Bipartite Causal Inference with Interference

Abstract: Statistical methods to evaluate the effectiveness of interventions are increasingly challenged by the inherent interconnectedness of units. Specifically, a recent flurry of methods research has addressed the problem of interference between observations, which arises when one observational unit's outcome depends not only on its treatment but also the treatment assigned to other units. We introduce the setting of bipartite causal inference with interference, which arises when 1) treatments are defined on observational units that are distinct from those at which outcomes are measured and 2) there is interference between units in the sense that outcomes for some units depend on the treatments assigned to many other units. Basic definitions and formulations are provided for this setting, highlighting similarities and differences with more commonly considered settings of causal inference with interference. Several types of causal estimands are discussed, and a simple inverse probability of treatment weighted estimator is developed for a subset of simplified estimands. The estimators are deployed to evaluate how interventions to reduce air pollution from 473 power plants in the U.S. causally affect cardiovascular hospitalization among Medicare beneficiaries residing at 23,458 zip code locations.