Interpretability Audits of Computer Vision Dermatology Classifiers Under Skin Tone Reference Card Absence: A Healthcare Fairness Estimation

Dermatology computer vision classifiers are increasingly evaluated for fairness across skin tones, yet the reference standards used to label tone in audit datasets are themselves inconsistent. The problem is framed as a measurement invariance failure: when tone labels are derived from uncalibrated sources, the audit's conditioning variable is contaminated, and apparent fairness gaps conflate classifier behaviour with labelling error. A formal framework is developed that decomposes the observed fairness gap into a classifier component and a tone-labelling error component, and a design-based estimation procedure is proposed for audits in which no reference card is available. The framework is characterised through a replication-based evaluation of the before-after-control-impact estimator 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. The evaluation indicates that 54 clusters are required to detect a 5 percentage point fairness gap at 80% power. The contribution is a measurement-theoretic account of what interpretability audits can and cannot establish when tone reference standards are absent, together with a design rule for sizing such audits.