Although randomized controlled trials have long been regarded as the ``gold standard'' for evaluating treatment effects, there is no natural prevention from post-treatment events. For example, non-compliance makes the actual treatment different from the assigned treatment, truncation-by-death renders the outcome undefined or ill-defined, and missingness prevents the outcomes from being measured. In this paper, we develop a statistical analysis framework using principal stratification to investigate the treatment effect in broken randomized experiments. The average treatment effect in compliers and always-survivors is adopted as the target causal estimand. We establish the asymptotic property for the estimator. We apply the framework to study the effect of training on earnings in the Job Corps Study and find that the training program does not have an effect on employment but possibly have an effect on improving the earnings after employment.

翻译：尽管随机对照试验长期以来被视为评估处理效应的"金标准"，但无法自然避免处理后事件的发生。例如，不依从行为导致实际处理与分配处理不一致，"死亡截断"使结果变量未定义或定义不清，而数据缺失则阻碍了结果的测量。本文提出一种基于主分层的统计分析框架，用于研究失效随机化实验中的处理效应。我们采用依从者与始终存活者的平均处理效应作为目标因果估计量，并建立了估计量的渐近性质。将该框架应用于职业培训研究中的培训对收入影响分析，发现培训项目对就业状况无显著影响，但可能对就业后的收入提升产生作用。