Sensitivity and specificity of multiple tests

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}

• sensitivity and specificity