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Sensitivity and specificity measure positive and negative test results within groups defined by a reference standard.
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Formula
Sensitivity and specificity are dimensionless, often reported as percentages · TP, FN, TN and FP are counts
| Symbol | Meaning | Unit |
|---|---|---|
| True positives: reference-positive people with a positive test | people | |
| False negatives: reference-positive people with a negative test | people | |
| True negatives: reference-negative people with a negative test | people | |
| False positives: reference-negative people with a positive test | people |
\mathrm{Sensitivitaet}=\frac{TP}{TP+FN}, \qquad \mathrm{Spezifitaet}=\frac{TN}{TN+FP}Sensitivity is TP/(TP+FN), the positive fraction among people classified as affected by the reference standard. Specificity is TN/(TN+FP), the negative fraction among reference-negative people. These conditional measures are not the probability that a person with a positive or negative result has the condition. They depend on the test threshold, how reference status is established, and the spectrum of the target population. A report should state all three. Predictive values additionally depend on prevalence, and an imperfect reference standard can bias apparent test performance.
Applies to a prespecified positive test threshold and a clearly described reference standard in a defined target population. An imperfect reference standard, verification bias or a different disease spectrum can change the estimates.
Measures condition on reference status: sensitivity among reference-positive people, specificity among reference-negative people.
False-negative fraction among reference-positive people
Applies to the same threshold and reference standard.
False-positive fraction among reference-negative people
Do not confuse this with the fraction of positive tests that are false positives.
A test correctly identifies 90 of 100 reference-positive and 180 of 200 reference-negative people. Calculate both measures.
TP=90, FN=10, TN=180, FP=20.
Sensitivity=90/(90+10)=90%; specificity=180/(180+20)=90%.
These values apply to the stated threshold and target population.
What typically changes when the threshold for a positive result is lowered?
More people test positive.
This may reduce false negatives and increase sensitivity, while increasing false positives and lowering specificity.
The result must be determined against the same reference standard in the target population.
Interpreting sensitivity as the probability of disease after a positive test.
Sensitivity is P(test+|reference-positive); positive predictive value is P(reference-positive|test+).
Comparing measures without threshold, reference standard and target population.
Differences may reflect different classification or disease spectrum rather than improved test performance.
Formula cluster
Conditional test measures depend on the reference standard, threshold and target population; predictive values additionally depend on prevalence.
Against a stated reference standard, a test is positive for 90 of 100 affected people and negative for 180 of 200 unaffected people. Sensitivity=90/(90+10)=90%; specificity=180/(180+20)=90%. Lowering the positive threshold may increase sensitivity while reducing specificity. These figures describe that threshold in the studied target population; they do not guarantee the same results in a different screening group or clinic.
Comparing diagnostic tests, choosing screening thresholds and interpreting false-negative and false-positive trade-offs in clinical studies
Here is how to work through a typical Diagnostic Test Sensitivity and Specificity (Sensitivität = TP/(TP+FN); Spezifität = TN/(TN+FP)) task step by step:
Task
A test correctly identifies 90 of 100 reference-positive and 180 of 200 reference-negative people. Calculate both measures.
Solution path
TP=90, FN=10, TN=180, FP=20.
Sensitivity=90/(90+10)=90%; specificity=180/(180+20)=90%.
These values apply to the stated threshold and target population.
Task
What typically changes when the threshold for a positive result is lowered?
Solution path
More people test positive.
This may reduce false negatives and increase sensitivity, while increasing false positives and lowering specificity.
The result must be determined against the same reference standard in the target population.
Sensitivity is the proportion of positive test results among all people classified as having the condition by the stated reference standard: TP/(TP+FN). Specificity is the proportion of negative results among all reference-negative people: TN/(TN+FP). Both are conditional proportions and depend on the test threshold. A study should state its reference standard, threshold and target population. Without these details, it is unclear which disease definition, decision and patient group a percentage describes. These measures do not directly answer how likely the condition is after an individual result; predictive values and prevalence are relevant for that question. Record the reference standard, threshold and target population. Only then can readers judge whether the measures transfer to another clinic, screening group or prevalence.
Assign test result and reference standard to four cells: TP are positive tests among reference-positive people, FN negative tests among reference-positive people, TN negative tests among reference-negative people, and FP positive tests among reference-negative people. Then sensitivity is TP/(TP+FN), and specificity TN/(TN+FP). With TP=90, FN=10, TN=180 and FP=20, both measures equal 90%. Check that only reference-positive people form the first denominator and only reference-negative people the second. Record the test threshold and target population; otherwise comparison with another study is unreliable. Record the reference standard, threshold and target population. Only then can readers judge whether the measures transfer to another clinic, screening group or prevalence.
A lower threshold makes it easier to classify a result as positive. Often more affected people are detected, so sensitivity may rise; more unaffected people also test positive, so specificity may fall. A higher threshold often produces the reverse trade-off. The exact relationship is estimated for a particular target population against a reference standard. Report how the threshold was selected and whether it was prespecified. An ROC curve displays the trade-off across possible thresholds, but does not itself decide which clinical threshold is right for the intended purpose. Record the reference standard, threshold and target population. Only then can readers judge whether the measures transfer to another clinic, screening group or prevalence.
No, values can change between populations. A clinic with severely ill, clear-cut cases may produce different test results from screening for mild or early disease. Comorbidities and the composition of the unaffected group also influence observed performance. A different or imperfect reference standard can shift classification into TP, FN, TN and FP. Do not transfer measures uncritically to a new target population. Check disease spectrum, threshold, test procedure and reference standard, and validate the test in its intended setting where possible. Record the reference standard, threshold and target population. Only then can readers judge whether the measures transfer to another clinic, screening group or prevalence.
No. Sensitivity and specificity condition on reference status; positive predictive value asks about reference status among people who test positive. Prevalence in the target population is also needed. At low prevalence, even high specificity can yield many false positives relative to the small number of affected people. The reference standard and threshold must also match those used for the measures. Calculate or report predictive values for the intended population rather than presenting sensitivity or specificity as an individual probability of disease. Record the reference standard, threshold and target population. Only then can readers judge whether the measures transfer to another clinic, screening group or prevalence.
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