Author

Lu Wang

Date of Award

Summer 2020

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Lianming Wang

Abstract

Both censored survival data and panel count data arise commonly in real-life studies in many fields such as epidemiology, social science, and medical research. In these studies, subjects are usually examined multiple times at periodical or irregular follow-up examinations. Censored data are studied when the exact failure times of the events are of interest but not all of these exact times are directly observed. Some of the failure times of event of interest are only known to fall within some intervals formed by the observation times. Panel count data are under investigation when the exact times of the recurrent events are not of interest but the counts of the recurrent events of interest occurring within the time intervals are available and of interest. This dissertation devotes to discussing three semiparametric regression models that can be used to analyze censored survival data and panel count data.

Chapter 1 of this dissertation proposes an estimation approach for regression analysis of arbitrarily censored survival data under the proportional odds model. Arbitrarily censored data contains a mixture of exactly observed, left-censored, intervalcensored, and right-censored observations. Existing research work on regression analysis on arbitrarily censored data is sparse and limited to the proportional hazards model only. In this chapter, a novel estimation approach based on an EM algorithm is proposed for analyzing arbitrarily censored data under the proportional odds model. The proposed EM algorithm is robust to initial values, easy to implement, converging fast, and providing the variance estimate of the regression parameter estimate in closed form. This method has shown excellent performance in estimating the regression parameters as well as the baseline survival function in an extensive simulation study. Several real-life data applications are provided for illustration purpose.

In Chapter 2, a novel Bayesian approach is proposed to analyze panel count data. The widely used gamma frailty Poisson process model has been shown to have good estimation performance and some robustness against misspecification of the frailty distribution but may still produce biased estimation in some cases when the gamma frailty assumption is violated. In this chapter, we tackle the problem by modeling the frailty distribution nonparametrically by adopting a Dirichlet Process Gamma Mixture (DPGM) prior for the frailty distribution. An easy-to-implement Gibbs sampler is developed to facilitate the Bayesian computation. The proposed Bayesian approach has an excellent performance in estimating the regression parameters and the baseline mean function in our simulation. It outperforms the gamma frailty Poisson model when the gamma frailty distribution is misspecified. The proposed method is applied to the famous bladder cancer data for illustration and comparison with existing methods.

In Chapter 3, a novel unified Bayesian approach is developed for analyzing panel count data under the Gamma frailty Poisson process mode and interval-censored data under Cox’s proportional hazards model and the proportional odds model. The baseline functions in these models share the same property of being nondecreasing positive functions and are modeled nonparametrically by assigning a Gamma process prior. Efficient and easy-to-implement Gibbs samplers are developed for the posterior computation under these three models for the two types of data. The proposed methods are evaluated in extensive simulation studies and illustrated by real-life data applications.

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