Leveraging baseline covariates to analyze small cluster-randomized trials with a rare binary outcome

Cluster-randomized trials (CRTs) involve randomizing entire groups of participants to treatment arms, but are often comprised of a limited number of available clusters. While covariate adjustment can account for chance imbalances between treatment arms and increase statistical efficiency in individually-randomized trials, analytical methods for covariate adjustment in small CRTs have received little attention to date. In this paper, we systematically investigate, through extensive simulations, the operating characteristics of propensity score weighting and multivariable regression as two covariate adjustment strategies for estimating the participant-average causal effect in small CRTs with a rare binary outcome and identify scenarios where each covariate adjustment strategy has a relative efficiency advantage over the other to make practical recommendations. Beyond efficiency considerations, we also examined the finite-sample performance of the sandwich variance estimators associated with propensity score weighting and multivariable regression for quantifying the uncertainty in estimating the participant-average treatment effect. We found that the \citet{mancl2001} type bias-corrected sandwich variance estimator tends to provide the closest to nominal coverage for both propensity score weighting and multivariable regression estimators, extending the existing recommendations for unadjusted analysis of CRTs to accommodate covariate adjustment in small CRTs with a rare binary outcome. To illustrate the practical consequences of these various adjustment approaches, we reanalyzed a recent CRT testing a sedation protocol in $31$ pediatric intensive care units.