Quantix Bio Labs / Paper 10
Karanvir Singh
Independent researcher, Quantix Bio, Cambridge, MA, USA
Correspondence: karanvir.singh@quantixmind.com
Manuscript draft, August 2026. Not yet peer reviewed.
Framing note, deliberately placed before the abstract. Self identified race and ethnicity is a social category, not a biological one. Its statistical reconstructability from clinical measurements reflects the joint imprint of ancestry structure, environment, socioeconomic exposure and differential healthcare access on measured biology. Nothing in this paper supports biological essentialism, and no causal claims are made. The question is an engineering one with policy consequences: when a clinical calculator is made "race blind" by deleting the race column, how much race information remains in its inputs and its output?
Background. In response to well documented harms of race adjusted clinical algorithms, the prevailing remedy has been removal of the race variable. Removal guarantees only that the model cannot use the deleted column; if routine clinical features jointly encode race and ethnicity, a race blind model can retain race dependent behaviour. We quantified both stages of this leakage, reconstructability from features and residual information in a deployed score, on national survey data.
Methods. NHANES 2011 to 2018, 14,080 adults in the four largest self identified race and ethnicity groups (6,537 non Hispanic white, 3,601 non Hispanic Black, 2,225 Mexican American, 1,717 other Hispanic). Reconstructability: one versus rest prediction of group membership from nested feature tiers, from age and sex alone through anthropometrics, blood pressure, routine labs (glycohemoglobin, total and HDL cholesterol), smoking, and finally income to poverty ratio as a deliberately social comparison anchor; L2 logistic regression and gradient boosted trees, five fold cross validation. Score leakage: the race blind diabetes risk score of our companion studies, evaluated for conditional mutual information with group given outcome, I(score; A | Y), by plug in estimation over score deciles against a within outcome permutation null, and for group flag rate gaps at clinical thresholds.
Results. Age and sex alone carried almost no group information (AUC 0.51 to 0.59). Adding routine anthropometrics raised reconstructability sharply (AUC 0.68 to 0.74), routine labs raised it further (0.69 to 0.76, gradient boosting), and smoking added little. Critically, adding the income to poverty ratio, an explicitly social variable, moved AUC by only 0.004 to 0.025: the large majority of reconstructable group information is already present in ordinary clinical measurements before any socioeconomic variable is seen. The race blind score itself carried statistically unambiguous residual group information beyond outcome: I(score; A | Y) = 0.015 bits (permutation null 0.003, p < 0.005), and at a 20 percent risk threshold the score flagged 26.5 percent of white against 17.8 percent of Mexican American participants, a nine point gap produced without any race input, driven by the score's understatement of risk in the groups where our companion study documented the largest calibration drift.
Conclusions. Race blindness by column deletion is a syntactic property; the semantic property, race independent behaviour, fails in both measurable senses on national data. Ordinary vitals, anthropometrics and labs reconstruct self identified group at AUC up to 0.76, and the blind score still distributes flags unequally. Fairness auditing of clinical calculators should measure leakage and subgroup calibration directly rather than certify blindness from the feature list, and the same measurements should guide whether explicit, carefully governed use of the attribute for calibration repair harms less than pretending it is absent.
Keywords. race blind algorithms, proxy variables, mutual information, algorithmic fairness, NHANES, clinical calculators
The removal of race coefficients from clinical calculators, kidney function foremost among them, followed persuasive demonstrations that race adjustment could misdirect care [1, 2], and the harms of race correlated algorithm behaviour extend beyond explicit adjustment, as the risk score studied by Obermeyer and colleagues showed while containing no race variable at all [3]. That last example carries the warning this paper quantifies: blindness of the feature list is not blindness of the function.
Two measurable quantities separate the syntax from the semantics. First, reconstructability: how accurately the remaining features predict the removed attribute, which upper bounds nothing but indicates how much attribute correlated structure the model can absorb. Second, score leakage: how much information about the attribute the model's output carries beyond what the outcome itself explains, I(score; A | Y), which is the quantity that connects to disparate behaviour of thresholded decisions; by Pinsker's inequality, small conditional mutual information bounds the achievable statistical disparity, so a large measured value certifies that the score is not behaviourally blind [4, 5].
We measure both on NHANES, whose standardized examination protocol makes it the right instrument: the features are the ordinary contents of a clinical encounter, collected identically across groups, with self identified race and ethnicity recorded. The study asks three questions with one design. How much group information do routine clinical features carry, tier by tier? How much of it is attributable to explicitly socioeconomic variables versus the clinical measurements themselves? And does a specific deployed style, race blind risk score, the diabetes model of our companion drift studies [6, 7], carry residual group information and unequal flag rates?
NHANES cycles 2011 to 2018, adults 20 and over with complete data on all study variables: n = 14,080 across the four largest RIDRETH1 categories. The category variable is self identification into coarse buckets; this coarseness is a measurement limitation discussed in section 4.4, not a claim about human variation.
Six nested tiers: T1 age, sex; T2 plus height, weight, body mass index, waist circumference; T3 plus systolic and diastolic blood pressure; T4 plus glycohemoglobin, total cholesterol, HDL cholesterol; T5 plus current smoking; T6 plus family income to poverty ratio. One versus rest classification per group, five fold stratified cross validation, reporting out of fold AUC for L2 logistic regression (standardized features) and gradient boosted trees, the latter to prevent "the model was too weak" as an objection.
