Sensitivity and specificity of multiple tests

Radiopaedia • CC-by-nc-sa 3.0 • de

Sensitivity and specificity of multiple tests is a common statistical problem in radiology because frequently two tests (A and B) with different sensitivities and specificities are combined to diagnose a particular disease or condition.

These two tests can be interpreted in an "and" or an "or" manner.

They can also be performed in two ways:

  • parallel: studies are performed at the same time or at approximately the same time
  • serial: studies are performed sequentially, with the second study dependent on the results of the first
Parallel testing
  • A "and" B
    • if both tests are positive, then the disease or condition is present
    • sensitivity: (A)sen x (B)sen
    • specificity: (A)spec + (B)spec - [(A)spec x (B)spec]
  • A "or" B
    • if either test is positive, then the disease or condition is present
    • sensitivity: (A)sen + (B)sen - [(A)sen x (B)sen]
    • specificity: (A)spec x (B)spec

When two studies are combined in an "or" manner:

  • the overall sensitivity is greater than for either alone
  • the overall specificity is less than for either alone

When two studies are combined in an "and" manner:

  • the overall sensitivity is less than for either alone
  • the overall specificity is greater than for either alone
Serial testing

Serial testing is more useful in some clinical scenarios to potentially eliminate the need for the second test.

  • A "and" B
    • sensitivity: (A)sen x (B)sen
    • specificity: (A)spec + [1 - (A)spec] x (B)spec
  • A "or" B
    • sensitivity: (A)sen + [1 - (A)sen] x (B)sen
    • specificity: (A)spec x (B)spec

For A "or" B, if A is positive, then the second test does not need to be performed. Sensitivity is higher than for either test alone.

For A "and" B, if A is negative, then the second test does not need to be performed. Specificity is higher than for either test alone.

See also