Negative Predictive Value - Definition

Definition

The Negative Predictive Value is defined as:

{\rm NPV} = \frac{\rm number\ of\ True\ Negatives}{{\rm number\ of\ True\ Negatives}+{\rm number\ of\ False\ Negatives}} = \frac{\rm number\ of\ True\ Negatives}{{\rm number\ of\ Negative\ calls}}

where a "true negative" is the event that the test makes a negative prediction, and the subject has a negative result under the gold standard, and a "false negative" is the event that the test makes a negative prediction, and the subject has a positive result under the gold standard.

The following diagram illustrates how the positive predictive value, negative predictive value, sensitivity, and specificity are related.


Condition
(as determined by "Gold standard")
Condition Positive Condition Negative
Test
Outcome		 Test
Outcome
Positive		 True Positive False Positive
(Type I error)		 Positive predictive value =
Σ True Positive Σ Test Outcome Positive
Test
Outcome
Negative		 False Negative
(Type II error)		 True Negative Negative predictive value =
Σ True Negative Σ Test Outcome Negative
Sensitivity =
Σ True Positive Σ Condition Positive 		Specificity =
Σ True Negative Σ Condition Negative

Note that the positive and negative predictive values can only be estimated using data from a cross-sectional study or other population-based study in which valid prevalence estimates may be obtained. In contrast, the sensitivity and specificity can be estimated from case-control studies.

If the prevalence, sensitivity, and specificity are known, the negative predictive value can be obtained from the following identity:

{\rm NPV} = \frac{({\rm specificity}) ({\rm 1 - prevalence})}{({\rm specificity}) ({\rm 1 - prevalence}) + (1 - {\rm sensitivity}) ({\rm prevalence})}.

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