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27% more risk, one extra case
Relative versus absolute risk
Relative risk compares two rates, and absolute risk is the actual gap between them. In the Women's Health Initiative, a large trial of hormone therapy in menopausal women, those taking estrogen plus a synthetic progesterone had a relative increase in breast cancer of about 25% to 27% compared with placebo. That figure became the only headline: hormone therapy increases the risk of breast cancer by 27%.
The absolute increase was 0.1%, one case in a thousand. Going from four in a thousand to five in a thousand is a 25% increase, which is how a tiny change produced an alarming number.
The estrogen-only arm
The trial's other arm, estrogen alone in women without a uterus, moved the other way: a 24% reduction in breast cancer, again about one in a thousand, with a P value of 0.06 or 0.07 that fell just short of statistical significance. The estrogen plus synthetic progesterone result barely reached significance, at a P value of 0.05.
Why do headlines favor relative risk?
A relative figure looks bigger than the absolute change behind it, which makes it travel better as a headline. Gerd Gigerenzer, a risk-communication researcher, has documented how the same data read very differently in each form. In October 1995, the UK Committee on Safety of Medicines warned that third-generation contraceptive pills doubled the risk of blood clots, a rise from about one in 7,000 women to two in 7,000. Analyses of national statistics, including work by the sociologist Frank Furedi, linked the scare to about 13,000 additional abortions in England and Wales the following year.
Why is a P value of 0.05 the cutoff?
A P value is the probability of seeing a result at least this extreme if there were no real effect, so 0.05 means roughly one chance in twenty. Under the usual convention, a result with a P value of 0.06 or 0.07 is labeled not significant even though it sits close to the line. The statistician Ronald Fisher suggested 0.05 as a convenient threshold in his 1925 book Statistical Methods for Research Workers.
How did the two arms diverge over time?
Rowan Chlebowski and colleagues published a long-term follow-up of the Women's Health Initiative hormone trials in JAMA in 2020, tracking participants for about 20 years. Estrogen plus progestin was associated with higher breast cancer incidence, with a hazard ratio near 1.28, while estrogen alone was associated with lower incidence, near 0.78. Women assigned to estrogen alone also had lower breast cancer mortality.
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