Numbers · 3 min read
Relative vs Absolute Risk: What "50% Higher Risk" Really Means
A headline says a food raises your risk by 50%. Should you worry? Relative versus absolute risk, and the one question to ask of any health scare.
By the Cognosc team ·
“Eating X raises your risk of Y by 50%.” It sounds alarming. Whether it is depends entirely on a number the headline usually leaves out.
Try it
What does “50% higher risk” look like?
Set the usual risk, then how much a headline says it rises. Each dot is one person in 1,000.
A 50% rise takes the risk from 2 in 1,000 to 3.0 in 1,000: 1.0 extra person per 1,000. The headline says “50% higher”; the change in your risk is 0.10 percentage points.
Two ways to describe the same change
Suppose your risk of an illness is 2 in 10,000, and a food raises it to 3 in 10,000.
- Relative risk: the risk went from 2 to 3, a rise of 50%.
- Absolute risk: the risk went up by 1 in 10,000, or 0.01 percentage points.
Both are true. They just answer different questions. The relative figure says how much bigger the risk got compared with before. The absolute figure says how much your actual chances changed.
Why headlines use relative risk
Relative numbers are bigger and more dramatic. “Doubles your risk” makes a better headline than “raises your risk from 1 in 50,000 to 2 in 50,000”. Press releases, adverts for treatments and even some scientific papers lean on relative figures for the same reason.
It works both ways. A drug that “cuts heart attacks by 30%” may take the risk from 10 in 1,000 to 7 in 1,000: three people in a thousand helped.
The one question to ask
Whenever you see a percentage rise or fall in risk, ask:
50% of what?
If the starting risk is tiny, even a big relative rise leaves it tiny. If the starting risk is large, a small relative change can matter a lot.
Number needed to treat
Doctors often use a figure that turns absolute risk into people: the number needed to treat. If a treatment takes the risk of something from 10 in 1,000 to 7 in 1,000, it prevents 3 cases for every 1,000 people treated. So about 333 people need to be treated for one of them to benefit. The same idea works for harms: the number needed to harm.
These numbers make trade-offs visible. A treatment that helps 1 in 333 people might be well worth it if it’s cheap and safe, and not worth it if it has serious side effects.
Worked example
A well-publicised 2015 report found that eating processed meat raises the risk of bowel cancer by about 18% per 50 g eaten a day. That’s relative. For a typical person in the UK, the lifetime risk of bowel cancer is roughly 6 in 100. An 18% rise takes it to about 7 in 100: around one extra case for every 100 people eating that much every day of their lives. Worth knowing, and far less alarming than “18% higher cancer risk” sounds.
Try it
Set a starting risk and a headline’s rise above, and see the change as people in a crowd of 1,000.
The free probability test has a risk-headline question, and why a positive test often isn’t what it seems covers the related trap of ignoring how common something is.