Occasional reflections on Life, the World, and Mathematics

Percents are hard


Some really bad science reporting from the BBC. They report on a new study finding the incidence of diagnosed coeliac disease increasing (and decreasing incidence of dermatitis herpetiformis, though this doesn’t rate a mention) in the UK. Diagnoses have gone up from 5.2 to 19.1 per 100,000 in about 20 years, which they attribute to increased awareness. Except, they don’t say what that is 100,000 of. You have to go back to the original article to see that it is person-years, and that they are talking about incidence, and not prevalence (in technical parlance); they use the word “rate”, which is pretty ambiguous, and commonly used — particularly in everyday speech — to refer to prevalence. If you read it casually — and, despite being a borderline expert in the subject, I misread it at first myself —  you might think they mean that 19 in 100,000 of the population of Britain suffers from coeliac; that would be about 12,000 people, hardly enough to explain the condition’s cultural prominence (and prominent placement on the BBC website). In fact, they estimate that about 150,000 have diagnosed CD in the UK.

As if aiming maximally to compound the confusion, they quote one of the authors saying

“This [increase] is a diagnostic phenomenon, not an incidence phenomenon. It is exactly what we had anticipated.”

In the article they (appropriately) refer to the rate of diagnosis as incidence, but here they say it’s not about “incidence”.

To make matters worse, they continue with this comment:

Previous studies have suggested around 1% of the population would test positive for the condition – but the data from this study suggests only 0.25% are diagnosed.

I think that normally, if you say “only x% are diagnosed” is meant relative to the number of cases; here it would mean 0.25% of the 1%. But, in fact, they mean to compare the 0.25% of the population who are diagnosed with the 1% who actually suffer from the disease.

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