On estimation of causal effects under the K-nearest-neighbor interference model with misspecified interference

Abstract

Interference in an experiment occurs when the response of a unit is not only affected by the treatment status given to that unit, but is also impacted by the interventions of other units around it. Interference in experiments is becoming increasingly common, especially in experiments performed within social networks. However, traditional causal models often assume no interference across experimental units. Estimating causal effects without considering interference when it is present may lead to biased estimation of causal quantities and may lead to incorrect conclusions. However, often it is impossible to know the interference structure prior estimating causal effects, and considerable work has been performed to improve estimation under unknown or misspecified interference structure. In this report, we investigate misspecification of treatment interference under the K-Nearest Neighbor Interference Model (KNNIM). The KNNIM model assumes that the response of an unit is affected by its own treatment status and treatments applied to the unit’s K “closest” units, where closeness may be a measure of the interaction between units. Of note, KNNIM allows for larger effects of treatment interference between units with stronger interactions. We perform a simulation study under KNNIM in which we inject uncertainty in the interaction measure to create misspecification in the interference structure. In our simulations, we assume that the magnitudes of interference effects are larger for closer units. We then perform Horvitz-Thompson estimation of direct, indirect, and nearest-neighbor causal effects, and we investigate how misspecification can impact estimates. We find, for our considered models, that the misspecification injects bias in estimates of the 1st nearest-neighbor effects, but have little impact on other causal effects. The bias of the 1st-nearest-neighbor effect grows with increasing sample sizes.