It helps to be literal here: 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
| Quantity | Value | Derivation |
|---|
| Control-arm event rate | 8.0 % | From the trial table, not the abstract |
| Hazard ratio | 0.80 | Reported |
| Treated event rate | 6.4 % | 8.0 × 0.80 |
| Absolute risk reduction | 1.6 pp | 8.0 − 6.4 |
| Number needed to treat | 63 | 1 ÷ 0.016 |
| Relative risk reduction | 20 % | 1 − 0.80 |
The last two rows describe the same finding. Only one of them is used in headlines.
The part that matters: 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 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.
The papers are readable. Read the paper rather than the summary of the paper, especially where the summary is enthusiastic.
Do you have a reference for the last claim? Not disputing it, just want to read it. – bac_or_bust 6 months ago add a comment