The Monotone Instrumental Variable in Randomized Trials with Noncompliance

Noncompliance is an important problem in randomized trials. The estimation and bounds of average causal effects (ACEs) have been discussed as a way to address this issue. Previous studies have considered ACEs under the instrumental variable (IV) assumption, which postulates that potential outcomes are constant across subject sub-populations assigned to separate treatment regimens. However, the IV assumption may not be valid in unmasked trials. In the present analyses, the IV assumption is relaxed to the monotone IV (MIV) assumption, which replaces equality in the IV assumption with inequality. We propose bounds on ACEs under the MIV assumption in addition to the other existing assumptions. The results demonstrate that the intention-to-treat effect is an upper or lower bound under one assumption and the per-protocol effect is an upper or lower bound under the other assumption, even using the MIV assumption in place of the IV assumption. These proposed bounds are illustrated using a classic randomized trial.