Monday, May 7, 2012

Sensitivity and Specificity

Sensitivity and specificity are measures used to assess the value of a diagnostic test. For any given test in any given patient, please remember that the disease or condition itself may be present or absent, and the patient may test positive or negative. Given this, we need to know how useful our test really is. We can construct a 2X2 contingency table, where across the top are two columns: disease present, disease absent. We can add along the side test positive, test negative. This creates 4 cells:

  • 1.       Disease present, test positive (true positives)
  • 2.       Disease absent, test positive (false positives)
  • 3.       Disease present, test negative (false negatives)
  • 4.       Disease absent, test negative (true negatives)

Keeping this in mind, we can now define sensitivity and specificity and calculate them from our table.

Sensitivity is defined as the ability of a test to correctly identify a patient who truly has the disease in question. It is equal to the number of people with the disease who test positive divided by all the people in which the disease is present: true positives/(true positives + false negatives).

Specificity is the ability of test to properly identify those people who do not have the disease in question. It is equal to the number of people without the disease divided by all the people in which the disease is absent: true negatives/(true negatives + false positives).

Imagine a orthopedic diagnostic test for a herniated intervertebral  disc, tried out on 100 people with acute low back pain. The actual presence absence of herniated disc was diagnosed from MRI and we are comparing the results of our own orthopedic test against that “gold standard.”  The results of our 2x2 table show that our diagnostic test was positive in 20 people in which MRI also demonstrated the presence of a herniated disc; it was negative in 5 people even though there was MRI proof of herniation (false negatives); it was positive in 30 people for which the MRI did not show evidence of herniation (false positives); and it was absent in 45 people when MRI also showed no evidence of herniation (true negatives).  Sensitivity would therefore be 20/(20 + 5) = 20/25 + 0.8, or 80%. If a herniation is present, there is an 80% chance of the test properly identifying it being present.  Specificity would therefore be 45/(30 + 45) =45/75 = 0.6, or 60%. If no herniation is present, there is a 60% chance of the test being negative. However, keep in mind that there is a 40% chance of having a false positive result.

Next week, we will look at some of the implications of sensitivity and specificity.

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