What is the Negative Likelihood Ratio (LR⁻)?
The negative likelihood ratio (LR⁻) is a diagnostic testing assessment that indicates how much less likely a negative test result is in someone with the condition compared to someone without it. A lower LR⁻ value means a stronger ability to rule out the disease. It does not tell you the probability that a person is disease-free if they test negative—that’s the negative predictive value, which incorporates disease prevalence.
The negative likelihood ratio formula expresses the ratio of two probabilities: the chance of a false negative result in someone with the condition, divided by the chance of a true negative result in someone without it. It is calculated using both sensitivity and specificity:
The negative likelihood ratio tells you how much less likely a person without the condition is to test negative compared to a person with the condition. For instance, a value of 0.2 means someone without the disease is only 20% as likely to test negative than someone with the disease.
The lower the LR⁻, the more informative a negative result is. A value of 1 means the test result provides no diagnostic value, while values below 0.1 are often considered strong evidence to rule out the condition.
Like sensitivity and specificity, the negative likelihood ratio reflects the inherent ability of the test to distinguish between those with and without the condition. It does not depend on how common the condition is in the population.
However, the likelihood ratio serves as a bridge between test accuracy and clinical decision-making. You can use it with a patient’s pre-test odds to calculate their post-test odds using Bayes’ theorem. Because pre-test odds typically reflect the condition’s prevalence in the relevant population, this approach incorporates prevalence into the interpretation, providing a more personalized assessment of the test result for that individual.
For the related measure that applies to positive test results, see the positive likelihood ratio (LR⁺).
LR⁻ Example Calculation and Interpretation
A test for influenza has a sensitivity of 95% and a specificity of 70%. The negative likelihood ratio is:
This value means that if a person has the disease, they are only about 7.1% as likely to test negative as someone without the disease. In other words, negative results are far more common in people who don’t have the condition. You can apply this likelihood ratio to a pre-test probability based on clinical symptoms or known prevalence to estimate the post-test probability that the person truly does not have the condition.
To express this in more intuitive terms, you can take the reciprocal:
This reciprocal of the negative likelihood ratio indicates that a person without influenza is about 14 times more likely to test negative than a person with influenza.
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