## Flesh Eating Bacteria and Probability

17 May

It’s well known that doctors are bad at probability:

Here’s a story problem about a situation that doctors often encounter:

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

[…]

Next, suppose I told you that most doctors get the same wrong answer on this problem – usually, only around 15% of doctors get it right. (“Really? 15%? Is that a real number, or an urban legend based on an Internet poll?” It’s a real number. See Casscells, Schoenberger, and Grayboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and many other studies. It’s a surprising result which is easy to replicate, so it’s been extensively replicated.)

On the story problem above, most doctors estimate the probability to be between 70% and 80%, which is wildly incorrect.

That’s why it is in your best interest to learn some probability theory so that you don’t die! Not knowing probability might increase your probability of death; look at the tail end anecdote in this story:

She said that many doctors have a mantra: “If you hear hooves outside your window, chances are it’s a horse and not a zebra,” meaning that you should first consider the obvious explanation. “Our point is, physicians need to be trained to look at necrotizing fasciitis as a horse and not a zebra.”

If you suspect the disease, ask doctors to rule it out. Batdorff cited the case of “a gentleman whose wife said to the emergency room staff ‘could this be the flesh-eating bacteria? They said no. And it was. And he died.”

There’s a lot right with this quote but one thing wrong. No, flesh eating bacteria shouldn’t be thought of as a horse. It’s still a zebra; meaning that it’s still less common than other infections.

But the sound advice — the best advice — is to ask doctors to rule out the more serious (though less probable) possibility. That’s not probability in and of itself, but decision theory. More to the point, ask doctors to do a high success rate/low false positive rate test to rule out the possibility. Like I wrote in the post right before this one: Disconfirming evidence is better than confirming evidence. If flesh eating bacteria give certain symptom 100 out of 100 times, this doesn’t mean you actually have the disease. That, again, is the Prosecutor’s or Base Rate fallacy.

Ask for disconfirming evidence. And don’t just accept “no” from a doctor like in the last sentence of the quote, because like I said, doctors suck at probability just like the rest of us. And that ignorance of probability might cost you a lot of money in repeated doctor’s visits… or cost you your life.

1 Comment

Posted by on May 17, 2012 in Bayes

### One response to “Flesh Eating Bacteria and Probability”

1. May 21, 2012 at 10:44 pm

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