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Robust Covariance Estimator for Small-Sample Adjustment in the Generalized Estimating Equations: A Simulation Study

Received: 21 January 2014     Published: 20 February 2014
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Abstract

The robust or sandwich estimator is common to estimate the covariance matrix of the estimated regression parameter for generalized estimating equation (GEE) method to analyze longitudinal data. However, the robust estimator would underestimate the variance under a small sample size. We propose an alternative covariance estimator to the robust estimator to improve the small-sample bias in the GEE method. Our proposed estimator is a modification of the bias-corrected covariance estimator proposed by Pan (2001, Biometrika88, 901—906) for the GEE method. In a simulation study, we compared the proposed covariance estimator to the robust estimator and Pan's estimator for continuous and binominallongitudinal responses for involving 10—50 subjects. The test size of Wald-type test statistics for the proposed estimator is relatively close to the nominal level when compared with those for the robust estimator and the Pan's approach.

Published in Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 1)
DOI 10.11648/j.sjams.20140201.13
Page(s) 20-25
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Bias, Binary Response, Continuous Response, Longitudinal Data, Test Size

References
[1] Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linearmodels. Biometrika73:13—22.
[2] Mancl, L. A. and DeRouen, T. A. (2001). A covariance estimator for GEE with improvedsmall-sample properties. Biometrics 57:126—134.
[3] Hardin, J. and Hilbe, J. (2013). Generalized Estimating Equations, 2nd edn. Chapman and Hall, London.
[4] Fay, M. P. and Graubard, B. I. (2001). Small-sample adjustments for Wald-type testsusing sandwich estimators. Biometrics 57:1198—1206.
[5] Pan, W. and Wall, M. M. (2002). Small-sample adjustments in using the sandwich variance estimator in generalized estimating equations. Statistics in Medicine21:1429—1441.
[6] Guo, X., Pan, W., Connett, J., Hannan, P., and French, S.A. (2005). Small-sample performance of the robust score test and its modifications in generalized estimating equations. Statistics in Medicine 24:3479—3495.
[7] Kauermann, G. and Carroll, R. (2001). A note on the efficiency of sandwich covariancematrix estimation. Journal of the American Statistical Association 96:1387—1396.
[8] Pan, W. (2001). On the robust variance estimator in generalisedestimatingequations. Biometrika88:901—906.
[9] Lu, B., Preisser, J. S., Qaqish, B. F., Suchindran, C., Bangdiwala, S. I., andWolfson, M. (2007). A comparison of two bias-corrected covariance estimators for generalizedestimating equations. Biometrics 63:935—941.
[10] MacKinnon, J. and White, H. (1985). Some heteroskedasticity-consistent covariancematrix estimators with improved finite sample properties. Journal of Econometrics 29:305—325.
[11] White, H. (1980). A heteroskedasticity-consistent covariance matrix estimatorand a direct test for heteroskedasticity. Econometrika 48:817—838.
[12] Qaqish, B. F. (2003). A family of multivariate binary distributions for simulatingcorrelated binary variables with specified marginal means and correlations.Biometrika 90:455—463.
Cite This Article
  • APA Style

    Masahiko Gosho, Yasunori Sato, Hisao Takeuchi. (2014). Robust Covariance Estimator for Small-Sample Adjustment in the Generalized Estimating Equations: A Simulation Study. Science Journal of Applied Mathematics and Statistics, 2(1), 20-25. https://doi.org/10.11648/j.sjams.20140201.13

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    ACS Style

    Masahiko Gosho; Yasunori Sato; Hisao Takeuchi. Robust Covariance Estimator for Small-Sample Adjustment in the Generalized Estimating Equations: A Simulation Study. Sci. J. Appl. Math. Stat. 2014, 2(1), 20-25. doi: 10.11648/j.sjams.20140201.13

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    AMA Style

    Masahiko Gosho, Yasunori Sato, Hisao Takeuchi. Robust Covariance Estimator for Small-Sample Adjustment in the Generalized Estimating Equations: A Simulation Study. Sci J Appl Math Stat. 2014;2(1):20-25. doi: 10.11648/j.sjams.20140201.13

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  • @article{10.11648/j.sjams.20140201.13,
      author = {Masahiko Gosho and Yasunori Sato and Hisao Takeuchi},
      title = {Robust Covariance Estimator for Small-Sample Adjustment in the Generalized Estimating Equations: A Simulation Study},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {2},
      number = {1},
      pages = {20-25},
      doi = {10.11648/j.sjams.20140201.13},
      url = {https://doi.org/10.11648/j.sjams.20140201.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140201.13},
      abstract = {The robust or sandwich estimator is common to estimate the covariance matrix of the estimated regression parameter for generalized estimating equation (GEE) method to analyze longitudinal data. However, the robust estimator would underestimate the variance under a small sample size. We propose an alternative covariance estimator to the robust estimator to improve the small-sample bias in the GEE method. Our proposed estimator is a modification of the bias-corrected covariance estimator proposed by Pan (2001, Biometrika88, 901—906) for the GEE method. In a simulation study, we compared the proposed covariance estimator to the robust estimator and Pan's estimator for continuous and binominallongitudinal responses for involving 10—50 subjects. The test size of Wald-type test statistics for the proposed estimator is relatively close to the nominal level when compared with those for the robust estimator and the Pan's approach.},
     year = {2014}
    }
    

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    AU  - Masahiko Gosho
    AU  - Yasunori Sato
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    AB  - The robust or sandwich estimator is common to estimate the covariance matrix of the estimated regression parameter for generalized estimating equation (GEE) method to analyze longitudinal data. However, the robust estimator would underestimate the variance under a small sample size. We propose an alternative covariance estimator to the robust estimator to improve the small-sample bias in the GEE method. Our proposed estimator is a modification of the bias-corrected covariance estimator proposed by Pan (2001, Biometrika88, 901—906) for the GEE method. In a simulation study, we compared the proposed covariance estimator to the robust estimator and Pan's estimator for continuous and binominallongitudinal responses for involving 10—50 subjects. The test size of Wald-type test statistics for the proposed estimator is relatively close to the nominal level when compared with those for the robust estimator and the Pan's approach.
    VL  - 2
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Author Information
  • Advanced Medical Research Center, Aichi Medical University, Aichi, Japan

  • Clinical Research Center, Chiba University Hospital, Chiba, Japan

  • Clinical Development Center, Asahikasei Pharma Corporation, Tokyo, Japan

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