Dental hygiene therapy powered toothbrush dispensing and caregiver-reported plaque control in Zambian orphanage dental hygiene programmes: a cluster-randomised implementation evaluation

Cluster-randomised evaluations of powered toothbrush dispensing in orphanage dental hygiene programmes face a design problem that is rarely quantified before fieldwork: with few clusters and high intraclass correlation, the before-after-control-impact estimator may lack power to detect the modest plaque-control differences that programmes can realistically deliver. Power was estimated across 2000 design cells defined by cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis found that 54 clusters were required for 80% power at a 5-percentage-point effect, that power rose steeply between 8 and 24 clusters, and that the minimum detectable effect at 80% power fell as cluster count increased. The intraclass correlation of 0.64 dominated the design, making cluster count the binding constraint rather than within-cluster sample size. Orphanage dental hygiene programmes in Zambia and comparable settings should treat cluster count as the primary design decision and should report the assumed intraclass correlation alongside any caregiver-reported plaque outcome.