Simple efficient bias corrected instrumental variable estimator for randomized trials with noncompliance

An instrumental variable (IV) estimator has been widely used to estimate causal effects among compliers in randomized trials with noncompliance. The estimator of complier average treatment effect can be expressed as a ratio of two unbiased estimators but the ratio estimator is not unbiased. The bias of IV estimator can be substantial when the sample size is small, or when there is substantial noncompliance. A simple adjustment to the standard instrumental variable estimator is studied to lower the bias. The bias corrected estimator can lower the bias in an order of magnitude, and we verify by numerical examples that the bias corrected estimator can have substantially lower bias and mean squared error compared to the usual IV estimator for small to moderate sample sizes. The proposed point estimator does not need an iterative procedure to implement and can perform well even when the outcome distributions of compliers and non-compliers do not overlap. We also discuss situations where the IV estimator and the proposed estimator can consistently estimate the population average treatment effect.