How do doctors diagnose extremely rare diseases with high confidence?
A commonly studied application of Bayes rule in probability suggests that a positive test result for a rare disease may not be a strong indicator of having the disease, if the disease is especially rare.
Does this phenomena ever pose a problem for clinicians in practice? If you're testing for a rare disease, does it make sense to repeat the test multiple times?
Of course your patient came to you because they are having relevant symptoms, so they are not a uniformly random member of the population, but I was wondering if this example you see often in statistics courses actually has any relevance to clinical practice.
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