Positive and Negative Predictive Value: Formula, Examples and Why Prevalence Matters

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-10-30

Positive predictive value (PPV) is the proportion of people with a positive test result who actually have the disease. Negative predictive value (NPV) is the proportion of people with a negative test result who truly do not have the disease.

A patient who tests positive does not want a lecture on test accuracy. They want to know the chance that the result is right. Sensitivity and specificity describe how a test behaves in people whose disease status is already known. PPV and NPV turn that around and answer the question from the result back to the person. The catch is that the answer depends on how common the disease is in the group being tested. That single fact explains most of the confusion around the predictive value of a test, and it is why a test can look excellent in one setting and misleading in another.

What PPV and NPV mean

Four terms carry the rest of the article.

The reference standard is the method used to decide whether disease is truly present. In a study of a rapid malaria test, the reference standard might be blood smear microscopy. In a study of a score meant to predict sepsis mortality, it might be death within 28 days.

Prevalence is the proportion of people in the tested population who have the disease at the time of testing.

Sensitivity is the probability of a positive result given that the disease is present. Specificity is the probability of a negative result given that the disease is absent. Both are properties of the test at a chosen cutoff, measured against the reference standard.

PPV and NPV reverse the direction of the question. PPV is the probability that disease is present given a positive result. NPV is the probability that disease is absent given a negative result.

The notation makes the distinction clear. Sensitivity is P(result positive | disease present). PPV is P(disease present | result positive). Those are different conditional probabilities, and they are not reciprocals. A test can catch 95% of cases and still have a PPV of 20% if the disease is rare in the population being tested.

The PPV formula and the 2x2 table

Every diagnostic accuracy study can be reduced to four counts. Arrange them in a 2x2 table with disease status across the top and test result down the side.

	Disease present	Disease absent	Total
Test positive	True positive (TP)	False positive (FP)	TP + FP
Test negative	False negative (FN)	True negative (TN)	FN + TN
Total	TP + FN	FP + TN	N

From those cells:

PPV = TP / (TP + FP). The denominator is all positive results.
NPV = TN / (TN + FN). The denominator is all negative results.
Sensitivity = TP / (TP + FN). The denominator is all people with disease.
Specificity = TN / (TN + FP). The denominator is all people without disease.
Prevalence = (TP + FN) / N. The share of the sample with disease.

A memory aid helps on exams. Sensitivity and specificity read down the columns, because they start from known disease status. PPV and NPV read across the rows, because they start from a known test result. The numerator is the same in each pair. Only the denominator changes.

The relationship can also be written with prevalence, sensitivity (Se), and specificity (Sp) directly:

PPV = (Se × prevalence) / [(Se × prevalence) + (1 - Sp) × (1 - prevalence)]

NPV = [Sp × (1 - prevalence)] / [Sp × (1 - prevalence) + (1 - Se) × prevalence]

This version is the one to use when a paper reports sensitivity and specificity but you need the predictive values for a population with a different prevalence. It is also the form that makes the prevalence dependence obvious. Prevalence appears in both the numerator and the denominator of each expression, so it cannot cancel out.

How to calculate PPV: a worked example

A 2026 study of sepsis-induced coagulopathy followed 150 ICU patients and calculated the JAAM-DIC score within 6 hours of admission. The reference standard was death within 28 days. Sixty-five patients died, and 72 had a score of 4 or higher. The reported sensitivity was 81.5%, specificity 77.6%, PPV 73.6%, and NPV 84.6%, with overall accuracy of 79.3% [1].

The cell counts can be reconstructed from those totals and percentages:

TP = 0.815 × 65 = 53
FN = 65 - 53 = 12
FP = 72 - 53 = 19
TN = 85 - 19 = 66

	Died by day 28	Survived	Total
JAAM-DIC score 4 or higher	53	19	72
JAAM-DIC score below 4	12	66	78
Total	65	85	150

Now compute each metric:

Sensitivity = 53 / 65 = 81.5%
Specificity = 66 / 85 = 77.6%
PPV = 53 / 72 = 73.6%
NPV = 66 / 78 = 84.6%
Accuracy = (53 + 66) / 150 = 79.3%

Each number matches the published report, which is a useful check that the table is built correctly.

