Likelihood Ratio Calculator
Compute positive and negative likelihood ratios for a diagnostic test from its sensitivity and specificity.
How it works
LR+ = sensitivity ÷ (1 − specificity) · LR− = (1 − sensitivity) ÷ specificity
Likelihood ratios measure how much a test result shifts the odds of disease, independent of how common the disease is. LR+ tells you how much more likely a positive result is in a sick person than a healthy one; LR− does the same for a negative result. As rules of thumb, LR+ above 10 or LR− below 0.1 produces large, often decisive changes in probability, while ratios near 1 barely move the needle. They plug directly into the odds form of Bayes theorem: post-test odds = pre-test odds × LR.
Worked example
A test with 90% sensitivity and 85% specificity has LR+ = 0.90 ÷ (1 − 0.85) = 0.90 ÷ 0.15 = 6.0 and LR− = (1 − 0.90) ÷ 0.85 = 0.10 ÷ 0.85 = 0.118. A positive result multiplies the odds of disease sixfold.
Sources: Likelihood ratios in diagnostic testing — Wikipedia
Frequently asked questions
Why use likelihood ratios instead of predictive values?
Predictive values depend on prevalence, so they change from one setting to another. Likelihood ratios are intrinsic to the test, so they transfer across populations — you combine them with each patient’s pre-test probability to get their post-test probability.
How do I turn a likelihood ratio into a post-test probability?
Convert the pre-test probability to odds (p ÷ (1 − p)), multiply by the likelihood ratio, then convert back to a probability (odds ÷ (1 + odds)). A Fagan nomogram does this graphically.
What counts as a strong likelihood ratio?
LR+ over 10 and LR− under 0.1 cause large probability shifts; 5–10 and 0.1–0.2 are moderate; values between about 0.5 and 2 rarely change management. A ratio of exactly 1 means the result is useless.
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Educational statistics tool, not medical advice.