Concept Architecture
Concept
Theoretically, Accuracy is a diagnostic performance measure that quantifies the overall ability of a test or classification model to correctly identify both the presence and absence of a target condition. It represents the proportion of all classifications that are correct and is founded on probability theory and binary classification. The concept exists to provide an overall summary of diagnostic correctness across positive and negative outcomes.
Mathematically, Accuracy is represented as the proportion of correctly classified observations among all observations evaluated. It is a probability ranging from 0 to 1 or equivalently 0% to 100%. Although Accuracy provides an overall measure of performance, it is influenced by disease prevalence and may therefore be misleading when applied to highly imbalanced datasets.
In practice, Accuracy is estimated from diagnostic accuracy studies by comparing an index test with an accepted reference standard. It is widely applied in clinical diagnostics, epidemiology, machine learning and health economic evaluation to assess diagnostic technologies, although it is typically interpreted alongside sensitivity, specificity and predictive values.
Purpose
Used to quantify the overall correctness of diagnostic tests or classification models, compare diagnostic performance and support clinical and health economic decision-making.
Mathematical Formulae
Primary Formula
Accuracy = (TP + TN) / (TP + TN + FP + FN)
where:
- TP = true positives
- TN = true negatives
- FP = false positives
- FN = false negatives
Supporting Formulae
Error Rate = (FP + FN) / (TP + TN + FP + FN)
Accuracy = 1 ? Error Rate
Prevalence = (TP + FN) / (TP + TN + FP + FN)
Related Mathematical Methods
- Sensitivity
- Specificity
- Positive Predictive Value
- Negative Predictive Value
- Receiver Operating Characteristic Analysis
- Confusion Matrix
- Brier Score
- F1 Score
Example
A diagnostic study reports:
- True positives = 180
- True negatives = 720
- False positives = 40
- False negatives = 60
Accuracy:
Accuracy = (180 + 720) / (180 + 720 + 40 + 60)
Accuracy = 900 / 1,000 = 0.90
Accuracy = 90%
The diagnostic test correctly classifies 90% of all individuals.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Division | =(B2+C2)/(B2+C2+D2+E2) | Calculates overall diagnostic Accuracy from the confusion matrix. |
| Percentage | =((B2+C2)/(B2+C2+D2+E2))*100 | Expresses Accuracy as a percentage. |
| IF | =IF((B2+C2+D2+E2)>0,(B2+C2)/(B2+C2+D2+E2),"") | Prevents division by zero when calculating Accuracy. |
| ROUND | =ROUND((B2+C2)/(B2+C2+D2+E2),3) | Formats Accuracy for reporting. |
VBA (Optional)
A VBA macro can automatically calculate Accuracy and related diagnostic performance measures for multiple tests and generate comparative performance reports.
Sources
- Altman DG, Bland JM. Diagnostic tests 1: Sensitivity and specificity. BMJ. 1994;308:1552.
- Zhou XH, Obuchowski NA, McClish DK. Statistical Methods in Diagnostic Medicine. 2nd ed.
- Bossuyt PM, Reitsma JB, Bruns DE, et al. STARD 2015: an updated list of essential items for reporting diagnostic accuracy studies. BMJ. 2015;351:h5527.
- Steyerberg EW. Clinical Prediction Models. 2nd ed.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is accuracy?
A general measure of how closely a test result, measurement, or prediction corresponds to the true underlying value, covering sensitivity and specificity.
Source: Altman & Bland 1994
What does accuracy describe about a measurement or test?
Accuracy describes how closely a test result, measurement, or prediction matches the true underlying value it aims to capture. For a diagnostic test it reflects how often the test is right overall, drawing together its ability to detect disease and to clear the healthy. Overall accuracy alone can mislead, since a test can score highly on a rare disease simply by calling almost everyone negative, which is why sensitivity and specificity are reported alongside it. Closeness to the truth is what it conveys. Sackett and colleagues (1991) describe this.
Source: Sackett et al. 1991
How is diagnostic accuracy measured?
Diagnostic accuracy is measured against a reference standard that establishes the true condition status, comparing test results with the truth. Overall accuracy can be expressed as the proportion of all results that are correct, but this depends on prevalence, so accuracy is more fully characterised by sensitivity and specificity, and by measures such as likelihood ratios and the area under the ROC curve. So diagnostic accuracy is measured by comparing test results against a reference standard and summarising performance through measures such as sensitivity, specificity, and the area under the curve, since a single overall proportion correct can be misleading, being influenced by how common the condition is.
Source: Altman & Bland 1994
How does accuracy differ from precision?
Accuracy concerns how close a result is to the true value, while precision concerns how consistent or reproducible results are when repeated, regardless of whether they are close to the truth. A measurement can be precise but inaccurate if it consistently gives the same wrong value, or accurate on average but imprecise if it scatters widely around the truth. So accuracy and precision are distinct: accuracy is about correctness relative to the true value, and precision about reproducibility, and a good measurement or test ideally has both, since being consistent is not the same as being correct.
Source: Altman & Bland 1994
Why can overall accuracy be misleading?
Overall accuracy, the proportion of all results that are correct, can be misleading because it depends on the prevalence of the condition: when a condition is rare, a test that simply calls everyone negative achieves high accuracy while detecting no cases. It also does not distinguish the types of error. So overall accuracy can mislead by masking poor detection of a rare condition and by combining false positives and false negatives into one figure, which is why sensitivity and specificity, which separate the two error types and do not depend on prevalence, are preferred for characterising a test's performance rather than a single accuracy figure.
Source: Altman & Bland 1994
How is accuracy characterised for a diagnostic test?
Accuracy for a diagnostic test is characterised by measures that separate its performance on those with and without the condition, chiefly sensitivity and specificity, and by summary measures such as likelihood ratios and the area under the ROC curve, which capture discrimination across thresholds. These give a fuller picture than a single proportion correct. So the accuracy of a diagnostic test is characterised through sensitivity, specificity, and related measures rather than overall accuracy alone, because these convey how well the test detects and excludes the condition independently of prevalence, which is what determines its usefulness in different settings and for different purposes.
Source: Altman & Bland 1994
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 10 Dec 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/accuracy
- Term code
- HE-ES-SA-002
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