Causal inference for interfering units with cluster and population level treatment allocation programs
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Interference arises when an individual's potential outcome depends on the individual treatment level, but also on the treatment level of others. A common assumption in the causal inference literature in the presence of interference is partial interference, implying that the population can be partitioned in clusters of individuals whose potential outcomes only depend on the treatment of units within the same cluster. Previous literature has defined average potential outcomes under counterfactual scenarios where treatments are randomly allocated to units within a cluster. However, within clusters there may be units that are more or less likely to receive treatment based on covariates or neighbors' treatment. We define estimands that describe average potential outcomes for realistic counterfactual treatment allocation programs taking into consideration the units' covariates, as well as dependence between units' treatment assignment. We discuss these estimands, propose unbiased estimators and derive asymptotic results as the number of clusters grows. Finally, we estimate effects in a comparative effectiveness study of power plant emission reduction technologies on ambient ozone pollution.
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