Healthy Skepticism Library item: 1562

Warning: This library includes all items relevant to health product marketing that we are aware of regardless of quality. Often we do not agree with all or part of the contents.

Publication type: Journal Article

Friedman R.
Mix Math and Medicine and Create Confusion
The New York Times 2005 Apr 26;

Full text:

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.”

Why do so many people have trouble with the notion of probability and chance? Mathematicians chalk it up to innumeracy, the arithmetic equivalent of illiteracy. Simply put, people are uncomfortable with mathematical concepts like probability because they never learned them in the first place.

Innumeracy explains much of the public’s confusion about the risks of various drugs and medical treatments. But not all of it. In a classic 1966 study, a group of subjects was told that a man had parked his car on a hill and that the car had rolled back into a hydrant after the man had left. The subjects were sympathetic to the man.

But a second group of subjects, told that the car had rolled into another person after the man walked away, held him responsible, even though the cause was the same.

People might chalk up a minor mishap to chance, but they are reluctant to blame a serious event on bad luck. Someone or something has to be held responsible.

Not long ago, I was consulted by the parents of a man who was dating the daughter of a depressed woman. They wanted to know what the chances were, if the couple married, that their children would also develop depression.

The worry was understandable: Someone with a depressed first-degree relative runs a 15 percent to 30 percent risk of the illness. But the risk is also 10 percent to 15 percent in the general population.

So although the young man might lower his chances of having a depressed child by avoiding women with depression in the family, he could never eliminate that risk.

The truth is that random events can make or break us. It is more comforting to believe in the power of hard work and merit than to think that probability reigns not only in the casino but in daily life.