[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Diagnostic tests](https://durgical.com/en/epidemiology/areas/diagnostic/) › Likelihood ratios

# 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.

Updated Nov 5, 2026

## Key points

- LR+ = sensitivity / (1 − specificity).
- LR− = (1 − sensitivity) / specificity.
- LR = 1: the test changes nothing; LR+ above 10 or LR− below 0.1: a large shift.
- LR+ of 5 to 10 or LR− of 0.1 to 0.2: moderate shift; 2 to 5 or 0.2 to 0.5: small.
- They do not depend on prevalence and are multiplied by the pre-test odds.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- How to read a likelihood ratio
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## 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.

## Memory aid

Above ten rules in, below a tenth rules out: the extremes of the LR are what change decisions.

## 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.

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## Connections

## Related 5

- [Pre-test and post-test probability](https://durgical.com/en/epidemiology/pre-test-and-post-test-probability/)
- [Sensitivity](https://durgical.com/en/epidemiology/sensitivity/)
- [Specificity](https://durgical.com/en/epidemiology/specificity/)
- [Positive and negative predictive values](https://durgical.com/en/epidemiology/positive-and-negative-predictive-values/)
- [ROC curve](https://durgical.com/en/epidemiology/roc-curve/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

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](https://europepmc.org/article/PMC/PMC5950618/) (Perspectives in Clinical Research, 2018); [Measures of Diagnostic Accuracy: Basic Definitions](https://europepmc.org/article/PMC/PMC4975285/) (EJIFCC, 2009); [Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff](https://www.fda.gov/regulatory-information/search-fda-guidance-documents/statistical-guidance-reporting-results-studies-evaluating-diagnostic-tests-guidance-industry-and-fda) (U.S. Food and Drug Administration, 2007).

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Representative model, for educational purposes only.

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License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/likelihood-ratios/