Dental hygiene therapy silver diamine fluoride arrest rates and lesion selection thresholds in Kenyan school caries programmes: a target-trial emulation of referral timing

School-based caries programmes in Kenya that deploy silver diamine fluoride (SDF) by dental hygienists face a referral-timing problem: which lesions should be arrested in situ and which should be referred for restorative care, given that the decision rule itself determines the arrest rate a programme can report. the present analysis treats that decision as a design parameter rather than a clinical afterthought and characterises the operating characteristics of a before-after-control-impact (BACI) estimator for programme-level arrest rates under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.640). No observational data are used or claimed; the analysis is a replication-based evaluation across 2000 design cells defined by 8, 16, 24 and 32 clusters and effect sizes of 3, 5 and 8 percentage points. Power was estimated for each cell, and the minimum detectable effect at 80% power was derived. Fifty-four clusters are required to detect a 5-percentage-point difference at 80% power under the declared variance structure. The results indicate that lesion-selection thresholds interact with cluster count in ways that make small programmes structurally unable to distinguish a genuine SDF effect from referral-driven case-mix change. Referral timing should be specified as an a priori design parameter in school caries programmes, and that the BACI estimator is defensible only when the threshold rule is held fixed across the before and after periods.