Power and sample size calculations for cluster randomized trials of vector control interventions with spillover: a simulation-based approximation

Background Field trials of vector control interventions, particularly those against malaria, generally use cluster randomisation with large clusters, to minimize spillover caused by mosquito movement which can bias efficacy estimates. Often trial arms are separated by buffer zones. There is little evidence on the suitable sizes of clusters and buffer zones, nor on the impact of spillover on power and required sample size in the absence of buffer zones. Methods Analyses of simulated trials with a dichotomous outcome were used to establish and parameterize a generalised linear model (GLM) for the efficacy estimate, as a function of the true efficacy, the operative distance of spillover effects, the intra-cluster correlation and cluster size. Standard power and sample size calculations applied to effect size predictions from the GLM gave estimates of optimal cluster size and the required total study population. Results Using a Western Kenyan set of locations, the required total sample size is similar irrespective of whether buffer zones are specified. This minimum is much less than the overall sample size of several recent major malaria CRTs. Conclusions The approach provides a generalisable method for determining the minimum required study size for CRTs with geographical spillover. Trials with relatively small clusters can achieve adequate power by accommodating spillover bias and inflating the number of clusters. Similar total trial sizes are obtained by optimisation of cluster size in trials with buffers. The method could be extended to identify the least expensive trial design for any specific setting and type of outcome.