How do I convert the SURPASS-3 hazard ratio into an absolute risk reduction?

I have the full paper rather than the abstract, and the supplementary appendix.

I can do the algebra. I am not confident about the conversion factors.

If there is a standard way to lay this out, I would rather learn that than invent one.

What is the general form of this calculation?

In practice, the relevant distinction is between a trial that measured cardiovascular safety and one powered to demonstrate benefit. Several early trials did the first and are quoted as though they did the second.

SELECT randomised people with established cardiovascular disease and overweight or obesity but without diabetes to semaglutide 2.4 mg, and reported roughly a twenty per cent relative reduction in the primary composite. The absolute difference over about three years was on the order of one and a half percentage points.

Concretely, benefit appears to track exposure duration rather than switching on at a threshold, which is what you would expect from a mechanism working partly through weight, blood pressure and glycaemia rather than instead of them.

The caveat that matters: none of this is a reason for anyone to alter cardiovascular medication, and I am not in a position to advise on that.

The outcome trials are the evidence; the mechanism is still an argument. Cite the first, be careful with the second.

Answering this properly needs the absolute risk reduction rather than the relative one, because the relative figure is stable across risk strata and the absolute figure is not.

Systolic blood pressure falls by about three to six millimetres of mercury at the doses studied, most of it early and much of it attributable to weight loss rather than to a direct vascular effect.

More usefully, the heart-failure question is separate again, and the evidence there is largely in the preserved-ejection-fraction population with obesity, where the trials measured symptoms and function rather than mortality.

The cardiovascular safety requirement for new glycaemic agents is why these trials exist at all: regulators required an outcome programme, and the benefit finding was in that sense an unexpected dividend.

Population, baseline risk, endpoint definition. In that order, then the effect size.

Blood pressure falls by a few millimetres of mercury in this class, which is small individually and not small across a population.

Baseline risk decides how much the relative reduction is worth. The same twenty per cent applied to a one per cent annual risk and a five per cent annual risk produce very different absolute numbers.

A relative risk reduction quoted without the baseline risk is close to meaningless, and it is how most of these numbers travel.

Heart rate up a few beats, blood pressure down a few millimetres, events down about a fifth in high-risk populations. That is the honest summary.

Start with the population. Cardiovascular benefit in established disease and cardiovascular benefit in primary prevention are different claims supported by different evidence.

A twenty per cent relative reduction on a baseline three-year event rate of eight per cent is an absolute reduction of about one and a half points, which is a number-needed-to-treat somewhere in the region of sixty to seventy. Both framings are true and they read very differently.

SELECT is the trial to read for primary-prevention-adjacent populations without diabetes; SUSTAIN-6 and LEADER are the diabetes-population outcome trials for semaglutide and liraglutide respectively.

Read SELECT for the without-diabetes population and the earlier outcome trials for the with-diabetes one. They are not the same result.