A fundamental problem in decision-making systems is the presence of inequity across demographic lines. However, inequity can be difficult to quantify, particularly if our notion of equity relies on hard-to-measure notions like risk (e.g., equal access to treatment for those who would die without it). Auditing such inequity requires accurate measurements of individual risk, which is difficult to estimate in the realistic setting of unobserved confounding. In the case that these unobservables "explain" an apparent disparity, we may understate or overstate inequity. In this paper, we show that one can still give informative bounds on allocation rates among high-risk individuals, even while relaxing or (surprisingly) even when eliminating the assumption that all relevant risk factors are observed. We utilize the fact that in many real-world settings (e.g., the introduction of a novel treatment) we have data from a period prior to any allocation, to derive unbiased estimates of risk. We demonstrate the effectiveness of our framework on a real-world study of Paxlovid allocation to COVID-19 patients, finding that observed racial inequity cannot be explained by unobserved confounders of the same strength as important observed covariates.

翻译：决策系统中的根本问题之一是不同人口群体间存在的不公平现象。然而，不公平性往往难以量化，尤其是当公平概念依赖于难以测量的风险指标时（例如，为未接受治疗将导致死亡的患者提供平等治疗机会）。审计此类不公平性需要精准测量个体风险，但在存在未观测混杂的现实场景中，这难以实现。若这些未观测变量"解释"了表面差异，我们可能低估或高估不公平性。本文证明，即使在放松（或令人惊讶地，甚至彻底放弃）所有相关风险因素均可观测的假设时，仍能对高风险人群的分配比例给出信息性界。我们利用现实场景中（如引入新型疗法）在分配实施前即存在历史数据的事实，推导出风险的无偏估计。我们通过一项针对新冠肺炎患者帕昔洛韦分配的真实研究验证了框架的有效性，发现观测到的种族间不公平性无法被与重要观测协变量同强度的未观测混杂因素所解释。