Journal Article

GEE ANALYSIS OF CLUSTERED BINARY DATA WITH DIVERGING NUMBER OF COVARIATES

Wang, Lan

2011

Overview

Clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines. This paper develops an asymptotic theory for generalized estimating equations (GEE) analysis of clustered binary data when the number of covariates grows to infinity with the number of clusters. In this \"large n, diverging p\" framework, we provide appropriate regularity conditions and establish the existence, consistency and asymptotic normality of the GEE estimator. Furthermore, we prove that the sandwich variance formula remains valid. Even when the working correlation matrix is misspecified, the use of the sandwich variance formula leads to an asymptotically valid confidence interval and Wald test for an estimable linear combination of the unknown parameters. The accuracy of the asymptotic approximation is examined via numerical simulations. We also discuss the \"diverging p\" asymptotic theory for general GEE. The results in this paper extend the recent elegant work of Xie and Yang [Ann. Statist. 31 (2003) 310-347] and Balan and Schiopu-Kratina [Ann. Statist. 32 (2005) 522-541] in the \"fixed p\" setting.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: 62F12 / 62J12 / Binary data / Cluster analysis / Clustered binary data / Consistent estimators / Correlations / Covariance matrices / Estimating techniques / Estimators / Exact sciences and technology / General topics / generalized estimating equations (GEE) / high-dimensional covariates / Infinity / Linear equations / Logical proofs / Mathematics / Multivariate analysis / Nonparametric inference / Parametric inference / Probability and statistics / Sample size / sandwich variance formula / Sandwiches / Sciences and techniques of general use / Statistical variance / Statistics / Studies