“Your risk goes up 40%.” From what, to what?

Transcript

Welcome to the sofidex Health Drive podcast series. Today is a skill rather than a subject, and the skill is reading a health headline that tells you your risk has gone up or down by some percentage. You will have seen hundreds of them. A food you eat most days raises your risk of a cancer by a fifth, a pill doubles your chance of a clot, a new drug cuts heart attacks by a third. Each one lands like a verdict, and most of us either change what we do that afternoon or decide the whole thing is nonsense.

And the advice people usually get is to be sceptical, which sounds wise and helps almost nobody. Being told to doubt a number does not tell you which number to look for instead, so the headline wins anyway. So this episode asks one question, and it is the one in the title. When somebody says your risk goes up by forty per cent, the thing to ask is from what, and to what.

We will follow one man through one headline, from the link his daughter sent him to what he decides about his breakfast. We will turn a percentage back into people, out of a thousand, over a lifetime. We will look at why headlines and adverts both prefer the bigger-sounding number, and at one time that preference did real harm. And you will leave with three questions that work on any risk you are ever shown.

One thing before we start. None of this means the risks in the news are made up, and none of it is a reason to ignore a warning. The numbers are usually real. It is the missing half of them that does the damage. One thing before we start. This is health information, not medical advice, and nothing in it is a substitute for talking to your own doctor about your own treatment. What we can tell you is where all of it came from — 6 published sources, all listed with the episode. I want to do this one through a single person again. Somebody we're making up, so we can follow him the whole way through. Call him Martin. He's fifty-two. He drives a delivery van, and most mornings he picks up a bacon roll from the café by the depot. And last Tuesday his daughter sent him a link. No message with it. Just the link. And the headline said that eating processed meat raises your risk of bowel cancer by seventeen per cent.

And Martin did what nearly everybody does with a sentence like that. He felt it land. Seventeen per cent sounds like a lot. It sounds like roughly one person in six. And it isn't anything of the sort — which is the whole reason I wanted to do this one. Because that headline isn't lying to him. And every word of it can be defended. But it's still left out the one thing he'd need to decide what to do about his breakfast. So here's the plan. Start with the sentence. Work out what's missing from it. Put it back. And by the end Martin has a number he can actually use, and three questions that'll work on the next headline too. And the one after that.

So start with what's missing. Because to me that reads like a complete sentence. Your risk goes up by seventeen per cent. What more is there to say?

The starting point. Seventeen per cent of what? That's the bit that's gone. When a headline says your risk goes up by seventeen per cent, it doesn't mean seventeen people in every hundred. It means whatever your risk was before, it's now that plus about a sixth of that again. So it's a percentage of a percentage. And that's what's called a relative risk. Relative, because it only tells you how one group compares with another. It tells you nothing at all about how many people we're talking about. If your starting risk is big, seventeen per cent more is big. If your starting risk is tiny, seventeen per cent more is still tiny. And the same headline describes both. Word for word.

Give me that with something concrete, though. Because "a percentage of a percentage" is exactly the kind of sentence I'd nod along to and not follow at all.

Fair. So forget meat for a minute. Say there's a rare side effect. One person in a million gets it. And say a new pill doubles that. That's a hundred per cent increase. Terrifying headline. Your risk doubles. But what it actually means is two people in a million instead of one. Now take something common. Say thirty people in every hundred get it. A seventeen per cent increase on that is about five more people in every hundred. Smaller headline. Much bigger change. And that's the trap. So the size of the percentage tells you almost nothing about the size of what's happening to people. You need the before. And you need the after.

From what, to what. Which is the title. But say why it has to be both, because I'd have thought just knowing the before was enough.

From what, to what. That's the question, and it's — well, it's really the whole episode. And you need both because either one alone lets the other hide. The before on its own is just a fact about everybody. The after on its own sounds alarming with nothing to measure it against. So if you only take one habit away from this, take that one. Every time you see a risk go up or down by a percentage, ask what it was before and what it became. Out loud, if you have to. Because the answer turns a percentage back into people. And people are something you can actually picture. A percentage of a percentage isn't. Nobody can picture that. I certainly can't.

So do it for Martin, then. What's his before, and what's his after? Because that's what he actually needs from all this.

And this is the good bit, because somebody has already done the conversion for us, in public, with their own figures. Cancer Research UK did exactly that conversion in an article they wrote when the meat story broke. They start from the same kind of figure Martin saw. The people who ate the most processed meat had around a 17 per cent higher risk of bowel cancer than the people who ate the least. Then they turn it into people. Out of every 1000 people in the UK, about 61 will develop bowel cancer at some point in their lives. Among the people who eat the least processed meat, it's about 56 in 1000. And among the people who eat the most, you'd expect 66. That's 10 more.

