Signature
Acc = p * Se + (1 - p) * Sp
| Inputs | Definition | Unit |
|---|---|---|
p | Prevalence of the target condition in the people tested | probability |
Se | Sensitivity of the test | proportion |
Sp | Specificity of the test | proportion |
Acc | Share of all people tested whose result agrees with the reference standard | proportion |
|---|
Function
Diagnostic test accuracy measures and the expected value of test results
Maps the cross-classification of index test results against a reference standard to the measures of accuracy, conditional on disease status (sensitivity, specificity) or on the test result (predictive values), and combines accuracy with prevalence and the consequences of true and false results into the expected net monetary benefit of testing. The notation follows the Diagnostic Accuracy article and its two triage tests.
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Implementations
Excel
Proportion correct from named prevalence, sensitivity and specificity
With Prev, Sens and Spec named, the formula returns the proportion of correct results, held in PropCorrect.
=Prev*Sens+(1-Prev)*Spec
Assumptions
Both kinds of error weighted equally in the proportion correct
A false negative and a false positive each count as one wrong result, whatever their consequences.
Prevalence of the population in which correctness is counted
The result applies only at the prevalence p; the same test has a different proportion correct elsewhere.
Worked examples
Proportion correct of the two triage tests at 5 per cent prevalence
Test A scores 0.048 plus 0.722, or 0.770, and test B 0.040 plus 0.912, or 0.952, as in the article.
p = 0.05; Se = 0.96; Sp = 0.76; Acc = 0.77
Rule that calls everyone negative at 5 per cent prevalence
With sensitivity 0 and specificity 1 the proportion correct is 0.95, barely below test B's 0.952, as the article notes.
p = 0.05; Se = 0; Sp = 1; Acc = 0.95
Common errors
Ranking tests by the proportion correct
Test B's 0.952 barely beats the 0.950 of calling everyone negative, and test A, with 0.770, gives the higher net monetary benefit at 5 per cent prevalence; NICE's 2011 diagnostics manual set this definition of accuracy aside because a test can be wrong in more than one way and the measure depends on prevalence.
Quoting a proportion correct without its prevalence
Test A's proportion correct is 0.770 at 5 per cent prevalence and 0.764 at 2 per cent, and it tends to specificity as prevalence falls, so the figure cannot be transferred between settings (computed here for illustration).
Sources
Proportion correct set aside in the NICE Diagnostics Assessment Programme manual
National Institute for Health and Clinical Excellence. Diagnostics Assessment Programme manual. Manchester: NICE; December 2011 (since replaced by the NICE HealthTech programme manual, PMG48, 2025). Section 2.1: in statistics test accuracy means the proportion of test results that are correct; this is not a useful definition because a test may be incorrect in more than one way and for more than one reason, and it is also dependent on the prevalence of the condition in the population tested.
Sensitivity, specificity and AUC do not show whether a test should be used
Vickers AJ, Van Calster B, Steyerberg EW. Net benefit approaches to the evaluation of prediction models, molecular markers, and diagnostic tests. BMJ. 2016;352:i6. doi:10.1136/bmj.i6. Decision making and net benefit: traditional measures such as sensitivity, specificity, area under the curve and calibration do not provide an answer as to whether the model, marker or test should be used in clinical practice.
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