Why most people misread a relative risk

"New study: eating processed meat doubles your risk of bowel cancer." Read that headline, and most people would consider cutting processed meat from their diet entirely. Now read the actual numbers.

Let's say the baseline risk of bowel cancer for someone who eats no processed meat is 5 in 1,000 over a lifetime. A study finds that people who eat processed meat daily have a risk of 10 in 1,000. The relative risk increase is 100% — it has doubled. The absolute risk increase is 5 in 1,000 — an increase of half a percentage point. These two sentences describe exactly the same finding. Health journalists almost always report the first one.

Three numbers, one study

Why relative risk is so widely reported

Relative risk figures are almost always larger and more dramatic than absolute risk figures. A headline that says "increases your risk by 0.5 percentage points" attracts far less attention than one that says "doubles your risk". This is not necessarily malicious — scientists and journalists both have incentives to communicate significance, and relative risk genuinely captures something real about the strength of an association. The problem arises when it is presented without the baseline, which is the number that gives the relative risk its actual meaning.

If your baseline risk is 50%, doubling it is catastrophic. If your baseline risk is 0.1%, doubling it is still very small. The relative risk figure alone cannot distinguish between these situations.

The number that matters for decisions: NNT

The Number Needed to Treat (NNT) — or its mirror, the Number Needed to Harm (NNH) — is the most useful single statistic for evaluating whether a treatment or exposure actually matters at the scale of an individual decision. It asks: how many people need to be exposed (or treated) for one additional person to experience the outcome?

An NNT of 5 means that for every 5 people who receive a treatment, one additional person benefits who would not have otherwise. That is a powerful intervention. An NNT of 500 means you would need to treat 500 people — with all the associated costs, risks, and side effects — to produce one additional benefit. That changes the calculus considerably, even if the relative risk reduction looks impressive.

NNT and NNH are calculated directly from absolute risk differences, which is why absolute risk is the number you want. Reporting requirements in clinical trial publications increasingly mandate the inclusion of absolute risk data. Health reporting has not caught up.

What to do when you read a health headline

When you encounter a statistic about health risk — in a newspaper, a podcast, or a conversation — ask two questions. First: what is the baseline risk? A doubling is meaningless without knowing what it is doubling from. Second: how large is the absolute difference? If the article does not provide these numbers, treat the finding with appropriate scepticism. The original paper almost always contains them.

Statistical literacy is not about distrust of science. It is about reading science well enough to act on it sensibly.