Sample size determination for external pilot cluster randomised trials with binary feasibility outcomes: a tutorial

Justifying sample size for a pilot trial is a reporting requirement, but few pilot trials report a clear rationale for their chosen sample size. Unlike full-scale trials, pilot trials should not be designed to test effectiveness, and so, conventional sample size justification approaches do not apply. Rather, pilot trials typically specify a range of primary and secondary feasibility objectives. Often, these objectives relate to estimation of parameters that inform the sample size justification for the full-scale trial, many of which are binary. These binary outcomes are referred to as "feasibility outcomes" and include expected prevalence of the primary trial outcome, primary outcome availability, or recruitment or retention proportions.For pilot cluster trials, sample size calculations depend on the number of clusters, the cluster sizes, the anticipated intra-cluster correlation coefficient for the feasibility outcome and the anticipated proportion for that outcome. Of key importance is the intra-cluster correlation coefficient for the feasibility outcome. It has been suggested that correlations for feasibility outcomes are larger than for clinical outcomes measuring effectiveness. Yet, there is a dearth of information on realised values for these correlations.In this tutorial, we demonstrate how to justify sample size in external pilot cluster trials where the objective is to estimate a binary feasibility outcome. We provide sample size calculation formulae for a variety of scenarios, make available an R Shiny app for implementation, and compile a report of intra-cluster correlations for feasibility outcomes from a convenience sample. We demonstrate that unless correlations are very low, external pilot cluster trials can be made more efficient by including more clusters and fewer observations per cluster.