What does it mean to say that something causes 16% of cancers?

A few days ago, news reports claimed that 16 per cent of cancers around the world were caused by infections. This isn’t an especially new or controversial statement, as there’s clear evidence that some viruses, bacteria and parasites can cause cancer (think HPV, which we now have a vaccine against). It’s not inaccurate either. The paper that triggered the reports did indeed conclude that “of the 12.7 million new cancer cases that occurred in 2008, the population attributable fraction (PAF) for infectious agents was 16·1%”.

But for me, the reports aggravated an old itch. I used to work at a cancer charity. We’d get frequent requests for such numbers (e.g. how many cancers are caused by tobacco?). However,

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