### Probability and Medicine

When he explained that

*she*would either respond or not respond, she became confused and said "You mean my chances of getting better are really only 50%?" Clearly, she was mistaking the binary aspect of the treatment outcome (getting better or not) with the

*probability*that she herself would get a response.

Friedman then speculated on why her patient might have had this misconception. He points out that mathematicians have attributed such problems on

*innumeracy "*the arithmetic equivalent of illiteracy". He also mentioned that some misunderstanding might arise from a natural human tendency to not attribute bad (or any striking) events to chance.

Personally, I think the example Friedman cited has more to do with innumeracy. However, I don't like the word because of its pejorative connotation. The fact is that

*most*of us have this type of innumeracy even doctors (if you can believe it). Probability is one of those terribly difficult philosophical problems that trouble just about all of us.

The dynamics of a clinical situation will determine the probability of a given patient developing a specific disease. A smoker has a higher probability of getting lung cancer than a nonsmoker, but an individual will either get it or not

*period*. This sounds straight forward but a lot of people have problems with it. Some smokers never get lung cancer and some nonsmokers do. The reason is that smoking is not the only factor that leads to lung cancer. The more factors we understand (for example age, exposure to other toxins such as oxidants and genetics), the more precise the probability estimate will become.

This becomes very important as physicians increasingly embrace evidence-based medicine (EBM). In the desire to cite statistics of medical outcomes (such as the chance of developing a certain disease or the likelihood that a certain treatment will work) it is very important to recognize that every patient is different. The study population of a particular study will surely have a cross-section of many different types of participants. The patient's observed probability will be closer to patients more like himself -- maybe closer in ways that weren't even imagined or assessed by the researchers.

The original studies looking at the impact of cholesterol on cardiac outcomes didn't subdivide patients by measuring the different

*types*of cholesterol such as LDL, HDL or triglycerides. Had they done so, individual probabilities of adverse outcomes could have been better stratified (as they have been subsequently).

As physicians, we have to do a better job of explaining these concepts to our patients. At the same time, we need to do a better job of understanding them ourselves! What's true in a study may not be true for a particular patient.

I want to close this post with my favorite probability brainteaser: If you flip a coin nine times and it comes up heads each time, what is the probability that it will come up heads the tenth time? I'll put the correct answer as the first comment to this post.

Labels: Art of Medicine, Education, Statistics

## 6 Comments:

The answer to my question paraphrases Bertrand Russell: I don't know but you're crazy if you say 50:50!

.

I vaguely recall from grade school that "Lady Luck has no memory."

That is, the odds of the 10th toss coming up heads (or tails) is still 50/50.

In support of this, a quick Google search yielded the following:

"If you flip a coin, what are the odds of it coming up heads 10 times in a row? The odds are 1 in 2 raised to 10th power, or 1 in 1024. But what if the coin has already been flipped 9 times and come up heads each time? What are the odds that the coin will come up heads 10 times in a row? The only remaining random event is the last coin toss. The coin will either come up heads, making 10 heads in a row, or tails, making 9 heads in a row followed by one tail. Thus, the conditional probability of a coin coming up heads 10 times in a row�if it�s already come up heads 9 times in a row�is 1 in 2, or 50 percent."

http://www.stevemcconnell.com/

ieeesoftware/eic18.htm

BTW, I had never heard the term "innumeracy" before; thanx for the new word!

Henry, you've traded mathematical purity for common sense: the odds of a "fair" coin coming up heads in the first 9 tosses is 2 raised to the 9th power. 1 in 512. Pretty bad odds.

My conclusion (and Sir Russell's)is that "that ain't no fair coin!" I stand by my answer which is that you're

crazyif you think it's 50:50!.

Ooookay...."Uncle!"

;-))

This reminds me of a guy I used to work with years ago: It had been raining steadily for some time that night (we were on the night shift). He lamented the fact that the weather service said there was something like a sixty percent chance of rain and yet it had been raining steadily all night.

It took some time for us to convince him that a sixty percent chance of rain didn't mean it was only going to rain sixty percent of the night. It meant there was a sixty percent chance of measurable precipitation and it may rain all night, not at all, or spordically through the night. I think he finally understood what we where trying to tell him.

If the coin is perfectly balanced, then we expect that the coin will land heads approximately 50 percent of the time. Anyway i could use some real help with Conditional probillity concepts in medicine. anyone who is Knowledgeable in subject and has a few moments please e-mail me at debraperna@gmail.com

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