Template:SensSpecPPVNPV

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A worked example
A diagnostic test with sensitivity 67% and specificity 91% is applied to 2030 people to look for a disorder with a population prevalence of 1.48%
Patients with bowel cancer
(as confirmed on endoscopy)
Condition positive Condition negative
Fecal
occult
blood

screen
test
outcome
Test
outcome
positive
True positive
(TP) = 20
False positive
(FP) = 180
Positive predictive value
= TP / (TP + FP)
= 20 / (20 + 180)
= 10%
Test
outcome
negative
False negative
(FN) = 10
True negative
(TN) = 1820
Negative predictive value
= TN / (FN + TN)
= 1820 / (10 + 1820)
99.5%
Sensitivity
= TP / (TP + FN)
= 20 / (20 + 10)
67%
Specificity
= TN / (FP + TN)
= 1820 / (180 + 1820)
= 91%

Related calculations

  • False positive rate (α) = type I error = 1 − specificity = FP / (FP + TN) = 180 / (180 + 1820) = 9%
  • False negative rate (β) = type II error = 1 − sensitivity = FN / (TP + FN) = 10 / (20 + 10) = 33%
  • Power = sensitivity = 1 − β
  • Likelihood ratio positive = sensitivity / (1 − specificity) = 66.67% / (1 − 91%) = 7.4
  • Likelihood ratio negative = (1 − sensitivity) / specificity = (1 − 66.67%) / 91% = 0.37

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

Note: This template is used as a portion of the articles on sensitivity, specificity, likelihood ratios in diagnostic testing, etc. See those articles for additional citations.