A General Framework for Design-Based Treatment Effect Estimation in Paired Cluster-Randomized Experiments

Paired cluster-randomized experiments (pCRTs) are common in education program impact evaluation trials. Although common, there is surprisingly no clear consensus regarding how to analyze this randomization design to estimate average treatment effects. Variance estimation is also complicated due to the dependency created through pairing clusters. Therefore, we aim to provide an intuitive and practical comparison between different estimation strategies for pCRTs to inform practitioners' choice of strategy. To this end, we present a general framework for design-based estimation of an average individual effect in pCRTs. This framework offers a novel and intuitive view on the bias-variance trade-off between point estimators and emphasizes the benefits of covariate adjustment for estimation with pCRTs. In addition to providing a general framework for estimation with pCRTs, the point and variance estimators we present support fixed-sample unbiased estimation with similar precision to a common regression model and conservative variance estimation. Through simulation studies based on an educational efficacy trial, we compare the performance of the point and variance estimators reviewed. Our analysis and simulation studies inform the choice of point and variance estimators for analyzing pCRTs in practice.