Ben Goldacre

Health scare stories often arise because their authors simply don’t understand numbers.

Competence always looks better from a distance, but I have a confession to make: I’m a doctor, and I just don’t understand most of the stories on health risks in the news. I don’t mean I can’t understand the fuss. I mean I literally can’t understand what they’re trying to communicate to me. Last week, we were told that red meat causes bowel cancer, and Nurofen causes heart attacks, but I was no wiser. Try this, on bowel cancer, from the Today programme: “A bigger risk meaning what, Professor Bingham?” “A third higher risk.” “That sounds an awful lot, a third higher risk; what are we talking about in terms of numbers, here?” “A difference ... of around about 20 people per year.” “So it’s still a small number?”

“Umm ... per 10,000 ...” HG Wells, 150 years ago, said that statistical thinking would one day be as important as the ability to read and write in a modern technological society. I disagree; probabilistic reasoning is difficult for everyone, but everyone understands normal numbers. Which is why “natural frequencies” are the only sensible way to communicate risk. Let’s say the risk of having a heart attack in your 50s is 50% higher if you have high cholesterol: that sounds pretty bad. Let’s say the extra risk of having a heart attack if you have high cholesterol is only 2%. That sounds OK to me. But they’re both talking about the same (hypothetical) figures. Out of a hundred men in their 50s with normal cholesterol, four will be expected to have a heart attack; whereas out of 100 men with high cholesterol, six will be expected to have a heart attack. That’s two extra heart attacks. Those are natural frequencies. Easy.

Natural frequencies are readily understandable, because instead of using probabilities, or percentages, they use concrete numbers, just like the ones you use every day to check if you’ve lost a kid on a coach trip, or got the right change in a shop. Lots of people have argued that we evolved to reason and do maths with concrete numbers like these, and not with probabilities, so we will find them more intuitive. I’ll start believing evolutionary psychologists on the day they start defecating in the back garden at dinner parties like the monkeys they extrapolate from, but the point stands. Simple numbers are simple. I’m not alone in finding percentages unhelpful, incidentally. There are studies of doctors, and commissioning committees for local health authorities, and people from the legal profession, that show that even people who interpret and manage risk for a living are much more likely to make the wrong decision when information about risk is presented as probabilities or percentages, rather than as natural frequencies.

So let’s read about painkillers and heart attacks, another front-page story this month. It was a study over four years, and it suggested, using natural frequencies, that you would expect one extra heart attack for every 1,005 people taking ibuprofen. Or as the Daily Mail, in an article titled “How pills for your headache could kill”, reported: “British research revealed that patients taking ibuprofen to treat arthritis face a 24% increased risk of suffering a heart attack.” Almost everyone reported the percentages: diclofenac increases the risk of heart attack by 55%, ibuprofen by 24%. Only the Daily Telegraph and the Evening Standard reported the natural frequencies, one extra heart attack in 1,005 people on ibuprofen. The Mirror, for example, reported that one in 1,005 people on ibuprofen “will suffer heart failure over the following year”. Several other papers repeated the mistake. No. It’s heart attacks, not heart failure, and it’s one extra person in 1,005, over the heart attacks you’d get anyway. I could be a lot more forgiving if I believed that a nefarious, knowing, numerate media was choosing to report the higher, scarier percentage figures, to mislead and titillate an innumerate public. Actually, I think that they just don’t understand what they are reporting.

So if anyone is listening, this is the information I want from a newspaper, to help me make decisions about my health: I want to know who you’re talking about (eg men in their 50s); I want to know what the baseline risk is (eg four out of 100 will have a heart attack over 10 years); and I want to know what the increase in risk is, as a natural frequency (two extra men out of that 100 will have a heart attack over 10 years); and I want to know exactly what’s causing that increase in risk - an occasional headache pill or daily pain relief for arthritis. Health journalists are perfectly well paid, and the ones I know get paid more than the NHS pays me; it’s not too much to ask.