Science

# Good Stories this Week: Critical Thinking and Cancer Statistics

Readers should demand to know how health statistics were derived

In his blog Not Exactly Rocket Science, Science writer Ed Yong took a good, critical look a number that was getting bandied about in the press. A recent report had stated that 16.1% of cancers are caused by infections, such as HPV.

Health statistics can be notoriously misleading, and it's always a good idea to understand how they were derived and what they really mean. Yong explains that the number in this report is what's called a population attributable fraction, and then he gives a little background on it was calculated:

Formally, these numbers – the population attributable fractions (PAFs) – represent the proportion of cases of a disease that could be avoided if something linked to the disease (a risk factor) was avoided. So, in this case, we're saying that if no one caught HPV or any other cancer-causing infection, then 16.1% of cancers would never happen. That's around 2 million cases attributable to these causes.

From answering enquiries and talking to people, I reckon that your average reader believes that we get these numbers because keen scientists examined lots of medical records, and did actual tallies. We used to get questions like "How do you know they didn't get cancer because of something else?" and "What, did they actually count the people who got cancer because of [insert risk factor here]?"

No, they didn't. Those numbers are not counts.

Yong also does us a service by pointing out that the number 16.1 implies more precision than the researchers could possibly measure. It's a little like me saying Higgs weights 13.3 pounds after attempting to weight him on my bathroom scale. (Who else can boast of measuring the mass of the Higgs on a weekly basis?). My digital scale does read to a tenth of a pound, but when I'm holding a wiggling Higgs I could step on it three times and get three different weights. And my weight, which I have to subtract, doesn't come up exactly the same if I step on the scale a couple of different times. In theory, his weight could be measured to a tenth of a pound – but not with the instrument that's in my bathroom.

Yong says he likes the suffix "ish" so we can say Higgs is 13ish pounds – only a little above the ideal weight according to the veterinarians.

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