🤖 AI Summary
In cluster-randomized trials, cross-cluster interference is often ignored—especially when units exhibit irregular spatial distributions and cluster boundaries are ill-defined—leading to systematic bias in causal effect estimation.
Method: We formally characterize the bias–variance trade-off under cross-cluster interference and propose a “boundary-unit exclusion” truncation estimator that mitigates interference by leveraging neighborhood homogeneity. We further establish interference-robust theoretical guarantees for k-medoids clustering.
Contribution/Results: Our approach significantly reduces asymptotic bias while keeping variance inflation bounded. We derive an optimal cluster-number selection criterion grounded in this bias–variance analysis. Crucially, the method requires no prior knowledge of community structure, thereby enhancing both estimation consistency and practical applicability in real-world settings with ambiguous clustering.
📝 Abstract
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.
