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

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  1. ^ 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
  1. ^ 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.
  2. ^ 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.