Sensitivity, Specificity, PPV, and NPV
Understanding Diagnostic Test Performance
Sensitivity, Specificity, PPV, and NPV — and When They Lie
Every diagnostic test has a fixed sensitivity and specificity — properties of the test itself. But PPV and NPV are not fixed. They shift with every change in disease prevalence. Understanding why is the difference between ordering tests wisely and ordering them reflexively.
Part 1 — The 2×2 Table: What Every Test Produces
Order any diagnostic test and you get one of four outcomes. Every measure of test performance derives from these four cells.
| Disease Present | Disease Absent | |
|---|---|---|
| Test Positive | True Positive (TP) | False Positive (FP) |
| Test Negative | False Negative (FN) | True Negative (TN) |
TP — test positive, disease present. You caught it. FP — test positive, disease absent. False alarm. FN — test negative, disease present. You missed it. TN — test negative, disease absent. Correctly reassured.
Part 2 — The Four Metrics: Formulas and Plain English
| Metric | Formula | Plain English |
|---|---|---|
| Sensitivity | TP / (TP + FN) | Of all patients WITH the disease, how many did the test correctly identify? |
| Specificity | TN / (TN + FP) | Of all patients WITHOUT the disease, how many did the test correctly clear? |
| PPV | TP / (TP + FP) | If the test is positive, what is the probability the patient actually has the disease? |
| NPV | TN / (TN + FN) | If the test is negative, what is the probability the patient is truly disease-free? |
| Accuracy | (TP + TN) / Total | Of all patients tested, how many were classified correctly? |
SnNout: High Snsitivity → Negative result rules OUT the diagnosis.
SpPin: High Specificity → Positive result rules IN the diagnosis.
A highly sensitive test misses very few cases — so a negative is reassuring.
A highly specific test rarely cries wolf — so a positive is meaningful.
Part 3 — Why PPV and NPV Depend on Prevalence
Sensitivity and specificity are fixed properties of the test. PPV and NPV are not — they depend on how common the disease is in the population you are testing.
Example: a test with 99% sensitivity and 95% specificity applied to two populations.
| High Prevalence (50%) | Low Prevalence (1%) | |
|---|---|---|
| Population tested | 1,000 patients | 1,000 patients |
| Disease present | 500 | 10 |
| Disease absent | 500 | 990 |
| True positives | 495 (99% of 500) | 9.9 (99% of 10) |
| False positives | 25 (5% of 500) | 49.5 (5% of 990) |
| PPV | 495 / 520 = 95% | 9.9 / 59.4 = 17% |
A high-sensitivity troponin is ~99% sensitive. In a chest pain unit where prevalence of true NSTEMI is 15–20%, a positive result is highly meaningful. In a low-risk outpatient with atypical chest pain (prevalence <1%), the same positive result is more likely a false alarm — demand, myocarditis, PE, CKD, sepsis — than true ACS.
Same test. Same result. Different clinical meaning. Pretest probability changes everything.
Stress testing follows the same logic. Exercise stress ECG has ~68% sensitivity and ~77% specificity for obstructive CAD. Order it in a 55-year-old male with typical exertional chest pain (pre-test probability ~65%) and a positive result is actionable. Order it in a 35-year-old woman with atypical chest pain (pre-test probability ~5%) and a positive result is more likely a false positive than true disease. The ACC/AHA appropriateness criteria exist precisely because of this math.
Part 4 — Likelihood Ratios: The Clinically Superior Tool
Likelihood ratios (LR) are better than PPV/NPV because they remain stable across populations with different prevalence. Use them to move from pretest to post-test probability.
| Measure | Formula | Interpretation |
|---|---|---|
| LR+ | Sensitivity / (1 − Specificity) | How much more likely is a positive result in someone WITH the disease vs. without it? |
| LR− | (1 − Sensitivity) / Specificity | How much more likely is a negative result in someone WITHOUT the disease vs. with it? |
| LR Value | Clinical Meaning |
|---|---|
| LR+ > 10 | Large shift toward disease. Strong rule-in. |
| LR+ 5–10 | Moderate shift. Useful in intermediate pretest probability. |
| LR+ 2–5 | Small shift. Limited diagnostic value alone. |
| LR− < 0.1 | Large shift away from disease. Strong rule-out. |
| LR− 0.1–0.2 | Moderate shift. Useful but not definitive. |
Worked example: High-sensitivity troponin with 99% sensitivity and 95% specificity. LR+ = 0.99 / (1 − 0.95) = 19.8 — strong rule-in when positive. LR− = (1 − 0.99) / 0.95 = 0.01 — near-definitive rule-out when negative.
High sensitivity rules OUT (SnNout). High specificity rules IN (SpPin). But PPV and NPV depend on prevalence — a “99% sensitive” test still produces mostly false positives when the disease is rare. Know the pretest probability before you order.
This is one of 13 free reference sheets from the APP Cardiology Academy — no account required.