Likelihood ratios
- Measure
How much more likely a result is in someone with the disease than in someone without; it shows how far a result shifts suspicion.
What it is
A likelihood ratio (LR) compares the probability of a result in diseased people with the probability of the same result in healthy people. The positive LR shows how much a positive result raises the odds of disease, and the negative LR how much a negative result lowers them. Because they are built from sensitivity and specificity, they do not depend on prevalence, and they convert pre-test probability into post-test probability.
Formula and reading
- LR+ = Se / (1 − Sp): probability of a positive in the diseased / probability of a positive in the healthy.
- LR− = (1 − Se) / Sp: probability of a negative in the diseased / probability of a negative in the healthy.
- Post-test odds = pre-test odds × LR.
- Reading: an LR+ of 6 multiplies the odds of disease by 6; an LR− of 0.12 cuts them to about an eighth.
Worked example
- Data: an ultrasound for a disease has 90% sensitivity and 85% specificity.
- LR+ = 0.90 / (1 − 0.85) = 0.90 / 0.15 = 6.0.
- LR− = (1 − 0.90) / 0.85 = 0.10 / 0.85 ≈ 0.12 (rounded to two decimals).
- On the usual scale, an LR+ of 6 is a moderate shift and so is an LR− of 0.12.
- Reading: a positive is 6 times as likely in a diseased person as in a healthy one; a negative is about 8 times less likely.
How to read a likelihood ratio
| LR+ | LR− | Shift in probability |
|---|---|---|
| Above 10 | Below 0.1 | Large, often decisive |
| 5 to 10 | 0.1 to 0.2 | Moderate |
| 2 to 5 | 0.2 to 0.5 | Small |
| 1 to 2 | 0.5 to 1 | Minimal, rarely useful |
Markers
- LR+
- LR−
How to read it
- LRs for history and examination findings let clinical findings and tests be combined quantitatively.
- One test can have different LRs for different result ranges (for example very high, intermediate or low).
Common pitfalls
- Inverting the formulas (putting specificity in the numerator of LR+).
- Multiplying the LR by the probability instead of by the odds.
- Chaining LRs from tests that are not independent of each other.
Test yourself
Think of the answer, then tap the question to see it.
Sensitivity 80% and specificity 95%. What is the LR+?
0.80 / 0.05 = 16: a large shift.
Sensitivity 98% and specificity 60%. What is the LR−?
0.02 / 0.60 ≈ 0.03: a negative greatly lowers the probability of disease.
Why do likelihood ratios not change with prevalence?
Because they are calculated only from sensitivity and specificity, which are measured within diseased and within healthy people.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Understanding the properties of diagnostic tests - Part 2: Likelihood ratios (Perspectives in Clinical Research, 2018); Measures of Diagnostic Accuracy: Basic Definitions (EJIFCC, 2009); Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff (U.S. Food and Drug Administration, 2007).
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Representative model, for educational purposes only.