| In this study, we will examine the time-varying coefficients models and their applications in the aging setting, the area in which fixed-coefficient models are commonly used. 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 inference with fixed-effect models.; In the epidemiological and statistical literature, the relationship between risk factors and the risk of an event is usually analyzed in terms of the cumulative risk within a follow-up period, methods include logistic regression models, relative risks and odds ratios from contingency tables. With the development of survival analysis, another commonly used method is the proportional hazards model. This model assumes that the hazard ratio of any covariate is fixed during the follow-up time, which is not satisfied in many real situations. We will investigate some classic epidemiological relationships, such as blood pressure and death, body weight and death, in a more flexible way, which describes the relationship between a baseline covariate and the risk of events as a changing process over time.; 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 method and the Markov Chain Monte Carlo (MCMC) sampling method. The linear Bayesian method is simpler, faster, and more flexible to calculate, but it requires specifications of some parameters. The MCMC method gets around the difficulty of specifying hyperparameters, but is much more computationally intensive. We will use a simulation study to investigate the performances of these two methods, and proposal methods on how to use them in better ways.; The Bayesian Dynamic Survival Model is applied to the Framingham Heart Study, investigating 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 concluded 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. |
