Screening Test PPV vs Prevalence

Screening Population

Prevalence 2.0%

Sensitivity 95%

Specificity 95%

Live PPV

P(has disease | tested positive)

–

– of – positive results are real

Truly sick

–

Truly healthy

–

True positive

False positive

False negative

True negative

Why PPV swings so hard

Sensitivity and specificity are properties of the test itself — they don't change no matter who you screen. But positive predictive value (PPV) depends on who you're testing, because of how many truly-sick vs truly-healthy people are in the pool to begin with.

PPV = (Sens × Prev)
      ────────────────────────────────────
      (Sens × Prev) + ((1 − Spec) × (1 − Prev))

High prevalence — most people tested are actually sick, so most positives are true positives. PPV stays high.
Low prevalence — almost everyone tested is actually healthy. Even a small false-positive rate, applied to that huge healthy pool, produces more false positives in raw numbers than the tiny sick pool can produce true positives. PPV collapses.
This is why a single positive result from a rare-disease screening test is usually followed by a confirmatory test — most of those first positives are false alarms.

True positive False positive False negative True negative

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.