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Clustering and the ICC

When people are grouped into wards, clinics or practices they resemble each other more than they resemble people picked at random, so each additional person carries less independent information than the count suggests.

What the ICC measures

The intracluster correlation coefficient is the share of total variation in the outcome that lies BETWEEN clusters rather than within them. A value of zero means grouping is irrelevant; larger values mean cluster membership explains more of who has the outcome, and each cluster's members are correspondingly more redundant.

What a low and a high ICC look like

Two panels of observations grouped into three clusters. With a low ICC the clusters overlap and barely differ. With a high ICC each cluster is tight and the clusters sit at different levels.Low ICC: clusters barely differClusterMost variation is within clusters.High ICC: members of a cluster are alikeClusterMost variation is between clusters.The higher the ICC, the less each extra member of an existing cluster adds, and the closer the effectivesample size gets to the number of clusters.
Conceptual diagram. It shows the structure of the idea, not data from any study.

The design effect

The practical consequence is the design effect: roughly one plus the ICC multiplied by the average cluster size minus one. Even a small ICC becomes expensive with large clusters. An ICC of 0.02 with clusters of fifty inflates the required sample size by about a factor of two, which is why an ICC that sounds negligible is not.

The acronym collision, which matters

An ICC is two different statistics sharing an abbreviation. The intraCLUSTER correlation coefficient described here is what a cluster trial states when it sizes itself. The intraCLASS correlation coefficient in an agreement study measures rater reliability. They are computed differently and mean different things, and reading a reliability ICC as a clustering one, or the reverse, produces nonsense in either direction.

An ICC is an estimate, not a constant

The value used in a sample size calculation is usually borrowed from a published study, and it carries its own uncertainty. Treating a borrowed ICC as known can leave a trial substantially underpowered, and protecting against that may require a considerably larger sample than the point estimate implies. ICCs also vary systematically: process measures tend to have higher ICCs than clinical outcomes, and secondary care differs from primary care.

Why Mallard warns about it

Mallard requires clustering to be modelled or explicitly justified whenever a group-level exposure meets an individual-level outcome, and it sizes clustered designs by simulation rather than a closed form, because no simple formula covers them honestly.

Key assumptions and design requirements

  • The ICC used for sizing is stated, with its source, and its uncertainty acknowledged.
  • The design effect is applied to the sample size, not mentioned and then ignored.
  • The analysis accounts for clustering with a random effect or cluster-robust inference.
  • Below about 30 clusters, a small-sample correction is named.
  • Which ICC is meant is unambiguous, given the acronym collision with reliability.

What to watch out for

An ICC is two different statistics sharing one acronym: the clustering coefficient used in cluster trials and the reliability coefficient used in agreement studies are not the same quantity. An ICC borrowed from a published study is an estimate with its own uncertainty, and treating it as known can leave a trial substantially underpowered.

Clinical example

A hand-hygiene programme is randomized across twenty wards averaging forty patients each. With an ICC of 0.02 the design effect is about 1.8, so eight hundred patients carry roughly the information of four hundred and fifty independent ones. Sizing on the patient count alone would leave the trial underpowered by nearly half.

Recent studies that used this
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Related Learn pages
Sources & further reading
  1. Allowing for imprecision of the intracluster correlation coefficient in the design of cluster randomized trials (opens in a new tab) · Stat Med · doi 10.1002/sim.1721
  2. Determinants of the intracluster correlation coefficient in cluster randomized trials: the case of implementation research (opens in a new tab) · Clin Trials · doi 10.1191/1740774505cn071oa
The first paper is the reason a borrowed ICC should not be treated as known. The second gives empirical ICC magnitudes and shows they depend on setting and outcome type, so a value from a different context is a weak guide.
Last source review: 2026-09-06
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