School-based fluoride varnish programmes and untreated caries inequality in South African primary schools: a target-trial emulation of nurse-delegation thresholds

Delegating school-based fluoride varnish application to nurses rather than dental therapists is often proposed to widen coverage in South African primary schools, but the minimum number of clusters at which such a programme can detect a policy-relevant reduction in untreated caries inequality has not been established. Power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points.56 clusters are required to detect a 5-percentage-point effect at 80% power, and that the minimum detectable effect at 80% power falls steeply as cluster count rises from 8 to 32. The intraclass correlation of 0.64 dominates the design: at 8 clusters, even an 8-percentage-point effect is detected with low probability, whereas at 32 clusters a 5-percentage-point effect becomes detectable. The results imply that nurse-delegation thresholds cannot be evaluated credibly with the small cluster counts typical of district-level pilot programmes, and that the BACI estimator's operating characteristics should be reported alongside any claim that nurse delegation reduces untreated caries inequality.