Wednesday, July 22, 2015

In a world...

Put on that deep voice that you only use to introduce dystopian near-future science fiction, and say, “In a world…”

Good. In a world where someone invents a cancer-screening machine that is nearly 100% accurate, how useful would it really be?

Let’s look at a population of, say, one million. Medical records stretching back over decades seem to suggest that there are 100 cases of cancer diagnosed each year. And this new machine is 99% accurate. That is, if you submit to screening and you have cancer, the Machine That Goes Ping will go ping 99% of the time. Of course, technology isn’t infallible, and the same machine typically goes ping and gives a false positive in 0.1% – 1 in 1000 – cases.

In summary, there is a 99% chance of being diagnosed, and a 0.1% chance of being misdiagnosed. So what is the overall success rate of the machine? Something approaching 99%? Perhaps surprisingly, not even close.

Let’s put everybody, all 1,000,000 citizens, through the Machine That Goes Ping.
  • In 100 cancer cases, the machine pings 99 times. 
  • In the remainder of the population, 999,900 people produce 999.9 (call it 1000) false-positive pings. 
  • Total suspected cancer cases = 1099, of which 99 are actually genuine. 
  • So the probability of diagnosing a cancer using this screening machine is 99/1099 = 9%. 
Nine percent? Only nine percent? That’s outrageous, ludicrous, ridiculous!

It’s pointless doing it then.

Well, no. If I get screened and I have cancer, the chance of getting it detected remains at 99%, and those are pretty good odds. The problem is the huge number of false positives that scare the crap out of too many cancer-free citizens. I suppose you can allay their fears by saying that only 9% of the pings actually indicate cancer. But that leaves the patient wondering why he did the test at all.

Statistics, eh? Of course, you can live healthily, avoid junk food, exercise, not smoke, and still get hit by a bus.


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