Template:SensSpecPPVNPV
Template:SensSpecPPVNPV
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
- Positive likelihood ratio = sensitivity / (1 − specificity) ≈ 0.67 / (1 − 0.91) ≈ 7.4
- Negative likelihood ratio = (1 − sensitivity) / specificity ≈ (1 − 0.67) / 0.91 ≈ 0.37
- Prevalence threshold = ≈ 0.2686 ≈ 26.9%
- 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%
Fecal occult blood screen test outcome | |||||
Total population (pop.) = 2030 |
Test outcome positive | Test outcome negative | Accuracy (ACC) = (TP + TN) / pop. = (20 + 1820) / 2030 ≈ 90.64% |
F1 score = 2 × precision × recall/precision + recall ≈ 0.174 | |
Patients with bowel cancer (as confirmed on endoscopy) |
Actual condition positive (AP) = 30 (2030 × 1.48%) |
True positive (TP) = 20 (2030 × 1.48% × 67%) |
False negative (FN) = 10 (2030 × 1.48% × (100% − 67%)) |
True positive rate (TPR), recall, sensitivity = TP / AP = 20 / 30 ≈ 66.7% |
False negative rate (FNR), miss rate = FN / AP = 10 / 30 ≈ 33.3% |
Actual condition negative (AN) = 2000 (2030 × (100% − 1.48%)) |
False positive (FP) = 180 (2030 × (100% − 1.48%) × (100% − 91%)) |
True negative (TN) = 1820 (2030 × (100% − 1.48%) × 91%) |
False positive rate (FPR), fall-out, probability of false alarm = FP / AN = 180 / 2000 = 9.0% |
Specificity, selectivity, true negative rate (TNR) = TN / AN = 1820 / 2000 = 91% | |
Prevalence = AP / pop. = 30 / 2030 ≈ 1.48% |
Positive predictive value (PPV), precision = TP / (TP + FP) = 20 / (20 + 180) = 10% |
False omission rate (FOR) = FN / (FN + TN) = 10 / (10 + 1820) ≈ 0.55% |
Positive likelihood ratio (LR+) = TPR/FPR = (20 / 30) / (180 / 2000) ≈ 7.41 |
Negative likelihood ratio (LR−) = FNR/TNR = (10 / 30) / (1820 / 2000) ≈ 0.366 | |
False discovery rate (FDR) = FP / (TP + FP) = 180 / (20 + 180) = 90.0% |
Negative predictive value (NPV) = TN / (FN + TN) = 1820 / (10 + 1820) ≈ 99.45% |
Diagnostic odds ratio (DOR) = LR+/LR− ≈ 20.2 |
This hypothetical screening test (fecal occult blood test) correctly identified two-thirds (66.7%) of patients with colorectal cancer.[lower-alpha 1] Unfortunately, factoring in prevalence rates reveals that this hypothetical test has a high false positive rate, and it does not reliably identify colorectal cancer in the overall population of asymptomatic people (PPV = 10%).
On the other hand, this hypothetical test demonstrates very accurate detection of cancer-free individuals (NPV ≈ 99.5%). Therefore, when used for routine colorectal cancer screening with asymptomatic adults, a negative result supplies important data for the patient and doctor, such as ruling out cancer as the cause of gastrointestinal symptoms or reassuring patients worried about developing colorectal cancer.