, Manoochehr Babanezhad and Els Goetghebeur
Ghent University and 
Harvard School of Public Health
Abstract: Instrumental variables (IV) estimators are well established in a broad range of fields to correct for measurement error on exposure. In a distinct prominent stream of research, IV's are becoming increasingly popular for estimating causal effects of exposure on outcome since they allow for unmeasured confounders which are hard to avoid. Because many causal questions emerge from data which suffer severe measurement error problems, we combine both IV approaches in this article to correct IV-based causal effect estimators in linear (structural mean) models for possibly systematic measurement error on the exposure. The estimators rely on the presence of a baseline measurement that is associated with the observed exposure and known not to modify the target effect. Simulation studies and the analysis of a small blood pressure reduction trial () with treatment noncompliance confirm the adequate performance of our estimators in finite samples. Our results also demonstrate that incorporating limited prior knowledge about a weakly identified parameter (such as the error mean) in a frequentist analysis can yield substantial improvements.
Key words and phrases: Causal inference, instrumental variables, measurement error, noncompliance, prior information, two-stage least squares estimators, weak identifiability.