Bias analysis of the instrumental variable estimator as an estimator of the average causal effect

Noncompliance is a common problem in drawing causal inference in randomized trials. The instrumental variable (IV) method estimates the average causal effect in randomized trials with noncompliance. However, the IV estimator generally yields a biased estimate under a non-null hypothesis, although it can yield an unbiased estimate under a null hypothesis. Therefore, it is important to evaluate the potential bias of the IV estimate quantitatively. This paper provides such a quantitative method, which is an extension of bias analysis for unmeasured confounders using the confounding risk difference in the context of observational studies. The proposed method will help investigators to provide a realistic picture of the potential bias of the IV estimate. It is illustrated using a field trial for coronary heart disease.