Summary
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.
SummaryThe intra-cluster correlation coefficient (ICC) of the primary outcome plays a key role in thedesign and analysis of cluster randomized trials (CRTs), but the precise definition of this parameteris 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 ICCthat may be expressed in different ways depending on the modelling approach used to describe thedata, 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 ICCcannot be related directly to the parameters of the logistic-normal model that is commonly usedfor dichotomous outcomes. We show how the definition of the ICC is different when covariates areintroduced. Finally, we use our framework and definition of the ICC to draw out implications forthose interpreting and choosing values of the ICC when planning CRTs.
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