Template:DiagnosticTesting Example

Patients with bowel cancer
(as confirmed on endoscopy)
Total population (pop.)
= 2030 		Condition positive Condition negative Prevalence
= (TP + FN) / pop.
= (20 + 10) / 2030
≈ 1.48%
 Accuracy (ACC)
= (TP + TN) / pop.
= (20 + 1820) / 2030
≈ 90.64%
Fecal
occult
blood
screen
test
outcome 		Test
outcome
positive 		True positive (TP)
= 20
(2030 × 1.48% × 67%) 		False positive (FP)
= 180
(2030 × (100% − 1.48%) × (100% − 91%)) 		Positive predictive value (PPV), precision
= TP / (TP + FP)
= 20 / (20 + 180)
= 10%
 False discovery rate (FDR)
= FP / (TP + FP)
= 180 / (20 + 180)
= 90.0%
Test
outcome
negative 		False negative (FN)
= 10
(2030 × 1.48% × (100% − 67%)) 		True negative (TN)
= 1820
(2030 × (100% − 1.48%) × 91%) 		False omission rate (FOR)
= FN / (FN + TN)
= 10 / (10 + 1820)
≈ 0.55%
 Negative predictive value (NPV)
= TN / (FN + TN)
= 1820 / (10 + 1820)
≈ 99.45%
True positive rate (TPR), recall, sensitivity
= TP / (TP + FN)
= 20 / (20 + 10)
≈ 66.7%
 False positive rate (FPR), fall-out, probability of false alarm
= FP / (FP + TN)
= 180 / (180 + 1820)
= 9.0%
 Positive likelihood ratio (LR+)
= ⁠TPR/FPR⁠
= (20 / 30) / (180 / 2000)
≈ 7.41
 Diagnostic odds ratio (DOR)
= ⁠LR+/LR−⁠
≈ 20.2
 F1 score
= 2 × ⁠precision × recall/precision + recall⁠
≈ 0.174
False negative rate (FNR), miss rate
= FN / (TP + FN)
= 10 / (20 + 10)
≈ 33.3%
 Specificity, selectivity, true negative rate (TNR)
= TN / (FP + TN)
= 1820 / (180 + 1820)
= 91%
 Negative likelihood ratio (LR−)
= ⁠FNR/TNR⁠
= (10 / 30) / (1820 / 2000)
≈ 0.366

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