Cluster-Randomized Trials with Cross-Cluster Interference

The literature on cluster-randomized trials typically assumes no interference across clusters. This may be implausible when units are irregularly distributed in space without well-separated communities, in which case clusters may not represent significant geographic, social, or economic divisions. In this paper, we develop methods for reducing bias due to cross-cluster interference. First, we propose an estimation strategy that excludes units not surrounded by clusters assigned to the same treatment arm. We show that this substantially reduces asymptotic bias relative to conventional difference-in-means estimators without substantial cost to variance. Second, we formally establish a bias-variance trade-off in the choice of clusters: constructing fewer, larger clusters reduces bias due to interference but increases variance. We provide a rule for choosing the number of clusters to balance the asymptotic orders of the bias and variance of our estimator. Finally, we consider unsupervised learning for cluster construction and provide theoretical guarantees for $k$-medoids.