Sensitivity and Specificity Calculator (with Confidence Intervals)

This calculator is designed for clinicians and researchers evaluating the diagnostic performance of a medical test. Use it when analyzing results from a diagnostic accuracy study or clinical dataset to determine the sensitivity and specificity of a test from empiric data.

Enter values from a 2×2 diagnostic contingency table
True Positives (TP) Diseased patients correctly identified
False Positives (FP) Non-diseased patients incorrectly positive
False Negatives (FN) Diseased patients missed by the test
True Negatives (TN) Non-diseased patients correctly identified

Formulas

Sensitivity

\( \text{Sensitivity} = \frac{\text{TP}}{\text{TP} + \text{FN}} \)

Specificity

\( \text{Specificity} = \frac{\text{TN}}{\text{TN} + \text{FP}} \)

Wilson Confidence Interval for a Proportion

Given \( x \) = number of successes, \( n \) = total observations, \( \hat{p} = x/n \), and \( z = 1.96 \) (for 95% CI):

\( \text{Wilson CI} = \frac{\hat{p} + \frac{z^2}{2n} \pm z \sqrt{\frac{\hat{p}(1 - \hat{p}) + \frac{z^2}{4n}}{n}}}{1 + \frac{z^2}{n}} \)

Understanding Sensitivity and Specificity

Sensitivity represents the probability that the test correctly identifies patients who truly have the disease. A highly sensitive test minimizes false negatives and is useful for ruling out disease when the test result is negative.

Specificity represents the probability that the test correctly identifies patients who do not have the disease. A highly specific test minimizes false positives and is useful for ruling in disease when the test result is positive.

Sensitivity and specificity are intrinsic characteristics of a diagnostic test and do not vary with disease prevalence.

Specific Examples

High Sensitivity Example

A highly sensitive test correctly identifies most patients who truly have the disease, resulting in few false negatives.

Example: D-dimer testing for pulmonary embolism has high sensitivity; a negative result makes clinically significant pulmonary embolism unlikely in low-risk patients.

Low Sensitivity Example

A low sensitivity test misses a substantial proportion of patients with the disease, resulting in more false negatives.

Example: Plain chest radiography for early pneumonia may miss subtle or early disease compared with CT imaging.

High Specificity Example

A highly specific test correctly identifies most patients without the disease, resulting in few false positives.

Example: Acid-fast bacilli smear positive for tuberculosis is highly specific when properly obtained and processed.

Low Specificity Example

A low specificity test incorrectly labels many healthy individuals as having the disease, resulting in more false positives.

Example: D-dimer testing is poorly specific because many non-thrombotic conditions elevate D-dimer levels.

Assumptions & Limitations

  • Assumes binary test outcomes
  • Requires an appropriate and accurate reference standard (in many cases, reference standards are not 100% accurate)
  • Does not incorporate disease prevalence or pre-test probability, so doesn't actually tell clinicians what to do with a positive or negative result (that depends on prevalence)
  • Does not reflect downstream clinical consequences of misclassification

Formula Reference

For additional information on sensitivity and specificity, see this StatPearls article on Sensitivity and Specificity.

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