When the hazard ratio misleads
Dispatch: non-proportional hazards, and the case for restricted mean survival time.
The hazard ratio is the reflex summary for any time-to-event trial. One number, one confidence interval, done. It rests on an assumption that is easy to skip over and quietly often false: proportional hazards.
What proportional hazards actually assumes
A Cox model’s hazard ratio is a single constant. It assumes the treatment’s effect on the instantaneous risk is the same in month two as in year four. When that holds, the HR is a clean summary. When it doesn’t, the reported HR becomes a weighted average of a time-varying effect, and the weights depend on the censoring pattern rather than on anything clinical. The number you report is then an artifact of when people happened to drop out, not a stable description of the treatment.
Non-proportional hazards are not exotic. They are the norm for therapies with a delayed effect (many immunotherapies do nothing for months and then separate the curves), for treatments whose benefit wanes, and for any setting where the survival curves cross. In all of these a single HR can look modest while the curves tell a dramatic story, or look impressive while the benefit is confined to a window that matters less than the average implies.
What to report instead
Two alternatives give a number that survives non-proportional hazards and that a clinician and a patient can actually interpret:
- Restricted mean survival time (RMST). The area under the survival curve up to a chosen horizon. The between-arm difference reads directly as “this many more event-free months over five years,” with no proportional-hazards assumption required.
- Milestone (landmark) analysis. The event rate at a fixed, pre-specified time, for example five-year survival. Blunt, but honest and easy to communicate.
Neither replaces the survival curve itself, which should always be shown.
The discipline is in the timing
The trap is choosing RMST after seeing the curves cross. That is a post-hoc switch, and reviewers will read it as one. The fix costs nothing if you do it early: pre-specify the primary analysis (Cox, RMST, or milestone), and name the proportional-hazards diagnostic that would trigger a switch, before the data are unblinded. The cheapest place to handle non-proportional hazards is the analysis plan, not the response to reviewers.
If you are designing a time-to-event study, the study-design chapter walks the endpoint and analysis-plan decisions this connects to.