Hybrid sample size calculations for cluster randomised trials using assurance

Sample size determination for cluster randomised trials is challenging because it requires robust estimation of the intra-cluster correlation coefficient. Typically, the sample size is chosen to provide a certain level of power to reject the null hypothesis in a two-sample hypothesis test. This relies on the minimal clinically important difference and estimates for the overall standard deviation, the intra-cluster correlation coefficient and, if cluster sizes are assumed to be unequal, the coefficient of variation of the cluster size. Varying any of these parameters can have a strong effect on the required sample size. In particular, it is very sensitive to small differences in the intra-cluster correlation coefficient. A relevant intra-cluster correlation coefficient estimate is often not available, or the available estimate is imprecise due to being based on studies with low numbers of clusters. If the intra-cluster correlation coefficient value used in the power calculation is far from the unknown true value, this could lead to trials which are substantially over- or under-powered.

In this article, we propose a hybrid approach using Bayesian assurance to determine the sample size for a cluster randomised trial in combination with a frequentist analysis. Assurance is an alternative to traditional power, which incorporates the uncertainty on key parameters through a prior distribution. We suggest specifying prior distributions for the overall standard deviation, intra-cluster correlation coefficient and coefficient of variation of the cluster size, while still utilising the minimal clinically important difference. We illustrate the approach through the design of a cluster randomised trial in post-stroke incontinence and compare the results to those obtained from a standard power calculation.

We show that assurance can be used to calculate a sample size based on an elicited prior distribution for the intra-cluster correlation coefficient, whereas a power calculation discards all of the information in the prior except for a single point estimate. Results show that this approach can avoid misspecifying sample sizes when the prior medians for the intra-cluster correlation coefficient are very similar, but the underlying prior distributions exhibit quite different behaviour. Incorporating uncertainty on all three of the nuisance parameters, rather than only on the intra-cluster correlation coefficient, does not notably increase the required sample size.

Assurance provides a better understanding of the probability of success of a trial given a particular minimal clinically important difference and can be used instead of power to produce sample sizes that are more robust to parameter uncertainty. This is especially useful when there is difficulty obtaining reliable parameter estimates.