Artificial Intelligence Causal Inference of Community Clinic Hypertension Treatment Escalation Under Unmeasured White-Coat Measurement Confounding: A Healthcare Doubly Robust Prescribing Safety Evaluation

White-coat measurement confounding threatens the validity of artificial-intelligence-guided hypertension treatment escalation in community clinics: when the decision to intensify therapy is informed by a blood pressure reading that is itself distorted by the measurement setting, the prescribing rule and the outcome share a common cause that no observed covariate set captures. No observational data are used or claimed. The analysis declares a variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, and estimates power across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design requires 56 clusters to detect a 5-percentage-point escalation effect at 80 per cent power. The framework separates the prescribing-safety estimand from the measurement-confounding nuisance, and the design evaluation shows how the doubly robust estimator's bias correction interacts with cluster-level heterogeneity. The contribution is a formal statement of the identification conditions under which an AI prescribing rule can be evaluated for safety when white-coat measurement is unobserved, together with the design parameters that make such an evaluation informative.