Sensitivity, Specificity, PPV, and NPV
Master the 2×2 table for diagnostic tests — and understand why positive predictive value changes dramatically with disease prevalence.
You'll learn
How to calculate and interpret sensitivity, specificity, PPV, NPV, and likelihood ratios for any diagnostic test.
Use this when
You are evaluating a diagnostic test, biomarker cutoff, or screening programme.
The 2×2 Diagnostic Table
Any binary diagnostic test can be evaluated by comparing its results against a gold standard. This produces four cells: true positives (TP), false positives (FP), false negatives (FN), and true negatives (TN).
| Disease Present (Gold +) | Disease Absent (Gold −) | Total | |
|---|---|---|---|
| Test Positive | TP | FP | TP+FP |
| Test Negative | FN | TN | FN+TN |
| Total | TP+FN | FP+TN | N |
Sensitivity, Specificity, PPV, NPV
| Measure | Formula | Question it answers |
|---|---|---|
| Sensitivity | TP / (TP + FN) | Of all patients WITH disease, what fraction does the test correctly identify? |
| Specificity | TN / (TN + FP) | Of all patients WITHOUT disease, what fraction does the test correctly exclude? |
| PPV (Positive Predictive Value) | TP / (TP + FP) | If a test is positive, what is the probability the patient has the disease? |
| NPV (Negative Predictive Value) | TN / (TN + FN) | If a test is negative, what is the probability the patient is disease-free? |
💡 Sensitivity and specificity are fixed properties of the test
Sensitivity and specificity are intrinsic to the test itself — they describe performance in a well-defined population. PPV and NPV depend on the prevalence of the disease in your population. The same test can have PPV = 90% in a high-risk clinic and PPV = 10% in a general screening population.
Why Prevalence Changes PPV
Imagine a test with sensitivity = 95%, specificity = 95%. Applied to 1,000 patients where prevalence = 50%: TP = 475, FP = 25, FN = 25, TN = 475. PPV = 475/(475+25) = 95%. Now apply to a population where prevalence = 1%: TP = 9.5, FP = 49.5. PPV = 9.5/(9.5+49.5) ≈ 16%.
⚠️ Screening in low-prevalence populations creates many false positives
Even an excellent test (95% sensitivity, 95% specificity) used for universal screening of a rare condition (1% prevalence) will have PPV around 16% — meaning 84% of positive results are false alarms. This drives overdiagnosis and unnecessary procedures.
Likelihood Ratios: A More Portable Measure
The positive likelihood ratio (LR+) and negative likelihood ratio (LR−) combine sensitivity and specificity into a single measure that can be applied to any prior probability using Bayes' theorem.
- ●LR+ = Sensitivity / (1 − Specificity) — how much more likely a positive result is in a diseased vs healthy person
- ●LR− = (1 − Sensitivity) / Specificity — how much less likely a negative result is in a diseased person
- ●LR+ > 10 or LR− < 0.1: large, clinically meaningful shift in probability
- ●LR between 0.5 and 2: the test barely changes the probability — not useful clinically
Trusted sources behind this lesson
Further reading
Read next
Table 1: Baseline Characteristics
Learn how to build and present the baseline characteristics table — the first table in nearly every clinical paper — correctly and completely.