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Estimation of covariate effects in generalized linear mixed models with informative cluster sizes

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  • John M. Neuhaus
  • Charles E. McCulloch

Abstract

In standard regression analyses of clustered data, one typically assumes that the expected value of the response is independent of cluster size. However, this is often false. For example, in studies of surgical interventions, investigators have frequently found surgery volume and outcomes to be related to the skill level of the surgeons. This paper examines the effect of ignoring response-dependent, informative, cluster sizes on standard analytical methods such as mixed-effects models and conditional likelihood methods using analytic calculations, simulation studies and an example from a study of periodontal disease. We consider the case in which cluster sizes and responses share random effects which we assume to be independent of the covariates. Our focus is on maximum likelihood methods that ignore informative cluster sizes, and we show that they exhibit little bias in estimating covariate effects that are uncorrelated with the random effects associated with cluster sizes. However, estimation of covariate effects that are associated with the random effects can be biased. In particular, for models with random intercepts only, ignoring informative cluster sizes can yield biased estimators of the intercept but little bias in estimation of all covariate effects. Copyright 2011, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:1:p:147-162
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    File URL: http://hdl.handle.net/10.1093/biomet/asq066
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    Cited by:

    1. Chun Yin Lee & Kin Yau Wong & Kwok Fai Lam & Dipankar Bandyopadhyay, 2023. "A semiparametric joint model for cluster size and subunit‐specific interval‐censored outcomes," Biometrics, The International Biometric Society, vol. 79(3), pages 2010-2022, September.
    2. Charles E. McCulloch & John M. Neuhaus & Rebecca L. Olin, 2016. "Biased and unbiased estimation in longitudinal studies with informative visit processes," Biometrics, The International Biometric Society, vol. 72(4), pages 1315-1324, December.
    3. Glen McGee & Marianthi‐Anna Kioumourtzoglou & Marc G. Weisskopf & Sebastien Haneuse & Brent A. Coull, 2020. "On the interplay between exposure misclassification and informative cluster size," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1209-1226, November.
    4. Anders Skrondal & Sophia Rabe-Hesketh, 2022. "The Role of Conditional Likelihoods in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 799-834, September.
    5. 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.
    6. Shaun R. Seaman & Menelaos Pavlou & Andrew J. Copas, 2014. "Methods for observed-cluster inference when cluster size is informative: A review and clarifications," Biometrics, The International Biometric Society, vol. 70(2), pages 449-456, June.
    7. Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2021. "Random Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models," International Statistical Review, International Statistical Institute, vol. 89(1), pages 186-206, April.

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