Characterisation of between-cluster heterogeneity in malaria cluster randomised trials to inform future sample size calculations.

Cluster randomised trials (CRTs) are important tools for evaluating the community-wide effect of malaria interventions. During the design stage, CRT sample sizes need to be inflated to account for the cluster heterogeneity in measured outcomes. The coefficient of variation (k), a measure of such heterogeneity, is typically used in malaria CRTs yet is often predicted without prior data. Underestimation of k decreases study power, thus increases the probability of generating null results. In this meta-analysis of cluster-summary data from 24 malaria CRTs, we calculate true prevalence and incidence k values using methods-of-moments and regression modelling approaches. Using random effects regression modelling, we investigate the impact of empirical k values on original trial power and explore factors associated with elevated k. Results show empirical estimates of k often exceed those used in sample size calculations, which reduces study power and effect size precision. Elevated k values are associated with incidence outcomes (compared to prevalence), lower endemicity settings, and uneven intervention coverage across clusters. Study findings can enhance the robustness of future malaria CRT sample size calculations by providing informed k estimates based on expected prevalence or incidence, in the absence of cluster-level data.