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Recurrent events data are rising in all areas of biomedical research. We present a model for recurrent events data with the same link for the intensity and mean functions. Simple interpretations of the covariate effects on both the intensity and mean functions lead to a better understanding of the covariate effects on the recurrent events process. We use partial likelihood and empirical Bayes methods for inference and provide theoretical justifications and as well as relationships between these methods. We also show the asymptotic properties of the empirical Bayes estimators. We illustrate the computational convenience and implementation of our methods with the analysis of a heart transplant study. We also propose an additive regression model and associated empirical Bayes method for the risk of a new event given the history of the recurrent events. Both the cumulative mean and rate functions have closed form expressions for our model. Our inference method for the simiparametric model is based on maximizing a finite dimensional integrated likelihood obtained by integrating over the nonparametric cumulative baseline hazard function. Our method can accommodate time-varying covariates and is easier to implement computationally instead of iterative algorithm based full Bayes methods. The asymptotic properties of our estimates give the large-sample justifications from a frequentist stand point. We apply our method on a study of heart transplant patients to illustrate the computational convenience and other advantages of our method.
Additive Intensity Model, Cumulative Mean Function, Intensity Function, Empirical Bayes Methods, Recurrent Events Data
Date of Defense
March 25, 2011.
A Thesis submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Debajyoti Sinha, Professor Directing Thesis; Isaac W. Eberstein, University Representative; Dan McGee, Committee Member; Xufeng Niu, Committee Member.
Florida State University
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