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

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.

[1]  Kosuke Imai,et al.  Survey Sampling , 1998, Nov/Dec 2017.

[2]  D. Ashby,et al.  Sample size for cluster randomized trials: effect of coefficient of variation of cluster size and analysis method. , 2006, International journal of epidemiology.

[3]  Simon G Thompson,et al.  Constructing intervals for the intracluster correlation coefficient using Bayesian modelling, and application in cluster randomized trials , 2006, Statistics in medicine.

[4]  B. Giraudeau.  Model mis‐specification and overestimation of the intraclass correlation coefficient in cluster randomized trials , 2006, Statistics in medicine.

[5]  N. Kerse,et al.  Intraclass correlation coefficients from three cluster randomised controlled trials in primary and residential health care , 2005, Australian and New Zealand journal of public health.

[6]  J. Crump,et al.  Household based treatment of drinking water with flocculant-disinfectant for preventing diarrhoea in areas with turbid source water in rural western Kenya: cluster randomised controlled trial , 2005, BMJ : British Medical Journal.

[7]  P. Fayers,et al.  Determinants of the intracluster correlation coefficient in cluster randomized trials: the case of implementation research , 2005, Clinical trials.

[8]  Evangelos Evangelou,et al.  Intraclass correlation coefficients for cluster randomized trials in primary care: the cholesterol education and research trial (CEART). , 2005, Contemporary clinical trials.

[9]  S. Chinn,et al.  Intraclass correlation coefficient and outcome prevalence are associated in clustered binary data. , 2005, Journal of clinical epidemiology.

[10]  Risto Lehtonen,et al.  Multilevel Statistical Models , 2005 .

[11]  Dongwoo Kang,et al.  A sample size computation method for non‐linear mixed effects models with applications to pharmacokinetics models , 2004, Statistics in medicine.

[12]  Sandra Eldridge,et al.  Patterns of intra-cluster correlation from primary care research to inform study design and analysis. , 2004, Journal of clinical epidemiology.

[13]  Wooi K. Lim,et al.  On intra-class correlation coefficient estimation , 2004 .

[14]  C. Griffiths,et al.  Specialist nurse intervention to reduce unscheduled asthma care in a deprived multiethnic area: the east London randomised controlled trial for high risk asthma (ELECTRA) , 2004, BMJ : British Medical Journal.

[15]  Andrew R Willan,et al.  Randomizing patients by family practice: sample size estimation, intracluster correlation and data analysis. , 2003, Family practice.

[16]  Harvey Goldstein,et al.  Partitioning variation in multilevel models , 2002 .

[17]  A. V. Peterson,et al.  A comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials , 2001, Statistics in medicine.

[18]  S L Normand,et al.  On determination of sample size in hierarchical binomial models , 2001, Statistics in medicine.

[19]  R Z Omar,et al.  Bayesian methods of analysis for cluster randomized trials with binary outcome data. , 2001, Statistics in medicine.

[20]  S. Chinn,et al.  Components of variance and intraclass correlations for the design of community-based surveys and intervention studies: data from the Health Survey for England 1994. , 1999, American journal of epidemiology.

[21]  D. Firth,et al.  Estimating Intraclass Correlation for Binary Data , 1999, Biometrics.

[22]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .

[23]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[24]  P. Vargha,et al.  A critical discussion of intraclass correlation coefficients. , 1997, Statistics in medicine.

[25]  P. Sham.  Statistics in human genetics , 1997 .

[26]  F B Hu,et al.  Intraclass correlation estimates in a school-based smoking prevention study. Outcome and mediating variables, by sex and ethnicity. , 1996, American journal of epidemiology.

[27]  S. Lipsitz,et al.  Efficient Estimation of the Intraclass Correlation for a Binary Trait , 1996 .

[28]  Bernard W. Silverman.  International Statistical Review , 1996 .

[29]  Allan Donner,et al.  Cluster randomization trials in epidemiology: theory and application , 1994 .

[30]  N Dubin,et al.  Estimation and sample size considerations for clustered binary responses. , 1994, Statistics in medicine.

[31]  D. Commenges,et al.  The intraclass correlation coefficient: distribution-free definition and test. , 1994, Biometrics.

[32]  C A Bodian,et al.  Intraclass correlation for two-by-two tables under three sampling designs. , 1994, Biometrics.

[33]  A Sommer,et al.  Estimation of design effects and diarrhea clustering within households and villages. , 1993, American journal of epidemiology.

[34]  J. Neuhaus.  Estimation efficiency and tests of covariate effects with clustered binary data. , 1993, Biometrics.

[35]  D. Coetzee,et al.  The effects of cluster sampling in an African urban setting. , 1992, The Central African journal of medicine.

[36]  Marshall Godwin,et al.  Health measurement scales , 1991 .

[37]  J. Kalbfleisch,et al.  A Comparison of Cluster-Specific and Population-Averaged Approaches for Analyzing Correlated Binary Data , 1991 .

[38]  Nicholas P. Jewell,et al.  Some Comments on Rosner's Multiple Logistic Model for Clustered Data , 1990 .

[39]  R. Prentice,et al.  Correlated binary regression with covariates specific to each binary observation. , 1988, Biometrics.

[40]  T. Mak.  Analysing Intraclass Correlation for Dichotomous Variables , 1988 .

[41]  A Donner,et al.  Adjustments to the Mantel-Haenszel chi-square statistic and odds ratio variance estimator when the data are clustered. , 1987, Statistics in medicine.

[42]  A. Donner,et al.  A comparison of confidence interval methods for the intraclass correlation coefficient. , 1986, Biometrics.

[43]  A. Donner.  A Review of Inference Procedures for the Intraclass Correlation Coefficient in the One-Way Random Effects Model , 1986 .

[44]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[45]  M. Schemper.  General Derivation of Intraclass Correlation Coefficients , 1986 .

[46]  W. Grove.  Statistical Methods for Rates and Proportions, 2nd ed , 1981 .

[47]  S Karlin,et al.  Sibling and parent--offspring correlation estimation with variable family size. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[48]  A Donner,et al.  The estimation of intraclass correlation in the analysis of family data. , 1980, Biometrics.

[49]  A computer program for calculating different kinds of intraclass correlation coefficients. , 1977, Computer programs in biomedicine.

[50]  J. Fleiss,et al.  Statistical methods for rates and proportions , 1973 .

[51]  S. R. Searle.  Generalized Inverse Matrices , 1971 .

[52]  S. R. Searle.  A Biometrics Invited Paper. Topics in Variance Component Estimation , 1971 .

[53]  J. A. Harris.  ON THE CALCULATION OF INTRA-CLASS AND INTER-CLASS COEFFICIENTS OF CORRELATION FROM CLASS MOMENTS WHEN THE NUMBER OF POSSIBLE COMBINATIONS IS LARGE , 1913 .