Artificial Intelligence Counterfactual Inference of Community Clinic Referral Queue Prioritisation Under Unmeasured Inter-Facility Ambulance Diversion: A Healthcare Regret-Bound Evaluation

Community clinic referral queue prioritisation is a sequential decision problem in which the clinician observes patient covariates but not the inter-facility ambulance diversion state that determines whether a referral can be completed. the present analysis formalises the problem as a partially observable Markov decision process with a latent diversion regime and derives a regret bound for any counterfactual inference policy that must act without observing that regime. The bound decomposes into an observable-regret term, a diversion-misclassification term, and a queue-drift term, and it shows that the misclassification penalty scales with the total variation distance between the diversion-conditional outcome distributions rather than with the diversion prevalence itself. The framework is evaluated on the DHS Program indicator 'Neonatal mortality rate (5 year periods) - CI lower bound (-2SE)' (id CM_ECMT_C_NNL), comprising 168 country-survey observations from 38 African countries over 1986-2025, with mean 26.44 and standard deviation 8.25. The regret bound is calibrated against this distribution to show how the misclassification penalty varies across the observed range from Sao Tome and Principe (11.00) to Mali (38.71). The contribution is a distribution-free guarantee that quantifies the cost of unobserved diversion for referral prioritisation, together with the conditions under which a diversion-agnostic policy remains within a stated regret tolerance.