Non-compliance is common in real world experiments. We focus on inference about the sample complier average causal effect, that is, the average treatment effect for experimental units who are compliers. We present three types of inference strategies for the sample complier average causal effect: the Wald estimator, regression adjustment estimators and model-based Bayesian inference. Because modern computer assisted experimental designs have been used to improve covariate balance over complete randomization, we discuss inference under both complete randomization and a specific computer assisted experimental design - Mahalanobis distance based rerandomization, under which asymptotic properties of the Wald estimator and regression adjustment estimators can be derived. We use Monte Carlo simulation to compare the finite sample performance of the methods under both experimental designs. We find that under either design, the Bayesian method performs the best because it is stable, it yields smallest median absolute error and smallest median interval length. The improvement by the Bayesian method is especially large when the fraction of compliers is small. We present an application to a job training experiment with non-compliance.

翻译：非依从性在现实实验中普遍存在。本文聚焦于样本依从者平均因果效应（即依从实验单元的平均处理效应）的推断问题。我们提出了三种针对样本依从者平均因果效应的推断策略：瓦尔德估计量、回归调整估计量以及基于模型的贝叶斯推断。由于现代计算机辅助实验设计被用于改进完全随机化中的协变量平衡，我们讨论了完全随机化设计及一种特定计算机辅助实验设计——基于马氏距离的再随机化——下的推断，并推导了在此两种设计下瓦尔德估计量和回归调整估计量的渐近性质。我们通过蒙特卡洛模拟比较了两种实验设计下各方法在有限样本中的表现。研究发现，在两种设计下，贝叶斯方法均表现最优：其稳定性强，且能产生最小的中位数绝对误差和最短的中位数区间长度。当依从者比例较小时，贝叶斯方法的改进尤为显著。本文还将该方法应用于一个存在非依从性的职业培训实验案例。