Concept Architecture
Concept
Theoretically, Diagnostic Accuracy is the ability of a diagnostic test or prediction model to correctly distinguish individuals with a target condition from those without it. It is founded on statistical decision theory and diagnostic test evaluation, where test performance is quantified by comparing observed test results with a recognised reference standard. In health economics, diagnostic accuracy is fundamental to evaluating screening programmes, diagnostic technologies and clinical decision pathways because inaccuracies directly influence healthcare costs, patient outcomes and cost-effectiveness.
Mathematically, diagnostic accuracy is quantified using measures derived from the confusion matrix, including sensitivity, specificity, predictive values, likelihood ratios and summary measures such as the receiver operating characteristic (ROC) curve and area under the curve (AUC). These measures characterise different aspects of test performance and provide the mathematical basis for evaluating diagnostic effectiveness under varying disease prevalence and decision thresholds.
In practice, diagnostic accuracy is estimated by comparing test results with the true disease status established using a reference standard. Health economists use diagnostic accuracy measures to populate decision trees, Markov models and cost-effectiveness models, allowing the economic consequences of true positives, false positives, true negatives and false negatives to be quantified.
Purpose
Used to evaluate the performance of diagnostic tests, quantify classification accuracy, inform diagnostic decision-making and populate health economic models assessing diagnostic interventions.
Mathematical Formulae
Primary Formula
Accuracy = (TP + TN) / (TP + FP + TN + FN)
where:
TP = true positives
TN = true negatives
FP = false positives
FN = false negatives
Supporting Formulae
Sensitivity = TP / (TP + FN)
Specificity = TN / (TN + FP)
Positive Predictive Value = TP / (TP + FP)
Negative Predictive Value = TN / (TN + FN)
Positive Likelihood Ratio = Sensitivity / (1 ? Specificity)
Negative Likelihood Ratio = (1 ? Sensitivity) / Specificity
Related Mathematical Methods
Sensitivity
Specificity
Receiver Operating Characteristic Curve
Area Under the Curve
Likelihood Ratios
Confusion Matrix
Diagnostic Odds Ratio
Example
A new diagnostic test is evaluated in 500 patients.
True positives = 170
False positives = 20
True negatives = 270
False negatives = 40
Diagnostic accuracy:
Accuracy = (170 + 270) / (170 + 20 + 270 + 40)
Accuracy = 440 / 500
Accuracy = 0.88
The test therefore correctly classifies 88% of patients relative to the reference standard.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUM | =SUM(B2:E2) | Calculate total study population |
| Formula | =(B2+D2)/SUM(B2:E2) | Calculate diagnostic accuracy |
| Formula | =B2/(B2+E2) | Calculate sensitivity |
| Formula | =D2/(D2+C2) | Calculate specificity |
| Formula | =B2/(B2+C2) | Calculate positive predictive value |
| Formula | =D2/(D2+E2) | Calculate negative predictive value |
VBA (Optional)
Automate calculation of diagnostic performance measures and generate summary reports for diagnostic accuracy studies and health economic models.
Sources
Zhou XH, Obuchowski NA, McClish DK. Statistical Methods in Diagnostic Medicine.
Pepe MS. The Statistical Evaluation of Medical Tests for Classification and Prediction.
Bossuyt PM, Reitsma JB, Bruns DE, et al. STARD 2015: An Updated List of Essential Items for Reporting Diagnostic Accuracy Studies.
Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Bayesian Methods in Health Economics — Gianluca Baio, 1st Edition ed., 2012 (Chapman & Hall / CRC Press)
An overview of Bayesian statistical methods for the analysis of health economic data, covering economic evaluation concepts, statistical cost-effectiveness analysis, Bayesian computation and MCMC, and applied health economic evaluation.
BookView source →
Frequently Asked Questions (6)
What is diagnostic accuracy?
The overall ability of a diagnostic test to correctly classify individuals as having or not having a condition, summarised using sensitivity and specificity.
Source: Altman & Bland 1994
What does diagnostic accuracy describe about a test?
Diagnostic accuracy describes how well a test correctly sorts people into those who have a condition and those who do not. It cannot be captured by a single number, because a test can be good at detecting disease yet poor at clearing the healthy, or the reverse, so it is described jointly by sensitivity and specificity. Together these show the two ways a test can be right and the two ways it can err. How well a test classifies disease status is what it captures. Sackett and colleagues (1991) describe this.
Source: Sackett et al. 1991
How is diagnostic accuracy measured?
Diagnostic accuracy is measured by comparing a test's results with a reference standard in a group of individuals whose true condition status is known, and computing measures such as sensitivity and specificity, predictive values, likelihood ratios, and the area under the ROC curve. Studies of diagnostic accuracy require a suitable reference standard and representative patients. So diagnostic accuracy is measured through studies that compare the test against the truth and summarise its performance with several complementary measures, since no single figure fully captures accuracy, and the design of such studies, including the choice of patients and reference standard, affects the validity of the estimates.
Source: Altman & Bland 1994
Why is diagnostic accuracy characterised by more than one measure?
Diagnostic accuracy is characterised by more than one measure because a single figure, such as overall accuracy, can be misleading, depending on prevalence and hiding the balance between missing cases and false alarms. Sensitivity and specificity separate the two types of error and are independent of prevalence, while predictive values convey what a result means for a patient. So diagnostic accuracy requires several measures because different aspects of performance, detecting the condition, excluding it, and interpreting results in context, matter for different purposes, and using sensitivity, specificity, and related measures together gives a fuller and less misleading picture than any one summary alone.
Source: Altman & Bland 1994
How does prevalence affect diagnostic accuracy measures?
Prevalence affects some diagnostic accuracy measures but not others: sensitivity and specificity are properties of the test and do not depend on prevalence, while predictive values do, so the probability that a positive or negative result is correct changes with how common the condition is. Overall accuracy is also prevalence-dependent. So prevalence affects the interpretation of diagnostic accuracy, since the same test yields different predictive values in different settings, which is why sensitivity and specificity are used to characterise the test itself and predictive values are interpreted in the context of the specific population, and why overall accuracy alone can mislead across settings.
Source: Altman & Bland 1994
How is diagnostic accuracy used in practice?
Diagnostic accuracy is used in practice to judge whether a test is suitable for a purpose, such as screening, diagnosis, or ruling conditions in or out, and to interpret results for individual patients by combining the test's sensitivity and specificity with the pre-test probability. So diagnostic accuracy informs the selection and interpretation of tests, guiding whether a test is good enough for its intended role and how its results should update the probability of disease, since understanding a test's accuracy, and how it translates into predictive values at a given prevalence, is what allows results to be applied appropriately in clinical decision-making.
Source: Altman & Bland 1994
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 15 Dec 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/diagnostic-accuracy
- Term code
- HE-ES-SA-050
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