Intraclass Correlation

A measure quantifying the proportion of total variance in an outcome attributable to differences between groups or clusters, relative to variance within them.

Source: Shrout & Fleiss 1979

The intraclass correlation reveals how much of the total variation in an outcome is due to differences between clusters rather than differences within them. A high value means people in the same cluster, such as a clinic, are much alike and differ mainly from those in other clusters, so the cluster explains a lot; a low value means location matters little. This governs how much clustering erodes a study's precision, which is why it is central to planning clustered trials. Gauging how much clusters matter is its purpose. Kirkwood and Sterne (2003) describe this measure.

Source: Kirkwood & Sterne 2003

The intraclass correlation is calculated as the ratio of the between-cluster variance to the total variance, the sum of the between-cluster and within-cluster variances, typically estimated from a model that partitions the variation into these components. So the intraclass correlation is calculated from the variance components, expressing the between-cluster variance as a fraction of the total, which gives the proportion of variation due to differences between clusters and equals the expected correlation between two members of the same cluster, with the variance components usually obtained from a hierarchical or analysis-of-variance model of the data.

Source: Shrout & Fleiss 1979

The intraclass correlation measures how strongly observations within the same cluster resemble one another, or equivalently the share of total variation that lies between clusters rather than within them; a high value means members of a cluster are very similar and clustering is strong, a low value that they are little more similar than members of different clusters. So the intraclass correlation measures the degree of clustering or within-cluster resemblance, and in a measurement context it measures reliability, the consistency of repeated ratings or measurements, with higher values indicating greater agreement, making it a versatile measure of similarity within groups.

Source: Shrout & Fleiss 1979

The intraclass correlation is important because it quantifies the clustering that affects the analysis and design of grouped data: it determines how much clustering inflates variance, feeding into the design effect and sample size calculations for clustered studies, and it indicates the reliability of measurements. So the intraclass correlation matters for both the planning and the analysis of studies with clustered or repeated data, since it captures the within-cluster correlation that must be accounted for to obtain valid inference and adequate power, and in measurement it quantifies reliability, which is why it is a key statistic in cluster randomised trials and in assessing rater agreement.

Source: Shrout & Fleiss 1979

The intraclass correlation is used in study design to plan clustered studies, since it, together with the cluster size, determines the design effect, the factor by which the sample size must be increased to account for clustering. A higher intraclass correlation implies a larger design effect and a bigger required sample. So the intraclass correlation is used to size cluster randomised and other clustered studies adequately, because it quantifies how much clustering reduces the effective information per observation, which must be offset by enrolling more participants, making an estimate of the intraclass correlation a necessary input to sample size calculation for such designs.

Source: Shrout & Fleiss 1979