# Sensitivity and specificity of multiple tests

Dr Tim Luijkx and Dr Matt A. Morgan et al.

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.

## Article information

rID: 34868
Section: Physics
Synonyms or Alternate Spellings: