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Negative predictive value



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

Contents

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
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 ≡ 10%
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

Hence with large numbers of false positives and few false negatives, a positive FOB screen test is in itself poor at confirming cancer (PPV=10%) and further investigations must be undertaken, it will though pickup 66.7% of all cancers (the sensitivity). However as a screening test, a negative result is very good at reassuring that a patient does not have cancer (NPV=99.5%) and at this initial screen correctly identifies 91% of those who do not have cancer (the specificity).

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,

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

See also

References

  • Altman DG, Bland JM (9 Jul 1994). "Diagnostic tests 2: Predictive values". BMJ 309 (6947): 102. PMID 8038641.
 
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Negative_predictive_value". A list of authors is available in Wikipedia.
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