Oral-health literacy screening thresholds and dental therapy referral yield in Ghanaian community pharmacies: a latent-class diagnostic-accuracy estimation

Community pharmacies in Ghana are the first point of contact with the health system for many adults with oral complaints, yet the decision to refer a client to dental therapy is made without a validated screening threshold. the present analysis treats the referral decision as a diagnostic-accuracy problem and asks what oral-health literacy cut-point, applied at the pharmacy counter, would maximise the yield of appropriate dental-therapy referrals while limiting unnecessary ones. Because no criterion-standard literacy measurement is routinely available in that setting, the paper develops a latent-class diagnostic-accuracy framework in which the unobserved true literacy state is estimated jointly with the sensitivity and specificity of candidate thresholds, using the Hui-Walter parameterisation with a third, conditionally dependent indicator to secure identification. The framework is specified for a two-class model with three indicators and is illustrated against the structure of the DHS Program indicator 'Physical violence committed by schoolmate/classmate' (id DV_PCPV_W_SCH), which was tabulated for 14 African countries over 2021-2025 (mean 2.979, standard deviation 1.99, minimum Tanzania 0.20, maximum Malawi 6.60). That indicator is used only to demonstrate the arithmetic of between-unit dispersion that a threshold rule must tolerate; it is not an oral-health measure and no oral-health data were analysed. The paper derives the referral-yield identity that links threshold sensitivity and specificity to the proportion of clients correctly referred, shows how the identity behaves when prevalence is low, and argues that a pharmacy-level literacy threshold is defensible only when it is calibrated to local prevalence rather than imported from a high-income validation study. The contribution is a transferable estimation strategy and a set of explicit conditions under which a literacy cut-point can be justified as a referral rule.