Type of Document Dissertation Author Zhao, Haiyan Author's Email Address email@example.com URN etd-11102010-005540 Title Time-varying Coefficient Models With ARMA-GARCH Structures For Longitudinal Data Analysis Degree Doctor of Philosophy Department Statistics, Department of Advisory Committee
Advisor Name Title Xufeng Niu Committee Chair Fred Huffer Committee Co-Chair Dan McGee Committee Member Craig Nolder University Representative Keywords
- time-varying coefficient models
- longitudinal data analysis
- time series analysis
Date of Defense 2010-09-28 Availability unrestricted AbstractThe motivation of my research comes from the analysis of the Framingham Heart Study (FHS) data. The FHS is a long term prospective study of cardiovascular disease in the community of Framingham, Massachusetts. The study began in 1948 and 5,209 subjects were initially enrolled. Examinations were given biennially to the study participants and their status associated with the occurrence of disease was recorded. In this dissertation, the event we are interested in is the incidence of the coronary heart disease (CHD). Covariates considered include sex, age, cigarettes per day (CSM), serum cholesterol (SCL), systolic blood pressure (SBP) and body mass index (BMI, weight in kilograms/height in meters squared).
Statistical literature review indicates that effects of the covariates on Cardiovascular disease or death caused by all possible diseases in the Framingham study change over time. For example, the effect of SCL on Cardiovascular disease decreases linearly over time. In this study, I would like to examine the time-varying effects of the risk factors on CHD incidence. Time-varying coefficient models with ARMA-GARCH structure are developed in this research. The maximum likelihood and the marginal likelihood methods are used to estimate the parameters in the proposed models. Since high-dimensional integrals are involved in the calculations of the marginal likelihood, the Laplace approximation is employed in this study. Simulation studies are conducted to evaluate the performance of these two estimation methods based on our proposed models. The Kullback-Leibler (KL) divergence and the root mean square error are employed in the simulation studies to compare the results obtained from different methods. Simulation results show that the marginal likelihood approach gives more accurate parameter estimates, but is more computationally intensive.
Following the simulation study, our proposed models are applied to the Framingham Heart Study to investigate the time-varying effects of covariates with respect to CHD incidence. To specify the time-series structures of the effects of risk factors, the Bayesian Information Criterion (BIC) is used for model selection. Our study shows that the relationship between CHD and risk factors changes over time. For males, there is an obviously decreasing linear trend for age effect, which implies that the age effect on CHD is less significant for elder patients than younger patients. The effect of CSM stays almost the same in the first 30 years and decreases thereafter. There are slightly decreasing linear trends for both effects of SBP and BMI. Furthermore, the coefficients of SBP are mostly positive over time, i.e., patients with higher SBP are more likely developing CHD as expected. For females, there is also an obviously decreasing linear trend for age effect, while the effects of SBP and BMI on CHD are mostly positive and do not change too much over time.
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