommodate both cure fractions and complex dependence structures. In this paper, we propose a novel bivariate cure frailty-copula model for paired survival data with a cure fraction. By incorporating a zero-inflated gamma frailty, the proposed framework simultaneously accommodates a cure fraction and continuous unobserved heterogeneity among uncured subjects. Dependence between cure statuses is modeled naturally via an odds-ratio parameter, while dependence between survival times conditional on frailty is captured through a copula. We show that the proposed model includes existing bivariate cure models as special cases. Population-level rank correlation coefficients are derived for the proposed model, namely tie-corrected versions of Kendall's tau and Spearman's rho. For suitable choices of marginal distributions and copula, the joint survival function admits a closed-form expression, enabling maximum likelihood estimation and likelihood ratio testing. Simulation studies and a real data application demonstrate the practical utility of the proposed approach. An R package, curecopula, implementing the proposed methods is publicly available on GitHub.

Problem

• bivariate cure model
• paired survival data
• cure fraction
• dependence structure
• frailty-copula

Innovation

• bivariate cure model
• zero-inflated gamma frailty
• copula
• paired survival data
• cure fraction