Tuesday, August 14, 2012

BTL reader question: How do you get to 2%?

I have started a FAQ page on the BTL book web site here, and I will cross-post the discussion here on the blog. This will give us an opportunity to have a more interactive discussion, if necessary, with additional comments and questions.

Here is the inaugural installment.

On August 13, 2012, this question came in via Twitter:

Well, here is the answer (and thank you for the question, Tia!)

First the problem. At the bottom of page 74 and going on to the top of page 75 I discuss the question posed in a 1978 New England Journal of Medicine paper by Casscells and colleagues to 60 physicians and physicians-in-training at Harvard Medical School. The problem went like this:
"If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5 per cent, what is the chance that a person found to have a positive result actually has the disease, assuming that you know nothing about the person's symptoms or signs?"

The question clearly mimics a disease screening situation. The answer is simple yet elusive. Let us assume that 1,000 people are tested. Among them only 1 person has the actual disease. However, given that the false positive rate is 5%, we also know that out of the 1,000 people tested, 50 will have a false positive test. Assuming that the single person with the disease also has a positive test, we can expect 51 people to test positive. But since only 1 out of these 51 people with a positive test has the disease, the answer to the question above is 1/51=2%. This is a pretty shocking realization, given that a large plurality of the Harvard doctors and trainees chose 95% as their answer. 

So, be careful not to let your intuition override the data when making medical decisions!

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  1. Thank you very much, Marya! And thank you for your most beautiful and useful book.

    It was the "false positive rate" concept that wasn't clear enough to me. But now it is.