A survival model for lifetime with long-term survivors and unobserved heterogeneity

. In this paper, we develop a new survival model induced by discrete frailty with Katz distribution. The new model encompasses as particular cases the mixture cure rate model and promotion cure rate model and has a proportional hazards structure when the covariates are modeled through mean frailty. Furthermore, we construct a regression model to evaluate the effects of covariates on both the cured fraction and risk of the event of interest. We discuss inference aspects of the proposed model in a classical approach, where an expectation maximization algorithm is developed to determine the maximum likelihood estimates of the models parameters. Finally, the model is fully illustrated with a dataset on cervical cancer.