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

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.;In particular, the first example considers early escape designs in which additional rescue medication is provided for patients that do not respond well to the assigned treatment in a placebo-controlled clinical trial. We demonstrate complications that arise in such trials as well as provide a Bayesian analysis of a dataset with such complications. Another example considers the case of binary outcomes in a randomized experiment. Binary outcomes, in combination with a binary treatment, necessarily lead to four principal strata that cannot be identified with the observed data. We consider inference for the average causal effect by testing null hypotheses that determine the number of units in the principal strata of interest. Fisher's randomization test, a standard randomization-based analysis, breaks down for such hypotheses because they are not sharp and rely on nuisance unknowns. We interpret the randomization test as a Bayesian posterior predictive check, which can integrate out the nuisance unknowns. The last example focuses on estimands that assess the efficacy of a prophylactic treatment of HIV, which fits into the more general framework of assessing causal effects of treatment for preventing infectious diseases. We focus on two issues involving information observed after treatment is assigned: exposure to the disease and interference between units. We link these two issues by showing how interference occurs because an effective treatment reduces the exposure in the population.