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.