Propensity-Adjusted AUC under Nuisance-Model Misspecification

Adjusted AUC under nuisance-model misspecification can drop below one half under Gaussian latent-index assumptions with exact linear-index strata, with a closed-form correlation boundary.

• Why it matters: Propensity adjustment is used to compare detector scores within matched measured properties, but its reliability depends on how the nuisance model defines those groups.
• What they did: The study derives a closed-form boundary for when adjusted AUC falls below 0.5, validates it by quadrature matching 36 simulation cells within 0.008, and adds overlap screening plus a self-stratified control.
• The result: In real pathology corpora, logistic and boosted-tree propensity models using the same 16 features disagree, and mean adjusted-AUC gaps are 0.057 on AFB, 0.048 on Kaggle, and 0.049 on PCam across the reported splits.

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