So the seventeen per cent is fifty-six becoming sixty-six. Out of a thousand. That's it? That's the whole of the scary number?

That's it. Fifty-six becoming sixty-six. And I want to be careful, because "that's it" can sound like I'm waving it away, and I'm not. Ten people in a thousand is ten real people. But look at what's happened to the size of the thing. Seventeen per cent sounded like one in six. What it actually describes is one extra person in every hundred. Over a whole lifetime. Comparing the people who eat the most with the people who eat the least. And Martin can now do something with that, which he couldn't with the headline. He can weigh it.

Can we picture the thousand? Because I think that's where it actually lands for me. Not the number. The people.

Yes. So picture a thousand men like Martin. Fill a big lecture hall with them, every seat taken. Now, if every one of them ate the least processed meat there is, about fifty-six of them would get bowel cancer at some point in their lives anyway. That's the starting point, and it's not zero. It never is. Now swap the whole hall over to eating the most. Bacon most mornings, ham at lunch, sausages on Saturday. You'd expect about sixty-six. So ten more people stand up. And now look at everybody else. Nine hundred and thirty-four of them don't get bowel cancer either way. Whatever they had for breakfast, for their whole lives. That's the picture the headline hides. Not because it's false. Because a percentage can't show you the people sitting down. And it can't show you the fifty-six who were standing before the bacon came into it at all. So when Martin sees seventeen per cent, the picture in his head is a hall full of people on their feet. And the real picture is a hall where almost everybody stays sitting, and ten more stand up.

But if you're one of the ten, the percentage doesn't really matter, does it? You've got bowel cancer either way.

No, and that's a real point, not a quibble. For the ten, it's everything. But that's the odd thing about risk. Nobody knows in advance which seat they're in. So the only question Martin can actually answer is the before-and-after one. And there's another way to look at the same ten. If you're running health policy for a whole country, ten in a thousand across millions of people is a lot of cancers. So a charity or a health body can be completely right to care about a number that an individual can be completely reasonable about. Both views are honest. They're just answering different questions. One is about a population. The other is about Martin.

Hang on, though. You said these figures came from a charity's article. How old is it? Because things move.

Good question, and the answer matters. It's ten years old now — the page says so itself, right at the top. And they call their own figures ball-park, and say everybody's risk will be different. So I'm not giving Martin a precise statistic about this year. I'm showing him the shape of the conversion. The relative figure was seventeen per cent. In people, it came to roughly ten in a thousand, over a lifetime. If the baseline has drifted a bit since, the shape doesn't change. A modest percentage on a modest starting risk gives you a modest number of people.

Then why is the headline seventeen per cent? If the people version is clearer, why does nobody print it?

Partly habit, and partly that it works. Somebody actually counted this. A team went through 207 news stories about three drugs used to prevent disease. A cholesterol drug, an osteoporosis drug, and aspirin. These were stories from the mid to late nineties. Of the stories that put a number on the benefit at all, 83 per cent gave only the relative figure. Only 2 per cent gave the absolute figure on its own, and 15 per cent gave both. So it isn't that one newspaper chose the scary number. It's that the relative number is what the coverage reaches for. Almost every time. And there's a reason it reaches for it.

Is that still true now, though? That's nearly thirty years ago. Surely people have caught on.

I can't tell you it's still true, because that counting was done then, and we haven't got a newer version of it in what we've sourced. So I won't pretend. But I'd say this. The reason it happened then hasn't gone anywhere. And you can test it yourself. Next time you see a health headline with a percentage in it, look for the before and the after. See how often they're there. My guess is you'll be doing a lot of looking. But that's a guess, and I'd rather you counted than took my word for it.

Fine. So what's the reason, then? Because I'd assumed it was just to make things sound dramatic.

It's more interesting than that. The Cochrane review on exactly this question pulled together 35 studies. People shown the same result in different ways. And what it concludes is that the relative version may be perceived to be larger and is more likely to be persuasive than the absolute version of the same result. Same facts. Bigger feeling. More likely to change what you do. And it found no differences between health professionals and consumers. So this isn't about people being bad at sums. And doctors feel it too. Everybody does. The relative number reaches the part of you that decides before the part of you that counts.

So nobody needs to be a villain for this to happen. It just sort of drifts that way on its own.

