  Three critical issues for causal inference that often occur in modern,
complicated experiments are interference, treatment nonadherence, and missing
outcomes. A great deal of research efforts has been dedicated to developing
causal inferential methodologies that address these issues separately. However,
methodologies that can address these issues simultaneously are lacking. We
propose a Bayesian causal inference methodology to address this gap. Our
methodology extends existing causal frameworks and methods, specifically,
two-staged randomized experiments and the principal stratification framework.
In contrast to existing methods that invoke strong structural assumptions to
identify principal causal effects, our Bayesian approach uses flexible
distributional models that can accommodate the complexities of interference and
missing outcomes, and that ensure that principal causal effects are weakly
identifiable. We illustrate our methodology via simulation studies and a
re-analysis of real-life data from an evaluation of India's National Health
Insurance Program. Our methodology enables us to identify new active causal
effects that were not identified in past analyses. Ultimately, our simulation
studies and case study demonstrate how our methodology can yield more
informative analyses in modern experiments with interference, treatment
nonadherence, missing outcomes, and complicated outcome generation mechanisms.
