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%

		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.