LogicalDUAL-USE

Relative vs. Absolute Risk

What it is

Reporting a change in risk as a ratio (“halves the risk”, “40 percent more likely”) without the base rates it is a ratio of, so that a tiny absolute change reads as large — or, run the other way, a large one reads as trivial.

How it works

A relative risk is one probability divided by another, and division throws away the scale. Doubling a risk from one in a million to two in a million and doubling it from 10 percent to 20 percent are both “a 100 percent increase”, yet one is a rounding error and the other is a public-health emergency. The audience cannot tell which it is without the base rate, and the base rate is exactly what the ratio omits. Gigerenzer and colleagues showed that patients, journalists and most physicians read relative figures as if they were absolute, and that leaflets routinely use “mismatched framing”: a treatment's benefit stated relatively (big number) and its harms absolutely (small number) on the same page. The lever is arithmetic illiteracy plus a vivid headline number. A worked case: a drug that cuts strokes from 2 in 1,000 to 1 in 1,000 is honestly described as a 50 percent reduction and as 0.1 of a percentage point; a thousand people must take it for one stroke to be prevented. Absolute figures can also mislead when the time window is short, so the defense is to demand both, with the window.

Real-world examples

  • •In October 1995 the UK Committee on Safety of Medicines warned that third-generation contraceptive pills “doubled” the risk of thrombosis. The absolute change was from about 1 in 7,000 to about 2 in 7,000; many women stopped taking the pill, and Gigerenzer and colleagues cite an estimated 13,000 additional abortions in England and Wales the following year.
  • •The VIGOR trial of rofecoxib (Vioxx), published in 2000, showed roughly half the rate of serious gastrointestinal events compared with naproxen (about 2 versus 4.5 per 100 patient-years) — a relative benefit that was marketed heavily — while the heart-attack signal, about 0.4 percent versus 0.1 percent, was presented as naproxen being protective. Merck withdrew the drug in September 2004.
  • •In October 2015 the IARC classified processed meat as a Group 1 carcinogen, citing an 18 percent higher colorectal-cancer risk per 50 grams eaten daily. Headlines placed bacon beside cigarettes; the absolute change is roughly one extra case per hundred people over a lifetime, because Group 1 describes the strength of evidence, not the size of the risk.
  • •In 2021 critics of the COVID-19 vaccines circulated the Pfizer trial's absolute risk reduction — under one percentage point, because there were 8 cases among the vaccinated and 162 among the placebo group over about two months — as if it were the whole benefit. The 95 percent relative figure was honest; the absolute figure was honest; what misled was quoting the absolute number without the short window that produced it.

Ethical guidelines

Where the line is

A relative risk is legitimate in a paper, a leaflet or a news story when the absolute figures it was computed from stand beside it with the population and time window; it becomes manipulation when the ratio is presented alone, or when benefits are framed relatively and harms absolutely, because the audience will predictably read the wrong size.

  • ●Whenever a relative risk is stated, put the two absolute figures beside it: from what, to what, in how many people, over how long.
  • ●Use the same frame for benefits and harms. Stating benefits relatively and harms absolutely on the same page is the single most reliable tell of a sales document.
  • ●When you know the audience lacks the base rate, supplying the ratio alone is not “technically true”; it is a decision to let them misread it.
  • ●Prefer natural frequencies (“2 in every 1,000 people”) over percentages and ratios; the evidence that they are understood is strong.

How to defend against it

  • ►Ask for the two numbers the ratio came from: how many out of how many, before and after. A source that cannot or will not give them has told you something.
  • ►Translate every relative claim into people: “out of 1,000 like me, how many are affected with and without this?” If the answer is 1 versus 2, you now know what “doubles” means.
  • ►Ask for the time window. An absolute risk over two months and over twenty years are different numbers for the same treatment.
  • ►Check for mismatched framing: if a leaflet gives benefits as percentages and side effects as “1 in 500”, convert both to the same format before deciding.
  • ►Ask for the number needed to treat — how many people must take it for one to benefit — which is the absolute risk reduction turned into a headcount.

From the Defense Playbook

Ask for Absolute Numbersseconds

When someone quotes a relative change ("cuts your risk by 50 percent", "doubles the danger"), ask what the risk was before and after in plain counts out of the same number of people, because the same fact sounds enormous as a ratio and modest as a difference.

Every playbook entry states how strong its evidence is and when not to use it. Browse the full playbook.

References

  1. Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., & Woloshin, S. (2007). Helping doctors and patients make sense of health statistics. Psychological Science in the Public Interest, 8(2), 53-96 · link
    Collective statistical illiteracy among patients and physicians, mismatched framing, the 1995 pill scare with the estimated 13,000 additional abortions, and the recommendation to use absolute risks and natural frequencies.
  2. Gigerenzer, G. (2002). Calculated Risks: How to Know When Numbers Deceive You. Simon & Schuster
    The book-length treatment of relative versus absolute risk and the translation of risk claims into natural frequencies.
  3. Bombardier, C., Laine, L., Reicin, A., Shapiro, D., Burgos-Vargas, R., Davis, B., Day, R., Ferraz, M. B., Hawkey, C. J., Hochberg, M. C., Kvien, T. K., & Schnitzer, T. J. (2000). Comparison of upper gastrointestinal toxicity of rofecoxib and naproxen in patients with rheumatoid arthritis. New England Journal of Medicine, 343(21), 1520-1528
    The VIGOR trial figures: the relative gastrointestinal benefit and the myocardial-infarction rates of 0.4 versus 0.1 percent.
  4. Polack, F. P., Thomas, S. J., Kitchin, N., Absalon, J., Gurtman, A., Lockhart, S., et al. (2020). Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine. New England Journal of Medicine, 383(27), 2603-2615
    The trial counts (8 versus 162 cases) behind the 95 percent relative efficacy and the sub-one-point absolute reduction over the trial window.
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