  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.
