U01.06.004 Likelihood ratio

Likelihood ratios (LRs) are a powerful tool in medicine for interpreting diagnostic tests. They go beyond simple sensitivity and specificity by providing a more nuanced understanding of how a test result influences the probability of disease.

What are Likelihood Ratios?

LRs express the likelihood of a particular test result in someone with a disease compared to someone without the disease. There are two main types:

Positive Likelihood Ratio (LR+):
- Compare the probability of a positive test in someone with the disease to the probability of a positive test in someone without the disease.
- An LR+ greater than 10 suggests a highly specific test, meaning a positive result strongly suggests the presence of the disease.
Negative Likelihood Ratio (LR-):
- Compare the probability of a negative test in someone with the disease to the probability of a negative test in someone without the disease.
- An LR- less than 0.1 suggests a highly sensitive test, meaning a negative result makes the disease very unlikely.

Formulas and Interpretation:

LR+ = Sensitivity / (1 – Specificity)
LR- = (1 – Sensitivity) / Specificity

Example Calculation:

Imagine a test for a disease with a sensitivity of 90% (90% of people with the disease will test positive) and a specificity of 80% (80% of people without the disease will test negative).

LR+ = 0.9 / (1 – 0.8) = 4.5
LR- = (1 – 0.9) / 0.8 = 0.1

LRs and Pretest Odds:

Likelihood ratios can be even more informative when combined with pretest odds, which represent the initial probability of a patient having the disease before the test. By multiplying the LR by the pretest odds, we can calculate the posttest odds, which represent the probability of disease after the test result is considered.

Key Points to Remember:

Likelihood ratios provide a more comprehensive picture of a test’s performance than just sensitivity and specificity.
A high LR+ suggests a positive test result makes the disease more likely, while a low LR- suggests a negative test result makes the disease less likely.
Likelihood ratios are best used in conjunction with pretest odds to estimate posttest odds and refine the diagnosis.

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U01.06.004 Likelihood ratio

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