Estimation method of the semiparametric mixture cure gamma frailty model.

Mixture cure frailty model has been proposed to analyze censored survival data with a cured fraction and unobservable information among the uncured patients. Different from a usual mixture cure model, the frailty model is employed to model the latency component in the mixture cure frailty model. In this paper, we extend the mixture cure frailty model by incorporating covariates into both the cure rate and the latency distribution parts of the model and propose a semiparametric estimation method for the model. The Expectation Maximization (EM) algorithm and the multiple imputation method are employed to estimate parameters of interest. In the simulation study, we show that both estimation methods work well. To illustrate, we apply the model and the proposed methods to a data set of failure times from bone marrow transplant patients.