A headline that says “20% lower risk” leaves an essential question unanswered: lower than what? A relative effect describes a comparison. The absolute event proportions show how common the outcome was in the groups observed. Both are useful, and neither should be presented as a personal forecast.
A real cardiovascular example
SELECT studied semaglutide in adults with established cardiovascular disease and overweight or obesity, without diabetes. A major cardiovascular event occurred in 6.5% of the semaglutide group and 8.0% of the placebo group during the trial. The reported hazard ratio was 0.80, with mean follow-up of 39.8 months. SELECT original trial.
Subtracting the reported proportions gives an absolute difference of 1.5 percentage points. Expressed as arithmetic using rounded trial percentages, that is about 15 fewer participants with an event per 1,000 enrolled over the observed follow-up. This is a description of the trial, not a claim about everyone taking the medicine.
Why the hazard ratio is not just a percentage subtraction
The hazard ratio comes from a time-to-event analysis, incorporating when events occur under the model used. The simple proportion difference above uses the reported aggregate percentages. These summaries answer related questions but are not the same calculation. Avoid presenting 0.80 as though it was obtained by subtracting 6.5 from 8.0.
Follow-up also matters. A difference observed during this trial cannot be relabeled as an annual difference without a suitable analysis. Nor should a reader’s personal probability be substituted into the study result without an individualized assessment. The study required established cardiovascular disease; it did not enroll a general low-risk population.
An explicitly invented comparison
Imagine two fictional settings with the same 25% relative reduction in risk. In one, risk changes from 4% to 3%, a one-percentage-point difference. In the other, it changes from 20% to 15%, a five-point difference. The arithmetic explains why the starting risk matters. These are teaching examples, not study findings or treatment estimates.
Bring benefits and harms into the same frame
A treatment decision also needs relevant adverse effects, tolerability, and uncertainty. Ask for comparable denominators and time frames when reading harms. The CONSORT Harms guidance calls for clear methods of harms collection and transparent reporting. CONSORT Harms guideline. A benefit percentage does not settle the whole benefit-risk question.
A useful reading note includes the population, event definition, group proportions, relative measure, and follow-up. If a summary omits any of those, find the original paper before repeating the number. That small habit makes impressive headlines more informative without dismissing a meaningful result.