Nobody needs to be a villain at all. And I think that's worth saying, because the easy version of this episode is "the media lies to you", and it doesn't, mostly. A relative risk is the natural thing a comparison produces. You compare two groups, and the cleanest summary is how much higher one is than the other. That's what goes at the top of the write-up. That's what goes in the press release. And then it's a short step to the headline. Every step is honest. And at the end of it, Martin's got seventeen per cent and no idea how many people it means. Which is the bit that matters to his breakfast.

Does it only go one way, though? Because everything we've said so far is about scary headlines. Does the same thing happen with good news?

It does, and that's the half people forget. Exactly the same trick sells benefits. "Cuts your risk by half" is a relative risk too. And there's a lovely made-up example that makes the point properly — the review's own plain-language summary uses it. A drug that cuts the risk of a hip fracture over the next three years by 50 per cent. Sounds enormous. Then they give you the before and after. 10 per cent of untreated people have the fracture, and 5 per cent of treated people do. So the drug halves the risk, and 5 fewer people in every hundred break a hip. Both true. Both the same drug. But only one of them tells you what you're actually buying.

And there's a third way of saying it, isn't there? The number you have to treat. I've heard doctors use that one.

There is. In the same example, 20 people take the drug for 3 years for one of them to avoid a fracture. That's called the number needed to treat. And it's honest. It's a useful way to think. But here's the odd part. It doesn't help most people understand. A second systematic review, in the Annals of Internal Medicine, looked at 91 studies of ways to show patients a risk. And the number needed to treat actually made understanding worse. So I wouldn't lead with it. The form that seems to work best is the plain one. Out of a hundred people like you. How many without it. How many with it. Over how long.

So what about adverts? If Martin's looking at a supplement in the chemist and the box says it cuts your risk of something by a third. What's he looking for?

The same questions, and one extra warning sign. A third of what? Out of how many? Over how long? And then watch for the words "up to". Up to a third. That's describing the best case, not the usual one. So it's the ceiling, not the average. And if Martin genuinely can't find the before and the after anywhere on the box or the website, that tells him something too. Because if the absolute numbers were impressive, they'd be printed in big letters. The missing number is often the most informative thing on the packet. So I'd have him treat silence as an answer.

Which brings me back to Martin, sort of. Because I'd imagine at some point somebody's going to offer him a tablet with a number attached.

Very likely. He's fifty-two. Say at his next check-up somebody tells him a tablet will cut his risk of a heart attack by a third. That's the same shape exactly. A third of what? If his chance over the next ten years is high, a third off it is a lot of heart attacks. If it's low, a third off it is very few. And I'm not going to give him numbers for that here, deliberately. Because the real numbers depend completely on his own starting risk. Which is the entire point. So nobody can tell him what a third means until they've told him what it's a third of. And that's a question he's allowed to ask. Out of a hundred men like me, over ten years, how many have a heart attack without it? How many with it?

Is there a case where this has actually gone wrong? Not just confused people. Actually done harm.

There's a famous one, and it's worth telling carefully. In October 1995 the UK's medicines safety committee warned that some brands of the contraceptive pill were associated with a higher risk of a blood clot in a vein. It was a real warning about a real risk. And it went everywhere. And then a significant number of women either switched brands or stopped contraception altogether. And a review of what followed reports a substantial increase in unintended pregnancies. Which matters, because an unplanned pregnancy isn't free of risk either. So people stepped away from one risk, without being told how big it was, and towards a different one they weren't weighing at all.

So was the warning wrong? Because that's how I've always heard that story told.

No. And I want to be precise here, because this story often gets told as "the warning was a mistake", and that's not what the sources we've used say. The warning was about something true. I'm not going to put figures on the clot risks themselves, because they aren't in what we've sourced for this episode. What the review does say is that the level of risk should in future be more carefully assessed, and the advice more carefully presented. That's the lesson. A risk with no starting point can't be weighed. Not against doing nothing. And not against the thing you'd do instead.

So what would a better version of that warning have sounded like? Not the numbers. Just the shape of it.

The shape is easy, and it's the same shape every time. Out of this many women taking this pill for a year, this many have a clot. Out of the same number taking the other kind, this many. And out of the same number who get pregnant, this many. So, same number of women, three rows, one year. That's it. Somebody reading that can see which row they're in and what moving rows would do. Somebody reading "higher risk" can only see the word higher. And so the decision gets made by the word.

Okay. So say Martin wants to get good at this. Not just for this headline. Is there a rule? Something written down somewhere he could actually hold onto?

