Proportional Hazards Assumption & Competing Risks
Two survival-analysis traps: a hazard ratio that isn’t constant over time, and rival events that block the one you’re measuring.
Two pitfalls that break naive survival analysis. (1) The PROPORTIONAL-HAZARDS assumption — a constant hazard ratio over time — underlies the Cox model and any single HR; if curves cross or the effect changes with time, one HR is misleading. (2) COMPETING RISKS — an event (e.g. death from another cause) that PREVENTS the event of interest from ever occurring; standard Kaplan–Meier then OVER-estimates the cumulative incidence.
When curves cross, the hazard ratio reverses over time — a single HR fits no part of the follow-up.
The treatment curve starts higher but crosses below the control curve partway through: the effect is beneficial early and harmful late. No single hazard ratio can describe this — an averaged HR near 1 would falsely suggest “no effect” when the truth is a time-varying one.
Crossing or converging curves are the visual signal of NON-proportional hazards — confirm with log–log survival plots, Schoenfeld residuals, or a time-by-treatment interaction term. Separately, when a rival event (death from another cause) can pre-empt your outcome, a Kaplan–Meier 1−survival curve over-counts the cumulative incidence.
In elderly, comorbid ED/ICU populations patients often die of OTHER causes before the studied non-fatal event can happen. Ignoring competing risks inflates incidence estimates; ignoring non-proportional hazards hides reversing or fading treatment effects — both can flip a trial’s conclusion.
Crossing curves→ non-proportional hazards- Check:
log–log plot · Schoenfeld · time-interaction - Competing risk = event that PREVENTS your outcome
- Use
cumulative incidence / Fine–Gray, not naive KM
Comorbid ED/ICU cohorts — in an elderly multimorbid cohort followed for a non-fatal outcome (e.g. re-admission or a specific complication), death from unrelated causes competes with the outcome: patients who die can never re-attend. A naive Kaplan–Meier estimate of cumulative incidence is then inflated, and a Fine–Gray cumulative-incidence analysis gives a lower, truer figure. If a survival paper in a frail population reports plain KM incidence with no mention of competing risks, treat the incidence as an over-estimate until proven otherwise.
- Quoting a single HR when the curves cross — non-proportional hazards make it meaningless.
- Ignoring competing risks in elderly/comorbid populations who die of other causes first.
- Forgetting that naive Kaplan–Meier OVER-estimates cumulative incidence under competing risks.
Quick check
Patients can die of other causes before the studied event occurs — what analysis do you need?
Answer: A competing-risks approach — a cumulative incidence function / Fine–Gray model — not a naive Kaplan–Meier estimate, which would over-state the incidence.
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