In this article, we derive and compare methods to derive \textit{p}-values and sets of confidence intervals with strong control of the family-wise error rates and coverage for estimates of treatment effects in cluster randomised trials with multiple outcomes. There are few methods for \textit{p}-value corrections and deriving confidence intervals, limiting their application in this setting. We discuss the methods of Bonferroni, Holm, and Romano \& Wolf (2005) and adapt them to cluster randomised trial inference using permutation-based methods with different test statistics. We develop a novel search procedure for confidence set limits using permutation tests to produce a set of confidence intervals under each method of correction. We conduct a simulation-based study to compare family-wise error rates, coverage of confidence sets, and the efficiency of each procedure in comparison to no correction using both model-based standard errors and permutation tests. We show that the Romano-Wolf type procedure has nominal error rates and coverage under non-independent correlation structures and is more efficient than the other methods in a simulation-based study. We also compare results from the analysis of a real-world trial.

翻译：本文推导并比较了在具有多个结局的集群随机试验中，通过强控制族系错误率与覆盖概率来获取治疗效应估计的p值及置信区间集合的方法。目前针对此类场景的p值校正与置信区间推导方法较为有限，限制了其应用。我们讨论了Bonferroni、Holm以及Romano & Wolf（2005）三种方法，并通过基于置换的检验框架及不同检验统计量将其适配至集群随机试验推断中。创新性地提出一种利用置换检验搜索置信集边界的算法，以在每种校正方法下生成对应的置信区间集合。通过模拟研究，结合基于模型的标准误与置换检验，比较了各方法与无校正方案在族系错误率、置信集覆盖概率及效率方面的表现。结果表明，在非独立相关结构下，Romano-Wolf型方法能维持名义错误率与覆盖概率，且在模拟研究中效率优于其他方法。此外，我们还对一项真实试验的分析结果进行了比较。