Negative predictive value

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The negative predictive value is the proportion of patients with negative test results who are correctly diagnosed.

1 Worked example
2 Definition
3 See also
4 References

[edit] Worked example

Relationships among terms

		Condition (as determined by "Gold standard")
		True	False
Test outcome	Positive	True Positive	False Positive (Type I error, P-value)	→ Positive predictive value
Test outcome	Negative	False Negative (Type II error)	True Negative	→ Negative predictive value
		↓ Sensitivity	↓ Specificity

A worked example: the Fecal occult blood (FOB) screen test is used in 203 people to look for bowel cancer:

		Patients with bowel cancer (as confirmed on endoscopy)
		True	False	?
FOB test	Positive	TP = 2	FP = 18	= TP / (TP + FP) = 2 / (2 + 18) = 2 / 20 = 0.1 = 10%
FOB test	Negative	FN = 1	TN = 182	= TN / (TN + FN) 182 / (1 + 182) = 182 / 183 = 99.5%
		↓ = TP / (TP + FN) = 2 / (2 + 1) = 2 / 3 = 66.67%	↓ = TN / (FP + TN) = 182 / (18 + 182) = 182 / 200 = 91%

Related calculations

False positive rate (α) = FP / (FP + TN) = 18 / (18 + 182) = 9% = 1 - specificity
False negative rate (β) = FN / (TP + FN) = 1 / (2 + 1) = 33% = 1 - sensitivity
Power = 1 − β

[edit] Definition

The Negative Predictive Value can be defined as:

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

or, alternatively,

                    specificity x (1 - prevalence)
NPV = ---------------------------------------------------------------
      specificity x (1 - prevalence) + (1 - sensitivity) x prevalence