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Design of Cluster-Randomized Trials with Cross-Cluster Interference

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  • Michael P. Leung

Abstract

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 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.

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  • Michael P. Leung, 2023. "Design of Cluster-Randomized Trials with Cross-Cluster Interference," Papers 2310.18836, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2310.18836
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    References listed on IDEAS

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    1. Timothy B. Armstrong & Michal Kolesár, 2018. "Optimal Inference in a Class of Regression Models," Econometrica, Econometric Society, vol. 86(2), pages 655-683, March.
    2. Hudgens, Michael G. & Halloran, M. Elizabeth, 2008. "Toward Causal Inference With Interference," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 832-842, June.
    3. Sandra M. Eldridge & Obioha C. Ukoumunne & John B. Carlin, 2009. "The Intra‐Cluster Correlation Coefficient in Cluster Randomized Trials: A Review of Definitions," International Statistical Review, International Statistical Institute, vol. 77(3), pages 378-394, December.
    4. Michael P. Leung, 2021. "Rate-Optimal Cluster-Randomized Designs for Spatial Interference," Papers 2111.04219, arXiv.org, revised Sep 2022.
    5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    6. Neal Alexander & Audrey Lenhart & Karim Anaya-Izquierdo, 2020. "Spatial spillover analysis of a cluster-randomized trial against dengue vectors in Trujillo, Venezuela," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 14(9), pages 1-13, September.
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