Accounting for the uncertainty in the ICC estimate when calculating the sample size for cluster-randomised trials with continuous outcomes

Poster presented at ICTMC 2022

Calculating the sample size for cluster-randomised controlled trials (cRCTs) requires an inflation factor to account for the intra-cluster correlation coefficient (ICC), a value that quantifies the degree of dependence within clusters. Estimates of the ICC are often taken from pilot or preliminary trials and are estimated with uncertainty. This uncertainty can have a marked impact on the resulting power of the trial being designed. 

We aimed to develop an approach to account for the uncertainty in the ICC estimate when calculating the sample size for a cRCT with a continuous outcome.

This was a methodological study using simulated data. 

We developed an approach to account for the imprecision in the ICC estimate using numerical methods to integrate the sample size for a cRCT over plausible values of the ICC. This gives a sample size which is the average over all these plausible values. 

We simulated 4 hypothetical scenarios which take an ICC estimate from pilot cRCTs of differing sizes. For each, we generated distributions of plausible values for the ICC estimated using Searle’s, Swiger’s and Fisher’s methods. Finally, we calculated the sample size for a main cRCT using our integrative adjustment over the plausible ICC values provided by the three different methods. We compared these with two other common approaches.

A sensitivity analysis explored the impact of this approach on the main trial power in a realistic scenario.

In each case the main trial sample size using our integrative adjustment was greater than using the point estimate for the ICC which does not account for its imprecision. The overall sample size also depended on the number of clusters in the main trial. We found that this approach consistently preserved main trial power at 10% or more above using a simple ICC point estimate for realistic conservative scenarios.

The proposed method estimates the sample size for a cRCT that accounts for the imprecision in the ICC and thus can help mitigate potential power loss that can result from using an uncertain point ICC estimate. This method can be used with any means of estimating distributions of plausible values for the ICC, allowing broad applicability.  This work has been published in Statistical Methods in Medical Research and R code for the calculation of the adjusted cRCT sample size is available.