Complications in Causal Inference: Incorporating Information Observed After Treatment is Assigned

Abstract

Randomized experiments are the gold standard for inferring causal effects of treatments. However, complications often arise in randomized experiments when trying to incorporate additional information that is observed after the treatment has been randomly assigned. The principal stratification framework has provided clarity to these problems by explicitly considering the potential outcomes of all information that is observed after treatment is randomly assigned. Principal stratification is a powerful general framework, but it is best understood in the context of specific applied problems (e.g., non-compliance in experiments and "censoring due to death" in clinical trials). This thesis considers three examples of the principal stratification framework, each focusing on different aspects of statistics and causal inference.