Two diagnostic tests are conditionally independent if...

• A. When the probability of getting a given result on one test does not depend on the result from the other test given the disease status of the animal
• B. When the test results are perfectly correlated
• C. When the probability of getting a given result on one test depends on the result from the other test regardless of disease status
• D. When the tests measure the same biomarker

Answer: (A)

Conditional independence means that within each disease status group (diseased or not diseased), knowing the result of one test gives no extra information about the result of the other test. In probability terms, for a given disease status the joint probability factors: P(Test A result, Test B result | disease) = P(Test A result | disease) × P(Test B result | disease). So the likelihood of a particular result on one test does not depend on the result of the other test once you know whether the animal is diseased or not. This is exactly what the statement describes.

If the tests were perfectly correlated, that would violate independence because knowing one result would perfectly determine the other. If the probability of one test result depended on the other test result regardless of disease status, that would break the conditional independence condition. Finally, whether the tests measure the same biomarker isn’t itself the definition of conditional independence; two tests could still be conditionally independent even if they assess related biological signals, depending on how disease status affects each test.