There is, and it's surprisingly blunt. NICE's guideline on shared decision making says it in one line. Use absolute risk rather than relative risk. Their example is the risk going from 1 in 1,000 to 2 in 1,000, rather than saying the risk doubles. That's the same shape as our side-effect example from earlier. Doubles sounds like an emergency. One in a thousand to two in a thousand sounds like what it is. And then it keeps going. Use natural frequencies, like 10 in 100, rather than percentages. Which means people, not per cents. So not ten per cent. Ten people in every hundred.

Why does that make a difference, though? Ten per cent and ten in a hundred are the same thing.

They're the same number. They aren't the same experience. A percentage is abstract. Ten in a hundred is a room with ten people standing up in it. And it isn't just a hunch. The Cochrane review found people understand a natural frequency better than a percentage. Professionals included. And the guideline has another one I really like. Use the same denominator when you compare two risks. Not 1 in 14 and 1 in 5, but 7 in 100 and 20 in 100. Because try comparing one in fourteen with one in five in your head. You can't. Not quickly. But seven in a hundred against twenty in a hundred you can do instantly.

Which is Martin's fifty-six and sixty-six. Same thousand, both times.

Exactly that. Same thousand, both times. That's why the conversion was so easy to read. Then there's one more thing it asks for, and it's the one that gets dropped most. Present a risk over a defined period of time. Because a risk with no time attached is close to meaningless. Ten in a thousand over a year would be one thing. Ten in a thousand over a whole lifetime is quite another. And Martin's figure was lifetime. At some point in their lives, the article says. So when you see a risk, ask: over how long? A year? Ten years? The rest of my life? It changes everything about what the number means.

And what about words, rather than numbers? Because half the time nobody gives you a number. They just say it's rare, or it's common.

That's in there too, and it's one of my favourite lines in the whole guideline. Be aware that different people interpret terms such as risk, rare, unusual and common in different ways. And that's a polite way of saying those words are nearly useless on their own. Rare to a doctor might mean one in a thousand. Rare to Martin might mean it's never going to happen to anyone he knows. Same word. Completely different picture. So if somebody tells him a side effect is rare, the follow-up is simple. How rare? Out of how many? And they'll usually be able to tell him.

And what about pictures? Because I'm the kind of person who'd much rather see it than hear it.

Pictures help. The second review is clear on it — icon arrays and bar graphs improved understanding. An icon array is just a grid of little figures. A hundred, or a thousand. Some coloured in. And Martin could draw his own. A thousand squares on the back of a delivery note. Fifty-six shaded for the starting risk. Ten more in a different colour. And then the rest left blank. He'd see the ten. But he'd also see how much blank there is. And the same review says absolute numbers beat relative ones for getting it right. So the picture and the people version are doing the same job.

Okay, devil's advocate for a second. Is relative risk ever the right number? Because we've been pretty hard on it.

It is, and I'd hate anyone to leave thinking it's a con. Relative risk is the bit that travels. You compare people who eat the most processed meat with people who eat the least, and you get a ratio. That ratio is roughly the thing that can carry across to people with different starting points. Your starting point is the bit that's yours. So the proper calculation is both. Your own starting risk, then the relative change applied to it. Neither one alone is enough. Relative risk without a baseline is the headline. And a baseline without the relative change is just a statistic about everybody else.

So whose baseline is Martin's? Because he's not "people in the UK". He's him.

Right. And that's exactly the gap. The fifty-six in a thousand is an average across a lot of very different people. Martin's own starting point could be higher or lower. If something about him puts his starting point higher, the same relative change means more people. And if something puts it lower, fewer. I'm not going to guess at that, because nothing we've sourced tells us about Martin. But the guideline covers this too. Make it clear how the information applies to the person personally. Which, for Martin, means it's a perfectly reasonable thing to ask his GP. Not "is bacon bad". But "what's my own starting point, and what does this change do to it?"

Can I ask about "doubles", specifically? Because that's the word that really frightens people. Your risk doubles.

It's the worst of the lot, because doubling feels catastrophic and it's completely silent about the starting point. Double a tiny risk and you've got a slightly less tiny risk. Double a big one and you've got a crisis. And here's a trick for it. When you hear "doubles", don't think twice as dangerous. Think: one more of the same again. If the starting point was one in a thousand, doubling is one more in a thousand. Then ask whether one more in a thousand is worth what it costs to avoid. Sometimes it absolutely is. Sometimes it isn't. But you can't tell until you know what's being doubled.

You mentioned framing earlier, too. Saying the same thing two different ways. Is that the same problem or a different one?

