What is the Positive Likelihood Ratio (LR⁺)?
The positive likelihood ratio (LR⁺) is a diagnostic testing assessment that indicates how much more likely a positive test result is in someone with the condition compared to someone without it. A higher LR⁺ value means a stronger ability to rule in the disease. It does not directly tell you the probability that a person has the disease if they test positive—that’s the positive predictive value, which incorporates disease prevalence.
The positive likelihood ratio formula expresses the ratio of two probabilities: the chance of a true positive result in someone with the condition, divided by the chance of a false positive result in someone without it. It is calculated using both sensitivity and specificity:
The positive likelihood ratio tells you how much more likely a person with the condition is to test positive compared to a person without the condition. For instance, a value of 2 means a person with the disease is twice as likely to test positive as someone without the disease.
The higher the LR⁺, the more informative a positive result is. A value of 1 means the test result provides no diagnostic value, while values above 10 are often considered strong evidence to rule in the condition.
Like sensitivity and specificity, the positive likelihood ratio reflects the inherent ability of the test to distinguish between those with and without the condition. It does not depend on the prevalence of the condition 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 complementary measure that describes how to interpret negative test results, see the negative likelihood ratio (LR⁻).
LR⁺ Example Calculation and Interpretation
A test for strep throat has a sensitivity of 90% and a specificity of 80%. The positive likelihood ratio is:
This result indicates that a person with strep throat is 4.5 times more likely to test positive than someone who does not have it. You can apply this positive likelihood ratio to a pre-test probability based on clinical symptoms or prevalence to estimate the post-test probability that the person truly has the condition.
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