Concept Architecture
Concept
Theoretically, Sensitivity is a diagnostic accuracy measure that quantifies the ability of a test to correctly identify individuals who truly have a target condition. It represents the probability that a diagnostic test yields a positive result when the condition is present and is founded on conditional probability theory. The concept exists to evaluate the capacity of a diagnostic test to minimise false-negative results and support accurate disease detection.
Mathematically, Sensitivity is represented as the proportion of true positive results among all individuals who truly have the condition according to a reference standard. It is a probability ranging from 0 to 1 or equivalently 0% to 100%. Higher sensitivity indicates a greater ability to detect disease and reduce missed diagnoses.
In practice, Sensitivity is estimated from diagnostic accuracy studies by comparing the results of an index test with those of an accepted reference standard. It is widely applied in screening programmes, diagnostic evaluation, health technology assessment and health economic modelling to assess test performance, estimate downstream healthcare consequences and inform diagnostic decision-making.
Purpose
Used to quantify the ability of a diagnostic test to correctly identify individuals with disease, evaluate diagnostic performance and support clinical and health economic decision-making.
Mathematical Formulae
Primary Formula
Sensitivity = TP / (TP + FN)
where:
- TP = true positives
- FN = false negatives
Supporting Formulae
False Negative Rate = FN / (TP + FN)
False Negative Rate = 1 ? Sensitivity
LR? = Sensitivity / (1 ? Specificity)
LR? = (1 ? Sensitivity) / Specificity
where:
- LR? = positive likelihood ratio
- LR? = negative likelihood ratio
Related Mathematical Methods
- Specificity
- Positive Predictive Value
- Negative Predictive Value
- Positive Likelihood Ratio
- Negative Likelihood Ratio
- Bayes' Theorem
- Receiver Operating Characteristic Analysis
- Diagnostic Odds Ratio
Example
A diagnostic study evaluates a new blood test for detecting sepsis.
Among 250 patients confirmed to have sepsis:
- True positives = 225
- False negatives = 25
Sensitivity:
Sensitivity = 225 / (225 + 25)
Sensitivity = 225 / 250 = 0.90
Sensitivity = 90%
The test correctly identifies 90% of patients who truly have sepsis.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Division | =B2/(B2+C2) | Calculates Sensitivity from true positives and false negatives. |
| Percentage | =(B2/(B2+C2))*100 | Expresses Sensitivity as a percentage. |
| IF | =IF((B2+C2)>0,B2/(B2+C2),"") | Prevents division by zero when calculating Sensitivity. |
| ROUND | =ROUND(B2/(B2+C2),3) | Formats Sensitivity for reporting in diagnostic evaluations. |
VBA (Optional)
A VBA macro can automatically calculate Sensitivity and related diagnostic performance measures for multiple diagnostic tests and generate comparative evaluation reports.
Sources
- Zhou XH, Obuchowski NA, McClish DK. Statistical Methods in Diagnostic Medicine. 2nd ed.
- Altman DG, Bland JM. Diagnostic tests 1: Sensitivity and specificity. BMJ. 1994;308:1552.
- 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.
- Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004;329:168?169.
- 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 sensitivity?
The proportion of individuals who truly have a condition who are correctly identified as positive by a diagnostic test.
Source: Altman & Bland 1994
What does the sensitivity of a test measure?
Sensitivity is the proportion of people who truly have a condition that a test correctly identifies as positive. It measures how well a test catches disease when it is present, so a highly sensitive test misses few true cases and produces few false negatives. This makes sensitivity important for ruling disease out, since a negative result from a very sensitive test is strong reassurance the condition is absent. How well a test detects true cases is what it captures. Sackett and colleagues (1991) describe this measure.
Source: Sackett et al. 1991
How is sensitivity calculated?
Sensitivity is calculated as the number of true positives divided by the total number of people who truly have the condition, that is true positives plus false negatives. It requires a reference standard to establish who genuinely has the condition. So sensitivity is calculated from the proportion of those with the condition who test positive, giving the true positive rate, which is determined by the test itself and does not depend on how common the condition is, distinguishing it from predictive values, and it is estimated by comparing test results against a definitive reference standard in people known to have or not have the condition.
Source: Altman & Bland 1994
What does high sensitivity mean?
High sensitivity means a test correctly identifies most people who have the condition, producing few false negatives, so a negative result from a highly sensitive test is fairly reliable for ruling the condition out. This is why highly sensitive tests are valued when missing a case would be serious, such as in screening. So high sensitivity indicates that the test rarely misses the condition when it is present, which makes a negative result useful for excluding disease, though a highly sensitive test may still give false positives, so sensitivity is considered alongside specificity to judge overall performance.
Source: Sackett et al. 1991
How does sensitivity differ from specificity?
Sensitivity is the proportion of those with the condition who test positive, the true positive rate, while specificity is the proportion of those without the condition who test negative, the true negative rate. Sensitivity concerns detecting the condition when present, and specificity correctly excluding it when absent. There is often a trade-off between the two, since making a test more sensitive can reduce its specificity. So sensitivity and specificity are complementary measures of a test's performance, one capturing how well it finds the condition and the other how well it rules it out, and both are needed to characterise a diagnostic test.
Source: Altman & Bland 1994
Why is sensitivity important?
Sensitivity is important because it shows how well a test detects a condition when it is present, which matters greatly where missing cases has serious consequences, as in screening or ruling out dangerous conditions. A highly sensitive test gives confidence that a negative result is unlikely to be a missed case. So sensitivity matters for judging a test's ability to catch disease, guiding its use where failing to detect the condition would be harmful, and because it is a property of the test independent of prevalence, it characterises the test's detection ability consistently across settings, complementing specificity and the prevalence-dependent predictive values.
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
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- HE-ES-RM-040
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