Assessing Algorithm Fairness Requires Adjustment for Risk Distribution Differences: Re-considering the Equal Opportunity Criterion

The proliferation of algorithm-assisted decision making has prompted calls for careful assessment of algorithm fairness. One popular fairness metric, equal opportunity, demands parity in true positive rates (TPRs) across different population subgroups. However, we highlight a critical but overlooked weakness in this measure: at a given decision threshold, TPRs vary when the underlying risk distribution varies across subgroups, even if the model equally captures the underlying risks. Failure to account for variations in risk distributions may lead to misleading conclusions on performance disparity. To address this issue, we introduce a novel metric called adjusted TPR (aTPR), which modifies subgroup-specific TPRs to reflect performance relative to the risk distribution in a common reference subgroup. Evaluating fairness using aTPRs promotes equal treatment for equal risk by reflecting whether individuals with similar underlying risks have similar opportunities of being identified as high risk by the model, regardless of subgroup membership. We demonstrate our method through numerical experiments that explore a range of differential calibration relationships and in a real-world data set that predicts 6-month mortality risk in an in-patient sample in order to increase timely referrals for palliative care consultations.