Why “halves the risk” can mean very little

In October 1995, British regulators warned doctors that newer "third-generation" contraceptive pills doubled the risk of a dangerous blood clot — a 100% increase. The warning was accurate. What it did not convey was the size of the risk: roughly 1 in 7,000 women on the older pills had a thrombosis, compared with about 2 in 7,000 on the newer ones. Many women stopped taking the pill, and the following year saw an estimated 13,000 additional abortions in England and Wales. The risk had indeed doubled — from very small to small. How a number is framed can matter as much as the number itself.

Two ways to describe the same result

Every trial result can be expressed in two ways. The relative risk reduction tells you by what proportion a treatment changes the risk: if 2 in 100 people have a heart attack instead of 4 in 100, the risk has fallen by 50%. The absolute risk reduction tells you the actual difference: 4% minus 2% is 2 percentage points.

From the absolute figure follows the most useful number of all, the number needed to treat (NNT): how many people must take a treatment for one of them to benefit. It is simply 1 divided by the absolute risk reduction — in the example above, 1 ÷ 0.02 = 50. Its mirror image is the number needed to harm (NNH): how many people must be treated for one to suffer a particular side effect. In the pill scare, the NNH for an extra thrombosis was about 7,000.

Take the JUPITER trial, in which 17,802 apparently healthy people with normal cholesterol but raised C-reactive protein received rosuvastatin or placebo. The trial was stopped early, after a median of 1.9 years.

Both statements describe the same data, yet they invite very different decisions.

Baseline risk changes everything

A relative effect is often fairly stable across groups; the absolute effect is not. The Cholesterol Treatment Trialists' Collaboration pooled individual data from 27 statin trials. Each 1 mmol/L reduction in LDL cholesterol lowered major vascular events by about 21% (rate ratio 0.79), and the proportional benefit was at least as large in people whose five-year risk was below 10%. Yet in that low-risk group, the authors estimated about 11 fewer events per 1,000 people over five years per 1 mmol/L reduction.

Apply the same 21% relative reduction to people with different starting risks over five years (our own illustrative arithmetic):

• 5% baseline risk: falls to about 4% — an absolute reduction of about 1 point, NNT ≈ 95.
• 10% baseline risk: falls to about 7.9% — about 2 points, NNT ≈ 48.
• 30% baseline risk (typical of people who have already had a heart attack): falls to about 23.7% — about 6 points, NNT ≈ 16.

The "same" drug is six times more useful to the high-risk person. That is why guidelines base treatment decisions on total cardiovascular risk, not on a headline percentage.

A screening example

The Harding Center for Risk Literacy summarises mammography screening for women aged 50 and over, followed for about 11 years, using the Cochrane review as its data source. Without screening, about 5 in 1,000 women died of breast cancer; with screening, about 4. That can be reported as "screening cuts breast cancer deaths by 20%" — or as "1 in 1,000 women avoids death from breast cancer." Deaths from all cancers combined were 22 per 1,000 in both groups. On the other side of the ledger, about 100 in 1,000 women experienced a false alarm leading to further tests or a biopsy, and about 5 had part or all of a breast removed unnecessarily.

The underlying Cochrane analysis is debated and other assessments are more favourable; the point here is the framing, not the verdict. When women in four countries were asked how many in 1,000 are saved from breast cancer death by screening, only 6% gave an answer in the right range (0 to 5); in a German survey the most frequent answer was 500.

How headlines and adverts frame results

Framing is not a neutral choice. In one study cited by Gigerenzer and colleagues, 80% of people shown a screening benefit as a relative risk reduction said they would probably accept the test; when the same benefit was shown as an absolute reduction or as an NNT, the figures fell to 53% and 43%. Physicians, too, rate a treatment as more effective when its benefit is given in relative terms.

Watch for two patterns:

• Relative benefit without a base rate. An analysis of medical press releases found that 45% of those comparing groups gave relative risks without the underlying absolute risks.
• Mismatched framing. Benefits in large relative numbers, harms in small absolute ones ("1% experienced side effects"). This makes the benefit look big and the harm look small.

Natural frequencies and icon arrays

The psychologist Gerd Gigerenzer showed that people reason far better with natural frequencies — counts of real people — than with percentages and conditional probabilities. In one session, 160 German gynaecologists were told that 1% of women in a screening group have breast cancer, that the test detects 90% of cancers, and that 9% of healthy women test positive. Asked what a positive result means, only 21% chose the correct answer. After training in natural frequencies, 87% did.

Here is the same information as natural frequencies. Of 1,000 women, 10 have breast cancer and 9 of them test positive. Of the 990 without cancer, about 89 also test positive. So of 98 women with a positive result, only 9 — about 1 in 10 — actually have cancer.

An icon array makes this visible. Picture a grid of 1,000 small figures. In the "no screening" grid, 5 are shaded for death from breast cancer; in the "screening" grid, 4 are shaded — and 100 others are marked for a false alarm. The Harding Center, now part of the Faculty of Health Sciences Brandenburg with a base at the University of Potsdam, publishes such fact boxes and icon arrays in German.

What this means for you

When you read about — or are offered — a treatment or test, ask:

• Out of how many? What happens to 1,000 people like me with and without it?
• What is my own baseline risk?
• How many people need to be treated (or screened) for one to benefit — and over how many years?
• How many will be harmed, and in what way?
• Are benefits and harms given in the same format?
• Does the result refer to something I care about — death, stroke, a fracture — or only to a lab value?

Small absolute benefits are not worthless: 1 in 100 may be well worth having if harms are rare and the outcome is serious. But the decision should be made with the real numbers on the table.

This article is general information and not individual medical advice. Decisions about tests and treatment belong in a conversation with your own physician.