Causal Inference in Experiments with Interference

David Choi (Carnegie Mellon University)

In experiments that study social phenomena, such as peer influence or herd immunity, the treatment of one unit may influence the outcomes of others. Such "interference between units" violates traditional approaches for causal inference, so that additional assumptions are often imposed to model or limit the underlying social mechanism; for example, one might assume that the units can be partitioned into non-interfering groups, or that an underlying dependency graph is unknown but sparse so that most units do not interfere with each other. For binary outcomes, we propose an approach that does not require such assumptions, allowing for interference that is both unmodeled and arbitrarily strong, with confidence intervals derived using only the randomization of treatment. However, the estimates will have wider confidence intervals and weaker causal implications than those attainable under stronger assumptions, essentially showing only that effects exist and are associated with specified measures of treatment exposure, such as the number of treated friends or neighborhood treatment rate. The approach allows for the usage of regression, matching, or weighting, as may best fit the application at hand. Inference is done by bounding the distribution of the estimation error over all possible values of the unknown counterfactual, using an integer program. Examples are shown using using a vaccination trial and two experiments investigating the effects of social influence.

https://arxiv.org/abs/2107.00248


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