Likelihood inference for semiparametric mixture cure generalized-gamma frailty model

The standard survival models for time-to-event data assume that every subject in the study population is susceptible to the event of interest and will eventually experience the event. However, many diseases are curable and a portion of patients will never experience the event of interest. In addition, unobservable effects or correlation among the subjects within the same cluster may exist and careful attention is needed. In this paper, we developed the EM-based likelihood inference for semiparametric mixture cure frailty model with Generalized-Gamma frailty distribution. The proposed model contains most existing mixture cure frailty model as special cases. Since the expectations in the E-step lack closed-form solutions, we employ a Markov chain Monte Carlo (MCMC) method for numerical approximation. The bootstrap method is adopted for variance estimation. We conducted comprehensive simulation study to assess the performance of our proposed model and its associated inference methods. To demonstrate practical applicability, we subsequently applied this model on a real data examining blood purification status and estimated amount effects on acute diquat poisoning cases.