What is non-collapsibility?

Take a randomised trial, where by construction there is no confounding. Fit an unadjusted model and get a hazard ratio. Now add a covariate that predicts the outcome but, because of randomisation, is unrelated to treatment. The hazard ratio moves — usually further from one. Nothing has gone wrong, and neither estimate is biased for what it estimates.

This is non-collapsibility. The marginal hazard ratio, comparing the whole treated population with the whole control population, is not a weighted average of the hazard ratios within strata of a covariate. The two are simply different quantities. The hazard ratio and the odds ratio behave this way; the risk difference and the risk ratio do not, which is why they can be averaged across strata and these cannot.

Two practical consequences follow. First, an adjusted and an unadjusted hazard ratio from the same trial are not competing estimates of one number, so a difference between them is not evidence of confounding — it is expected. Second, hazard ratios from different papers adjusted for different covariate sets are not on a common scale, and meta-analysing them or carrying them between models treats different quantities as interchangeable.

If the estimand you want is a population-level contrast — the effect of treating everyone versus no one — then say so and estimate it directly, for example by fitting an adjusted model and standardising its predictions over the observed covariate distribution. That gives a marginal estimate with the precision benefit of adjustment, rather than an adjusted conditional estimate reported as though it were marginal.

MethodSurvival analysis