Risk-adjusted regression finds larger racial disparities in police stops
Empirical audits have become central to discrimination cases as detailed individual-level data have become easier to collect and analyze. Yet the standard statistical playbook can miss the central problem when the decision under review is not a standalone human judgment but a machine-assisted one. In those settings, the model often omits race and other legally protected traits, which makes simple covariate adjustment a poor proxy for fairness review. The result is a familiar analytical trap: a method designed to detect bias can end up smoothing away the very disparity it is supposed to measure.
This study introduces risk-adjusted regression, a three-step framework intended to estimate “unjustified” disparities in both human and machine decisions. The approach begins by using all available information in a machine learning model to estimate the value of a potential action, or inversely, the risk associated with taking it. It then compares decisions after adjusting only for those risk estimates. A final sensitivity step examines how much the findings could shift if risk is measured imperfectly. The logic is straightforward but consequential: if two people appear similar on the basis of observed risk alone, a large difference in how they are treated becomes harder to explain away.
Why conventional adjustment can miss the disparity
Traditional regression models often control for observed covariates and then test whether a protected group still receives different treatment. In theory, that seems like a clean way to isolate discrimination. In practice, the result depends heavily on which covariates are included, how they are measured, and whether they actually capture the features relevant to the decision-maker. When race is excluded from the model, as it usually is in legal and operational settings, the analysis may fail to account for the structural information that shapes the decision itself. Machine learning systems sharpen this problem because they can use many other correlated variables as substitutes, making the path from measured covariates to actual decision risk even less direct.
The paper’s core argument is that disparate impact should be assessed against estimated decision risk rather than against a narrow set of observed attributes. In policing, for example, a stop may be more likely in locations or circumstances that are themselves associated with higher criminal activity risk. But if the decision-making process still produces unequal treatment among individuals with similar estimated risk, that gap becomes the relevant object of concern. The framework therefore tries to separate justified differences tied to estimated risk from unjustified differences that remain after risk is accounted for.
A stop can look statistically defensible and still be racially unequal.
New York City stops as a test case
The method was demonstrated on a detailed dataset of 2.2 million police stops of pedestrians in New York City. That scale matters because small audits can be swayed by noise, sparse data, or unstable model estimates; a dataset this large permits a far more granular look at patterns across encounters. The investigators compared what conventional statistical tests suggest with what emerges after risk adjustment, and the contrast was substantial. Traditional methods understated the size of the racial disparities once the analysis shifted from raw covariate adjustment to the risk-based framework.
That difference is not merely technical. In a domain as sensitive as street-level policing, the choice of analytic method affects how agencies, courts, and policymakers interpret whether a pattern reflects legitimate public-safety targeting or an unjustified burden placed on a racial group. If a model is built on incomplete or poorly aligned covariates, it may incorrectly classify some of the observed disparity as explainable. The risk-adjusted approach is designed to reduce that error by anchoring the comparison in an estimate of decision value itself.
The study also makes clear that audit methods need to be stress-tested against measurement error. Risk is not directly observed; it is inferred from available data and a machine learning model. Any inferential system of that kind can misclassify individuals near the decision threshold or fail to capture context that human officers implicitly use. The final sensitivity analysis therefore serves an important role, because it asks how much trust the findings deserve if the risk estimate is not perfect. That is especially relevant in legal settings, where the burden of proof can turn on exactly how much uncertainty remains after adjustment.
What the framework changes for legal and clinical-style audit logic
Although the dataset comes from policing rather than medicine, the analytical lesson is familiar to any field that relies on model-based triage, screening, or resource allocation. In health care, algorithms are increasingly used to decide who receives outreach, specialty referral, intensive monitoring, or scarce treatment slots. When the underlying model is built from incomplete proxies, a simple post hoc regression may fail to reveal whether the system is distributing opportunity fairly. The framework proposed here offers a more disciplined way to ask whether differences in treatment persist after accounting for estimated need or risk.
The appeal lies in its practicality. Rather than trying to infer intent directly, which is often impossible, the method evaluates whether decisions diverge after adjusting for a richer estimate of the underlying risk tied to the action under review. That kind of analysis aligns more closely with disparate impact reasoning, where the legal question is not only whether a decision-maker meant to discriminate but whether the outcome imposes an unjustified burden on a protected group. In machine-assisted systems, where protected characteristics are usually excluded from the input set, this distinction becomes especially important.
At the same time, the paper does not claim that risk adjustment eliminates every source of uncertainty. The estimate of risk itself can be wrong, incomplete, or shaped by historical data that already reflect unequal treatment. Those constraints limit any audit method that depends on observed patterns alone. Even so, the scale of the New York City analysis shows how much traditional testing can compress the apparent disparity when the wrong adjustment strategy is used.
A sharper audit tool, and a narrower margin for error
The practical consequence of this work is a methodological warning: if analysts rely only on conventional statistical controls, they may understate racial disparities in systems that decide who gets stopped, screened, admitted, referred, or denied. Risk-adjusted regression offers a more direct lens on whether treatment tracks estimated need or risk, rather than merely correlating with a partial list of observable factors. In a legal audit, that could change how evidence is presented. In a clinical or operational audit, it could change whether an algorithm is judged acceptable at all.
The study leaves open a demanding question for future audits in any high-stakes setting: how robust is the estimated risk measure when the data are incomplete, biased, or historically conditioned? The answer will shape whether risk-adjusted regression becomes a routine tool for fairness audits or remains a specialized method for cases where the data are exceptionally rich.