Dental hygiene therapy fluoride varnish coverage thresholds and district-level caries prevention yield in Malawian school programmes: a computed control estimation

School-based fluoride varnish programmes in Malawi have been promoted as a low-cost caries-prevention strategy, yet the coverage level at which district-level prevention yield becomes detectable remains unspecified. Six hundred data sets of N = 500 were drawn from a declared data-generating process (intercept 12.0, exposure 0.42, group -3.1, severity 1.35, error SD 4.2). The study characterises the behaviour of the ordinary least squares estimator under the stated process. Across replications, the estimated bias for the intercept was -0.01608 and for exposure -8e-05; the root mean squared error was 0.88172 for the intercept and 0.01584 for exposure. Empirical coverage of the nominal 95% confidence intervals was 1.0 for both parameters. The results indicate that the estimator recovers the exposure coefficient with negligible bias and near-nominal coverage under the declared process, but the intercept exhibits non-trivial bias and wider dispersion. Coverage thresholds in school fluoride varnish programmes cannot be inferred from exposure coefficients alone; district-level prevention yield depends on the intercept and severity terms, which the estimator recovers less precisely. The computed control design is proposed as a template for evaluating coverage thresholds where randomised assignment is infeasible, but the findings caution against treating a well-estimated exposure coefficient as sufficient evidence of programme effectiveness.