Which equations describe the false positive and false negative fractions?

• A. false positive = 1 - sensitivity; false negative = 1 - specificity.
• B. false positive = specificity; false negative = sensitivity.
• C. false positive = 1 - specificity; false negative = 1 - sensitivity.
• D. false positive = prevalence; false negative = 1 - prevalence.

Answer: (C)

In diagnostic testing, the false positive rate and false negative rate are the misclassification fractions that come from the test’s performance against true disease status. The false positive rate is the portion of people without the disease who test positive, which is the complement of specificity: FPR = 1 − specificity. The false negative rate is the portion of people with the disease who test negative, which is the complement of sensitivity: FNR = 1 − sensitivity.

So the correct way to describe the two fractions is: false positive = 1 − specificity and false negative = 1 − sensitivity. For example, if specificity is 95%, the false positive rate is 5%; if sensitivity is 90%, the false negative rate is 10%.

The alternatives don’t fit because using specificity as the false positive rate would misrepresent the actual misclassification, and relying on prevalence would mix in how common the disease is rather than how often the test errs.