Design of Cluster-Randomized Trials with Cross-Cluster Interference

Cluster-randomized trials often involve units that are irregularly distributed in space without well-separated communities. In these settings, cluster construction is a critical aspect of the design due to the potential for cross-cluster interference. The existing literature relies on partial interference models, which take clusters as given and assume no cross-cluster interference. We relax this assumption by allowing interference to decay with geographic distance between units. This induces a bias-variance trade-off: constructing fewer, larger clusters reduces bias due to interference but increases variance. We propose new estimators that exclude units most potentially impacted by cross-cluster interference and show that this substantially reduces asymptotic bias relative to conventional difference-in-means estimators. We then study the design of clusters to optimize the estimators' rates of convergence. We provide formal justification for a new design that chooses the number of clusters to balance the asymptotic bias and variance of our estimators and uses unsupervised learning to automate cluster construction.