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 $$ , ratio of mean cluster-level event rates $$ , ratio of event rates $$ , double ratio of counts $$ , and double ratio of event rates $$ . In the absence of an indirect effect, they all estimate the direct effect of the intervention. Otherwise, $$ , $$ and $$ estimate the total effect, which comprises the direct and indirect effects, whereas $$ and $$ 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, $$ performs comparably with $$ and $$ in trials with a large but realistic number of clusters. When the variability of baseline event rate is large and there is no indirect effect, $$ and $$ tend to offer higher power than $$ , $$ and $$ . We discuss the implications of these findings to the planning and analysis of cluster randomized trials.