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

Abstract

Randomized experiments in which the treatment of a unit can affect the outcomes of other units are becoming increasingly common in healthcare, economics, and in the social and information sciences. From a causal inference perspective, the typical assumption of no interference becomes untenable in such experiments. In many problems, however, the patterns of interference may be informed by the observation of network connections among the units of analysis. Here, we develop elements of optimal estimation theory for causal effects leveraging an observed network, by assuming that the potential outcomes of an individual depend only on the individual's treatment and on the treatment of the neighbors. We propose a collection of exclusion restrictions on the potential outcomes, and show how subsets of these restrictions lead to various parameterizations. Considering the class of linear unbiased estimators of the average direct treatment effect, we derive conditions on the design that lead to the existence of unbiased estimators, and offer analytical insights on the weights that lead to minimum integrated variance estimators. We illustrate the improved performance of these estimators when compared to more standard biased and unbiased estimators, using simulations.

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