Estimation of shared Gamma frailty models by a modified EM algorithm

Standard survival models assume independence between survival times and frailty models provide a useful extension of the standard survival models by introducing a random effect (frailty) when the survival data are correlated. Several estimation methods have been proposed to find the parameters of shared frailty models. Among them, the EM algorithm (Survival Analysis—Techniques for Censored and Truncated Data, 1997) and the penalized likelihood method (Penalized Survival Models and Frailty, Technical Report No. 66, Mayo Foundation, 2000) are two popular ones. However, the variance estimates involve the calculation of matrix inverse, so the current methods are not able to handle the data with a large number of clusters. This paper provides a modified EM algorithm for the shared frailty models. The new method utilizes standard statistical procedures to find the maximum likelihood estimates (MLE) and it can handle data sets with large numbers of clusters and distinct event times. The confidence intervals of the parameters can be constructed by multiple imputation. Simulation studies were carried out to compare different approaches for the frailty models.