A worked example on the COMPAS dataset
You are a clinician, compliance officer, or data-science auditor. A deployed risk-scoring model has landed on your desk with a request: audit this for disparate performance across protected groups, in a form the FDA or your IRB will accept. You cannot re-train it. You do not have its training weights. You have its outputs, the observed outcomes, and the protected attribute.
This is the problem clinicalfair (CRAN 0.1) is designed for — post-hoc fairness auditing. It takes predictions, labels, and a protected attribute, and returns the set of metrics and visual diagnostics that a regulator or review board expects. No GLM re-fitting, no access to the original training pipeline.
As a worked example I use the COMPAS dataset — the canonical recidivism-prediction audit in the algorithmic-fairness literature, shipped with clinicalfair as compas_sim (predictions + outcomes + race, based on ProPublica (2016) and Angwin et al.). COMPAS is a criminal-justice tool, not a clinical one, but the audit workflow applies identically to a clinical risk score; the final section generalises back.
suppressPackageStartupMessages({
library(clinicalfair)
library(ggplot2)
library(dplyr)
})
data(compas_sim)
dim(compas_sim)[1] 1000 3head(compas_sim, 3) risk_score recidivism race
1 0.4864 1 Black
2 0.2680 0 Black
3 0.1677 0 Whitecompas_sim contains 1 000 rows with the deployed model’s risk score, the binary recidivism outcome, and the protected race attribute (Black vs White). Because we are in audit mode, we treat the risk score as an opaque input — the question is not how it was produced but how its errors distribute across groups.
fd <- fairness_data(
predictions = compas_sim$risk_score,
labels = compas_sim$recidivism,
protected_attr = compas_sim$race,
threshold = 0.5
)
fm <- fairness_metrics(fd,
metrics = c("selection_rate", "tpr", "fpr",
"ppv", "accuracy", "brier"),
ci = TRUE, n_boot = 2000)fm |>
mutate(metric = factor(metric,
levels = c("selection_rate", "tpr", "fpr",
"ppv", "accuracy", "brier"),
labels = c("Selection rate", "TPR", "FPR",
"PPV", "Accuracy", "Brier"))) |>
ggplot(aes(x = group, y = value, fill = group)) +
geom_col(width = 0.6) +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper),
width = 0.2, colour = "grey20") +
facet_wrap(~ metric, scales = "free_y", nrow = 2) +
scale_fill_manual(values = c(Black = "#546E7A", White = "#E65100"),
guide = "none") +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01)) +
labs(x = NULL, y = "Metric value") +
theme_minimal(base_size = 12) +
theme(panel.grid.minor = element_blank(),
strip.text = element_text(face = "bold"))
The four-fifths rule (EEOC, 29 CFR 1607.4(D); also used by FDA AI/ML guidance as a screening heuristic) flags any group whose metric value falls below 0.8× or above 1.25× the reference group’s value. fairness_report() runs this automatically.
fr <- fairness_report(fd)
frThe report flags 3 metric(s) that violate the four-fifths rule: selection_rate (ratio 0.51), tpr (ratio 0.64), fpr (ratio 0.26). Selection rate and error-rate disparities are large, formally triggering a disparate impact finding. PPV and Brier are not flagged — the model is approximately equally calibrated across groups, even though its errors land very differently.
plot_roc(fd) + theme_minimal(base_size = 12) +
theme(panel.grid.minor = element_blank())
plot_roc(). Both curves sit well above the 45° diagonal (AUC is comparable across groups), but at any fixed threshold the two groups’ false-positive and true-positive rates differ. A single global threshold cannot match both TPR and FPR across groups — this is the geometric reason for the disparity above.
plot_calibration(fd, n_bins = 10) + theme_minimal(base_size = 12) +
theme(panel.grid.minor = element_blank())
Changing the global 0.5 threshold to group-specific thresholds is the simplest post-hoc mitigation. threshold_optimize() searches the product of per-group thresholds for the choice that minimises a disparity objective subject to a minimum accuracy floor.
topt_eo <- threshold_optimize(fd, objective = "equalized_odds",
min_accuracy = 0.5)
topt_dp <- threshold_optimize(fd, objective = "demographic_parity",
min_accuracy = 0.5)
topt_eo
topt_dpcompare_df <- bind_rows(
mutate(topt_eo$before, policy = "Global threshold 0.5"),
mutate(topt_eo$after, policy = "Equalized odds"),
mutate(topt_dp$after, policy = "Demographic parity")
) |>
filter(metric == "selection_rate") |>
mutate(policy = factor(policy, levels = c("Global threshold 0.5",
"Equalized odds",
"Demographic parity")))
ggplot(compare_df, aes(x = policy, y = value, fill = group)) +
geom_col(position = position_dodge(width = 0.7), width = 0.6) +
geom_text(aes(label = scales::percent(value, accuracy = 1)),
position = position_dodge(width = 0.7),
vjust = -0.3, size = 3.6, fontface = "bold") +
scale_fill_manual(values = c(Black = "#546E7A", White = "#E65100"), name = NULL) +
scale_y_continuous(labels = scales::percent_format(accuracy = 1),
expand = expansion(mult = c(0, 0.18))) +
labs(x = NULL, y = "Selection rate") +
theme_minimal(base_size = 12) +
theme(panel.grid.minor = element_blank())
The accuracy cost of the two mitigations relative to the global threshold is small: -1.4% for equalized odds and -1.4% for demographic parity. Whether that cost is acceptable, and which fairness objective to choose, are policy questions — see below.
Three observations from this audit reproduce the most-cited tension in algorithmic fairness:
clinicalfair makes both views visible in the same report. The choice between them is a policy decision about which kind of harm matters more — systematic over-flagging of one group (an error-rate concern) versus unequal reliability of the score at equivalent predicted risks (a calibration concern). Statisticians can identify the tension; deciding whose harm counts more is a role for clinical leadership, ethics review, and the regulator.
The identical workflow applies to a deployed clinical risk score — for example, a hospital-acquired-infection predictor, a mortality early-warning score, or a readmission model — simply by passing the relevant columns:
fd <- fairness_data(
predictions = hospital_df$score,
labels = hospital_df$event,
protected_attr = hospital_df$race # or sex, insurance, language, etc.
)
fairness_report(fd)clinicalfair is deliberately model-agnostic. It doesn’t care whether the score came from logistic regression, gradient boosting, or a vendor black-box — only that predictions and outcomes share an index. That constraint — not access to training code, only access to outputs — is what makes it suitable for audits of deployed systems, which are typically the ones actually affecting patients.
The compas_sim dataset records race as a binary Black/White attribute, analytically convenient but not representative of clinical populations: real audits must handle multi-category race and ethnicity, insurance status, primary language, and their intersections, each of which introduces smaller per-cell sample sizes and ethical questions about which axes to prioritise that a two-group worked example cannot surface. The mathematical impossibility result (Chouldechova 2017) means satisfying both calibration parity and equalised odds when base rates differ is formally infeasible; the choice between them is a value judgement rather than a modelling one, and clinicalfair is deliberately agnostic about which to prefer. The threshold-optimisation policy we apply was fit on the same data it is evaluated on; out-of-sample performance typically degrades, and production use should validate on a held-out cohort. Finally, an audit is a diagnosis, not a prescription — identifying a disparity leaves open whether the appropriate response is threshold adjustment, model redesign, better training data, or not deploying the model at all.