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Agent of change
September 29, 2003
Statistical Innumeracy
The science fiction writer H G Wells predicted that in modern technological societies statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. How far have we got, a hundred or so years later? A glance at the literature shows a shocking lack of statistical understanding of the outcomes of modern technologies, from standard screening tests for HIV infection to DNA evidence…
— Gigerenzer & Edwards, British Medical Journal 327 (2003), 741–744
1) A woman goes to her doctor’s office for a mammogram. She is told that
- The incidence of breast cancer is 0.8%.
- The “sensitivity” of the mammogram is 90%. (If she has breast cancer, the probability is 90% that it will show up on the mammogram.)
- The “false positive” rate is 7%. (If the woman doesn’t have breast cancer, there’s a 7% chance the mammogram will nonetheless yield a positive result.)
The mammogram comes back “positive”. What is the probability that the woman has breast cancer?
- 1%
- 7%
- 9%
- 15%
- 24%
- 47%
- 63%
- 83%
- 90%
In a recent study, a stunning majority of doctors tested (22/24) could not answer this question correctly.
The abstract to the paper
Bad presentation of medical statistics such as the risks associated with a particular intervention can lead to patients making poor decisions on treatment. Particularly confusing are single event probabilities, conditional probabilities (such as sensitivity and specificity), and relative risks. How can doctors improve the presentation of statistical information so that patients can make well informed decisions?
if, anything, soft-pedals the issue, for it seems that a shocking proportion of doctors themselves don’t understand garden-variety medical statistics.
Matters improved considerably, when the data was presented in terms of “natural”, rather than conditional probabilities (11/24 doctors in the “control group” got the above question right, when it was thus reframed). But that’s not the way this sort of data is conventionally presented to medical practitioners (let alone to patients).
The authors would like to believe that — if one could only “frame” the information in the right way, all would be well with the world. But I don’t see it.
2) Say various factors put the woman in a high risk group for breast cancer. Rather than the 0.8% risk faced by the general population, she faces a 2.4% risk of breast cancer. If the test comes back positive, what is the probability now that she has breast cancer?
More to the point, how do you even decide whether to administer a test or perform a procedure in the first place, without having to grapple with these “icky” statistical considerations. (Positive test results may require invasive/expensive followups, procedures carry their own risks, …)
Maybe patients don’t need to understand this stuff (though that makes a mockery of “informed consent”), but doctors surely do.
And it scares the bejeesus out of me that they, apparently, don’t.
Tip 'o the hat to Chris Bertram at Crooked Timber for making my day.
September 28, 2003
Happy 5764!
שנה טובה ומתוקה לכל אורחי הblog הזה.
September 26, 2003
You Can’t Buy Publicity this Bad
The Boston Globe reports that the RIAA has dropped its lawsuit against Sarah Seabury Ward, a 66 year old sculptress whom they had accused of sharing 2000 songs on Kazaa. Trouble was that:
- She’s a self-professed computer neophyte, who’d never installed any file-sharing software on her computer.
- She seems a rather unlikely aficionado of gangsta rap (among the music she was specifically accused of having traded).
- Her computer is a Macintosh. So, even if she knew how, and even if she’d wanted to, she couldn’t have shared those songs on Kazaa, which is Windows-only.
You’d think that, after such an obvious screw-up, the RIAA would be gracious, apologize to Mrs. Ward, offer to pay her legal expenses, and give her a gift-certificate to Tower Records. You’d think that, but you’d be wrong.
“Please note, however, that we will continue our review of the issues you raised and we reserve the right to refile the complaint against Mrs. Ward if and when circumstances warrant.”
was what their Law Firm wrote to her lawyer, in agreeing to drop their suit.
One of the signs of Depression is that the individual no longer cares about “keeping up appearances.” The RIAA’s rhetoric may still be that of an aggrieved party seeking redress for injuries sustained. Their body language say differently.
September 24, 2003
Old and New
My previous post on Dvali and Kachru’s recent paper stimulated a lot of interest. I got into a really wonderful physics conversation with Konstantin Savvidis of the Perimeter Institute and with Sonia Paban down the hall.
In my previous post, I basically asserted that Dvali and Kachru’s proposal would not work with the sorts of parameters they envisage. But we thought it would be more fruitful to ask what range of parameters would be required to make it work.
Mozilla Sucks
Sometimes I get depressed about this whole weblog thing. On the authoring side, it’s just about as good as I could wish for — compose an entry in a LaTeX dialect, click post and bingo! it’s converted to XHTML+MathML and posted to the web.
On the client side, however, it sucks. Never mind that only Gecko-based browsers support MathML. Even their rendering is piss-poor and, at least under MacOSX, getting worse.
Consider the humble minus sign. Up until recently, Mozilla rendered this as a hyphen, “-”. That’s wrong, and looks horrible. The most recent Mozilla builds have, instead, shifted to using the real minus sign glyph from the Symbol font as the default.
There’s one wee