Positive and negative predictive values
- Measure
If the test is positive (or negative), how likely the person is to have (or not have) the disease.
What it is
Predictive values answer the question a patient asks while holding the result. The positive predictive value (PPV) is the proportion of diseased people among those who tested positive; the negative predictive value (NPV) is the proportion of healthy people among those who tested negative. They are read across the rows of the 2×2 table and, unlike sensitivity and specificity, they change a lot with the prevalence of the group tested.
Formula and reading
- PPV = TP / all positives; NPV = TN / all negatives.
- Reading: a PPV of 33% means 2 of every 3 positives are false positives.
- PPV equals the post-test probability after a positive result; NPV equals 1 − the post-test probability after a negative one.
- They hold only for a prevalence similar to that of the study that measured them.
Worked example
- Data: a clinic tests 1,000 people; 100 have the disease. The test has 90% sensitivity and 80% specificity.
- Diseased: 90% of 100 = 90 true positives and 10 false negatives.
- Healthy: 80% of 900 = 720 true negatives and 180 false positives.
- PPV = 90 / (90 + 180) = 90 / 270 ≈ 0.333, that is 33%.
- NPV = 720 / (720 + 10) = 720 / 730 ≈ 0.986, that is 98.6%.
- Reading: a positive is right 1 time in 3; a negative is right almost 99 times in 100.
The example table, read across rows
| Result | Diseased | Healthy | Total | Predictive value |
|---|---|---|---|---|
| Positive | 90 | 180 | 270 | PPV = 90/270 ≈ 33% |
| Negative | 10 | 720 | 730 | NPV = 720/730 ≈ 98.6% |
| Total | 100 | 900 | 1,000 | Prevalence = 10% |
Markers
- PPV
- NPV
How to read it
- When explaining a positive screening result, it helps to say that it may be false and needs confirmation.
- A high NPV allows reassurance for someone who tests negative on a screening test with good sensitivity.
Common pitfalls
- Calculating predictive values down columns.
- Using the PPV published by a referral centre in a population with much less disease.
- Confusing PPV with sensitivity.
Test yourself
Think of the answer, then tap the question to see it.
There are 40 true positives and 60 false positives. What is the PPV?
40 / (40 + 60) = 0.40, that is 40%.
Which question does the negative predictive value answer?
If the test is negative, how likely it is that the person truly does not have the disease.
Why is a test's PPV different in a referral hospital and in the community?
Because it depends on prevalence: the community has fewer diseased people, so a larger share of positives are false.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Sensitivity, Specificity, and Predictive Values: Foundations, Pliabilities, and Pitfalls in Research and Practice (Frontiers in Public Health, 2017); Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff (U.S. Food and Drug Administration, 2007).
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Representative model, for educational purposes only.