An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model

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 develop a new estimation method for the semiparametric accelerated failure time gamma frailty model based on the EM-like algorithm and the rank-like estimation method. The proposed method is compared with the existing EM algorithm, which incorporates the M-estimator in the M-step. From simulation studies, we show that the rank-like estimation method in the M-like step simplifies the estimation procedure and reduces the computational time by the linear programming approach. With respect to the accuracy of estimates and length of computational time, the proposed method outperforms the existing estimation methods. 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.