How do I convert the REDEFINE-1 hazard ratio into an absolute risk reduction?

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

I would rather understand the derivation than memorise the outcome.

Two people I asked gave two answers that differ by a factor of ten, which is suggestive.

Can someone show the working rather than just the answer?

A hazard ratio from REDEFINE-1 cannot be converted into an absolute risk reduction without the control-arm event rate, and that rate is the number people forget to carry across. The arithmetic: absolute reduction equals the control event rate minus the treated event rate, and the treated rate is approximately the control rate multiplied by the ratio. A hazard ratio of 0.80 against a 10 per cent control rate is a 2-point absolute reduction and a number needed to treat of 50; the same 0.80 against a 2 per cent control rate is 0.4 points and a number needed to treat of 250. Identical ratio, six-fold difference in what it is worth. Take the control-arm rate and the follow-up duration from the REDEFINE-1 paper, not from the abstract, and do the subtraction yourself.

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.

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 part that matters: 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.

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.

Ask for the absolute risk reduction and the number needed to treat. If a source will not give you both, it is selling something.

On the detail: heart-rate increase and blood-pressure reduction both occur in this class, in opposite directions, and both are modest. Reading one without the other gives a misleading picture.

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.

The underlying point is that 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.

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

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

The short version: real effect, modest absolute size, largest in those with the highest baseline risk — which is the ordinary shape of a cardiovascular result.

Cardiovascular composites in this programme are typically cardiovascular death, non-fatal myocardial infarction and non-fatal stroke. When one component drives the result, that is worth knowing, because the components differ in how much they matter.

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.

Heart-rate elevation in this class is documented consistently enough across agents that it should be treated as a class effect rather than as a finding about any one molecule.

These are trial populations on licensed product. Research-grade material of unverified content is not the thing that was studied.

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.

The relevant detail is that blood pressure falls by a few millimetres of mercury in this class, which is small individually and not small across a population.

Resting heart rate rises by roughly two to four beats per minute across the class. The mechanism is not fully settled, the magnitude is consistent, and it has not translated into an adverse outcome signal in the trials that looked.

Where a cardiovascular claim is made for an agent with no completed outcome trial, the honest statement is that the class evidence is suggestive and the agent-specific evidence does not yet exist.

Nothing here is medical advice. If cardiovascular risk is the actual question, it is a conversation for a clinician with your numbers in front of them.

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

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

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.

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.

The caveat is the population. Trial participants were screened, monitored and supported; the effect size in an unmonitored setting is not the trial effect size, and it is not obvious in which direction the difference runs.

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