Generalized Accelerated Failure Time Frailty Model

Survival analysis is a kind of statistical method for survival data. The traditional survival model is based on the independent survival time. But the dependent time is very common in practice. Those classical survival models such as proportion hazard model or accelerated failure time model could not be used to fit the data. So we need develop a new model for this situation. The frailty model is one of the most popular models used to analyze clustered failure time data. And the frailty term in the model is used to assess associations in each cluster. The frailty model based on the semiparametric accelerated failure time model attracts less attention than the one based on the proportional hazards model due to its computational difficulties. In this paper, we first modified the model to make sure our model is more closed to the generalized accelerated failure time model than the others. Under this assumption, we develop two different new estimation methods for the semiparametric accelerated failure time frailty model based on the EM-like algorithm and the ML-EM like estimation method. The first proposed method is compared with the existing EM algorithm, which incorporates the kernel smoothing in the M-step. We extend the frailty distribution to the generalized gamma distribution which makes our method is more flexible. Then we develop a new method based on the ML-EM algorithm. We incorporate the Maximum Likelihood method and the normal EM algorithm in this method. We improve our estimation efficiency through it. For illustration, we apply the proposed method to the data set of sublingual nitroglycerin and oral isosorbide dinitrate on angina pectoris of coronary heart disease patients.