School-Based Fluoride Varnish Delivery Interval and Dental Caries Prevention Among South African Children: A Target-Trial Emulation of Application Frequency Thresholds

School-based fluoride varnish programmes in South Africa face a delivery-interval problem that existing trials have not resolved: whether the caries-preventive benefit of varnish depends on application frequency in a threshold manner, and what cluster counts are required to detect such thresholds in a school-randomised design. No observational data were used or claimed. Under a declared variance structure with between-cluster standard deviation of 6.0, residual standard deviation of 4.5 and intraclass correlation of 0.64, 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. The analysis indicates that 52 clusters are required to detect a 5-percentage-point effect at 80% power, and that the minimum detectable effect falls steeply as cluster count rises from 8 to 32. The intraclass correlation of 0.64 dominates the design's operating characteristics, and the before-after-control-impact interaction is sensitive to cluster count in a way that frequency-threshold hypotheses must accommodate. Frequency-threshold questions in school-based varnish delivery are best framed as target-trial emulations whose design parameters are specified before data collection, and that the cluster counts used in current South African school programmes are insufficient for threshold detection.