Diagnostic test accuracy

Last revised by Joachim Feger on 3 Dec 2023

The accuracy of a diagnostic test is defined as how often the test correctly classifies someone as having or not having the disease. The formula for accuracy is:

  • (true positive + true negative) / (true positive + true negative + false positive + false negative)

  • or correct results / all results

Superficially, accuracy seems to be a useful metric for diagnostic tests, but it can be extremely misleading. For example, if you screened for lung cancer using ultrasound in 100 patients, 3 of whom had lung cancer, the test would probably be negative in all 100 patients, yielding an accuracy of 97%. This seems impressive, but all 3 lung cancers would be missed.

The purpose of a diagnostic test is to distinguish the ill from the well. In that sense, a test has 2 roles:

  1. to correctly identify the ill and

  2. to correctly identify the well

The appropriate metrics for these two functions are sensitivity (ability to correctly identify the ill) and specificity (ability to correctly identify the well).

 

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