What to Do When You See a Scary Statistic: Relative and Absolute Risk

"Risk doubles!" sounds alarming until you learn that it went from one in a million to two in a million. A percentage change says nothing about how many people are affected until you know where it started. Before deciding how worried to be, turn the number back into people: out of how many, over what period, compared with whom?

What is happening

The same result can be written two ways. A relative figure ("cuts the risk by 25%") and an absolute one ("one fewer person in 1000") can describe exactly the same data. A Cochrane review of 35 studies on how risk is presented found that people perceive relative figures as larger and find them more persuasive, while understanding them no better (Akl et al., 2011). No bad intent is needed for this: written as a relative change, the same effect simply reads bigger.

Counts beat probabilities. Both doctors and patients grasp "10 out of 1000 people" more easily than "a 1% probability" (Akl et al., 2011; Gigerenzer et al., 2007). That is why the most useful move with any risk figure is to turn it into a count of people.

Three examples.

• A made-up one. Something affects 1 person in a million. A new factor "doubles the risk": now it is 2 in a million. That is a 100% increase and one extra case per million people.
• Mammography, a historical teaching example. Gerd Gigerenzer's often-quoted illustration uses screening-trial data: over 10 years, about 4 in 1000 women who were not screened died of breast cancer, against about 3 in 1000 who were. That is the "25% reduction" — and also one fewer death per 1000 women over 10 years. These are older trial figures used to teach the arithmetic, not a current estimate of what screening achieves; for your own decision, ask your doctor or your national screening programme.
• Processed meat. The International Agency for Research on Cancer (IARC, part of WHO) estimated that every 50 g of processed meat eaten daily raises the risk of colorectal cancer by about 18%. Cancer Research UK put a related analysis into people for the UK: out of 1000 people, about 61 develop bowel cancer at some point in their lives; about 56 among those who eat the least processed meat and about 66 among those who eat the most — 10 more per 1000. These are two different analyses with different comparisons (each extra 50 g a day versus the highest and lowest eaters), so do not combine them; the charity itself calls its figures ballpark. For scale, in 2011 about 3 in 100 UK cancers, around 8,800 a year, were linked to red and processed meat, against about 64,500 a year caused by smoking (Cancer Research UK).

The missing piece is the base rate. A relative change applied to an unknown starting point gives no absolute number — that is arithmetic, not opinion. Starting from how common something is in general is what the outside view means.

What to do

• Translate into "out of 1000": how many before, how many after?
• Ask about the period: per year, over 10 years, over a lifetime?
• Ask who was studied: age, sex, existing illness. A figure from people unlike you may not describe you.
• Work out the NNT. The number needed to treat is 1 divided by the absolute difference: how many people must take something for one to benefit. In the mammography example, a difference of 1 in 1000 means 1000 women screened for 10 years for one breast-cancer death prevented. The number needed to harm (NNH) works the same way for side effects. Ask for both.
• Check the study behind the headline: the sample size, and whether it shows a cause or only a correlation.
• Ask the same questions of hopeful numbers. "Halves the risk" needs a baseline as much as "doubles" does, and a remedy that seemed to work needs a comparison: see it got better after the treatment.
• Notice when a vivid story makes a risk feel common: that is the availability heuristic. Thinking in ranges rather than yes-or-no helps: probabilistic thinking.

When this is not the case

• A high baseline makes a relative change matter. With made-up numbers: a 20% increase on a 1-in-2 risk is 10 more people in every 100. Relative figures are not a trick; they just need their denominator.
• Same category does not mean same danger. IARC places processed meat in the same group as tobacco smoking because the evidence that each causes cancer is strong, not because they are equally harmful (IARC).
• You are not the average. Population figures blend people with very different risks; family history, age and other factors move your own number.
• Rare but irreversible is a separate conversation. A tiny absolute risk of something permanent can still deserve care. The numbers inform a decision; they do not make it for you.
• A headline is not a reason to change treatment. Talk to your doctor before stopping or starting anything because of a number in the news. Medical numbers of your own — lab results — have their own logic: how to read a blood test and an abnormal test result: what next.

Sources

• Akl et al., Cochrane 2011 — Using alternative statistical formats for presenting risks and risk reductions
• Gigerenzer et al., 2007 — Helping doctors and patients make sense of health statistics
• Gigerenzer, APS Observer — Helping physicians understand screening tests will improve health care
• IARC — Q&A on the carcinogenicity of the consumption of red meat and processed meat
• Cancer Research UK — Processed meat and cancer: what you need to know (2015)

Checked: 24 September 2026