Date of Award

6-9-2006

Degree Type

Closed Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Yichuan Zhao - Chair

Second Advisor

Yu-Sheng Hsu

Third Advisor

Pulak Ghosh

Fourth Advisor

Jun Han

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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