A flexible bivariate cure model with shared random effect and associated inference and application to diabetic retinopathy data

In lifetime studies, a proportion of subjects may never experience the event of interest, giving rise to the notion of cure rate. While traditional cure models address this in univariate set-up, many applications involve paired lifetimes, such as twin survival studies, paired organs, or dependent components in a system. In such cases, both the possibility of cure in one or both marginals and the dependence between lifetimes need to be modeled simultaneously, motivating bivariate cure models. We propose here a flexible framework for analyzing bivariate cure data by combining parametric modeling of each marginal survival distribution with a shared frailty term for capturing dependence. The shared frailty is assumed to follow a generalized gamma distribution, providing substantial flexibility in representing diverse dependence structures induced by unobserved frailty. This formulation accommodates cured individuals in one or both marginals and captures the joint survival dynamics of susceptible pairs. Likelihood-based inference for the proposed model is then developed, with estimation carried out using the expectation-maximization algorithm. The performance of the model and the associated inferential method are then evaluated through extensive simulation studies, demonstrating the efficiency and accuracy in estimating model parameters. A real data application, concerning diabetic retinopathy, further illustrates how the model provides insights into cure dynamics and associations that will not be evident in univariate analyses. The proposed bivariate cure model offers a comprehensive statistical tool for jointly studying cure fractions and survival dependence in paired lifetime settings, broadening the applicability of cure rate methodology in biomedical research.