What absolute versus relative risk really means

A relative risk describes how a risk compares between two groups; an absolute risk describes how large it actually is, in cases per person or per thousand. A widely cited example comes from the Women's Health Initiative's 2002 report, where hormone therapy in postmenopausal women was headlined as raising heart disease risk by roughly 29 percent — a relative figure that amounted to about seven additional cases per 10,000 women per year. Both numbers were true. Only one told a reader what to expect.

Engevity News publishes information, not medical advice, and this piece is a reader's guide to risk reporting rather than guidance about any therapy. The arithmetic, once habitual, takes ten seconds per headline.

What is a relative risk?

Relative risk is a ratio: the rate of an outcome in an exposed group divided by the rate in an unexposed group. If three people in a thousand experience an event in one group and two in a thousand in the other, the relative risk is 1.5 — commonly reported as a 50 percent increase. The ratio is scale-free, which makes it useful for comparing effects across studies and populations. Its weakness is that it discards the baseline: a 50 percent increase applied to a 2-in-1,000 risk and to a 2-in-10 risk produce wildly different numbers of affected people, and the ratio cannot show which world the reader lives in.

What is an absolute risk?

Absolute risk states the chance of an outcome in plain counts: per person, per hundred, per thousand, per year. The absolute difference between two groups — sometimes called the absolute risk increase or reduction — subtracts one rate from the other and answers the question a reader actually has: how many more or fewer cases does this produce. In the arithmetic example above, the 50 percent relative increase is an absolute increase of one case per thousand. Absolute numbers are what make risk comparable to the risks of daily life, which is why clinicians and statisticians, including the U.S. Preventive Services Task Force in its communications, lean on them when explaining screening and prevention to patients.

Why does the same study produce such different headlines?

Because the two framings are both correct, and relative numbers are almost always larger and more dramatic. A risk moving from 2 percent to 3 percent is a 50 percent increase or a single percentage point — the same event described two ways. In 2007, researchers writing in the Annals of Internal Medicine documented how framing the same effect in relative or absolute terms changed patients' willingness to take a treatment, with relative framing reliably inflating perceived benefit. The choice between framings is not statistical; it is rhetorical. A report that gives only the relative figure is not lying, but it is showing the reader the reflection and hiding the object.

How do we know the difference matters?

The evidence comes both from landmark studies and from experiments on communication. The Women's Health Initiative's 2002 results, published in JAMA, reported both framings — the approximate 29 percent relative increase in coronary heart disease and the corresponding small absolute excess per 10,000 women per year — yet much of the coverage carried only the percentage. Studies of risk communication since the 1990s have repeatedly found that absolute risks, and especially natural frequencies such as "eight more cases per 10,000 people", produce more accurate public understanding than percentages alone. The mismatch between how effects are measured and how they are headlined is one of the best-documented distortions in science journalism.

Which framing should a reader convert to?

Convert to counts per thousand or per ten thousand, because counts are what human intuition handles. The conversion needs two numbers: the baseline risk and the relative change. The table shows how one identical relative increase — 50 percent — translates across baselines.

The illustrative arithmetic above is hypothetical and chosen to be easy to check in one's head; real studies report their own baselines, and those baselines — age, sex, health status — decide how large any percentage really is.

What about risk reductions in good news headlines?

The same asymmetry runs in the encouraging direction, and it powers some of the most repeated numbers in medicine. "Cuts the risk in half" sounds transformative; if the baseline is four cases per thousand, halving it prevents two cases per thousand, and a thousand people still need to act for two to benefit. This is not an argument against acting — population-wide, two per thousand is many people. It is an argument for knowing the denominator. Benefit framings deserve the same question harm framings do: out of how many, over how long?

What is the number needed to treat?

One further step turns absolute risk into perhaps the most intuitive statistic in medicine: the number needed to treat. Divide 100 by the absolute risk reduction expressed as a percentage, and the result is how many people must receive an intervention for one to benefit. An absolute reduction of two cases per hundred means one benefit per fifty people treated. The companion figure, number needed to harm, applies the same arithmetic to side effects, and the two numbers together frame nearly every medical decision: is one benefit per fifty worth one harm per two hundred? Researchers have used these measures since the late 1980s precisely because patients and clinicians reason more accurately with them than with percentages. A reader who converts a headline's figure into "one person per how many" has performed the entire exercise of this article in one division.

How can a reader do the conversion in a headline?

Three questions, in order.

1. What was the baseline risk in each group, in counts?
2. Is the percentage relative to that baseline, or is it a difference in percentage points?
3. Over what period, and in what population?

Headlines rarely carry all three answers, but the underlying paper's abstract almost always does. Ten seconds with the abstract's counts restores the scale that the headline's percentage removed.