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A Covariance Estimator for GEE with Improved Small‐Sample Properties

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  • Lloyd A. Mancl
  • Timothy A. DeRouen

Abstract

Summary. In this paper, we propose an alternative covariance estimator to the robust covariance estimator of generalized estimating equations (GEE). Hypothesis tests using the robust covariance estimator can have inflated size when the number of independent clusters is small. Resampling methods, such as the jackknife and bootstrap, have been suggested for covariance estimation when the number of clusters is small. A drawback of the resampling methods when the response is binary is that the methods can break down when the number of subjects is small due to zero or near‐zero cell counts caused by resampling. We propose a bias‐corrected covariance estimator that avoids this problem. In a small simulation study, we compare the bias‐corrected covariance estimator to the robust and jackknife covariance estimators for binary responses for situations involving 10–40 subjects with equal and unequal cluster sizes of 16–64 observations. The bias‐corrected covariance estimator gave tests with sizes close to the nominal level even when the number of subjects was 10 and cluster sizes were unequal, whereas the robust and jackknife covariance estimators gave tests with sizes that could be 2–3 times the nominal level. The methods are illustrated using data from a randomized clinical trial on treatment for bone loss in subjects with periodontal disease.

Suggested Citation

  • Lloyd A. Mancl & Timothy A. DeRouen, 2001. "A Covariance Estimator for GEE with Improved Small‐Sample Properties," Biometrics, The International Biometric Society, vol. 57(1), pages 126-134, March.
  • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:126-134
    DOI: 10.1111/j.0006-341X.2001.00126.x
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    1. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    2. Keener, Robert W. & Kmenta, Jan & Weber, Neville C., 1991. "Estimation of the Covariance Matrix of the Least-Squares Regression Coefficients When the Disturbance Covariance Matrix Is of Unknown Form," Econometric Theory, Cambridge University Press, vol. 7(1), pages 22-45, March.
    3. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
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