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

TL;DR

This paper introduces a new bivariate cure model with zero-inflated gamma frailty for paired survival data, capturing dependence in cure fractions and survival times, with practical estimation and an available R package.

Contribution

It develops a novel statistical framework that models complex dependence structures in paired survival data with cure fractions, including a new copula-based approach and an R package.

Findings

Model includes existing cure models as special cases.

Closed-form joint survival function enables maximum likelihood estimation.

Simulation and real data demonstrate the model's practical utility.

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.