Framing & context

Relative risk without the baseline

“Raises your risk 18%.” Of what, from what, by how many?

a.k.a. relative vs absolute risk · the naked percentage increase · missing baseline risk · risk ratio · hazard is not magnitude

A percentage increase is a ratio, and a ratio means nothing until you know what it multiplied. Eighteen percent more of a one-in-a-million chance and eighteen percent more of a coin flip are the same number on the page and different worlds to live in. Charts drawn in ratio space — axes labelled “% increased risk”, indexes pinned to 100, bars whose height is a change rather than an amount — cannot show the baseline, because the baseline is not on the axis. The reader supplies it from imagination, and imagination runs high.

How to spot it

Read the axis label. “% increase”, “× risk”, “relative to baseline” — nothing on that axis is a quantity of anything.
Ask “increase from what?” If the chart, the caption and the press release all decline to say, that silence is the finding.
A multiplier with no denominator in sight: “doubles”, “50% more likely”, “three times the risk”.
Rare outcomes make the most quotable multipliers, so the biggest ratios tend to sit on the smallest baselines.
A category being read as a quantity: a classification says whether something causes an outcome, never how much of it.

The fix

Put both risks on one absolute scale and let the reader see the gap and the ground it stands on — 61 in 1,000 against 66 in 1,000, on an axis that runs to 1,000. An icon array of a hundred or a thousand does that in a single picture. Give the difference as well as the ratio: the difference is the number a person can act on, and it is the one the ratio hides. Keep the ratio too — it is the right way to carry an effect across populations with different baselines — just never let it travel alone. And when the chart is really about a classification, plot the magnitudes underneath it, because a category and a quantity are different questions and only one of them has a scale.

In the gallery

Dark navy briefing slide, masthead “Morning Health Briefing · Lyon, 26 October 2015”, headlined “Your breakfast is now a Group 1 carcinogen”. A subhead reads: twenty-two scientists from ten countries, convened by the World Health Organization’s cancer agency, considered more than 800 studies on cancer in humans and reached a verdict; processed meat — bacon, ham, sausages, hot dogs — is carcinogenic to humans, the agency’s top category, the one that already holds tobacco smoking and asbestos, and every 50 g eaten daily raises the risk of bowel cancer by 18%. The main panel is labelled “Group 1 · carcinogenic to humans · sufficient evidence in humans” and holds seven bars of identical length, one per agent: tobacco smoking, asbestos, plutonium, ultraviolet radiation, alcoholic beverages and formaldehyde in blue, processed meat in gold at the bottom. Every bar is annotated “sufficient evidence”, and a caption underneath reads “Every agent above sits at the top of the agency’s scale”. Below it, a second chart headed “Increase in bowel-cancer risk per 50 g of processed meat eaten daily” shows a single gold bar reaching +18% on an axis marked +0%, +5%, +10%, +15%, +20% — an axis of percentage increases, with no case counts anywhere on the slide. Three ticked boxes run along the bottom: “Twenty-two experts, ten countries — a Working Group convened by the WHO’s cancer agency in Lyon, sitting for eight days”, “More than 800 studies — considered on cancer in humans, across more than a dozen types of cancer”, and “The top category — Group 1, sufficient evidence in humans. There is no higher class to be put in.” Down the right, a card carries the figure +18% in large gold type over the words “increase in the risk of bowel cancer for every 50 g portion of processed meat eaten daily. IARC Monographs, Volume 114.” A second card, “Where the agency filed it”, lists processed meat, tobacco smoking, asbestos and plutonium at Group 1 and red meat at Group 2A. A third, “The agency’s ladder”, gives Group 1 carcinogenic to humans, Group 2A probably carcinogenic, Group 2B possibly carcinogenic, Group 3 not classifiable. A gold-bordered card headed “The verdict” reads: sufficient evidence in humans that the consumption of processed meat causes colorectal cancer — twenty-two experts, ten countries, one category, the same one as tobacco. Beneath it, in small grey type, sits the disclosure: “The agency’s classifications describe the strength of the scientific evidence about an agent being a cause of cancer, rather than assessing the level of risk.” A footnote credits IARC Monographs Volume 114 (2015) and the WHO Q&A on the carcinogenicity of red meat and processed meat, and calls the slide a demonstration drawn by us in the style of the coverage that followed.

The 18% that never says 18% of what

Relative risk without the baseline The convenient comparison