The Annals of Statistics

GEE analysis of clustered binary data with diverging number of covariates

Lan Wang

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Abstract

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.

Article information

Source
Ann. Statist., Volume 39, Number 1 (2011), 389-417.

Dates
First available in Project Euclid: 3 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.aos/1291388380

Digital Object Identifier
doi:10.1214/10-AOS846

Mathematical Reviews number (MathSciNet)
MR2797851

Zentralblatt MATH identifier
1209.62138

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 62J12: Generalized linear models

Keywords
Clustered binary data generalized estimating equations (GEE) high-dimensional covariates sandwich variance formula

Citation

Wang, Lan. GEE analysis of clustered binary data with diverging number of covariates. Ann. Statist. 39 (2011), no. 1, 389--417. doi:10.1214/10-AOS846. https://projecteuclid.org/euclid.aos/1291388380


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Supplemental materials

  • Supplementary material: Supplement to “GEE analysis of clustered binary data with diverging number of covariates”. The proofs of (3.3), Lemma 3.5, (3.11) and Theorem 5.1 are provided in this supplementary article [Wang (2010)].