Precision-Recall Lab

Precision & Recall Screening Lab

The Precision-Recall curve answers: when you raise an alarm, how trustworthy is it? (Precision) — and how many true cases did you catch? (Recall).

Drag the yellow dot on the P-R curve to explore the trade-off at every threshold.

Precision vs Recall

Both are computed from the confusion matrix at a given threshold:

Precision = TP / (TP + FP) → of all patients flagged malignant, how many actually are? Recall = TP / (TP + FN) → of all malignant patients, how many did we flag?

Raising the threshold → higher Precision, lower Recall. Lowering it → vice versa.

The F1 Score

F1 is the harmonic mean of Precision and Recall — it balances both into one number:

F1 = 2 × (Precision × Recall) / (Precision + Recall) F1 = 1.0 → perfect F1 = 0.0 → completely wrong The F-beta score generalises this: Fβ = (1+β²) × P×R / (β²×P + R) β > 1 → prioritise Recall (screening) β < 1 → prioritise Precision (follow-up)

⚖️ Ethical Reality

In cancer screening, Recall is life-critical. Missing a malignancy has severe consequences. A model optimised for Precision alone may achieve 95% precision by only flagging the most obvious cases — missing early-stage cancers entirely.

① Patient Input

Fasting Glucose

mg / dL

Patient BMI

kg / m²

② Threshold & Model

Decision Threshold0.50

or drag yellow dot on the P-R curve

β₀ · Risk Baseline-9.0

intercept

β₁ · Glucose Weight0.045

mg/dL discriminating power

Fβ Beta Weight1.0

>1 prioritises Recall (screening)

③ Metrics at Threshold

F1 Score (harmonic mean)

—

Precision (PPV)

—

Recall (Sensitivity)

—

Avg Precision (AP)

—

Threshold

④ Precision-Recall Curve — Recall (x) vs Precision (y) · F1 iso-curves shown · drag yellow dot to explore · AP = area under curve