Bounds on the complier average causal effect in randomized trials with noncompliance

Noncompliance is a common concern in drawing causal inference in randomized trials. There is a large body of literature on methods for dealing with this issue. Specifically, it is well known that the average causal effect within the principal strata of compliance behavior (complier average causal effect, CACE) is equal to the instrumental variable estimator under the monotonicity assumption. However, there is only a small amount of published literature that discusses CACE without this assumption. Here, we present bounds on the CACE without the monotonicity assumption. To derive the bounds, we utilize the idea considered to derive bounds on the principal strata effects in the context of causal mediation analysis and those on the average causal effects among the whole population. The bounds presented here are illustrated using a classic randomized trial.