Researchers designing a clinical trial to demonstrate superiority or non-inferiority of a new treatment to an established control face an important choice: to conduct a randomized controlled trial (RCT), or to take advantage of historical data on the control treatment and conduct a single-arm historically controlled trial (HCT). The primary advantage of the RCT is that it minimizes bias between the treatment and control arms with respect to known and unknown confounders (i.e., it ensures exchangeability), while the advantage of the HCT is potentially greater efficiency leading to smaller required sample size. However, a naïve comparison of sample size requirements, which suggests a 4-fold sample size ratio, is flawed because the sample size calculations involve different null hypotheses and therefore have different error rates for the null hypothesis of interest. In this paper, we define four approaches for calibrating the error rates for the RCT and HCT under that common null hypothesis, which allows for a fair comparison of sample size requirements. We show that the HCT has an inflated type 1 error rate for the null hypothesis of interest even in the absence of bias, that with appropriately calibrated error rates the sample size advantage of the HCT is always less than that suggested by a naïve calculation, and that the RCT can in some cases be more efficient.

研究人员设计一项临床试验以证明新疗法对既定对照的优越性或劣势，这是一个重要的选择：进行随机对照试验（RCT）或利用对照疗法的历史数据并进行一次臂历史对照试验（HCT）。RCT的主要优点是，它可以最大程度地减少治疗和控制臂之间相对于已知和未知混杂因素的偏倚（即，它确保了可交换性），而HCT的优势可能是更高的效率，从而导致所需的样本量更小。但是，由于样本量的计算涉及不同的原假设，因此对于所关注的原假设的错误率也不同，因此对样本数量要求进行单纯的比较（表明样本数量比率为4倍）是有缺陷的。在本文中，我们定义了四种在该通用无效假设下校准RCT和HCT错误率的方法，从而可以公平地比较样本数量要求。我们显示，即使在没有偏差的情况下，对于感兴趣的零假设，HCT的虚假的1型错误率也会升高，如果使用适当校准的错误率，则HCT的样本量优势始终小于单纯计算所暗示的优势，