Model-assisted complier average treatment effect estimates in randomized experiments with non-compliance

Non-compliance is a common problem in randomized experiments in various fields. Under certain assumptions, the complier average treatment effect is identifiable and equal to the ratio of the intention-to-treat effects of the potential outcomes to that of the treatment received. To improve the estimation efficiency, we propose three model-assisted estimators for the complier average treatment effect in randomized experiments with a binary outcome. We study their asymptotic properties, compare their efficiencies with that of the Wald estimator, and propose the Neyman-type conservative variance estimators to facilitate valid inferences. Moreover, we extend our methods and theory to estimate the multiplicative complier average treatment effect. Our analysis is randomization-based, allowing the working models to be misspecified. Finally, we conduct simulation studies to illustrate the advantages of the model-assisted methods and apply these analysis methods in a randomized experiment to evaluate the effect of academic services or incentives on academic performance.