Training Scores for Conditional Audits: Overlap Weighting and Power under Confounding

Conditional audits often test a score trained for marginal prediction, even though that objective rewards the very confounders the audit conditions on. We study whether train-only overlap weighting can recover conditional signal lost during score construction. The procedure estimates discrete-stratum label proportions in training data, fits a weighted classifier, and freezes its scores before an independent exact-stratum permutation test. We establish its training-balance target and explain why independent testing preserves the randomization guarantee. A Gaussian power ceiling separates score-learning loss from limited overlap. Across 25 synthetic configurations, we evaluate effect size, overlap, sample size, noise, and confounder measurement error. In a fresh 500-seed alternative block, overlap weighting raises forest detection from 61.6% to 79.4%, a paired gain of 17.8 percentage points [13.4, 22.4], while its null rejection rate is 4.0%. Global class balancing yields 60.8% detection. Additional continuous-confound and repeated-clip experiments delineate the test's assumptions. The contribution is a controlled score-training study and reproducible audit procedure built from established weighting and randomization tools.