Calculate Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value

For any given test administered to a given population, it is important to calculate the sensitivity[1], specificity[1], positive predictive value[2], and negative predictive value[3], in order to determine how useful the test is to detect a disease or characteristic in the given population. If we want to use a test to test a specific characteristic in a sample population, we would like to know:

  • How likely is the test to detect the presence of a characteristic in someone with the characteristic (sensitivity)?
  • How likely is the test to detect the absence of a characteristic in someone without the characteristic (specificity)?
  • How likely is someone with a positive test result to actually have the characteristic (positive predictive value)?
  • How likely is someone with a negative test result to actually not have the characteristic (negative predictive value)?

These values are very important to calculate in order to determine whether a test is useful for measuring a specific characteristic in a given population. This article will demonstrate how to calculate these values.

Steps

Calculator

Doc:Sensitivity and Specificity Calculator

Doing Your Own Calculation

  1. Define a population to sample, e.g. 1000 patients in a clinic.
  2. Define the disease or characteristic of interest, e.g. syphilis.
  3. Have a well-established gold standard test to determine the prevalence of disease or characteristic, e.g. darkfield microscopic documentation of presence of the Treponema pallidum bacteria from scrapes off a syphilitic sore, in collaboration with clinical findings. Use the gold standard test to determine who has the characteristic and who does not. For illustration, let us say 100 people have it and 900 do not.
  4. Have a test that you are interested in determining its sensitivity, specificity, positive predictive value, and negative predictive value for this population, and run this test on everyone within the chosen population sample. For example, let this test be a rapid plasma reagin (RPR) test to screen for syphilis. Use it to test the 1000 people in the sample.
  5. For people that have the characteristic (as determined by the gold standard), record the number of people who tested positive and the number of people who tested negative. Do the same for people that do not have the characteristic (as determined by the gold standard). You will end up with four numbers. People with the characteristic AND tested positive are the true positives (TP). People with the characteristic AND tested negative are the false negatives (FN). People without the characteristic AND tested positive are the false positives (FP). People without the characteristic AND tested negative are the true negatives (TN) For example, let us suppose you did the RPR test on the 1000 patients. Among the 100 patients with syphilis, 95 of them tested positive, and 5 tested negative. Among the 900 patients without syphilis, 90 tested positive, and 810 tested negative. In this case, TP=95, FN=5, FP=90, and TN=810.
  6. To calculate the sensitivity, divide TP by (TP+FN). In the case above, that would be 95/(95+5)= 95%. The sensitivity tells us how likely the test is come back positive in someone who has the characteristic. Among all people that have the characteristic, what proportion will test positive? 95% sensitivity is pretty good.
  7. To calculate the specificity, divide TN by (FP+TN). In the case above, that would be 810/(90+810)= 90%. The specificity tells us how likely the test is to come back negative in someone who does not have the characteristic. Among all people without the characteristic, what proportion will test negative? 90% specificity is pretty good.
  8. To calculate the positive predictive value (PPV), divide TP by (TP+FP). In the case above, that would be 95/(95+90)= 51.4%. The positive predictive value tells us how likely someone is to have the characteristic if the test is positive. Among all people that test positive, what proportion truly has the characteristic? 51.4% PPV means that if you test positive, you have a 51.4% chance of actually having the disease.
  9. To calculate the negative predictive value (NPV), divide TN by (TN+FN). In the case above, that would be 810/(810+5)= 99.4%. The negative predictive value tells us how likely someone is to not have the characteristic if the test is negative. Among all people that test negative, what proportion truly does not have the characteristic? 99.4% NPV means that if you test negative, you have a 99.4% chance of not having disease.



Tips

  • Accuracy, or efficiency, is the percentage of test results correctly identified by the test, i.e. (true positives + true negatives)/total test results = (TP+TN)/(TP+TN+FP+FN).
  • Good screening tests have high sensitivity, because you want to be able to pick up all those that have the characteristic. Tests with very high sensitivity are useful to rule out diseases or characteristics if they come back negative. ("SNOUT": SeNsitivity-rule OUT)
  • Try drawing out a 2x2 table to make things easier.
  • Know that sensitivity and specificity are intrinsic properties of a given test, and do not depend on the given population, i.e. these two values should be the same when the same test is applied to different populations.
  • Good confirmatory tests have high specificity, because you want your test to be specific and not mislabel those without the characteristic as having it. Tests with very high specificity are useful to rule in diseases or characteristics if they come back positive. ("SPIN": SPecificity-rule IN)
  • Positive predictive value and negative predictive value, on the other hand, depend upon the prevalence of the characteristic in a given population. The rarer the characteristic, the lower the positive predictive value and the higher the negative predictive value (because pre-test probability is low for rare characteristic). Conversely, the more common the characteristic, the higher the positive predictive value and the lower the negative predictive value (because pre-test probability is high for common characteristic).
  • Try to understand these concepts well.

Warnings

  • It is easy to make careless mistakes in calculation. Check your math carefully. Drawing out a 2x2 table will help.

Related Articles

Sources and Citations

  1. ↑ 1.0 1.1 https://en.wikipedia.org/wiki/Sensitivity_and_specificity
  2. ↑ https://en.wikipedia.org/wiki/Positive_predictive_value
  3. ↑ https://en.wikipedia.org/wiki/Negative_predictive_value

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