New Estimands for Experiments with Strong Interference

Abstract: 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 binary outcomes, we propose new estimands that can be estimated without such assumptions, allowing for interval estimates assuming only the randomization of treatment. However, the causal implications of these estimands are more limited than those attainable under stronger assumptions, showing only that the treatment effects under the observed assignment varied systematically as a function of each unit's direct and indirect exposure, while also lower bounding the number of units affected.