A cousin of it. And the guideline's answer is to use both. Say it works for 97 out of 100 people, and say it doesn't for 3 out of 100. Because the same fact feels different depending on which side you hear first. Ninety-seven out of a hundred sounds wonderful. Three out of a hundred failing sounds a bit worrying. They're one sentence said two ways. And Martin can do it with his. Sixty-six in a thousand of the biggest meat eaters get bowel cancer. Nine hundred and thirty-four don't. Both are true. And hearing both is how you get an accurate feeling rather than just an accurate number.

So give me the toolkit. If Martin had to fit it on a sticky note on the dashboard of the van. What's on it?

Three questions. First. From what, to what? Turn any percentage change back into a before and an after. Second. Out of how many? Make it people, and make it the same number of people both times. Fifty-six in a thousand and sixty-six in a thousand, not seventeen per cent. And third. Over how long? A year, ten years, a lifetime. That's it. Three questions. They work on a scary headline. They work on a leaflet selling a supplement. They work on a GP offering a tablet. And they work on the link your daughter sends you at seven in the morning.

Is there one I'd add? Like — compared with what? Because that seems to be where the pill story went wrong.

That's a good fourth, and yes, it's the pill scare question. Compared with what I'd do instead. Because the choice is never between a risk and no risk. Martin's choice isn't bacon roll or immortality. It's bacon roll or something else. And the something else has its own risks and its own costs. They might be tiny. They might be bigger. Often they're just a question of what he'd enjoy. So yes. Put it on the note. From what to what. Out of how many. Over how long. Compared with what.

Right, so take him back to the café. It's Monday morning. What does Martin actually do?

He does two things. First, he replies to his daughter. Not with "it's fine", and not with "I'm giving up meat". He writes back: fifty-six in a thousand to sixty-six in a thousand, over a lifetime, comparing the people who eat the most with the people who eat the least. That's a much better conversation than the one the headline started. And then he decides about breakfast with an actual number in his head. And the same article that gave him the number gives him something useful there too. It says a bacon sandwich or a sausage bap a few times a week probably isn't much to worry about. So maybe the roll's a Friday thing now. Maybe it isn't. But it's his decision, made on the real size of the thing.

And the daughter? Because she didn't send that link to be annoying. She sent it because she worries about him.

She did, and I'd want Martin to keep that in mind. The link was a way of saying look after yourself. So the worst reply is the dismissive one, because it answers the headline and ignores her. What the numbers let him do is take her seriously and still be accurate. Something like: I looked it up, it's about ten more in a thousand over a lifetime for the heaviest eaters, so I'm cutting back a bit, and thank you. That's kinder than either "don't be daft" or a panic. And it might just teach her the question, too.

And if he decides to keep the roll every day? Is that allowed in this episode?

Completely allowed. That's the point of the skill. It isn't there to make anybody give anything up. It's there so the decision is made with the right-sized number. If Martin looks at ten in a thousand over a lifetime and decides the roll is worth it to him, that's a real choice. Made with real information. What I'd want him to avoid is the two bad versions. Panic, where seventeen per cent sounds like one in six and he gives up something he loves for a risk he's overestimated. Or the shrug, where he decides it's all nonsense and stops listening. Including to the next warning, which might be a big one.

Before we finish, what don't we know? Because I'd like you to draw that line for this one too.

A few things. The first is that the figures Martin used are ball-park and a decade old, and I've tried to treat them that way. The shape holds. The exact numbers might not. The second is that these are averages across groups of people. Most and least, which are broad bands. Martin isn't a group. He's one man with his own starting point, and nobody's handed him that number yet. And the third is something about the conversion itself. It assumes the relative change applies the same way at every starting point. That's a reasonable working assumption. It's not a law of nature. So the whole thing is a better estimate. Not a certainty.

If Martin takes one thing away from this, what is it? One sentence, if you can manage it.

That a percentage change on its own is half a fact. It's true, and it's incomplete, and the missing half is the number of people. Seventeen per cent turned out to be ten in a thousand, over a lifetime. That's not nothing. But it's also not one in six. And he only found that out because he asked from what, to what.

And three things he could take to his doctor. Because I'd guess that's where most people actually meet these numbers.

First. What's my own starting risk for this, out of a hundred people like me? Ask for the number, not a reassurance. Second. If I take this, or change this, what does that number become? And over how many years? Get both numbers, the before and the after, and get the time. And third. What's the risk of the alternative? Of doing nothing, or doing something different instead? Because that's the pill scare lesson, and it works for almost every decision there is. Three questions, and none of them needs any maths. Which is good news, because the maths is never really the hard part. Asking is.