Bayes for medical diagnosis

Here’s a cool little paper by Christopher Gill, Lora Sabin, and Chris Schmid, on the use of Bayesian methods for medical diagnosis. (The paper will appear in the British Medical Journal.) The paper has a very readable explanation of Bayesian reasoning in a clinical context.

I don’t really agree with their claim that “clinicians are natural Bayesians” (see here for my comments on that concept) but I agree that Bayesian inference seems like the right way to go, at least in the examples discussed in this paper.

2 thoughts on “Bayes for medical diagnosis

  1. Thanks for the heads up on an excellent example of a failure of the peer review system. These authors are confused about the difference between frequentists and Bayesians.

    p. 3 "The Frequentist approach asks the question: “What is the probability of this test result, given that the patient has the disease?”

    p. 4 "The Bayesians reverse the statistical question of the Frequentists to ask, “What is the probability that this patient has the disease, given this test result?”

    Well, they are right about the Bayesian question but deeply confused about how a frequentist would approach this question.

    In addition to their almost comical cluelessness about the contrast between Bayesians and frequentists, they seem not to have heard about the Nobel-prize winning research on this topic by Kahneman and Tversky, showing that people (including physicians) are not very Bayesian. They haven't heard about Gigerenzer's work claiming that people are frequentists.

    My mind is truly boggled that this paper that would get a C- in Decision Science 101 will be published in BMJ.

  2. Lefty,

    The paper is not perfect (as I noted in my blog entry, I don't think that anyone is a natural Bayesians–I'm a big fan of the Kahneman, Tversky, etc, work on this), but I liked how it illustrated the ideas of base rate and individual data in the context of medical examples. These examples make it clear why the overall operating characteristics of a test are not enough when applying it to cases in which there is additional local information.

    Actually, this is an interesting set of examples, partly because in the usual Bayesian/frequency comparison, the non-Bayesians are just using local data properties. Here, the non-Bayesians are using the operating characteristics unconditional on the local data.

    So . . . I wouldn't quite say that they are "deeply confused about how a frequentist would approach this question." Rather, there are many different frequentist approaches. (In fact, as Rubin always said, one possibly frequentist approach is to use Bayesian inference and evaluate its frequency properties!) The real point, which they make well, I think, is that aggregate frequency properties aren't enough–it can be necessary to use local information as well.

    But I'll pass your comments on to the authors. At the very least, they should communicate the debates in the decision theory literature and distinguish between normative and descriptive approaches to decision making.

    P.S. I've never taught Decision Science 101, but I have taught Decision Analysis at Berkeley and Columbia and, lemme tell ya, a C- paper would look a lot worse than this!

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