Joint Frailty Mixture Cure Model for Recurrent Event Data With Dependent Censoring: An MCEM Approach

Advancements in modern medical technology have enabled cures for a fraction of patients while extending survival times for those who are not cured. For non-cured patients, disease recurrence is influenced by observed covariates and unobserved individual heterogeneity (random effects). In biomedical studies, dependent censoring is frequently encountered, for example, in cancer patients, where right censoring can be caused by death from unrelated diseases or due to an (unobservable) cure status. This study introduces a joint frailty model for recurrent event data with a cure fraction, effectively capturing heterogeneity and inducing dependent censoring. The proposed multivariate joint frailty mixture cure models incorporate covariates and frailties, together with the event incidence time and latent cure status. The model accounts for the probability of a cure after each recurrence using both the complementary log-log and the logistic link function. A likelihood-based estimation method is developed using the Monte Carlo Expectation-Maximization (MCEM) algorithm. Through Monte Carlo simulation, we examine the finite sample properties of the MCEM estimators, supplemented by a real-world application using secondary data on hospital readmissions for colorectal cancer recurrence post-surgery. Simulation results suggest lifetime and frailty parameter estimates are unbiased and consistent. Compared to models with identical frailty structure, both the complementary log-log and the logistic cure frailty models with dependent frailties demonstrate a better fit with the real data, as evidenced by lower Akaike information criteria values.