In this study, we will examine the Bayesian Dynamic Survival Models, time-varying coefficients models from a Bayesian perspective, and their applications in the aging setting. The specific questions we are interested in are: Do the relative importance of characteristics measured at a particular age, such as blood pressure, smoking, and body weight, with respect to heart diseases or death change as people age? If they do, how can we model the change? And, how does the change affect the analysis results if fixed-effect models are applied? In the epidemiological and statistical literature, the relationship between a risk factor and the risk of an event is often described in terms of the numerical contribution of the risk factor to the total risk within a follow-up period, using methods such as contingency tables and logistic regression models. With the development of survival analysis, another method named the Proportional Hazards Model becomes more popular. This model describes the relationship between a covariate and risk within a follow-up period as a process, under the assumption that the hazard ratio of the covariate is fixed during the follow-up period. Neither previous methods nor the Proportional Hazards Model allows the effect of a covariates to change flexibly with time. In these study, we intend to investigate some classic epidemiological relationships using appropriate methods that allow coefficients to change with time, and compare our results with those found in the literature. After describing what has been done in previous work based on multiple logistic regression or discriminant function analysis, we summarize different methods for estimating the time varying coefficient survival models that are developed specifically for the situations under which the proportional hazards assumption is violated. We will focus on the Bayesian Dynamic Survival Model because its flexibility and Bayesian structure fits our study goals. There are two estimation methods for the Bayesian Dynamic Survival Models, the Linear Bayesian Estimation (LBE) method and the Markov Chain Monte Carlo (MCMC) sampling method. The LBE method is simpler, faster, and more flexible to calculate, but it requires specifications of some parameters that usually are unknown. The MCMC method gets around the difficulty of specifying parameters, but is much more computationally intensive. We will use a simulation study to investigate the performances of these two methods, and provide suggestions on how to use them effectively in application. The Bayesian Dynamic Survival Model is applied to the Framingham Heart Study to investigate the time-varying effects of covariates such as gender, age, smoking, and SBP (Systolic Blood Pressure) with respect to death. We also examined the changing relationship between BMI (Body Mass Index) and all-cause mortality, and suggested that some of the heterogeneity observed in the results found in the literature is likely to be a consequence of using fixed effect models to describe a time-varying relationship. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester, 2007. / May 7, 2005. / Bayesian Analysis, Time-Varying Coefficient Model, Survival Analysis / Includes bibliographical references. / Daniel L. McGee, Professor Co-Directing Dissertation; Xufeng Niu, Professor Co-Directing Dissertation; Suzanne B. Johnson, Outside Committee Member; Fred W. Huﬀer, Committee Member.
|Contributors||He, Jianghua (authoraut), McGee, Daniel L. (professor co-directing dissertation), Niu, Xufeng (professor co-directing dissertation), Johnson, Suzanne B. (outside committee member), Huﬀer, Fred W. (committee member), Department of Statistics (degree granting department), Florida State University (degree granting institution)|
|Publisher||Florida State University, Florida State University|
|Source Sets||Florida State University|
|Format||1 online resource, computer, application/pdf|
|Rights||This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them.|
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