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 andmatched-pair cluster randomized trials, including ratio of mean counts (r1), ratio of mean cluster-level event rates (r2), ratio of event rates (r3), double ratio of counts (r4), and double ratio of event rates (r5). In the absence of an indirect effect, they all estimate the direct effect of the intervention. Otherwise, r1, r2, and r3 estimate the total effect, which comprises the direct and indirect effects, whereas r4 and r5 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, r1 performs comparably with r2 and r3 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, r4 and r5 tend to offer higher power than r1, r2, and r3. We discuss the implications of these findings to the planning and analysis of cluster randomized trials.