Suppose that based on symptoms a patient has, his doctor is 60% certain that the patient...

Suppose that based on symptoms a patient has, his doctor is 60% certain that the patient has a

particular disease. If doctor's suspicions would be overwhelming, say at least 85%, then he would

recommend a surgery. Under these circumstances, the doctor opts for quite an invasive and

expensive procedure, which unfortunately is not 100% reliable. In particular, the test can show

positive even if the patient does not have the disease (false positive), because of his diabetes.

Chances of this is 30%. On the other hand, the test can show negative if the patient does have the

disease (false negative) in 10% of all cases. Question is, in the event the test shows positive, how

much higher the prior estimate of 60% should increase to make the test worth rendering. Can we

accurately predict the results of this before running the test in order to see if a positive test will

elevate the prior from 60% to 85% or higher?

Expert Solution

orchestra answered 1 year ago

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