Race in Clinical Models

Q: What is Race in Clinical Models?

The race-in-clinical-models question is whether a prediction model for care should take race (or an ethnicity field) as an input, given that race is a social category that can stand in for differences in access and exposure but is not itself a biological cause.

Whether a clinical model should see a patient's race is argued as if it were a statistical question. On real data it is often a values question with a small statistical effect.

The One-Sentence Definition

The race-in-clinical-models question is whether a prediction model for care should take race (or an ethnicity field) as an input, given that race is a social category that can stand in for differences in access and exposure but is not itself a biological cause.

Why It Matters

Several clinical formulas used a race term for years, and Race Correction in Clinical Algorithms describes how that delayed care for some patients. The same question now arises for every machine-learning risk model trained on hospital data: leave race in and the model can be checked for calibration by group and can correct for real differences in data quality; take it out and the model cannot use it, but the information often leaks back through proxies (Proxy Variables).

Two arguments are common and both are partly empirical. For including it: a model that ignores a group variable can be systematically off for that group, and you cannot see it without the variable. Against: using race as a predictor can hard-code a historical disparity into a score that allocates care. This explainer runs the comparison on the benchmark's hospital data so the empirical half has numbers.

Core Concept: Three Things to Compare

Accuracy: does the model with race predict better overall?
Calibration by group: does the predicted risk match the observed rate in each group, with and without race?
Allocation: if the score picks who gets a limited resource, how does the share of places and the share of the truly high-risk who get one change?

Only the third is what a patient experiences, and it needs a rule for how many places there are. The example uses the top 10% of scores.

Concrete Example: Healthcare Readmission

Healthcare Readmission: 30-day readmission after a hospital stay with diabetes, about 99,500 patients, logistic regression on the audit's core and proxy columns, the benchmark's split. One model also receives race, gender and age; the other receives none of them.

with race in the model
  AUC 0.635
  African American: mean predicted risk 0.115 vs observed 0.103 | given a place 0.114 | of those who were readmitted, given a place 0.213
  other patients : mean predicted risk 0.112 vs observed 0.114 | given a place 0.097 | of those who were readmitted, given a place 0.203
without race (and without gender and age)
  AUC 0.633
  African American: mean predicted risk 0.114 vs observed 0.103 | given a place 0.111 | of those who were readmitted, given a place 0.213
  other patients : mean predicted risk 0.112 vs observed 0.114 | given a place 0.097 | of those who were readmitted, given a place 0.205

Accuracy barely moves: AUC 0.635 with race and 0.633 without. For this model race adds almost no predictive information beyond the clinical columns.
Calibration differs by group either way: African American patients have a mean predicted risk of 0.115 and an observed rate of 0.103, so the model over-predicts for them by about 1.2 points with race and 1.1 without; for other patients predicted 0.112 against observed 0.114. Removing race does not fix it, because the over-prediction comes from the other columns.
Allocation shifts by under a point: the share of African American patients given a place is 11.4% with race and 11.1% without, against 9.7% for others. Of the patients who really were readmitted, 21.3% of African American patients and 20.3% of others receive a place with race, 21.3% and 20.5% without.

So on this model the debate is not a trade between accuracy and fairness: the variable carries almost no signal, and the group-level calibration gap exists with or without it. A model where race carried real signal would tell a different story, and the check above is how to find out.

Detection/Implementation Code

Run from the repo root (PYTHONPATH=. python3 explainers/code/race-in-clinical-models.py; that file is generated from the block below).

import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_auc_score
from faircode.benchmark import load_audit        # same loader, encoding and split as the benchmark harness

with_race = load_audit("Healthcare Readmission", strategy="baseline")      # core + proxy + race, gender and age
without = load_audit("Healthcare Readmission", strategy="unawareness")     # the same without the protected columns
train, test = with_race.idx_train, with_race.idx_test
y = with_race.y.to_numpy()
black = (with_race.df["race"] == "AfricanAmerican").to_numpy().astype(int)[test]

def fit(data):
    X = data.X.to_numpy(dtype=float)
    Z = (X - X[train].mean(axis=0)) / (X[train].std(axis=0) + 1e-9)
    model = LogisticRegression(max_iter=2000).fit(Z[train], y[train])
    return model.predict_proba(Z[test])[:, 1]

def report(name, p):
    y_te = y[test]
    # Use the score to pick the 10% of patients for a follow-up programme with a fixed number of places.
    chosen = p >= np.quantile(p, 0.90)
    print(f"{name}")
    print(f"  AUC {roc_auc_score(y_te, p):.3f}")
    for g, label in ((1, "African American"), (0, "other patients ")):
        rows = black == g
        print(f"  {label}: mean predicted risk {p[rows].mean():.3f} vs observed {y_te[rows].mean():.3f} "
              f"| given a place {chosen[rows].mean():.3f} | of those who were readmitted, given a place {chosen[rows & (y_te == 1)].mean():.3f}")

report("with race in the model", fit(with_race))
report("without race (and without gender and age)", fit(without))

Limitations

One dataset, one outcome. Readmission is a weak signal here (AUC about 0.63), which is why race adds little. A model with stronger signal can behave very differently.
The "other patients" group is mixed. It combines several groups, and a gap for one group can be hidden inside it. Report each group you have enough rows for.
A small allocation shift is not a small harm. At a few thousand patients per percentage point, the number of people affected can still be large.
Removing race does not remove it. The model without race still sees the proxy columns, and its calibration gap is unchanged.
Whether to include it is not settled by this table. The choice also turns on how the score will be used and on what the clinical and ethical consensus is, see Race Correction in Clinical Algorithms.

Race Correction in Clinical Algorithms - formulas that took race as an explicit input
Proxy Variables - why removing the column does not remove the information
Clinical Score Miscalibration - calibration by group in detail
Underdiagnosis Bias - how the labels themselves can differ by group
Fairness Through Unawareness - the general case for dropping an attribute

Healthcare Readmission/ - the audit used for the example above