Generalized gamma frailty model

In this article, we present a frailty model using the generalized gamma distribution as the frailty distribution. It is a power generalization of the popular gamma frailty model. It also includes other frailty models such as the lognormal and Weibull frailty models as special cases. The flexibility of this frailty distribution makes it possible to detect a complex frailty distribution structure which may otherwise be missed. Due to the intractable integrals in the likelihood function and its derivatives, we propose to approximate the integrals either by Monte Carlo simulation or by a quadrature method and then determine the maximum likelihood estimates of the parameters in the model. We explore the properties of the proposed frailty model and the computation method through a simulation study. The study shows that the proposed model can potentially reduce errors in the estimation, and that it provides a viable alternative for correlated data. The merits of proposed model are demonstrated in analysing the effects of sublingual nitroglycerin and oral isosorbide dinitrate on angina pectoris of coronary heart disease patients based on the data set in Danahy et al. (sustained hemodynamic and antianginal effect of high dose oral isosorbide dinitrate. Circulation 1977; 55:381-387).