Interpretability Audits of Computer Vision Cervical Cytology Screeners Under Staining Reagent Substitution: A Healthcare Fairness Evaluation

Staining reagent substitution in cervical cytology alters the colour distributions on which computer vision screeners depend, yet the fairness consequences of such substitutions remain uncharacterised. The framework defines a fairness gap functional over stain strata and derives its sampling distribution under a before-after-control-impact design with eight, sixteen, twenty-four and thirty-two clusters, an intraclass correlation of 0.64, a between-cluster standard deviation of 6.0 and a residual standard deviation of 4.5. Power analysis across 2000 replications per design cell shows that fifty-six clusters are required to detect a five-percentage-point fairness gap at eighty per cent power. The contribution is a design-theoretic account of how interpretability evidence should be collected when stain chemistry is not held fixed, together with the operating characteristics that such an audit must satisfy before its findings can be trusted.