Estimation of Causal Effects Under K-Nearest Neighbors Interference

TL;DR

This paper introduces a model and estimators for causal effects in experiments with treatment interference among units, specifically focusing on the influence of K-nearest neighbors, with applications to social network experiments.

Contribution

It develops a K-nearest neighbors interference model, derives causal estimands, proposes unbiased estimators, and validates them through simulations and real-world application.

Findings

Estimators effectively capture indirect effects in KNN interference scenarios.

Treatment effects mainly propagate through closest connections.

Method performs well under various interference conditions.

Abstract

Considerable recent work has focused on methods for analyzing experiments which exhibit treatment interference -- that is, when the treatment status of one unit may affect the response of another unit. Such settings are common in experiments on social networks. We consider a model of treatment interference -- the K-nearest neighbors interference model (KNNIM) -- for which the response of one unit depends not only on the treatment status given to that unit, but also the treatment status of its $K$ ``closest'' neighbors. We derive causal estimands under KNNIM in a way that allows us to identify how each of the $K$-nearest neighbors contributes to the indirect effect of treatment. We propose unbiased estimators for these estimands and derive conservative variance estimates for these unbiased estimators. We then consider extensions of these estimators under an assumption of no weak interaction between direct and indirect effects. We perform a simulation study to determine the efficacy of these estimators under different treatment interference scenarios. We apply our methodology to an experiment designed to assess the impact of a conflict-reducing program in middle schools in New Jersey, and we give evidence that the effect of treatment propagates primarily through a unit's closest connection.