Bayesian Semiparametric Methods for Analyzing Panel Count Data

Panel count data commonly arise in epidemiological, social science, medical studies, in which subjects have repeated measurements on the recurrent events of interest at different observation times. Since the subjects are not under continuous monitoring, the exact times of those recurrent events are not observed but the counts of such events within the adjacent observation times are known. Panel count data can be considered as a special type of longitudinal data with a count response variable in the literature. Compared to the frequentist literature, very limited Bayesian approaches have been developed to analyze panel count data. In this dissertation, several Bayesian estimation approaches are proposed for analyzing panel count data under different semiparametric regression models. Chapter 1 of this dissertation provides some description of panel count data, literature review on existing methods, and background knowledge of related tools used in the proposed methods. Chapter 2 proposes a Bayesian estimation approach under the Poisson proportional mean model, in which we model the baseline mean function with the monotone splines of Ramsay (1988) [1]. An efficient Gibbs sampler is proposed, all parameters can be either sampled directly from their full conditional distributions in standard forms or updated through automatic adaptive rejection sampling. Our proposed method is evaluated through extensive simulations and compared with two exiting methods. Our method is applied to a bladder cancer data set for illustration. Chapter 3 proposes a new Bayesian estimation approach for analyzing panel count data when there is heterogeneity in the population (that cannot be described by the available covariates). A frailty Poisson proportional mean model is proposed with the unobserved gamma frailties representing the heterogeneity among the subjects. Simulation studies suggest that our method not only has a good performance when such frailty exists but also provides robust estimation when there is no frailty. The bladder cancer tumor data is analyzed for illustration. Chapter 4 investigates the robustness of our proposed Bayesian approaches in Chapter 2 and Chapter 3 through simulations. We draw the conclusion that our proposed Bayesian methods still have a good performance in most cases when the assumptions are invalid