The frozen diabetes score of the companion studies (logistic in age, sex, body mass index, waist, systolic pressure; fit on NHANES 1999 to 2002) was applied to all 14,080 participants. Conditional mutual information I(score; A | Y) was estimated by the plug in over score deciles within outcome strata, debiased against and tested on a permutation null that shuffles group labels within outcome strata (200 permutations). Flag rate by group was computed at thresholds 0.10 and 0.20. The score's marginal ability to predict each group (AUC) is also reported for completeness.
Feature extraction from the SAS transport files uses the lab's numpy XPT reader; models use scikit-learn; the information estimates are implemented from first principles. Everything regenerates from public data with one command.
Table 1. One versus rest reconstruction AUC by feature tier (gradient boosting; logistic in parentheses).
| Tier | Mexican American | Other Hispanic | White NH | Black NH |
|---|---|---|---|---|
| T1 age, sex | 0.56 (0.56) | 0.55 (0.51) | 0.59 (0.55) | 0.55 (0.52) |
| T2 + anthropometrics | 0.74 (0.74) | 0.68 (0.68) | 0.69 (0.66) | 0.69 (0.67) |
| T3 + blood pressure | 0.74 (0.74) | 0.68 (0.68) | 0.70 (0.67) | 0.71 (0.69) |
| T4 + routine labs | 0.74 (0.75) | 0.69 (0.69) | 0.74 (0.69) | 0.76 (0.72) |
| T5 + smoking | 0.75 (0.75) | 0.69 (0.69) | 0.75 (0.70) | 0.76 (0.72) |
| T6 + income | 0.76 (0.76) | 0.69 (0.69) | 0.76 (0.71) | 0.77 (0.72) |
Three observations. The jump occurs at anthropometrics: four entirely ordinary body measurements move reconstruction from near chance to AUC around 0.7. Routine labs add most for the Black non Hispanic group (0.71 to 0.76), consistent with well described population differences in HDL and glycohemoglobin distributions whose interpretation is contested precisely because they blend ancestry and environment [8]. And the income to poverty ratio, the most explicitly social variable available, adds 0.004 to 0.025 AUC on top of the clinical tiers: the reconstructable information is overwhelmingly already inside the clinical measurements. Gradient boosting exceeds logistic regression modestly (up to 0.05 AUC), so nonlinear structure contributes but the phenomenon is not a nonlinearity artifact.
The score's conditional mutual information with group, given outcome, was 0.015 bits against a permutation null of 0.003 bits (debiased 0.012 bits, p < 0.005 with no permuted value reaching the observed one). Against the 1.81 bits of marginal group entropy this is small in absolute terms, which is exactly why the behavioural statement matters more: at the 0.20 risk threshold the score flags 26.5 percent of white, 22.4 percent of Black, 17.8 percent of Mexican American and 17.8 percent of other Hispanic participants; at 0.10, the gap between white and Mexican American participants is 8.4 points (51.4 versus 43.1 percent). Read jointly with the companion subgroup drift study [7], the direction is the harmful one: the groups with the highest measured miscalibration, whose true risk the frozen score most understates, are flagged least.
As a lone feature the score predicts group at AUC 0.47 to 0.53, essentially chance. This is the instructive contrast: a score can be almost useless as a group classifier and still behave unequally at thresholds, because disparity lives in the tails of the score distribution, not in average separability. Auditing tools that test whether the output "predicts race" and stop there will pass models that fail at the decision boundary.
Column deletion delivered neither of the two properties it is deployed to deliver. The feature space reconstructs self identified group at up to AUC 0.76 from measurements no one proposes to delete, and the blind score's decisions distribute unequally across groups, in the direction that compounds the calibration disparity documented in the companion study. The socioeconomic anchor result sharpens the point: this is not primarily leakage through income; the clinical measurements themselves are the proxy.
Not a return to race adjusted medicine, and not despair about fairness: measurement. First, "race blind" should be demoted from a certification to a feature list description, and fairness claims should rest on measured subgroup calibration and threshold behaviour, which our companion studies show can be monitored with a few hundred labelled cases per group. Second, the finding reframes the live policy debate about explicit, governed use of race and ethnicity for calibration repair [9]: the alternative to explicit use is not race independence, it is implicit, unaudited race dependence of exactly the kind measured here. Whether repair should use the attribute is an ethical and clinical decision; that blindness does not exist as a technical option is now a measured fact for this calculator class.
The eGFR debate established the harms of explicit race adjustment [1, 2]; Obermeyer and colleagues established that race free features can carry racially disparate behaviour through label choice [3]; the machine learning fairness literature has long noted proxy encodings in principle [4, 5]. The contribution here is quantification on standardized national examination data with tiered attribution (clinical versus social sources of leakage), plus the two stage audit design, features and deployed score, with the information theoretic and threshold level measurements connected through the same dataset.
RIDRETH1 categories are coarse social administrative buckets; heterogeneity within them is large, and reconstructability of the bucket is not reconstructability of any individual's identity or ancestry. NHANES examines a survey sample, unweighted here (the companion study's weighted machinery applies directly and is released). The score studied is one transparent calculator; deep models over richer features would plausibly leak more, making our estimates conservative. Conditional mutual information on deciles is a coarse lower bound style estimate; finer partitions raise it. Reconstruction AUC does not imply any deployed system attempts reconstruction; it bounds what any system could absorb.
For clinical calculators, race blindness is not an achievable property of the feature list; it is an empirical property of behaviour, to be measured. The measurements are cheap, and this paper supplies the design and the code.
All NHANES files are public. Complete source regenerates every number with one command.
The author declares no competing interests. The work received no funding.
Figure 1. Reconstruction AUC by feature tier and group (leakage_tiers.svg).