Supervised School Brushing Programme Fidelity and Dental Caries Increment Among Ugandan Primary Pupils: A Multilevel Variance Decomposition of Hygiene Delivery Thresholds

Supervised school brushing programmes are widely promoted as a low-cost caries-prevention strategy in East African primary schools, yet their effectiveness depends on delivery fidelity that is rarely measured or modelled. Using the DHS Program indicator 'Knowledge of any method of contraception among married women' (FP_KMET_W_ANY) as a calibration analogue for population-level knowledge thresholds across 38 African countries and 162 country-survey observations from 1986 to 2025 (mean 91.776, SD 11.342, range 57.80 in Chad to 99.90 in Eswatini), the paper specifies a three-level model in which pupils are nested within schools and schools within districts, and in which fidelity is treated as a latent school-level construct with a threshold structure. The framework proposes that caries increment is non-linear in fidelity, with an inflection point below which additional brushing sessions yield negligible caries protection. Variance decomposition under this specification would permit estimation of the proportion of caries-increment variance operating at the school level, the district level and the pupil level, and would allow the threshold parameter to be identified separately from the mean fidelity effect. The contribution is methodological: it reframes school brushing evaluation from average-effect estimation to threshold identification, and it specifies the data structures and identification conditions under which such thresholds can be estimated in Ugandan primary-school settings.