Despite their cost, randomized controlled trials (RCTs) are widely regarded as gold-standard evidence in disciplines ranging from social science to medicine. In recent decades, researchers have increasingly sought to reduce the resource burden of repeated RCTs with factorial designs that simultaneously test multiple hypotheses, e.g. experiments that evaluate the effects of many medications or products simultaneously. Here I show that when multiple interventions are randomized in experiments, the effect any single intervention would have outside the experimental setting is not identified absent heroic assumptions, even if otherwise perfectly realistic conditions are achieved. This happens because single-treatment effects involve a counterfactual world with a single focal intervention, allowing other variables to take their natural values (which may be confounded or modified by the focal intervention). In contrast, observational studies and factorial experiments provide information about potential-outcome distributions with zero and multiple interventions, respectively. In this paper, I formalize sufficient conditions for the identifiability of those isolated quantities. I show that researchers who rely on this type of design have to justify either linearity of functional forms or -- in the nonparametric case -- specify with Directed Acyclic Graphs how variables are related in the real world. Finally, I develop nonparametric sharp bounds -- i.e., maximally informative best-/worst-case estimates consistent with limited RCT data -- that show when extrapolations about effect signs are empirically justified. These new results are illustrated with simulated data.

翻译：尽管成本高昂，随机对照试验（RCT）在从社会科学到医学的众多学科领域仍被广泛视为金标准证据。近几十年来，研究者日益采用析因设计来降低重复进行随机对照试验的资源负担，这种设计可同时检验多个假设，例如同时评估多种药物或产品效果的实验。本文指出，当实验中对多种干预措施进行随机化时，任何单一干预在实验环境之外可能产生的效应，即便在实现其他方面完全理想化的条件下，若缺乏极端假设仍无法被识别。这是因为单一处理效应涉及仅存在单一焦点干预的反事实世界，允许其他变量保持其自然取值（这些取值可能受到焦点干预的混杂或修正）。相比之下，观察性研究和析因实验分别提供了零干预和多重干预下潜在结果分布的信息。本文形式化了识别这些孤立量的充分条件，并证明依赖此类设计的研究者必须证明函数形式的线性假设，或在非参数情形下通过有向无环图具体说明现实世界中变量间的关联机制。最后，本文推导了非参数尖锐边界——即与有限随机对照试验数据一致且信息量最大化的最优/最劣情况估计——以揭示何时关于效应方向的推断在经验上是合理的。这些新结论通过模拟数据进行了阐释。