The interpretation is concrete. About three out of four patients with a high score died within 28 days. About six out of seven patients with a low score survived. Neither result is a verdict. The score shifts probability, and the shift is large enough to matter in an ICU where the pretest risk is already high.

The arithmetic is simple. The hard part is choosing the cells. PPV uses the row total for positive results (72), not the column total for deaths (65). Mixing those up produces a number that looks plausible and means nothing.

Why prevalence matters

Take a test with 90% sensitivity and 90% specificity and apply it to 10,000 people at three different prevalences. The test does not change. Only the population changes.

Prevalence	Diseased	Not diseased	TP	FP	FN	TN	PPV	NPV
1%	100	9,900	90	990	10	8,910	8.3%	99.9%
10%	1,000	9,000	900	900	100	8,100	50.0%	98.8%
50%	5,000	5,000	4,500	500	500	4,500	90.0%	90.0%

Read the PPV column from top to bottom. It moves from 8.3% to 50% to 90% while sensitivity and specificity stay fixed at 90%. At 1% prevalence, 1,080 people test positive and only 90 of them have the disease. The other 990 are false positives drawn from the enormous disease-free group. A false-positive rate of 10% is small in relative terms and enormous in absolute terms when 9,900 people do not have the disease.

Read the NPV column and the pattern reverses. At 1% prevalence, a negative result is almost certainly correct because almost everyone is disease-free to begin with. At 50% prevalence, a negative result still leaves a 10% chance of disease, which is not reassuring.

Real studies show the same arithmetic in clinical settings.

In a Vietnamese cohort of 127 patients with cirrhotic ascites, esophageal varices were present in 78%. At a FIB-4 cutoff of 2.375, sensitivity was 79.8%, specificity 75.0%, PPV 91.9%, and NPV 51.3% [2]. The test looks strong on the positive side and weak on the negative side. That is not a flaw in the assay. It is what happens when three out of four patients already have the condition. A negative FIB-4 in that population is close to a coin flip, while a positive one is usually correct.

The mirror case is a low-prevalence disease. In 185 patients with systemic lupus erythematosus, interstitial lung disease was present in 22, or 12%. A thoracic ultrasound threshold of at least 10 B-lines had a sensitivity of 64% and an NPV of 97% [3]. The test missed about a third of cases, yet a negative result was reassuring because most patients did not have ILD in the first place. A positive result in that setting would need confirmation, since a modest specificity combined with a low prevalence produces a meaningful number of false positives.

Prevalence is not always a fixed biological constant. It depends on how the disease is defined and who is in the sample. A study of 420 young healthcare workers found metabolic syndrome prevalence of 15.5%, 18.6%, and 10.2% under three different diagnostic criteria [4]. Each definition produces a different denominator and therefore a different set of predictive values, even if the test itself is unchanged.

Prevalence in a study is not prevalence in your clinic

Diagnostic accuracy studies often enroll selected patients. A Lung-RADS validation study included only patients whose pulmonary lesions had already been sent for histopathology. Malignancy prevalence in that cohort was 75.8%, and PPV was 80.1% [5]. The sensitivity was 99.2% and the specificity was only 23.1%, which means the rule generated many false positives. The PPV stayed high anyway because true cases were abundant. Transplant that PPV into a community screening program where most nodules are benign and it will collapse. The same rule, the same cutoff, a different population.

This is why a low-prevalence screening cascade can bury a program in false-positive referrals. A Bayesian cost model of sequential screening showed that when prevalence is low, repeated screening generates large numbers of false positives that go on to confirmatory testing, adding cost, delay, and patient burden [6]. The model treats prevalence as the variable that drives the whole economics of screening, not as an afterthought.

PPV vs sensitivity: two different questions

Sensitivity asks: among people who have the disease, what fraction test positive? PPV asks: among people who test positive, what fraction have the disease?

Consider a multicenter eye study of paracentral acute middle maculopathy (PAMM) on optical coherence tomography as a sign of arteritic anterior ischemic optic neuropathy (AAION). AAION was present in 27 of 119 patients, about 23%. PAMM had a sensitivity of 19%, a specificity of 94.6%, and a PPV of 50% [7]. The sign was specific, meaning it was rare in the alternative condition, but insensitive, meaning it missed most cases of AAION. A positive finding raised the probability from roughly 23% to 50%. That is a real shift and still short of a diagnosis. A negative finding barely changed anything, because the test missed four out of five cases.

