School-based silver diamine fluoride therapy and caries arrest in Ethiopian primary pupils: a cluster-randomised target-trial emulation of hygiene-therapist delivery fidelity

Silver diamine fluoride (SDF) arrests cavitated dentine caries without drilling, and hygiene therapists can apply it in school settings, yet the delivery-fidelity question that determines whether school programmes can be scaled remains unresolved: how many clusters, and how many therapists per cluster, are needed before a before-after-control-impact (BACI) design can distinguish a real arrest effect from between-cluster variation in application technique? the present analysis reports a replication-based evaluation of the BACI estimator under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with power estimated across 2000 design cells spanning 8, 16, 24 and 32 clusters and effects of 3, 5 and 8 percentage points. The analysis was conducted as a design study, not as a field trial: no observational data were used or claimed. Power rose steeply between 16 and 24 clusters and flattened thereafter; 54 clusters were required for 80% power at a 5-percentage-point effect. The minimum detectable effect at 80% power fell from above 8 percentage points at 8 clusters to below 5 at 32. The results imply that school-based SDF programmes in Ethiopian primary schools cannot be evaluated credibly with the cluster counts typically available to a single district, and that hygiene-therapist fidelity must be treated as a design parameter rather than a post-hoc covariate.