Chapter 10: Medical diagnostics – Sensitivity and specificity

Aside from performing a test, we also need to know if it is diagnostically valid. That is, is it sufficiently sensitive and specific to be clinically useful?

In the perfect diagnostic test for a disease:

  • all the people who have a positive test result really would be ill (true positives)
  • there would be no positive test results in people who are not ill (false positives)
  • all the people with a negative test result would not be ill (true negatives)
  • people who are ill would not have a negative test result (false negatives).

Imagine a screening test for early cancer detection. There are 10 people without symptoms. The 2 people highlighted in orange have cancer.

A stylised diagram showing 10 people – 2 are diseased and 8 are not.
Figure 10.1: The two “orange” individuals have cancer and the eight “blue” individuals do not

With a perfect diagnostic test, all the blue figures would test negative, and all the orange figures would test positive.

A stylised diagram showing 10 people – 2 are diseased and 8 are not. Above the individuals is the result of a diagnostic test indicating positive for the diseased and negative for the healthy individuals.
Figure 10.2: A perfect test. The signs indicate the results for a cancer diagnostic. Only individuals with cancer test positive and those without test negative.

However, most tests are not perfect. In the following image the test has given a positive result in only 1 of the people who has cancer and there is a false alarm in 2 of the people who do not have cancer! In this test there are 2 false positives and 1 false negative.

A stylised diagram showing 10 people – 2 are diseased and 8 are not. Above the individuals is the result of a diagnostic test indicating two false positive tests, and one false negative test.
Figure 10.3: An imperfect test. One individual with cancer has tested negative (a false negative) and two without cancer have tested positive (false positives).

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