Template:SensSpecPPVNPV
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Revision as of 11:53, 19 May 2020 by imported>Jworkorg (import)
- 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 | Prevalence = (TP+FN)/Total_Population
= (20+10)/2030 ≈1.48% |
Accuracy (ACC) = (TP+TN)/Total_Population
= (20+1820)/2030 ≈90.64% | |||
Fecal occult blood screen test outcome |
Test outcome positive |
True positive (TP) = 20 (2030 x 1.48% x 67%) |
False positive (FP) = 180 (2030 x (100 - 1.48%) x (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 x 1.48% x (100 - 67%)) |
True negative (TN) = 1820 (2030 x (100 -1.48%) x 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% | ||
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 |
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) = 0.67 / (1 − 0.91) = 7.4
- Likelihood ratio negative = (1 − sensitivity) / specificity = (1 − 0.67) / 0.91 = 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.