Generalized frailty models for analysis of recurrent events

In this paper, we propose an extension of the frailty modeling to analyze the recurrent events data. We proposed a class of models, based on nonlinear mixed effects modeling, that takes into consideration of the between subject heterogeneity in the model. We propose an estimation method for estimating parameters of the proposed model and their standard deviations. The estimating equations are shown to give consistent estimates under commonly satisfied regularity conditions. A method for consistently estimating the covariance matrix of between subject random effects is also given. We prove the consistency and asymptotical normality of the estimators. We apply the proposed generalized frailty model to the Mammary Tumor data of 48 rats that was previously analyzed by Gail et al. (1980) and Cook and Lawless (2007). We compare the result of the our proposed model with results from the commonly used fixed effect model and frailty model. Both fixed effects model and frailty models result in biased estimates of the variance function for cumulative number of tumors. Simulation results suggest that the proposed generalized frailty model and estimation method is computationally feasible and provides unbiased estimates of the parameters and standard errors of their estimators.