  Sample size determination for cluster randomised trials (CRTs) is challenging
as it requires robust estimation of the intra-cluster correlation coefficient
(ICC). Typically, the sample size is chosen to provide a certain level of power
to reject the null hypothesis in a hypothesis test. This relies on the minimal
clinically important difference (MCID) and estimates for the standard
deviation, ICC and possibly the coefficient of variation of the cluster size.
Varying these parameters can have a strong effect on the sample size. In
particular, it is sensitive to small differences in the ICC. A relevant ICC
estimate is often not available, or the available estimate is imprecise. If the
ICC used is far from the unknown true value, this can lead to trials which are
substantially over- or under-powered. We propose a hybrid approach using
Bayesian assurance to find the sample size for a CRT with a frequentist
analysis. Assurance is an alternative to power which incorporates uncertainty
on parameters through a prior distribution. We suggest specifying prior
distributions for the standard deviation, ICC and coefficient of variation of
the cluster size, while still utilising the MCID. We illustrate the approach
through the design of a CRT in post-stroke incontinence. We show assurance can
be used to find a sample size based on an elicited prior distribution for the
ICC, when a power calculation discards all information in the prior except a
single point estimate. Results show that this approach can avoid misspecifying
sample sizes when prior medians for the ICC are very similar but prior
distributions exhibit quite different behaviour. Assurance provides an
understanding of the probability of success of a trial given an MCID and can be
used to produce sample sizes which are robust to parameter uncertainty. This is
especially useful when there is difficulty obtaining reliable parameter
estimates.
