Artificial Intelligence Counterfactual Scheduling of Echocardiography Referrals Under Variable Queue Abstraction Completeness: A Distributionally Robust Evaluation of Healthcare Diagnostic Delay

Queue abstraction completeness—the degree to which a scheduling model observes the true state of a diagnostic waiting list—is rarely treated as a formal source of uncertainty in counterfactual scheduling evaluations. The framework characterises the ambiguity set of queue-state distributions induced by missing abstraction, derives a robust scheduling policy that minimises worst-case diagnostic delay, and establishes finite-sample bounds on the delay gap between the robust policy and its complete-information counterpart. A replication-based evaluation of the before-after-control-impact estimator was conducted under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with power estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 54 clusters are required for 80% power at a 5-percentage-point effect. The contribution is a formal treatment of abstraction completeness as a distributional ambiguity that propagates into delay estimates, together with a design-level characterisation of the cluster counts needed to detect clinically meaningful scheduling effects.