Nonparametric Bounds for Causal Effects in Imperfect Randomized Experiments

Nonignorable missingness and noncompliance can occur even in well-designed randomized experiments, making the intervention effect that the experiment was designed to estimate nonidentifiable. Nonparametric causal bounds provide a way to narrow the range of possible values for a nonidentifiable causal effect with minimal assumptions. We derive novel bounds for the causal risk difference for a binary outcome and intervention in randomized experiments with nonignorable missingness that is caused by a variety of mechanisms, with both perfect and imperfect compliance. We show that the so-called worst-case imputation, whereby all missing subjects on the intervention arm are assumed to have events and all missing subjects on the control or placebo arm are assumed to be event-free, can be too pessimistic in blinded studies with perfect compliance, and is not bounding the correct estimand with imperfect compliance. We illustrate the use of the proposed bounds in our motivating data example of peanut consumption on the development of peanut allergies in infants. We find that, even accounting for potentially nonignorable missingness and noncompliance, our derived bounds confirm that regular exposure to peanuts reduces the risk of development of peanut allergies, making the results of this study much more compelling.

即便在设计精良的随机试验（randomized experiments）中，也可能出现不可忽略缺失（nonignorable missingness）与不依从（noncompliance）的情况，导致试验原本旨在估计的干预效应（intervention effect）无法被识别。非参数因果界（nonparametric causal bounds）为在最小化假设的前提下，缩小不可识别因果效应的可能取值范围提供了可行路径。针对由多种机制引发、同时存在完全依从（perfect compliance）与不完全依从（imperfect compliance）情况的不可忽略缺失随机试验，我们推导了二分类结局（binary outcome）与干预下的因果风险差（causal risk difference）的新型界值。我们证明，所谓的最坏情况插补（worst-case imputation）——即假设干预组（intervention arm）中所有缺失受试者均发生结局事件，而对照组或安慰剂组（control or placebo arm）中所有缺失受试者均未发生结局事件——在完全依从的盲法研究（blinded studies）中往往过于保守，且在不完全依从的情况下无法对正确的目标估计量（estimand）界定范围。我们以婴儿花生摄入与花生过敏发生风险的关联研究作为动机示例数据集，演示了所提界值的应用方法。我们发现，即便考虑到潜在的不可忽略缺失与不依从情况，我们推导得到的界值仍证实了规律摄入花生可降低婴儿花生过敏的发生风险，从而使本研究的结论更具说服力。