Mixed Effects Modeling of Recurrent Events: A Generalized Frailty Model Approach
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In this dissertation, I propose an extension of frailty modeling to analysis recurrent events data. A class of models based on nonlinear mixed effects modeling is proposed that takes into consideration additional sources of between subject heterogeneity in the model. The model specification is an alternative to the hierarchical nonlinear random coefficient model specification of Lindstrom and Bates (1990) that includes, as a special case, the pseudo nonlinear mixed effects model approximation of Sheiner and Beal (1980). Iteratively re-weighted nonlinear estimated generalized least square (EGLS) estimation of the mixed model fixed effects is proposed. The estimating equations are shown to gives consistent estimates of parameters and their variances under commonly satisfied regularity conditions. A method for consistently estimating the covariance matrix of between subject random effects is given. Then the consistency and asymptotically normality of the EGLS fixed effects estimators is proven. The proposed mixed effect model is applied 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 fully random coefficient mixed model with results from the application of the commonly used the frailty model (i.e., a random intercept model). The results show that the estimated mean function of either model fits well but the frailty model results in biased estimates of the variance function while the fully mixed model fit the variance function well. Simulation results suggest that the proposed nonlinear mixed effect model and estimation method is computationally feasible and that the pseudo nonlinear mixed effects model approximation provides unbiased estimates of the parameters and standard errors of their estimators.