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Inference on the marginal distribution of clustered data with informative cluster size

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  • Jaakko Nevalainen
  • Somnath Datta
  • Hannu Oja

Abstract

In spite of recent contributions to the literature, informative cluster size settings are not well known and understood. In this paper, we give a formal definition of the problem and describe it from different viewpoints. Data generating mechanisms, parametric and nonparametric models are considered in light of examples. Our emphasis is on nonparametric and robust approaches to the inference on the marginal distribution. Descriptive statistics and parameters of interest are defined as functionals and they are accompanied with a generally applicable testing procedure. The theory is illustrated with an example on patients with incomplete spinal cord injuries. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Jaakko Nevalainen & Somnath Datta & Hannu Oja, 2014. "Inference on the marginal distribution of clustered data with informative cluster size," Statistical Papers, Springer, vol. 55(1), pages 71-92, February.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:1:p:71-92
    DOI: 10.1007/s00362-013-0504-3
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    References listed on IDEAS

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    1. Ralitza V. Gueorguieva, 2005. "Comments about Joint Modeling of Cluster Size and Binary and Continuous Subunit-Specific Outcomes," Biometrics, The International Biometric Society, vol. 61(3), pages 862-866, September.
    2. Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2007. "A weighted multivariate sign test for cluster-correlated data," Biometrika, Biometrika Trust, vol. 94(2), pages 267-283.
    3. Somnath Datta & Glen A. Satten, 2008. "A Signed-Rank Test for Clustered Data," Biometrics, The International Biometric Society, vol. 64(2), pages 501-507, June.
    4. John M. Williamson & Somnath Datta & Glen A. Satten, 2003. "Marginal Analyses of Clustered Data When Cluster Size Is Informative," Biometrics, The International Biometric Society, vol. 59(1), pages 36-42, March.
    5. Datta, Somnath & Satten, Glen A., 2005. "Rank-Sum Tests for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 908-915, September.
    6. E. Benhin & J. N. K. Rao & A. J. Scott, 2005. "Mean estimating equation approach to analysing cluster-correlated data with nonignorable cluster sizes," Biometrika, Biometrika Trust, vol. 92(2), pages 435-450, June.
    7. John M. Neuhaus & Charles E. McCulloch, 2011. "Estimation of covariate effects in generalized linear mixed models with informative cluster sizes," Biometrika, Biometrika Trust, vol. 98(1), pages 147-162.
    8. David B. Dunson & Zhen Chen & Jean Harry, 2003. "A Bayesian Approach for Joint Modeling of Cluster Size and Subunit-Specific Outcomes," Biometrics, The International Biometric Society, vol. 59(3), pages 521-530, September.
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    Cited by:

    1. Xiaobing Zhao & Xian Zhou, 2020. "Partial sufficient dimension reduction on additive rates model for recurrent event data with high-dimensional covariates," Statistical Papers, Springer, vol. 61(2), pages 523-541, April.
    2. Omer Ozturk & Asuman Turkmen, 2016. "Quantile inference based on clustered data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 867-893, October.
    3. Ling Lan & Dipankar Bandyopadhyay & Somnath Datta, 2017. "Non-parametric regression in clustered multistate current status data with informative cluster size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(1), pages 31-57, January.

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