I have recently discovered David Spiegelhalter (and by recently, I mean “yesterday”). He was the lead speaker on one of the lectures on my iTunes playlist (yes, I’m that guy), and he’s a statistician.
Not the kind of profession where you’d expect to find entertainment. Although, I guess there’s also Nate Silver, with his correct prediction of the US presidential election and his bringing the gay fabulous into the world of math.
Here’s a short youtube clip of him explaining some statistics about breast cancer screening.
If you don’t feel like watching the video, here is the basic summary:
- Mammography tests, which I’m given to understand can be quite painful, correctly diagnose women 90% of the time.
- Which sounds like a pretty good result, right? Definitely worth the time.
- Only it isn’t always, really (and I guess that’s unsurprising – I’d hardly be writing about it if there was no underlying problem).
- Taking South Africa as an example (and using the stats I found on women24), one in 600 women over the age of 50 will have breast cancer (hence the annual mammogram recommendation for women over the age of 30/40).
- So if 600 women go and get tested, then there is a 90% chance that the woman with breast cancer will get an accurate positive result. So that’s good.
- But of the other 599 women, only 90% of them will get an accurate diagnosis of “no breast cancer”.
- That is: about 59 women who will get a false positive for breast cancer.
- So putting that altogether, if you’re diagnosed as positive for breast cancer from a mammography exam, there is a 98% chance that you actually don’t have breast cancer at all.
And when you throw that statistic against others like “95% survival rate” and:
In Western societies 60 to 70 women for every 100 000 develop breast cancer, whereas 25 for every 100 000 Asian women do so. However when Japanese or Chinese women move to the USA or Australia for example, the rate rises to that of the West within two generations. This suggests an environmental influence, such as a high fat diet or alcohol use.
You begin to wonder how much of that is simply a result of false positives…
Which is not to say that women shouldn’t go for mammograms. Although there are many that might – especially when you consider how many of those women end up undergoing painful and life-altering treatments on the back of that, and subsequent, false positives tests.
But we should be more wary of statistics. To quote another real world example: when scientists discovered that there was a genetic variant in 10% of people that was “found to prevent high blood pressure”, the story wasn’t news until a journalist retold the story as “a genetic variant has been found that increases the risk of high blood pressure in 90% of people”.
It’s all about the way you frame it.