ROC-AUC Lab | EpiSense

ROC & AUC Diagnostic Lab

The Receiver Operating Characteristic curve shows how a model's Sensitivity and Specificity trade off at every possible threshold — all at once.

Drag the yellow dot on the curve to pick a threshold. Watch all metrics update live.

How the ROC Curve Is Built

For every possible threshold (0→1), we compute TPR (Sensitivity) and FPR (1 − Specificity):

TPR = TP / (TP + FN) → of all diabetics, how many caught? FPR = FP / (FP + TN) → of all healthy, how many falsely flagged? Plot (FPR, TPR) for each threshold → ROC curve

A perfect classifier hugs the top-left corner. A random classifier lies on the diagonal.

Area Under the Curve (AUC)

AUC = probability that the model ranks a random positive higher than a random negative.

AUC = 1.0 → perfect model AUC = 0.5 → random guessing AUC = 0.0 → perfectly inverted model AUC is threshold-independent — a single number summarising overall discrimination.

Youden's J = TPR − FPR. The optimal clinical threshold maximises J.

⚖️ Ethical Reality

AUC treats all thresholds equally. In cancer screening, missing a malignancy (FN) is far worse than a false alarm (FP). The optimal threshold must reflect the cost asymmetry of clinical errors — not just mathematical balance.

① Patient Input

Fasting Glucose

mg / dL

Patient BMI

kg / m²

② Threshold & Model

Decision Threshold0.50

or drag yellow dot on the ROC curve

β₀ · Risk Baseline-9.0

intercept (MLE learns this)

β₁ · Glucose Weight0.045

mg/dL discriminating power

β₂ · BMI Weight0.12

kg/m² discriminating power

③ Metrics at Threshold

Area Under Curve (AUC)

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Sensitivity (TPR)

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Specificity (TNR)

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FPR (1−Spec)

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Youden's J

④ ROC Curve — FPR vs TPR across all thresholds · AUC shaded · drag the yellow dot to explore · diagonal = random classifier