How this calculator works
Sensitivity measures positive test results among reference-positive observations. Specificity measures negative results among reference-negative observations. Their error complements are the false-negative and false-positive rates. Likelihood ratios compare how probable a result is under the two reference conditions; the Youden index is sensitivity plus specificity minus one. A missing reference class leaves its rate undefined. Study design, spectrum of participants and reference-standard quality matter; these point estimates omit sampling intervals and should not be treated as individual diagnostic advice.
Formula
Sensitivity = TP/(TP + FN). Specificity = TN/(TN + FP). LR+ = sensitivity/(1 - specificity). LR- = (1 - sensitivity)/specificity. Youden index = sensitivity + specificity - 1.
Worked example
For TP = 40, FN = 10, TN = 90 and FP = 10, sensitivity is 80% and specificity is 90%. LR+ is 0.8/0.1 = 8, while LR- is 0.2/0.9 = 2/9.
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Frequently asked questions
Is specificity the same as negative predictive value?
No. Specificity conditions on absence of the condition. Negative predictive value conditions on a negative result and depends on prevalence.
Why is a likelihood ratio infinite?
When the model assigns zero probability to a result in the denominator condition but positive probability in the numerator condition, their ratio is infinite.
Should sensitivity and specificity be reported together?
Yes. They describe different error types. FDA guidance recommends presenting both with appropriate uncertainty and reference-standard information.