Analysis of Broken Randomized Experiments by Principal Stratification

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.