Prior distributions for the intracluster correlation coefficient, based on multiple previous estimates, and their application in cluster randomized trials

Abstract

Numerous estimates for the intracluster correlation coefficient (ICC) are available in research databases and publications. When planning a cluster randomized trial, an anticipated value for the ICC is required; currently, researchers base their choice informally on the magnitude of previous ICC estimates. In this paper, we make use of the wealth of ICC information by formally constructing informative prior distributions, while acknowledging the varying relevance and precision of the estimates available. Typically, for a planned trial in a given clinical setting, multiple relevant ICC estimates are available from each of several completed studies. Our preferred model allows for the imprecision in each ICC estimate around its underlying true value and, separately, allows for the similarity of ICC values from the same study. The relevance of each previous estimate to the planned clinical setting is considered, and estimates corresponding to less relevant outcomes or population types are given less influence. We find that such downweighting can increase the precision of the anticipated ICC. In trial design, the prior distribution constructed allows uncertainty about the ICC to be acknowledged, and we describe how to choose a design that provides adequate power across the range of likely ICC values. Prior information on the ICC can also be incorporated in analysis of the trial data, when taking a Bayesian approach. The methods proposed enable available ICC information to be summarised appropriately by an informative prior distribution, which is of direct practical use in cluster randomized trials.