While within a clinical study there may be multiple doses and endpoints, across different studies each study will result in either an approval or a lack of approval of the drug compound studied. The False Approval Rate (FAR) is the proportion of drug compounds that lack efficacy incorrectly approved by regulators. (In the U.S., compounds that have efficacy and are approved are not involved in the FAR consideration, according to our reading of the relevant U.S. Congressional statute). While Tukey's (1953) Error Rate Familwise (ERFw) is meant to be applied within a clinical study, Tukey's (1953) Error Rate per Family (ERpF), defined alongside ERFw,is meant to be applied across studies. We show that controlling Error Rate Familwise (ERFw) within a clinical study at 5% in turn controls Error Rate per Family (ERpF) across studies at 5-per-100, regardless of whether the studies are correlated or not. Further, we show that ongoing regulatory practice, the additive multiplicity adjustment method of controlling ERpF, is controlling False Approval Rate FAR exactly (not conservatively) at 5-per-100 (even for Platform trials). In contrast, if a regulatory agency chooses to control the False Discovery Rate (FDR) across studies at 5% instead, then this change in policy from ERpF control to FDR control will result in incorrectly approving drug compounds that lack efficacy at a rate higher than 5-per-100, because in essence it gives the industry additional rewards for successfully developing compounds that have efficacy and are approved. Seems to us the discussion of such a change in policy would be at a level higher than merely statistical, needing harmonizsation/harmonization. (In the U.S., policy is set by the Congress.)

翻译：尽管在单一临床研究中可能存在多个剂量和终点，但在不同研究间，每个研究将导致所研究的药物化合物获得批准或未获批准。错误批准率（FAR）是指监管机构错误批准缺乏疗效的药物化合物的比例。（根据我们对美国相关国会法规的理解，在美国，具有疗效并获得批准的化合物不纳入FAR考量。）虽然Tukey（1953）提出的族系错误率（ERFw）旨在应用于单个临床研究，但与之同时定义的每族系错误率（ERpF）则旨在跨研究应用。我们证明：将单个临床研究中的族系错误率（ERFw）控制在5%，即可跨研究地将每族系错误率（ERpF）控制在每百项研究5例的水平，且无论这些研究是否相关。进一步，我们表明现行监管实践——即控制ERpF的加性多重性调整方法——能精确（而非保守地）将错误批准率（FAR）控制在每百项研究5例的水平（即便在平台试验中也是如此）。相比之下，若监管机构选择跨研究将错误发现率（FDR）控制在5%，则这种从ERpF控制向FDR控制的政策转变，将导致缺乏疗效的药物化合物被错误批准的比例超过每百项研究5例，因为这实质上为行业额外奖励了那些成功开发出具有疗效且获批的化合物。在我们看来，此类政策转变的讨论已超出纯统计学层面，需要达成协调统一。（在美国，政策由国会制定。）