  In randomized experiments, the actual treatments received by some
experimental units may differ from their treatment assignments. This
non-compliance issue often occurs in clinical trials, social experiments, and
the applications of randomized experiments in many other fields. Under certain
assumptions, the average treatment effect for the compliers is identifiable and
equal to the ratio of the intention-to-treat effects of the potential outcomes
to that of the potential 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.
