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Bayes’ Theorem App

In this article in the hospitalist, the author reports on a new app for the iPhone that is designed to doctors make use of Bayes’ Theorem in making decisions about treating patients.  The app is called Medicine Toolkit, and its major function is called Bayes at the Bedside, which contains a database of likelihood ratios of different outcomes based on test results. The idea is that doctors will be able to use Bayes’ Theorem in the application that is often used to explain the theorem: determining the likelihood a patient has a disease given the probability that any person has the disease and the probability of testing positive for the disease. Given that Bayes’ Theorem is often explained by how it can be applied to medicine (including in this class), it is ironic that most doctors do not know how to apply the theorem. According to this article in the Wall Street Journal (not the primary focus of this blog post, but it has relevant data that is worth considering)

most American doctors were not able to determine the answer to the following problem: The probability that a woman of a certain age has breast cancer is 0.8%, and the probability that if she does have breast cancer her mammogram will be positive is 90%, the probability that if she does not have breast cancer her mammogram will be positive is 7%. If her test comes back positive, what is the probability that she actually has breast cancer? Using Bayes’ Theorem: P(breast cancer|positive mammogram)= P(positive mammogram|breast cancer)×P(breast cancer)/(P(positive mammogram|breast cancer)+P(positive result|no breast cancer))= 0.9*0.008/(0.9*0.008+0.7*0.992)= 9.4%. Almost all of the American doctors said 75% when they were asked this question. Clearly doctors do not understand the power of the tests they are using, which means that they cannot correctly inform patients about what their test results mean.

The Bayes at the Bedside app would change all of that. If doctors learn how to use it, they will understand better what the tests can actually tell them about a patient, which will help them and their patients make better decisions about treatment.  I think that this is only the most obvious application of Bayes’ Theorem to everyday decision making. In my first blog post, I described how I think that game theory, used in conjunction with mobile computing devices like smartphones, could change the way we make decisions about certain kinds of problems. This iPhone app is an example of how mobile technology is being used to make math a practical tool in decision making, and I think it is only the beginning.


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