# Mix math and medicine and create confusion

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Mix math and medicine and create confusion
New York Times, April 26, 2005, F 11
Richard Friedman, M.D

This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer). We give the entire exchange as presentied in this article by Dr. Friedman.

Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'

Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.

For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her.

"That means that 60 percent of the time I will feel better on this, right?" she asked.

Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant.

But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked.

"You mean my chances of getting better are really only 50 percent?" she asked with dismay.

Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained "You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening."

For example, Dr. Singer said, "Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant."

A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it. If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, "she is more likely than not to get better on that antidepressant."

DISCUSSION QUESTIONS:

(1) The doctor explained 60% chance of a response from the antidepressant as "If 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. The statistician's explanation was: If my patient was typical of the subjects in the clinical trial she read about, she is more likely than not to get the better on that antidepressant. What are the pros and cons of these explanations? How would you answer the question?

(2) If your doctor would answer one of the two questions that make doctors cringe, which would you prefer? Why?