Only one out of 21 obstetricians could estimate the probability that an unborn child had Down syndrome given a positive test
Say the doctor knows false positive/negative rates of the test, and also the overall probability of Down syndrome, but doesn't know how to combine these into the probability of Down syndrome given a positive test result.
Okay, so to the extent that it's possible, why doesn't someone just tell them the results of the Bayesian updating in advance? I assume a doctor is told the false positive and negative rates of a test. But what matters to the doctor is the probability that the patient has the disorder. So instead of telling a doctor, "Here is the probability that a patient with Down syndrome will have a negative test result," why not just directly say, "When the test is positive, here is the probability of the patient actually having Down syndrome. When the test is negative, here is the probability that the patient has Down syndrome."
Bayes theorem is a general tool that would let doctors manipulate the information they're given into the probabilities that they care about. But am I crazy to think that we could circumvent much of their need for Bayes theorem by simply giving them different (not necessarily much more) information?
There are counterpoints to consider. But it seems to me that many examples of Bayesian failure in medicine are analogously simple to the above, and could be as simply fixed. The statistical illiteracy of doctors can be offset so long as there are statistically literate people upstream.
The incidence of the disease may be different for different populations while the test manufacturer may not know where and on which patients the test is going to be used.
Also, serious diseases are often tested multiple times by different tests. What would a Bayes-ignorant doctor do with positives from tests A and B which are accompanied with information: "when test A is positive, the patient has 90% chance of having the syndrome" and "when test B is positive, the patient has 75% chance of having the syndrome"? I'd guess most statistically illiterate doctors would go with the estimate of the test done last.
In a world where 85% of doctors can't solve simple Bayesian word problems...
In a world where only 20.9% of reported results that a pharmaceutical company tries to investigate for development purposes, fully replicate...
In a world where "p-values" are anything the author wants them to be...
...and where there are all sorts of amazing technologies and techniques which nobody at your hospital has ever heard of...
...there's also MetaMed. Instead of just having “evidence-based medicine” in journals that doctors don't actually read, MetaMed will provide you with actual evidence-based healthcare. Their Chairman and CTO is Jaan Tallinn (cofounder of Skype, major funder of xrisk-related endeavors), one of their major VCs is Peter Thiel (major funder of MIRI), their management includes some names LWers will find familiar, and their researchers know math and stats and in many cases have also read LessWrong. If you have a sufficiently serious problem and can afford their service, MetaMed will (a) put someone on reading the relevant research literature who understands real statistics and can tell whether the paper is trustworthy; and (b) refer you to a cooperative doctor in their network who can carry out the therapies they find.
MetaMed was partially inspired by the case of a woman who had her fingertip chopped off, was told by the hospital that she was screwed, and then read through an awful lot of literature on her own until she found someone working on an advanced regenerative therapy that let her actually grow the fingertip back. The idea behind MetaMed isn't just that they will scour the literature to find how the best experimentally supported treatment differs from the average wisdom - people who regularly read LW will be aware that this is often a pretty large divergence - but that they will also look for this sort of very recent technology that most hospitals won't have heard about.
This is a new service and it has to interact with the existing medical system, so they are currently expensive, starting at $5,000 for a research report. (Keeping in mind that a basic report involves a lot of work by people who must be good at math.) If you have a sick friend who can afford it - especially if the regular system is failing them, and they want (or you want) their next step to be more science instead of "alternative medicine" or whatever - please do refer them to MetaMed immediately. We can’t all have nice things like this someday unless somebody pays for it while it’s still new and expensive. And the regular healthcare system really is bad enough at science (especially in the US, but science is difficult everywhere) that there's no point in condemning anyone to it when they can afford better.
I also got my hands on a copy of MetaMed's standard list of citations that they use to support points to reporters. What follows isn't nearly everything on MetaMed's list, just the items I found most interesting.
90% of preclinical cancer studies could not be replicated:
http://www.nature.com/nature/journal/v483/n7391/full/483531a.html