False Positives, False Negatives and Test Accuracy

Four possible outcomes

Every test result falls into one of four boxes.

A false positive says there is a problem when there is not. A false negative misses a problem that is there. This page explains the terms and does not interpret anyone's results.

Sensitivity and specificity

• Sensitivity is the probability that the test is positive when the condition is present. [1]
• Specificity is the probability that the test is negative when the condition is absent. [1]

A very sensitive test rarely misses the condition but may raise many false alarms; a very specific test rarely raises false alarms but may miss cases. Few tests are perfect at both, and the NHS reminds readers that screening tests are not perfect and can lead to difficult decisions about further tests or treatment. [2]

The part most people miss: predictive values

What you actually want to know after a positive result is "how likely is it that I have the condition?" That is the positive predictive value. Positive and negative predictive values are directly related to how common the condition is in the group tested. [1]

A published teaching example makes this concrete: a new test had a positive predictive value of 95% in a study with 50% of people affected. Applied to a population where only 1% were affected, its positive predictive value fell to 15%. Sensitivity and specificity had not changed. [1] The example comes from eye disease, but the arithmetic applies to any test. The practical lesson is that a positive result from a broad direct-to-consumer panel in healthy people is more likely to be a false alarm than the same result in someone with symptoms and a clinical reason to be tested. (This is our reading of the principle, not a statement about any specific product.)

What false alarms cost

The National Cancer Institute notes that a false-positive screening result can cause anxiety and is usually followed by more tests and procedures, which also have risks. [3] Results that fall outside a reference range do not necessarily indicate disease. [4] See Reference Ranges vs "Optimal" Ranges.

Accuracy in two senses

• Technical accuracy (analytical validity): is the number right? See Analytical Validity, Clinical Validity and Clinical Utility.
• Diagnostic accuracy: does a positive or negative result correctly sort people with and without the condition?

Both are different from benefit: knowing the answer is only worthwhile if acting on it helps.

Reading a claim like "95% accurate"

Ask: 95% of what? Sensitivity, specificity, both, or a predictive value? Tested in whom, compared against what reference method? Was the group similar to the people now being sold the test? Consumer test sellers often do not say. For related pitfalls see False Positives, Multiple Testing and Incidental Findings.