How do I convert the STEP 5 hazard ratio into an absolute risk reduction?

I have three data points across nine months, which I hope is enough to see a trend.

I would like the arithmetic checked rather than the conclusion asserted.

I have deliberately not used an online calculator because I want to be able to check the result.

Can someone walk through the arithmetic step by step?

Read the estimand before the effect size. Almost every apparent contradiction between two published figures from the same trial resolves once you notice that one is a trial-product estimand and the other is a treatment-policy estimand.

Absolute risk reduction, worked: if the control-arm event rate is 8.0 per cent over the follow-up period and the hazard ratio is 0.80, the treated rate is approximately 6.4 per cent, the absolute risk reduction is 1.6 percentage points, and the number needed to treat is 1 ÷ 0.016 ≈ 63 over that period. A 20 per cent relative reduction and a number needed to treat of 63 are the same finding stated two ways, and only one of them sounds impressive.

Relative to absolute, worked

The last two rows describe the same finding. Only one of them is used in headlines.

To be exact about it, estimated average glucose from HbA1c: eAG in mg/dL = 28.7 × A1c − 46.7, or in mmol/L, 1.59 × A1c − 2.59. An A1c of 6.5 per cent is therefore about 140 mg/dL or 7.8 mmol/L. The relationship is a population regression, so an individual can sit well off the line.

The papers are readable. Read the paper rather than the summary of the paper, especially where the summary is enthusiastic.

A single laboratory value is a point on a noisy curve. What you want is a trend across at least three draws under comparable conditions, and "comparable" is doing a lot of work in that sentence.

The rodent thyroid C-cell findings that generated the labelled warning appear to be species-specific: rodent C-cells express GLP-1 receptors at high density, human C-cells at very low density, and human calcitonin data across large trial populations has not reproduced the signal. A family history of medullary thyroid carcinoma or MEN2 is nonetheless a genuine contraindication rather than a theoretical one.

A fasting lipid panel drawn during rapid weight loss reads oddly for a mechanical reason: mobilised adipose tissue delivers free fatty acids to the liver, and hepatic triglyceride export rises. Triglycerides can transiently increase while the person is doing exactly the right thing. Draw the panel when weight has been stable for a few weeks if you want an interpretable number.

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.

Convert everything to an absolute effect before you compare two interventions. Relative effects are not comparable across different baseline risks.