Post-test probability

Post-test probability is a concept in medical statistics that refers to the probability of a person having a disease or condition after a diagnostic test has been performed. It is a key component of Bayesian statistics, which is a mathematical framework for updating probabilities based on new data.

Definition

The post-test probability of a disease is the probability that a patient has the disease after the test results are known. It is calculated using the sensitivity and specificity of the test, the pre-test probability of the disease, and the result of the test. The pre-test probability is the probability of the disease before the test is performed, based on the patient's symptoms, medical history, and epidemiological data.

Calculation

The post-test probability can be calculated using Bayes' theorem, which is a mathematical formula for updating probabilities based on new data. The formula for the post-test probability is:

P(D|T) = [P(T|D) * P(D)] / [P(T|D) * P(D) + P(T|~D) * P(~D)]

where:

• P(D|T) is the post-test probability of the disease,
• P(T|D) is the probability of a positive test result given the disease,
• P(D) is the pre-test probability of the disease,
• P(T|~D) is the probability of a positive test result given no disease, and
• P(~D) is the probability of no disease.

Clinical significance

The post-test probability is a crucial concept in clinical decision making. It helps clinicians to interpret the results of diagnostic tests and to make decisions about further testing or treatment. A high post-test probability may indicate the need for aggressive treatment, while a low post-test probability may suggest that further testing is needed to confirm the diagnosis.

See also

• Pre-test probability
• Likelihood ratios in diagnostic testing
• Predictive value of tests

Post-test probability Resources
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