Fluoride Varnish Application Interval and Dental Caries Survival in Kenyan School Hygiene Programmes: A Target-Trial Emulation of Reapplication Windows

School-based fluoride varnish programmes in Kenya face a scheduling problem: the interval between reapplications is set by administrative convention rather than by evidence about how caries survival responds to different reapplication windows. No observational data are 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 identifies 52 clusters as the number required for 80% power at a 5-percentage-point effect, and shows that the minimum detectable effect at 80% power falls steeply as cluster count rises from 8 to 32. The contribution is a design specification: it states what a credible target-trial emulation of varnish reapplication windows in Kenyan school programmes would need to measure, how it would need to be structured, and what it could and could not detect.