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Intraclass Correlation Coefficient

The intraclass correlation coefficient (ICC) measures the correlation of responses within class when responses are grouped into classes or groups, and there are a number of classes or groups. The ICC quantifies the variation between the clusters and can be defined as a proportion of total variation that is attributed to differences between the clusters (groups). Variation of a quantity is spread around its mean measured mainly by variance and standard deviation. Many situations in decision-making science make use of the ICC for drawing inference and assessing reliability. The ICC is used in a variety of situations for different purposes, including assessing homogeneity of outcomes or responses within a class or cluster in the context of a cluster survey, group randomized trial and multilevel studies, interrater agreement, and similarity of health/social responses within couples. Accounting for correlation of responses within group in a cluster or group randomized trial has important implications in terms of required sample size and statistical significance. Assessing agreement of raters on health states has been an important aspect of clinical decision making.

Thus, the ICC is used in studies involving correlation of responses within groups, assessment of interrater reliability, and similarity of responses in the dyads where dyad members are exchangeable. This entry provides an overview of the use of the ICC in studies involving groups or clusters with an example, followed by the use of the ICC in assessing rater agreements in reliability assessment and special cases of interrater reliability.

Studies Involving Clustering

Health outcomes of individuals in the same household or community tend to be more similar than those of individuals in other households and communities. This phenomenon may be due to similar levels of exposures, similar behaviors, or genetic predispositions. Due to this similarity, individuals in a group sharing some characteristics are unlikely to be independent with respect to their health outcomes, since responses of the individuals in a group show positive intraclass correlation. For example, transmission of an infectious agent or exposure to air pollution with its related health outcomes such as asthma will be more common among people within a particular community than in other communities due to different levels of exposures.

In developing countries, sampling frames are often not available for epidemiological surveys; the cluster sampling technique is recommended due to its logistic efficiency. Another advantage of cluster sampling is the comparative ease in enumerating groups of households or larger units such as census block, county, village, and so on, as clusters than as individuals. In studies at places where responses are naturally clustered, such as patients in general practices (patients within practitioners) or worksites (workers within worksites), a similar sampling scheme is applied. Similarly, in community trials, the unit of randomization is a group of people rather than an individual because intervention is applied to all people in a group that decreases the risk of contamination and increases the administrative efficiency. In all these situations involving some kind of clustering, there are two components of variation of responses: within-cluster/group variation and between-cluster/group variation. The ICC can be used to quantify and account for these two components of variations.

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