What is an intracluster correlation coefficient? Crucial concepts for primary care researchers

Abstract

Background: Primary care research often involves clustered samples in which subjects are randomized at a group level but analyzed at an individual level. Analyses that do not take this clustering into account may report significance where none exists. This article explores the causes, consequences, and implications of cluster data.

Methods: Using a case study with accompanying equations, we show that clustered samples are not as statistically efficient as simple random samples.

Results: Similarity among subjects within preexisting groups or clusters reduces the variability of responses in a clustered sample, which erodes the power to detect true differences between study arms. This similarity is expressed by the intracluster correlation coefficient, or p (rho), which compares the within-group variance with the between-group variance. Rho is used in equations along with the cluster size and the number of clusters to calculate the effective sample size (ESS) in a clustered design. The ESS should be used to calculate power in the design phase of a clustered study. Appropriate accounting for similarities among subjects in a cluster almost always results in a net loss of power, requiring increased total subject recruitment. Increasing the number of clusters enhances power more efficiently than does increasing the number of subjects within a cluster.

Conclusions: Primary care research frequently uses clustered designs, whether consciously or unconsciously. Researchers must recognize and understand the implications of clusters to avoid costly sample size errors.

Figure 1.

Two-level nesting, or clustering.

Figure 2.

Three-level nesting.