BACKGROUND Recent work has shown that cluster-randomised trials can estimate two distinct estimands: the participant-average and cluster-average treatment effects. These can differ when participant outcomes or the treatment effect depends on the cluster size (termed informative cluster size). In this case, estimators that target one estimand (such as the analysis of unweighted cluster-level summaries, which targets the cluster-average effect) may be biased for the other. Furthermore, commonly used estimators such as mixed-effects models or generalised estimating equations with an exchangeable correlation structure can be biased for both estimands. However, there has been little empirical research into whether informative cluster size is likely to occur in practice. METHOD We re-analysed a cluster-randomised trial comparing two different thresholds for red blood cell transfusion in patients with acute upper gastrointestinal bleeding to explore whether estimates for the participant- and cluster-average effects differed, to provide empirical evidence for whether informative cluster size may be present. For each outcome, we first estimated a participant-average effect using independence estimating equations, which are unbiased under informative cluster size. We then compared this to two further methods: (1) a cluster-average effect estimated using either weighted independence estimating equations or unweighted cluster-level summaries, and (2) estimates from a mixed-effects model or generalised estimating equations with an exchangeable correlation structure. We then performed a small simulation study to evaluate whether observed differences between cluster- and participant-average estimates were likely to occur even if no informative cluster size was present. RESULTS For most outcomes, treatment effect estimates from different methods were similar. However, differences of >10% occurred between participant- and cluster-average estimates for 5 of 17 outcomes (29%). We also observed several notable differences between estimates from mixed-effects models or generalised estimating equations with an exchangeable correlation structure and those based on independence estimating equations. For example, for the EQ-5D VAS score, the independence estimating equation estimate of the participant-average difference was 4.15 (95% confidence interval: -3.37 to 11.66), compared with 2.84 (95% confidence interval: -7.37 to 13.04) for the cluster-average independence estimating equation estimate, and 3.23 (95% confidence interval: -6.70 to 13.16) from a mixed-effects model. Similarly, for thromboembolic/ischaemic events, the independence estimating equation estimate for the participant-average odds ratio was 0.43 (95% confidence interval: 0.07 to 2.48), compared with 0.33 (95% confidence interval: 0.06 to 1.77) from the cluster-average estimator. CONCLUSION In this re-analysis, we found that estimates from the various approaches could differ, which may be due to the presence of informative cluster size. Careful consideration of the estimand and the plausibility of assumptions underpinning each estimator can help ensure an appropriate analysis methods are used. Independence estimating equations and the analysis of cluster-level summaries (with appropriate weighting for each to correspond to either the participant-average or cluster-average treatment effect) are a desirable choice when informative cluster size is deemed possible, due to their unbiasedness in this setting.

中文翻译：

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整群随机试验中提供信息的聚类大小：TRIGGER 试验的案例研究。

背景最近的工作表明，整群随机试验可以估计两个不同的估计值：参与者平均治疗效果和整群平均治疗效果。当参与者结果或治疗效果取决于簇大小（称为信息簇大小）时，这些可能会有所不同。在这种情况下，针对一个估计值的估计器（例如针对聚类平均效应的未加权聚类级别摘要的分析）可能会对另一个估计值产生偏差。此外，常用的估计量，例如混合效应模型或具有可交换相关结构的广义估计方程，可能会对两个估计量产生偏差。然而，关于信息簇大小在实践中是否可能发生的实证研究却很少。方法 我们重新分析了一项整群随机试验，比较了急性上消化道出血患者红细胞输注的两种不同阈值，以探讨参与者平均效应和整群平均效应的估计是否不同，为集群大小是否具有信息性提供经验证据。可能存在。对于每个结果，我们首先使用独立估计方程估计参与者平均效应，该方程在信息丰富的簇大小下是无偏的。然后，我们将其与另外两种方法进行比较：（1）使用加权独立估计方程或未加权的簇级摘要估计的簇平均效应，以及（2）根据混合效应模型或具有可交换相关性的广义估计方程进行估计结构。然后，我们进行了一项小型模拟研究，以评估即使不存在提供信息的聚类大小，聚类平均估计值和参与者平均估计值之间是否可能出现观察到的差异。结果 对于大多数结果，不同方法的治疗效果估计是相似的。然而，17 项结果中的 5 项 (29%) 的参与者平均估计值和集群平均估计值之间存在 >10% 的差异。我们还观察到混合效应模型或具有可交换相关结构的广义估计方程与基于独立估计方程的估计之间存在一些显着差异。例如，对于 EQ-5D VAS 评分，参与者平均差异的独立性估计方程估计值为 4.15（95% 置信区间：-3.37 至 11.66），相比之下为 2.84（95% 置信区间：-7.37 至 13.04）聚类平均独立性估计方程估计为 3.23（95% 置信区间：-6.70 至 13.16），来自混合效应模型。同样，对于血栓栓塞/缺血事件，参与者平均比值比的独立估计方程估计值为 0.43（95% 置信区间：0.07 至 2.48），而集群中的独立估计方程为 0.33（95% 置信区间：0.06 至 1.77）。平均估计量。结论 在这次重新分析中，我们发现各种方法的估计可能有所不同，这可能是由于存在信息丰富的簇大小。仔细考虑估计值以及支撑每个估计量的假设的合理性有助于确保使用适当的分析方法。当信息簇大小被认为是可能的时候，独立性估计方程和簇级摘要分析（对每个方程进行适当的权重，以对应于参与者平均或簇平均治疗效果）是一个理想的选择，因为它们在这方面是无偏的。环境。