- 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.