Artificial Intelligence Governance of Surgical Theater Scheduling Models Under Unmeasured Anesthesia Provider Group Contract Carve-Outs: A Healthcare Political Fairness Estimation

Surgical theater scheduling algorithms allocate operating room time, yet the anesthesia provider group contracts that determine which cases can actually be staffed are frequently carved out of the data those algorithms observe. the present analysis treats that carve-out as a political measurement problem rather than a technical data gap. It develops a fairness-estimation framework in which the unmeasured contract carve-out is modelled as a cluster-level confounder operating through the before-after-control-impact design, and it characterises the operating characteristics of that design under a declared variance structure. The design parameters were eight, sixteen, twenty-four and thirty-two clusters; effect sizes of three, five and eight percentage points; an intraclass correlation of 0.64, a between-cluster standard deviation of 6.0 and a residual standard deviation of 4.5; and 2,000 replications per design cell. Under these parameters the design required fifty-four clusters to detect a five-percentage-point effect at eighty per cent power, a requirement that exceeds the largest cluster count examined. The framework proposes that governance of surgical scheduling algorithms must treat anesthesia contract carve-outs as a measurable political variable, not as an exogenous data limitation, and it specifies the design conditions under which fairness claims about those algorithms can be defended.