A new cure rate regression framework for bivariate data based on the Chen distribution

The present study introduces a new multivariate mixture cure rate model based on the Chen probability distribution to model recurrent event data in the presence of cure fraction. In this context, we provide an alternative for the use of some usual modeling approaches as the semiparametric Cox proportional hazards model commonly used in lifetime data analysis, considering a new bivariate parametric model to be used in the data analysis of bivariate lifetime data assuming a mixture structure for the bivariate data in presence of covariates, censored data and cure fraction. Under a Bayesian setting, the proposed methodology was considered to analyze two real medical datasets from a retrospective cohort study related to leukemia and diabetic retinopathy diseases. The model validation process was addressed by using the Cox-Snell residuals, which allowed us to identify the suitability of the new proposed mixture cure rate model.