Type of Document Master's Thesis Author Jian, Wen Author's Email Address wjian1@student.gsu.edu URN etd-04272006-083906 Title Analysis of Longitudinal Data in the Case-Control Studies via Empirical Likelihood Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Yichuan Zhao Committee Chair Jun Han Committee Member Pulak Ghosh Committee Member Yu-Sheng Hsu Committee Member Keywords
- confidence region; GEE; logistic regression; empir
Date of Defense 2006-03-31 Availability restricted Abstract The case-control studies are primary tools for the study of risk factors (exposures) related to the disease interested. The case-control studies using longitudinal data are cost and time efficient when the disease is rare and assessing the exposure level of risk factors is difficult. Instead of GEE method, the method of using a prospective logistic model for analyzing case-control longitudinal data was proposed and the semiparametric inference procedure was explored by Park and Kim (2004). In this thesis, we apply an empirical likelihood ratio method to derive limiting distribution of the empirical likelihood ratio and find one likelihood-ratio based confidence region for the unknown regression parameters. Our approach does not require estimating the covariance matrices of the parameters. Moreover, the proposed confidence region is adapted to the data set and not necessarily symmetric. Thus, it reflects the nature of the underlying data and hence gives a more representative way to make inferences about the parameter of interest. We compare empirical likelihood method with normal approximation based method, simulation results show that the proposed empirical likelihood ratio method performs well in terms of coverage probability.
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