Bayesian Approach to Two-Stage Randomized Experiments in the Presence of Interference and Noncompliance

No interference between experimental units is a critical assumption in causal inference. Over the past decades, there have been significant advances to go beyond this assumption using the design of experiments; two-stage randomization is one such. The researchers have shown that this design enables us to estimate treatment effects in the presence of interference. On the other hand, the noncompliance behavior of experimental units is another fundamental issue in many social experiments, and researchers have established methods to deal with noncompliance under the assumption of no interference between units. In this article, we propose a Bayesian approach to analyze a causal inference problem with both interference and noncompliance. Building on previous work on two-stage randomized experiments and noncompliance, we apply the principal stratification framework to compare treatments adjusting for post-treatment variables yielding special principal effects in the two-stage randomized experiment. We illustrate the proposed methodology by conducting simulation studies and reanalyzing the evaluation of India's National Health Insurance Program, where we draw more definitive conclusions than existing results.