Analysis of longitudinal data in the case-control studies via empirical likelihood

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 article, 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 vector of regression parameters. 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 and interval width.