Shrinkage Empirical Likelihood Estimator in Longitudinal Analysis with Time-Dependent Covariates: Application to Modeling the Health of Filipino Children

• Activity Number: 347
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Dylan Small* and Denis Heng-Yan Leung and Min Zhu and Jing Qin
• Companies: University of Pennsylvania and Singapore Management University and Queensland University of Technology and National Institute of Allergy and Infectious Diseases
• Keywords: empirical likelihood ; longitudinal data ; time-dependent covariates

Abstract

The method of generalized estimating equations (GEE) is a popular tool for analyzing longitudinal (panel) data. Often, the covariates collected are time-dependent in nature. When using GEE to analyze longitudinal data with time-dependent covariates, crucial assumptions about the covariates are necessary for valid inferences to be drawn. When those assumptions do not hold or cannot be verified, Pepe and Anderson (1994) advocated using an independence working correlation assumption in the GEE model as a robust approach. However, using GEE with the independence correlation assumption may lead to significant efficiency loss (Fitzmaurice, 1995). In this paper, we propose an empirical likelihood method that extracts additional information from the estimating equations that are excluded by the independence assumption. The method always includes the estimating equations under the independence assumption and the contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries. We apply the method to a longitudinal study of the health of a group of Filipino children.