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The Intra‐Cluster Correlation Coefficient in Cluster Randomized Trials: A Review of Definitions

Author

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  • Sandra M. Eldridge
  • Obioha C. Ukoumunne
  • John B. Carlin

Abstract

The intra‐cluster correlation coefficient (ICC) of the primary outcome plays a key role in the design and analysis of cluster randomized trials (CRTs), but the precise definition of this parameter is somewhat elusive, especially in the context of non‐normally distributed outcomes. In this paper, we provide a unified treatment of ICC as used in CRTs. We present a general definition of the ICC that may be expressed in different ways depending on the modelling approach used to describe the data, illustrating how this general definition is applied to continuous and dichotomous outcomes. Greater complexity arises for dichotomous outcomes; in particular, the usual definition of the ICC cannot be related directly to the parameters of the logistic‐normal model that is commonly used for dichotomous outcomes. We show how the definition of the ICC is different when covariates are introduced. Finally, we use our framework and definition of the ICC to draw out implications for those interpreting and choosing values of the ICC when planning CRTs. Le coefficient de corrélation intraclasse (CCI) associé au critère de jugement principal joue un rôle majeur lors de la planification et de l'analyse des essais randomisés en clusters, mais la définition précise de ce paramètre reste malgré tout évasive, notamment lorsque les données ne sont pas normalement distribuées. Dans cet article, nous proposons de gérer les CCI utilisés dans le cadre des essais en cluster d'une façon uniforme. Nous présentons une définition générale du CCI qui peut s'exprimer différemment selon le modèle statistique utilisé, notamment lorsqu'il s'agit d'un modèle à corrélation commune ou d'un modèle hiérarchique. Nous montrons comment cette définition générale s'applique aussi bien à des données continues qu'à des données binaires. Le niveau de complexité est plus important lorsqu'il s'agit de données binaires; en particulier, le CCI usuel ne peut être liée directement aux paramètres du modèle de régression logistique classiquement utilisé pour les données binaires. Nous montrons que le CCI se définit différemment lorsque des covariables sont prises en compte. Enfin, nous utilisons la définition générale du CCI que nous proposons pour en tirer des conséquences lorsqu'il s'agit d'interpréter un CCI ou d'en fixer une valeur lors de la planification d'un essai randomisé en cluster.

Suggested Citation

  • Sandra M. Eldridge & Obioha C. Ukoumunne & John B. Carlin, 2009. "The Intra‐Cluster Correlation Coefficient in Cluster Randomized Trials: A Review of Definitions," International Statistical Review, International Statistical Institute, vol. 77(3), pages 378-394, December.
    • Handle: RePEc:bla:istatr:v:77:y:2009:i:3:p:378-394
    DOI: 10.1111/j.1751-5823.2009.00092.x
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    References listed on IDEAS

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    1. Nabendu Pal & Wooi Lim, 2004. "On intra-class correlation coefficient estimation," Statistical Papers, Springer, vol. 45(3), pages 369-392, July.
    2. Martin S. Ridout & Clarice G. B. Demétrio & David Firth, 1999. "Estimating Intraclass Correlation for Binary Data," Biometrics, The International Biometric Society, vol. 55(1), pages 137-148, March.
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    2. Michael P. Leung, 2023. "Design of Cluster-Randomized Trials with Cross-Cluster Interference," Papers 2310.18836, arXiv.org, revised Nov 2023.
    3. Sheng Wu & Weng Kee Wong & Catherine M. Crespi, 2017. "Maximin optimal designs for cluster randomized trials," Biometrics, The International Biometric Society, vol. 73(3), pages 916-926, September.
    4. Simon D French & Joanne E McKenzie & Denise A O'Connor & Jeremy M Grimshaw & Duncan Mortimer & Jill J Francis & Susan Michie & Neil Spike & Peter Schattner & Peter Kent & Rachelle Buchbinder & Matthew, 2013. "Evaluation of a Theory-Informed Implementation Intervention for the Management of Acute Low Back Pain in General Medical Practice: The IMPLEMENT Cluster Randomised Trial," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-15, June.
    5. Anneke Vang Hjort & Mirte A. G. Kuipers & Maria Stage & Charlotta Pisinger & Charlotte Demant Klinker, 2022. "Intervention Activities Associated with the Implementation of a Comprehensive School Tobacco Policy at Danish Vocational Schools: A Repeated Cross-Sectional Study," IJERPH, MDPI, vol. 19(19), pages 1-19, September.
    6. Intarapak Sukanya & Supapakorn Thidaporn, 2019. "An Alternative Matrix Transformation To The F Test Statistic For Clustered Data," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 153-169, March.

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