Date of Award

2017

Document Type

Open Access Dissertation

Department

Statistics

Sub-Department

College of Arts and Sciences

First Advisor

Lianming Wang

Abstract

Interval-censored data are a special type of survival data, in which the survival time is not accurately observed but known to fall within a specific time interval. Intervalcensored data commonly arise in real-life epidemiological and medical studies that involve periodic examinations. In this dissertation, several semiparametric regression models are investigated to provide flexible modeling and robust inference for intervalcensored data from Bayesian perspectives.

Chapter 1 provides a detailed description about interval-censored data and gives several examples. Existing models and methods for analyzing such interval-censored data are reviewed as well. Chapter 2 develops a unified Bayesian estimation approach under the framework of semiparametric linear transformation models for regression analysis of current status data, which is a special type of interval-censored data. This work provides an alternative estimation approach to the existing methods for the proportional hazards, proportional odds, and probit models. As a unified Bayesian estimation approach, the proposed method allows direct comparison of three different semiparametric regression models in the same framework of the Gibbs Sampler. Chapter 3 proposes a Bayesian estimation approach for analyzing general intervalcensored data under the generalized odds-rate hazards (GORH) models. The GORH models are a general class of semiparametric regression models including the proportional hazards and proportional odds models as special cases. Submodels of GORH models can be specified by indexing a non-negative value v, where the "sub" prefix refers to the fact that for each v, a semiparametric regression model is well-specified for regression analysis of general interval-censored data. It is found that treating v as an unknown parameter leads to biased estimation, which in this case is a consistent research result for right-censored data in the literature. To solve this issue, a Bayesian approach with a known v is proposed and has shown excellent performance in the simulation study. Chapter 4 extends the semiparametric probit model for regression analysis of arbitrarily censored data. The proposed method has been implemented using two sets of latent variables for posterior computation. The proposed method can be easy to implement in the estimation of regression parameters for two special types of arbitrarily censored data: right-censored data and general interval-censored data.

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