How the harm test works

Why a separate test

An observed score shift may be harmless. This page explains test_harm, which compares a reference group (source) with a group under review (target). See Benign vs harmful shift for the null of no adverse shift and guidance on which test to use.

For this derivation, recode the score so larger values mean more harm. If lower values are worse, pass worse="lower"; the test flips the sign before applying the same statistic. Choose the direction from the score's meaning, not from the p-value.

Tail-focused separation

For the recoded score S and threshold t, define the false-positive rate (FPR, the share of source scores above t) and true-positive rate (TPR, the share of target scores above t):

\[ \operatorname{FPR}(t) = P(S > t \mid \text{source}), \qquad \operatorname{TPR}(t) = P(S > t \mid \text{target}). \]

The ordinary shift statistic is ROC AUC, the area under the receiver operating characteristic curve. Each part of the FPR range contributes equally. The harm statistic gives more weight to thresholds the source rarely exceeds:

\[ \operatorname{AUC} = \int \operatorname{TPR}(t)\,d\operatorname{FPR}(t), \qquad T = \int \operatorname{TPR}(t)\,[1-\operatorname{FPR}(t)]^2\, d\operatorname{FPR}(t). \]

T is the weighted AUC reported by test_harm. Since 1 - FPR(t) is the share of source scores at or below the threshold, the weight is largest where few source observations exceed it. Target scores that enter this rare tail affect T more than changes among values the source often produces.

Compare T with its permutation null—the distribution from shuffling group labels—not with 0.5, because the weights change the scale.

Same samples, different question

Both tests hold scores fixed and permute the source and target labels. test_shift uses a two-sided ROC AUC statistic to test for rank-based separation. test_harm uses the tail-focused threshold weights above and a one-sided alternative.

Signatures are in Shift testing. A complete workflow is in Get started.

Reference

Kamulete, V. M. (2022). Test for non-negligible adverse shifts (D-SOS). Proceedings of UAI, PMLR 180:959-968. PMLR and arXiv:2107.02990.