Estimation of the accelerated failure time frailty model under generalized gamma frailty

The frailty model is one of the most popular models used to analyze clustered failure time data, where the frailty term is used to assess an association within 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 relax the frailty distribution to the generalized gamma distribution, which can accommodate most of the popular frailty assumptions. The estimation procedure is based on the EM-like algorithm by employing the MCMC algorithm in the E-step and the profile likelihood estimation method in the M-step. We conduct an extensive simulation study and find that there is a significant gain in the proposed method with respect to the estimation of the frailty variance with a slight loss of accuracy in the parameter estimates. For illustration, we apply the proposed model and method to a data set of sublingual nitroglycerin and oral isosorbide dinitrate on angina pectoris of coronary heart disease patients.