How do I convert the STEP 8 hazard ratio into an absolute risk reduction?

This is a question about interpretation, not about whether to act — I will take action questions elsewhere.

I have worked this out and I would like someone to find the error, because I suspect there is one.

My working so far, for the record, is below, and I am fairly sure the error is in the unit conversion rather than the algebra.

Where is my error, and what is the correct working?

A hazard ratio from STEP 8 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 STEP 8 paper, not from the abstract, and do the subtraction yourself.

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.

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.

Headline results, principal programmes

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.

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

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

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.

On the detail: 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.

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

What the outcome trials established is that the class does not increase cardiovascular risk and, in the higher-risk populations studied, reduces it. Those are two separate findings from the same programme.

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.

Worth being precise here: 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.

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.

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.