Template:SensSpecPPVNPV
- 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 | |||
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%
This hypothetical screening test (fecal occult blood test) correctly identified two-thirds (66.7%) of patients with colorectal cancer.[a] 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.
Note
[edit]- ^ There are advantages and disadvantages for all medical screening tests. Clinical practice guidelines, such as those for colorectal cancer screening, describe these risks and benefits.[1][2]
References
[edit]- ^ Lin, Jennifer S.; Piper, Margaret A.; Perdue, Leslie A.; Rutter, Carolyn M.; Webber, Elizabeth M.; O'Connor, Elizabeth; Smith, Ning; Whitlock, Evelyn P. (21 June 2016). "Screening for Colorectal Cancer". JAMA. 315 (23): 2576–2594. doi:10.1001/jama.2016.3332. ISSN 0098-7484. PMID 27305422.
- ^ Bénard, Florence; Barkun, Alan N.; Martel, Myriam; Renteln, Daniel von (7 January 2018). "Systematic review of colorectal cancer screening guidelines for average-risk adults: Summarizing the current global recommendations". World Journal of Gastroenterology. 24 (1): 124–138. doi:10.3748/wjg.v24.i1.124. PMC 5757117. PMID 29358889.
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.