Principal stratification for causal inference with extended partial compliance

Many randomized experiments, especially those in social sciences, suffer from non-compliance behavior, which would generate non-trivial consequences on the estimation for the causal effects of treatment assignments. Standard analyses using the Intention-to-Treat effect, which directly compares the average outcomes of the treatment group and the control group, may be biased for scientific estimands with the presence of non-compliance. Some widely used statistical techniques to address this issue, such as the standard instrumental variable estimate, rely heavily on certain implicit assumptions and thus are not flexible enough to handle more complicated situations in various settings. The Principal Stratification framework, which is a developed version of the Rubin Causal Model based on the potential outcome concept, has provided another perspective to analyze such a complication. By treating potential compliance behavior as a characteristic of the units in the experiments, previous applications of this framework have successfully addressed simple binary non-compliance problems.; Our work is to expand the application scope of this framework to "extended partial compliance" through two case studies, where units may comply with neither treatment nor control and compliance is only partial. The first case study is a revisit to Efron-Feldman (1991), which was among the earliest statistical articles to address non-compliance and has stimulated many active discussions including the original idea of Principal Stratification. By making weaker assumptions on the same dataset, we can diagnose the validity of the Efron-Feldman assumptions in the context of our model. We also address the necessary framework in order to estimate "dose-response" from such an experiment in which dose is not randomized. The second case study is the analysis of the New York City School Choice Scholarship Program, which encounters both missing data problems and non-compliance. Our research based on the framework reveals interesting information about the participants' potential compliance behavior and their school performances. These two studies exemplify the advantages of Principal Stratification: it possesses more flexibility and can examine individual assumptions explicitly.