The relationship between the two metrics runs through the likelihood ratio and the pretest probability. A positive likelihood ratio is sensitivity divided by (1 - specificity). It describes how much a positive result multiplies the pretest odds. PPV is what you get when you convert the resulting posttest odds back into a probability. This is why predictive values can be estimated through likelihood ratios in meta-analysis, a point made in a multinomial modeling study of multicategory diagnostic tests [8].

That same study flags a reporting problem. Predictive values for each test category are often reported as raw proportions that ignore pretest probability or prevalence [8]. A PPV printed without the prevalence of the study population is an incomplete number. It describes the sample, not the test.

A common reasoning error follows from this. Specificity is not PPV. A specificity of 95% means 95% of disease-free people test negative. It says nothing direct about the 5% of positive results that may be false. In a low-prevalence population, that 5% can outnumber the true positives.

How NPV responds to prevalence

NPV moves in the opposite direction from PPV. As prevalence rises, the number of false negatives rises with any fixed sensitivity, so a negative result becomes less reassuring. As prevalence falls, a negative result becomes more reassuring because there are fewer cases to miss.

A dengue study in southern Nigeria illustrates the point from the high-prevalence side. Of 145 archived plasma samples, 95 (65.5%) were positive by RT-PCR. An NS1 antigen rapid test had a sensitivity of 94.7%, a specificity of 100%, a PPV of 100%, and an NPV of 90.9% [9]. Specificity was perfect, so there were no false positives and PPV hit 100%. NPV was lower because sensitivity was not perfect and prevalence was high. In a population where two out of three samples were positive, even a small false-negative rate produced a meaningful number of missed cases.

The practical rule is straightforward. A negative result carries the most information when the disease is rare and the test is sensitive. A positive result carries the most information when the disease is common and the test is specific.

Predictive values in screening and confirmatory testing

Serial and parallel testing change PPV and NPV in predictable ways.

In serial testing, both tests must be positive for the combined result to count as positive. This raises specificity and PPV, which suits confirmation. In parallel testing, either test being positive counts as positive. This raises sensitivity and NPV, which suits initial screening. A 2026 methods review of serial and parallel diagnostic testing states the trade-off directly: serial testing improves specificity and PPV, while parallel testing improves sensitivity and NPV [10].

A veterinary study of body temperature measurement in dogs shows the same logic in a different species. Eye temperature and rectal temperature both had high specificity and low-to-moderate sensitivity. A series rule maximized PPV and a parallel rule maximized NPV across the observed prevalences [11]. The study used a Bayesian latent-class model, which is a way to estimate sensitivity and specificity when no perfect reference standard exists, and then projected predictive values across a range of pretest probabilities rather than reporting a single pair.

Combining tests adds a statistical assumption. The usual calculations assume that the tests are conditionally independent given disease status. When two tests measure the same underlying process, that assumption fails and the combined PPV or NPV is overestimated. The Bayesian screening model referenced earlier makes conditional independence an explicit assumption and notes that it may not hold in practice [6].

The choice between rules is a decision about error costs. A false negative may mean a missed treatable disease. A false positive may mean an unnecessary biopsy, an extra scan, or a frightened patient. Screening programs accept more false positives to avoid false negatives. Confirmatory programs accept more false negatives to avoid false positives. PPV and NPV are the metrics that quantify that trade.

What near-perfect tests look like

Some tests are close enough to perfect that the prevalence effect becomes small, though it never disappears.

The RESIST-5 O.K.N.V.I. immunochromatographic assay detects five major carbapenemase genes in Gram-negative bacteria. Compared with real-time PCR, it had a sensitivity of 99.66%, a specificity of 99.90%, a PPV of 99.66%, and an NPV of 99.90% [12]. Both predictive values were high because both operating characteristics were near 100%. Even here, the predictive values still depend on prevalence in principle. A specificity of 99.9% means one false positive per 1,000 disease-free tests, and in a very large low-prevalence population those false positives accumulate.

