  Paired cluster-randomized experiments (pCRTs) are common across many
disciplines because there is often natural clustering of individuals, and
paired randomization can help balance baseline covariates to improve
experimental precision. Although pCRTs are common, there is surprisingly no
obvious way to analyze this randomization design if an individual-level (rather
than cluster-level) treatment effect is of interest. 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 in pCRTs in order to inform practitioners'
choice of strategy. To this end, we present a general framework for
design-based estimation in pCRTs for average individual effects. This framework
offers a novel and intuitive view on the bias-variance trade-off between
estimators and emphasizes the benefits of covariate adjustment for estimation
with pCRTs. In addition to providing a general framework for estimation in
pCRTs, the point and variance estimators we present support fixed-sample
unbiased estimation with similar precision to a common regression model and
consistently conservative variance estimation. Through simulation studies, we
compare the performance of the point and variance estimators reviewed. Finally,
we compare the performance of estimators with simulations using real data from
an educational efficacy trial. Our analysis and simulation studies inform the
choice of point and variance estimators for analyzing pCRTs in practice.
