Math Stumps Your Doctor

In Bloomberg View, there is an article discussing the changing nature of healthcare. Doctors are now being presented with complex statistics that require mathematical skills to parse. Here is an example:

Take the famous hypothetical example of a test that is 95 percent accurate for a disease that affects 0.1 percent of the population. Imagine you’re a doctor and your patient tests positive. What is the chance that she has the disease? Most people’s intuitive answer is a rather dire 95 percent. This is wrong in a big way. Despite the ominous test result, the patient is unlikely to be sick. 

“Even doctors and medical students are prone to this error,” wrote Aron Barbey, a cognitive neuroscientist at the University of Illinois, in a paper on risk literacy published last month in the journal Science.

Some people do get the right answer: that the patient has about a 2 percent chance of having the disease.

To be honest, I did not know that answer. The article goes on to provide one way to illustrate how they came up with the answer. Once I read that, I started to see how that made logical sense.

But there’s also an intuitive approach that requires no formula at all. Imagine 1,000 people getting the test. On average, one will have the disease. The 5 percent error rate means that about 50 of the 999 healthy people will test positive. Now it’s easy to see that the group of false positives is about 50 times bigger than the group of real positives. In other words, just 2 percent of the people testing positive are likely to be sick.

I found the discussion of inside versus outside views interesting.

In an interview, Barbey said that when dealing with conditional probabilities, people often make the mistake of focusing on just the population statistics (what he calls the outside view) or just the patient’s individual statistics (the inside view). In the ALS story, the doctor saw only the outside view, focusing on the low rate of the disease in the whole population. In the problem of the test that's 95-percent accurate, people often take the inside view, ignoring the rarity of the disease.

Here is the link to the full article:  http://www.bloombergview.com/articles/2016-05-05/math-stumps-your-doctor-too