Replication studies for scientific research are an important part of ensuring the reliability and integrity of experimental findings. In the context of clinical trials, the concept of replication has been formalised by the 'two-trials' rule, where two pivotal studies are required to show positive results before a drug can be approved. In experiments testing multiple hypotheses simultaneously, control of the overall familywise error rate (FWER) is additionally required in many contexts. The well-known Bonferroni procedure controls the FWER, and a natural extension is to introduce weights into this procedure to reflect the a-priori importance of hypotheses or to maximise some measure of the overall power of the experiment. In this paper, we consider analysing a replication study using an optimal weighted Bonferroni procedure, with the weights based on the results of the original study that is being replicated and the optimality criterion being to maximise the disjunctive power of the trial (the power to reject at least one non-null hypothesis). We show that using the proposed procedure can lead to a substantial increase in the disjunctive power of the replication study, and is robust to changes in the effect sizes between the two studies.

翻译：科学研究的复制实验是确保实验结果可靠性与完整性的重要环节。在临床试验领域，复制概念已通过"双试验"规则形式化，该规则要求药物获批前必须有两项关键研究呈现阳性结果。在同时检验多重假设的实验中，许多场景还要求控制整体族系错误率。著名的Bonferroni方法可控制FWER，其自然扩展是引入权重以反映假设的先验重要性，或最大化实验整体功效的某种度量。本文提出使用最优加权Bonferroni方法分析复制研究，其权重基于被复制原始研究的结果，最优性准则为最大化试验的析取功效（即拒绝至少一个非零假设的能力）。研究表明，采用所提方法可显著提升复制研究的析取功效，且对两项研究间效应量变化具有稳健性。