How to Calculate 95% Confidence Interval for a Test's Sensitivity

PDF download Download Article
PDF download Download Article

The sensitivity of a test is the percentage of individuals with a particular disease or characteristic correctly identified as positive by the test. Tests with high sensitivity are useful as screening tests to exclude the presence of a disease. Sensitivity is an intrinsic test parameter independent of disease prevalence; the confidence level of a tests sensitivity, however, depends on the sample size. Tests performed on small sample sizes (e.g. 20-30 samples) have wider confidence intervals, signifying greater imprecision. 95% confidence interval for a tests sensitivity is an important measure in the validation of a test for quality assurance. To determine the 95% confidence interval, follow these steps.

Steps

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a1\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-1.jpg\/v4-460px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-1.jpg","bigUrl":"\/images\/thumb\/a\/a1\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-1.jpg\/aid1354406-v4-728px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    This is generally given for a specific test as part of the tests intrinsic characteristic. It is equal to the percentage of positives among all tested persons with the disease or characteristic of interest. For this example, suppose the test has a sensitivity of 95%, or 0.95.
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/1\/1a\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-2.jpg\/v4-460px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-2.jpg","bigUrl":"\/images\/thumb\/1\/1a\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-2.jpg\/aid1354406-v4-728px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    For our example, we have 1-0.95 = 0.05.
    Advertisement
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/af\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-3.jpg\/v4-460px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-3.jpg","bigUrl":"\/images\/thumb\/a\/af\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-3.jpg\/aid1354406-v4-728px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    [1] For our example, we have 0.05 x 0.95 = 0.0475.
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/f2\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-4.jpg\/v4-460px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-4.jpg","bigUrl":"\/images\/thumb\/f\/f2\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-4.jpg\/aid1354406-v4-728px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    [2] Suppose 30 positive cases were in the data set. For our example, we have 0.0475/30 = 0.001583.
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/38\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-5.jpg\/v4-460px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-5.jpg","bigUrl":"\/images\/thumb\/3\/38\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-5.jpg\/aid1354406-v4-728px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-5.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    [3] In our example, it would be sqrt(0.001583) = 0.03979, or approximately 0.04 or 4%. This is the standard error of the sensitivity.
  6. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/33\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-6.jpg\/v4-460px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-6.jpg","bigUrl":"\/images\/thumb\/3\/33\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-6.jpg\/aid1354406-v4-728px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    [4] For our example, we have 0.04 x 1.96 = 0.08. (Note that 1.96 is the normal distribution value for 95% confidence interval found in statistical tables. The corresponding normal distribution value for a more stringent 99% confidence interval is 2.58, and for a less stringent 90% confidence interval is 1.64.)
  7. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/ff\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-7.jpg\/v4-460px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-7.jpg","bigUrl":"\/images\/thumb\/f\/ff\/Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-7.jpg\/aid1354406-v4-728px-Calculate-95%25-Confidence-Interval-for-a-Test%27s-Sensitivity-Step-7.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    In this example, the confidence interval ranges from 0.95-0.08 to 0.95+0.08, or 0.87 to 1.03.
    8. Advertisement

Community Q&A

Search
Add New Question
  • Question
    What method is used here to calculate confidence intervals?
    Community Answer
    Work out the average standard deviation for your values and then the confidence Interval = average + and - 1.95 x standard deviation. Usually as most data is normal.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 2 Helpful 10
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Tips

      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Submit
      Thanks for submitting a tip for review!

      You Might Also Like

      How to
      Calculate Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value
      How to
      Calculate Weighted Average
      How to Find the Perfect Sample Size for Your Research Study
      How to
      Calculate Standard Deviation
      How to
      Calculate Lotto Odds
      How to
      Calculate Probability
      How to
      Calculate Cumulative Frequency
      How to
      Calculate Range
      How to
      Find Standard Deviation on the TI–84
      How to
      Calculate Odds
      How to
      Read Odds
      How to
      Calculate Variance
      How to
      Draw a Pie Chart from Percentages
      How to
      Calculate Uncertainty
      Advertisement

      References

      1. ↑ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7500131/
      2. ↑ https://www.medcalc.org/calc/diagnostic_test.php
      3. ↑ https://www.ncbi.nlm.nih.gov/books/NBK305683/
      4. ↑ https://www.ncbi.nlm.nih.gov/books/NBK305683/

      About This Article

      In other languages
      Thanks to all authors for creating a page that has been read 133,987 times.

      Did this article help you?

      Advertisement