In the quest to make defensible causal claims from observational data, it is sometimes possible to leverage information from "placebo treatments" and "placebo outcomes" (or "negative outcome controls"). Existing approaches employing such information focus largely on point identification and assume (i) "perfect placebos", meaning placebo treatments have precisely zero effect on the outcome and the real treatment has precisely zero effect on a placebo outcome; and (ii) "equiconfounding", meaning that the treatment-outcome relationship where one is a placebo suffers the same amount of confounding as does the real treatment-outcome relationship, on some scale. We instead consider an omitted variable bias framework, in which users can postulate non-zero effects of placebo treatment on real outcomes or of real treatments on placebo outcomes, and the relative strengths of confounding suffered by a placebo treatment/outcome compared to the true treatment-outcome relationship. Once postulated, these assumptions identify or bound the linear estimates of treatment effects. While applicable in many settings, one ubiquitous use-case for this approach is to employ pre-treatment outcomes as (perfect) placebo outcomes. In this setting, the parallel trends assumption of difference-in-difference is in fact a strict equiconfounding assumption on a particular scale, which can be relaxed in our framework. Finally, we demonstrate the use of our framework with two applications, employing an R package that implements these approaches.

翻译：在通过观测数据提出可辩护的因果主张的过程中，有时可以利用"安慰剂治疗"和"安慰剂结果"（或"阴性结果对照"）的信息。现有利用这些信息的方法主要关注点识别，并假设：（i）"完全安慰剂"，即安慰剂治疗对结果的影响精确为零，而真实治疗对安慰剂结果的因果效应也精确为零；（ii）"等混杂"，即当其中一个变量为安慰剂时，治疗与结果关系受到的混杂程度与真实治疗-结果关系在某种尺度上相同。我们转而考虑遗漏变量偏倚框架，在该框架下研究者可以假设：安慰剂治疗对真实结果存在非零效应，或真实治疗对安慰剂结果存在非零效应，以及安慰剂治疗/结果相对于真实治疗-结果关系所受混杂程度的相对强度。一旦设定这些假设，就能识别或界定治疗效应的线性估计量。虽然该方法适用于多种场景，但一个普遍的应用案例是将治疗前结果作为（完全）安慰剂结果。在此情境下，双重差分法的平行趋势假设实际上是在特定尺度上的严格等混杂假设，而我们的框架可以放宽该假设。最后，我们通过两个应用案例演示该框架的使用，并采用一个实现这些方法的R包。