Automated screening systems report PPV and NPV for the same reason. A retrospective validation of an artificial intelligence system for diabetic retinopathy screening in a Philippine community program evaluated PPV, NPV, sensitivity, specificity, and likelihood ratios against expert human graders [13]. The predictive values tell the program what a positive or negative output means in its own population, which is the number a clinician or program manager needs.

Common Mistakes and Limitations

Treating PPV as a fixed property of the test. PPV belongs to the test, the cutoff, and the population. Change the population and the number changes.
Confusing PPV with sensitivity. Sensitivity starts with disease. PPV starts with a positive result. They answer different questions and move independently when prevalence changes.
Confusing NPV with specificity. Specificity is the share of disease-free people who test negative. NPV is the share of negative results that are correct.
Computing PPV from sensitivity and specificity alone. The formula requires prevalence. Without it, the calculation is missing its most influential input.
Borrowing a PPV from an enriched cohort. Case-control designs and referral populations inflate prevalence. A PPV measured there does not transfer to a screening setting.
Trusting a PPV built on a tiny number of positives. A PPV of 50% is unstable when only a handful of patients tested positive. Confidence intervals around predictive values can be very wide in small subgroups.
Assuming independence in serial or parallel testing. Correlated tests break the standard combined formulas and overstate the combined predictive value.
Ignoring the quality of the reference standard. If the reference standard misclassifies disease, the cell counts are wrong and every derived metric, including PPV and NPV, inherits the error.
Collapsing a multicategory test into one number. Tests with ordered or partially ordered categories need category-specific predictive values. A single overall PPV hides the performance of individual categories [8].
Reporting PPV without prevalence. A predictive value without its denominator population is a number that cannot be interpreted or transported.

Two limitations deserve their own sentence. First, PPV and NPV are estimates. They should be reported with confidence intervals, especially when the positive or negative cell is small. Second, they are population-level summaries. They describe what a result means on average in a defined group, not what it means for one person with a particular history, exposure, and clinical picture. Individual patient decisions belong with a clinician who can weigh those details.

Quick Review

PPV = TP / (TP + FP). It is the share of positive results that are true positives.
NPV = TN / (TN + FN). It is the share of negative results that are true negatives.
Sensitivity and specificity read down the columns of a 2x2 table. PPV and NPV read across the rows.
PPV rises as prevalence rises. NPV falls as prevalence rises. Sensitivity and specificity stay put.
A test with 90% sensitivity and 90% specificity has a PPV of 8.3% at 1% prevalence and 90% at 50% prevalence.
Serial testing raises PPV and lowers sensitivity. Parallel testing raises NPV and lowers specificity.
Always report prevalence alongside PPV and NPV. Without it, the numbers cannot be compared across studies.

Frequently Asked Questions

What is the difference between PPV and sensitivity?

Sensitivity is the probability of a positive result in someone who has the disease. PPV is the probability that someone with a positive result has the disease. They run in opposite directions and change independently when prevalence changes.

How do I calculate PPV from a 2x2 table?

Divide the number of true positives by the total number of positive results, which is true positives plus false positives. In symbols, PPV = TP / (TP + FP). NPV is the matching calculation for negative results: TN / (TN + FN).

Why does prevalence change PPV but not sensitivity?

Sensitivity is measured within the group that already has the disease, so the size of the disease-free group does not enter the calculation. PPV is measured within the group that tested positive, and that group mixes true positives with false positives drawn from the disease-free population. A larger disease-free population means more false positives and a lower PPV.

Can a test have high sensitivity and low PPV?

Yes. A highly sensitive test used in a population where the disease is rare will produce many true positives and many false positives, and the false positives can outnumber the true positives. The PAMM eye sign study is a useful example of a specific sign with a PPV near 50% in a modest-prevalence cohort [7].

What is a good PPV?

There is no universal cutoff. A PPV is good if it is high enough to justify the action that follows a positive result, and that threshold depends on the cost of a false positive. A PPV of 50% may be excellent for triggering a cheap confirmatory test and unacceptable for triggering surgery.

Do PPV and NPV apply outside medicine?

Yes. Any binary classifier with a reference standard has predictive values, including spam filters, credit risk models, machine learning classifiers, and quality control assays. The arithmetic is identical, and the prevalence dependence is identical too.