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Definition — what does that mean?
How much more likely a positive result is in someone with the condition than in someone without it: sensitivity divided by one minus specificity.
In Swedish: Positiv sannolikhetskvot
LR+
How much more likely a positive result is in someone with the condition than in someone without it: sensitivity divided by one minus specificity.
LR+=4.5
LR+ equals 0.9 divided by (1 minus 0.8), equals 0.9 divided by 0.2, equals 4.5
You are given
Se is the sensitivity, the share of cases that test positive, and 1 − Sp the false positive rate, the share of healthy people who test positive. The ratio says how many times more often a positive result turns up in a case than in a healthy person.
Sensitivity 0.90 and specificity 0.80: LR+ = 0.90 / 0.20 = 4.5. A positive result is four and a half times as likely from a case as from a healthy person. With specificity 0.95 the same sensitivity gives 0.90 / 0.05 = 18.
The likelihood ratio is the factor by which a result multiplies the odds of the condition: odds after = odds before × LR+. A person with a 1 in 10 chance before the test has odds of 1 : 9; a positive result with LR+ = 4.5 makes them 4.5 : 9, or 1 : 2, a chance of 33%. The positive predictive value is that same probability worked out as counts; the likelihood ratio does it in one multiplication and belongs to the test, not to the population.
A ratio of 1 means the result carries no information. Above 10 a positive result moves the odds a great deal; between 2 and 5, a little; below 2, hardly at all. The negative likelihood ratio, (1 − Se) / Sp, does the same for a negative result and is read the other way: below 0.1 is strong.
Why odds and not probability?
Because Bayes’ theorem is a multiplication in odds and an unwieldy fraction in probabilities; the
Bayes’ theorem page shows both.
How does it relate to the odds ratio?
LR+ divided by LR− is the diagnostic odds ratio, a single number for the whole test.
Where is it calculated with an interval?
In the sensitivity and specificity calculator, from a 2×2 table.
| Solve for | Rearranged | With the numbers | Comes to |
|---|---|---|---|
| LR+ | Se1 | 0.91 | 4.5 |
| Se | LR+(1 | 4.5(1 | 0.9 |
| Sp | 1 | 1 | 0.8 |
Last reviewed October 20, 2026 ·How pages are reviewed
Statistics and probabilityAll formulas
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