Artificial Intelligence Benchmarking of Cross-Hospital Transferable Chest Radiograph Triage Models Under Unmeasured Acquisition Protocol Heterogeneity: A Healthcare Fairness-Transfer Evaluation

Chest radiograph triage models are frequently reported as transferable across hospitals, yet the acquisition protocol that produced each image is rarely recorded in the metadata that accompany benchmark datasets. the present analysis treats that omission as a structural feature of the evaluation problem rather than a data-cleaning nuisance, and asks what a fairness-transfer benchmark can legitimately conclude when the acquisition protocol is an unmeasured cluster-level confounder. The analysis is a design study, not an empirical audit: it characterises the operating characteristics of a before-after-control-impact (BACIP) estimator under a declared variance structure with between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.64, using 2000 replications per design cell across cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. Under that structure, 54 clusters are required to detect a 5-percentage-point transfer gap at 80% power, a requirement that exceeds every cluster count in the design grid. The paper derives the bias of the naive pooled estimator under protocol-driven clustering, shows that the BACIP contrast remains identified when protocol is time-invariant within cluster, and specifies the conditions under which a reported cross-hospital fairness gap is an artefact of protocol heterogeneity rather than a property of the model. The contribution is a benchmark design specification and an identification argument, not a set of measured transfer gaps.