Diagnostic tests: why a positive result is not enough

A test advertised as “99% reliable” does not, by itself, tell us what proportion of positive results corresponds to the disease being sought. We need to know what that percentage measures, in which population and against which reference. Counting people rather than comparing slogans is a useful way to understand the problem.

This analysis helps readers assess a publication or technology announcement. The calculations below are fictional and cannot be used to interpret an individual’s medical result.

Three questions behind three indicators

Sensitivity asks: among people who have the condition, how many test positive? Specificity starts with the other group: among people who do not have the condition, how many test negative? Positive predictive value starts with the results: among people who test positive, how many actually have the condition? The denominators differ. The FDA recommends presenting sensitivity and specificity together, specifying the reference used and the population studied. FDA, statistical guidance on diagnostic tests.

This distinction has practical consequences. A company may announce that its test identifies almost all known cases. That does not yet tell us how many people without the disease will also be flagged. Conversely, a test that produces very few false alarms may miss cases. Readers need both sides of the table.

A calculation involving 10,000 fictional people

Take an imaginary test with 90% sensitivity and 99% specificity. Assume a population of 10,000 people in which 1% have the condition. These parameters were chosen solely to make the arithmetic visible.

Assumed actual situation	Positive test	Negative test	Total
Condition present	90	10	100
Condition absent	99	9,801	9,900
Everyone	189	9,811	10,000

The calculation has three steps. There are 100 people with the condition; the test identifies 90. There are 9,900 people without it; with a 1% false-positive rate in that group, 99 nevertheless receive a positive result. There are therefore 189 positive results, of which 90 correspond to the condition.

Positive predictive value is 90 ÷ 189, or approximately 47.6%. This does not contradict 99% specificity. The 1% false-positive rate applies to a much larger group than the group with the condition.

We can repeat the calculation without a complex formula: count existing cases, apply sensitivity, count people without the condition, apply the false-positive rate, then combine the two positive categories. This representation avoids confusing “positive among people with the disease” with “disease among people who test positive”.

What changes with the population tested

Keep exactly the same fictional performance, but move to a population where 10% have the condition. There are 900 true positives among 1,000 affected people and 90 false positives among 9,000 unaffected people. The proportion becomes 900 ÷ 990, or approximately 90.9%.

Assumed prevalence	True positives	False positives	Actual cases among positive results
1%	90	99	47.6%
10%	900	90	90.9%

Prevalence is the proportion of people with the condition in the group considered. The National Cancer Institute explains that predictive values depend on this proportion as well as sensitivity and specificity. It also distinguishes screening test performance from demonstrated benefits of a screening programme. NCI, screening assessment.

Calculation limit: we held sensitivity and specificity constant to isolate the mathematical effect of prevalence. In a real study, different recruitment, disease stages or conditions of use may also alter measured performance. Our second row therefore cannot be used as a forecast for another service or country.

Read the study behind the percentage

First check the reference: how was the presence or absence of the condition established? Comparison against an imperfect method does not become a measure of truth through arithmetic alone. Then check the participants: were they recruited in the intended context of use? Finally, sample size matters. The FDA notes that observed performance values are estimates and requests confidence intervals to make their uncertainty visible. FDA, statistical guidance.

To examine a claim, we suggest a short checklist: target condition; population; reference method; true and false results; sample sizes; uncertainty. An empty field is a question to ask, not evidence of poor quality. Above all, this checklist reveals when two announcements concern different uses.

Uninterpretable results also deserve attention. A paper presenting only usable results leaves a practical question: what happens to everyone else? Look for the number of inconclusive examinations, how they were handled in the analysis and the planned next step, rather than assuming that they count as negative results.

From result to decision

A laboratory result is interpreted alongside other information. MedlinePlus, a service of the National Library of Medicine, highlights symptoms, medical history and other examinations; a result may require further checks. MedlinePlus, understanding lab results.

For a new technology, the editorial question becomes: what does the result trigger, and is there evidence for that step? Our guide to medical AI and patient benefit (in French) addresses this transition from technical performance to clinical utility. The calculation here answers a narrower question: why the meaning of a positive result depends on the group being tested.

Before repeating “99% reliable”, ask: 99% of what, among whom, and compared with which reference? These three details make a claim much more informative without promising certainty the test does not measure.

Sources and scope

Definitions and interpretive limits come from the FDA, NCI and MedlinePlus. Both populations are fictional and the percentages are educational calculations, not measured performance or individual medical advice. Sources consulted on 22 October 2026.