Examples
Worked examples
- Is an instance
Referral population, 10% prevalence: of 1,000 people (100 with the condition, 900 without) tested with a 90%-sensitivity, 90%-specificity test, TP=90, FN=10, FP=90, TN=810, giving PPV = 90/(90+90) = 50% and NPV = 810/(810+10) = 98.8%.
- Is an instance
Screening population, 1% prevalence: the identical test (same 90% sensitivity, 90% specificity) applied to 1,000 people with only 10 truly having the condition gives TP=9, FN=1, FP≈99, TN≈891, so PPV = 9/(9+99) ≈ 8.3% — the same test's PPV falls from 50% to about 8% purely because prevalence dropped from 10% to 1%.
Counter-examples
Looks similar, but isn't
- Not an instance
Assuming a test with 99% sensitivity and 99% specificity must have a high PPV is a common error: applied to a condition with 0.1% true prevalence, that test still produces a PPV under 10%, because the vast pool of true negatives generates more false positives than the small true-positive pool generates true positives — sensitivity/specificity alone never determines PPV without also knowing prevalence.
Editorial commentary
Positive predictive value (PPV) is the proportion of all positive test results that are true positives — the probability, after a positive result, that the condition is actually present. It is calculated within the test-positive row of a diagnostic accuracy study’s 2×2 table, which is what separates it from sensitivity and specificity (calculated within the disease-status columns of the same table) and is also why PPV moves with how common the condition is in the population being tested, while sensitivity and specificity in principle do not.
The 2×2 table PPV comes from
Every diagnostic accuracy statistic is built from the same four counts, produced by cross-tabulating an index test’s result against a reference standard:
| Condition present | Condition absent | |
|---|---|---|
| Test positive | True positive (TP) | False positive (FP) |
| Test negative | False negative (FN) | True negative (TN) |
Sensitivity and specificity are column statistics — each is calculated within people of known true disease status. PPV and negative predictive value (NPV) are row statistics — each is calculated within people who received a given test result, before their true status is known. That row/column distinction is the entire reason PPV behaves differently from sensitivity and specificity in practice. See Sensitivity vs. Specificity for the full build-up of this table and the likelihood ratios and ROC curve derived from it.
Formula
PPV = TP / (TP + FP) — of everyone who tested positive, what fraction truly has the condition.
Negative predictive value (NPV), the natural complement asked about alongside PPV, is NPV = TN / (TN + FN) — of everyone who tested negative, what fraction truly does not have the condition.
Worked example: the same test, two populations
Take a test with 90% sensitivity and 90% specificity, applied to 1,000 people.
Referral population, 10% prevalence (100 with the condition, 900 without): TP = 90, FN = 10, FP = 90, TN = 810.
- PPV = 90 / (90 + 90) = 50%
- NPV = 810 / (810 + 10) = 98.8%
Screening population, 1% prevalence (10 with the condition, 990 without), same test, same 90%/90% sensitivity and specificity: TP = 9, FN = 1, FP ≈ 99, TN ≈ 891.
- PPV = 9 / (9 + 99) ≈ 8.3%
- NPV = 891 / (891 + 1) ≈ 99.9%
Nothing about the test changed between the two rows — sensitivity and specificity are identical in both. What changed is the prevalence, and PPV collapsed from 50% to about 8% because of it. This is the standard “screening paradox”: a test that looks excellent by its own sensitivity/specificity numbers can still mean most positive results in a low-prevalence population are false alarms. It’s the reason a manuscript or clinical guideline reporting a bare PPV number without stating the prevalence (or pretest probability) it was measured at is reporting a number that cannot be reused in a different-prevalence setting.
PPV vs. NPV
| Positive Predictive Value (PPV) | Negative Predictive Value (NPV) | |
|---|---|---|
| Answers | Given a positive result, how likely is disease? | Given a negative result, how likely is no disease? |
| Formula | TP / (TP + FP) | TN / (TN + FN) |
| Table row used | Test-positive row | Test-negative row |
| Effect of lower prevalence | Falls | Rises |
| Most informative when | Ruling a condition in | Ruling a condition out |
Both PPV and NPV depend on prevalence in opposite directions: as prevalence falls, PPV falls and NPV rises, because there are proportionally fewer true positives to find and proportionally more true negatives among anyone testing negative.
PPV vs. sensitivity and specificity
These are frequently confused because both pairs sound like “how good is this test,” but they answer different questions asked in opposite directions:
- Sensitivity/specificity start from the true disease state and ask how the test performed — useful for characterizing a test itself, and (in principle) stable across populations.
- PPV/NPV start from the test result and ask how likely the true state is — the number a clinician or a test-taker actually wants after seeing a result, but one that shifts with the prevalence of the population the test is being used in.
A test can have excellent sensitivity and specificity and still have a low PPV in a low-prevalence setting — the worked example above is exactly that case. Reporting sensitivity and specificity alone, without PPV/NPV at a stated prevalence, does not tell a reader what a given result actually means for an individual.
Related diagnostic-accuracy metrics
PPV and NPV are two entries in a wider toolkit for evaluating diagnostic and prognostic tests:
- Diagnostic odds ratio — a single summary number combining sensitivity and specificity, prevalence-independent but harder to interpret clinically than PPV/NPV.
- Net reclassification improvement — measures whether adding a marker to a prediction model improves classification, a different question from a single test’s PPV.
- Youden’s J index — a threshold-selection statistic built from sensitivity and specificity, not from predictive values.
- Calibration plots — for multivariable prediction models rather than single binary tests, evaluate whether predicted probabilities match observed outcome rates.
Prevalence itself, the variable driving everything in this article, is covered in Prevalence vs. Incidence.
Reporting PPV correctly
Diagnostic accuracy studies reporting PPV/NPV should follow the STARD reporting guideline (for diagnostic accuracy studies) or TRIPOD (for multivariable prediction models), both of which require stating the prevalence or pretest probability the predictive values were calculated at, since PPV/NPV reported without that context cannot be validly applied to a population with a different prevalence.
Frequently asked questions
What is negative predictive value (NPV)?
Negative predictive value is the proportion of all negative test results that are true negatives: NPV = TN / (TN + FN). Like PPV, it is a row statistic calculated within a test result rather than within true disease status, and it moves with prevalence — in the opposite direction from PPV, rising as prevalence falls.
What’s the difference between PPV and NPV?
PPV answers “given a positive result, how likely is the condition actually present?” NPV answers the mirror question for a negative result. They are calculated from opposite rows of the same 2×2 table (TP/(TP+FP) vs. TN/(TN+FN)) and respond to prevalence in opposite directions: PPV falls and NPV rises as a condition becomes rarer in the population tested.
Is PPV the same as sensitivity?
No. Sensitivity is TP / (TP + FN) — calculated within people who truly have the condition (a column of the 2×2 table) and used to describe the test. PPV is TP / (TP + FP) — calculated within people who tested positive (a row of the table) and used to interpret a specific result. A test’s sensitivity does not change with prevalence; its PPV does.
Does a high-sensitivity, high-specificity test always have a high PPV?
No, and this is the most commonly missed point about PPV. In a low-prevalence population, even a test with 90%+ sensitivity and specificity can produce a PPV well under 50%, because the much larger pool of true negatives still generates enough false positives to outnumber the true positives. PPV always has to be evaluated at a stated prevalence, not read off a test’s sensitivity/specificity alone.
Machine-readable encodings
Use in your systems
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