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.

翻译：整群随机试验的样本量确定具有挑战性，因为需要稳健估计群内相关系数。通常，样本量选择旨在为假设检验提供特定检验功效以拒绝零假设，这依赖于最小临床重要差异值，以及标准差、ICC和可能的群组大小变异系数的估计值。这些参数的变化会对样本量产生显著影响，尤其是对ICC的微小差异十分敏感。由于往往缺乏相关ICC估计值，或现有估计不精确，若使用的ICC与未知真实值偏差较大，可能导致试验功效严重不足或过剩。我们提出一种混合方法，利用贝叶斯保障度来确定基于频率学派分析的CRT样本量。保障度是传统检验功效的替代方案，通过先验分布纳入参数不确定性。建议为标准差、ICC和群组大小变异系数设定先验分布，同时仍使用MCID。通过脑卒中后尿失禁CRT设计实例展示该方法，结果表明：当功效计算仅丢弃先验中除单一估计点外的所有信息时，保障度可基于推导出的ICC先验分布确定样本量。当ICC先验中位数相似但先验分布行为显著不同时，该方法能避免样本量误设。保障度能基于MCID评估试验成功概率，可生成对参数不确定性稳健的样本量，尤其适用于难以获得可靠参数估计的情形。