October 2022 Rate-optimal cluster-randomized designs for spatial interference
Michael P. Leung
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Ann. Statist. 50(5): 3064-3087 (October 2022). DOI: 10.1214/22-AOS2224


We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz–Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator’s rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.


The author thanks the referees and Associate Editor for helpful comments that improved the exposition of the paper.


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Michael P. Leung. "Rate-optimal cluster-randomized designs for spatial interference." Ann. Statist. 50 (5) 3064 - 3087, October 2022. https://doi.org/10.1214/22-AOS2224


Received: 1 April 2022; Revised: 1 August 2022; Published: October 2022
First available in Project Euclid: 27 October 2022

MathSciNet: MR4500634
zbMATH: 07628851
Digital Object Identifier: 10.1214/22-AOS2224

Primary: 62G20 , 62K05 , 62M30

Keywords: Causal inference , Experimental design , interference , spatial dependence

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 5 • October 2022
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