Does it decay? Obtaining decaying correlation parameter values from previously analysed cluster randomised trials

A frequently applied assumption in the analysis of data from cluster randomised trials is that the outcomes from all participants within a cluster are equally correlated. That is, the intracluster correlation, which describes the degree of dependence between outcomes from participants in the same cluster, is the same for each pair of participants in a cluster. However, recent work has discussed the importance of allowing for this correlation to decay as the time between the measurement of participants in a cluster increases. Incorrect omission of such a decay can lead to under-powered studies, and confidence intervals for estimated treatment effects can be too narrow or too wide, depending on the characteristics of the design. When planning studies, researchers often rely on previously reported analyses of trials to inform their choice of intracluster correlation. However, most reported analyses of clustered data do not incorporate a correlation decay. Thus, often all that is available are estimates of intracluster correlations obtained under the potentially incorrect assumption of no decay. In this article, we show that it is possible to use intracluster correlation values obtained from models that incorrectly omit a decay to inform plausible choices of decaying correlations. Our focus is on intracluster correlation estimates for continuous outcomes obtained by fitting linear mixed models with exchangeable or block-exchangeable correlation structures. We describe how plausible values for decaying correlations may be obtained given these estimated intracluster correlations. An online app is presented that allows users to obtain plausible values of the decay, which can be used at the trial planning stage to assess the sensitivity of sample size and power calculations to decaying correlation structures.