The Importance and Role of Intracluster Correlations in Planning Cluster Trials

Cluster trials evaluate interventions delivered to intact social groups or clusters, such as communities, churches, schools, workplaces, and medical practices, whereas outcomes are measured on members of those groups.1,2 The distinctive feature of cluster trials is the presence of intracluster (or intraclass) correlation among members within groups that arises from restricting assignment of the interventions to groups instead of to individuals. Failure to account for the intracluster correlation within clusters will likely lead to 2 shortcomings: an underpowered study and inflated Type I error rate of hypothesis tests relating to the intervention.1,2 Proper planning of cluster trials is based upon sample size formulae that use hypothesized intracluster correlation values, often based on estimates from earlier trials.3-6 Although sample size formulae based upon the intracluster correlation for a posttest-only cluster trial design are fairly well established, many cluster trials have multiple time points for which more than one type of intracluster correlation arises. In the case of a pretest–posttest nested cross-sectional design, characterized by different groups of individuals within clusters sampled at 2 time points, 2 intracluster correlations may be defined. The traditional intracluster correlation is the correlation among individuals within the same community at a specific time point. A second intracluster correlation is the correlation among individuals within the same community at different points in time. Extensions of the posttest-only sample size formulae are needed to refine sample size determination for multiple time point designs. The sample size formula adopted in planning a cluster trial depends upon the statistical analysis to be used and, more specifically, the test statistic for the null hypothesis of “no intervention effect.” The proposed analysis will depend upon the trial's experimental design, including whether the intervention condition is randomized to groups. For example, in a randomized pretest–posttest nested cross-sectional design, the trial planners are concerned with how the statistical analysis should handle the pretest data to maximize statistical power for the test of intervention, given that a sufficiently large number of clusters are enrolled to ensure baseline balance among covariates and outcome. In short, the focus is on the comparison of posttest means. In contrast, potential bias from baseline imbalance is an additional concern in planning a nonrandomized cluster trial. In this case, a “time × condition” analysis may be appropriate because its test statistic is the difference in change in the mean outcome over time between intervention and control conditions. If the pretest intervention and control condition means are equal, a time × condition analysis will tend to have lower statistical power than a posttest only analysis because the former uses a test statistic that is a function of 4 means, resulting in greater variance than a test statistic that is a function of only 2 (posttest) means. In sum, the manner of accounting for pretest information in the analysis of a randomized cluster trial has implications for statistical power, whereas the choice may affect both power and bias for nonrandomized trials. This article discusses the estimation of intracluster correlations and particularly their use in sample size formulae in the design of cluster trials. Although statistical analysis and power have received attention for modeling change in Gaussian outcomes,7,8 insufficient consideration has been given to binary outcomes.9,10 Focusing on large cluster trials with binary outcomes, a generalized estimating equations (GEE) approach is applied for the estimation of the 2 types of intracluster correlation.11 In planning a nonrandomized cluster trial with a pretest–posttest nested cross-sectional design, the paper discusses a sample size formula for a GEE time × condition analysis that incorporates the 2 types of intracluster correlations.12 Finally, the paper reports intracluster correlation estimates and estimates of their precision for several dichotomous measures of underage drinking from a large nonrandomized cluster trial to enforce underage drinking laws.12