Ratio estimators of intervention effects on event rates in cluster randomized trials

We consider five asymptotically unbiased estimators of intervention effects on event rates in non‐matched and matched‐pair cluster randomized trials, including ratio of mean counts [Formula: see text] , ratio of mean cluster‐level event rates [Formula: see text] , ratio of event rates [Formula: see text] , double ratio of counts [Formula: see text] , and double ratio of event rates [Formula: see text]. In the absence of an indirect effect, they all estimate the direct effect of the intervention. Otherwise, [Formula: see text] , [Formula: see text] and [Formula: see text] estimate the total effect, which comprises the direct and indirect effects, whereas [Formula: see text] and [Formula: see text] estimate the direct effect only. We derive the conditions under which each estimator is more precise or powerful than its alternatives. To control bias in studies with a small number of clusters, we propose a set of approximately unbiased estimators. We evaluate their properties by simulation and apply the methods to a trial of seasonal malaria chemoprevention. The approximately unbiased estimators are practically unbiased and their confidence intervals usually have coverage probability close to the nominal level; the asymptotically unbiased estimators perform well when the number of clusters is approximately 32 or more per trial arm. Despite its simplicity, [Formula: see text] performs comparably with [Formula: see text] and [Formula: see text] in trials with a large but realistic number of clusters. When the variability of baseline event rate is large and there is no indirect effect, [Formula: see text] and [Formula: see text] tend to offer higher power than [Formula: see text] , [Formula: see text] and [Formula: see text]. We discuss the implications of these findings to the planning and analysis of cluster randomized trials.