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Template:DiagnosticTesting Example

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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