What is a Post-Test Probability?
Post-test probability is the probability that a person has (or does not have) a condition after receiving the results of a diagnostic test. It provides a personalized estimate based on both the individual’s pre-test probability (such as their symptoms, risk factors, or local disease prevalence) and the accuracy of the test.
Unlike sensitivity, specificity, and likelihood ratios, which are fixed characteristics applicable only to the test itself, the post-test probability varies with the pre-test probability and applies to individual patients. It answers the question, “Given this test result, how likely is it that this person has the condition?”
Clinicians estimate post-test probability using Bayes’ theorem, which updates the pre-test probability based on the test’s positive or negative likelihood ratio. A positive test result uses the positive likelihood ratio (LR⁺) to raise the probability of disease. A negative test result uses the negative likelihood ratio (LR⁻) to lower it.
How to Calculate the Post-Test Probability
To calculate post-test probability, you first convert the pre-test probability into odds:
Then apply the appropriate likelihood ratio (LR⁺ or LR⁻) depending on the test result:
Finally, convert the post-test odds back into a probability:
A higher post-test probability suggests the condition is more likely after a positive test result. A lower value suggests the condition is less likely after a negative test result.
Example Calculations
A patient has a 30% pre-test probability of having strep throat based on symptoms and local prevalence. The test result is positive, and the rapid strep test has a positive likelihood ratio (LR⁺) of 4.5.
First, convert the pre-test probability to odds:
Multiply by LR⁺ to obtain the post-test odds:
Convert to post-test probability:
The post-test probability is about 66%, meaning that after the positive result, the patient is more likely than not to have strep, though it’s not certain.
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