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Randomized experiments in which the treatment of a unit can affect theoutcomes of other units are becoming increasingly common in healthcare,economics, and in the social and information sciences. From a causal inferenceperspective, the typical assumption of no interference becomes untenable insuch experiments. In many problems, however, the patterns of interference maybe informed by the observation of network connections among the units ofanalysis. Here, we develop elements of optimal estimation theory for causaleffects leveraging an observed network, by assuming that the potential outcomesof an individual depend only on the individual's treatment and on the treatmentof the neighbors. We propose a collection of exclusion restrictions on thepotential outcomes, and show how subsets of these restrictions lead to variousparameterizations. Considering the class of linear unbiased estimators of theaverage direct treatment effect, we derive conditions on the design that leadto the existence of unbiased estimators, and offer analytical insights on theweights that lead to minimum integrated variance estimators. We illustrate theimproved performance of these estimators when compared to more standard biasedand unbiased estimators, using simulations.

Elements of estimation theory for causal effects in the presence of network interference