Cox Proportional-Hazards Model
A regression for time-to-event data that gives adjusted hazard ratios without specifying the baseline hazard’s shape.
A SEMI-PARAMETRIC regression for time-to-event outcomes. It estimates each predictor’s effect as a HAZARD RATIO while handling censoring and allowing adjustment for multiple covariates — WITHOUT having to specify the shape of the underlying baseline hazard. Its central assumption is PROPORTIONAL HAZARDS: the hazard ratio between groups is constant over time.
A single Cox HR is trustworthy only when the curves don’t cross — the hazard ratio stays roughly constant over time.
Two non-crossing survival curves summarised by one hazard ratio (HR 0.72). The Cox model converts the whole survival experience — adjusted for covariates — into that single HR, the relative rate of the event in one group versus the other at any instant.
HR <1 favours treatment, HR >1 favours control, HR = 1 means no difference. The HR is a RATE ratio, not a risk ratio. Before trusting it, confirm the proportional-hazards assumption holds — if the curves cross or the effect changes over time, a single HR is the wrong summary.
Cox regression is the workhorse of adjusted survival analysis in EM, critical-care and cohort studies: it lets you compare groups while correcting for confounders (age, comorbidity, severity) and uses all the follow-up that censoring would otherwise waste.
Output = adjusted hazard ratioSemi-parametric: baseline hazard left unspecifiedAssumes proportional hazards(constant HR)- HR is a rate ratio, NOT a risk ratio
Adjusted hazard ratios in survival trials — many EM and critical-care trials report a Cox-derived adjusted HR as the headline effect, for example a mortality HR around 0.8 (a 20% lower hazard) after adjusting for age and illness severity. The HR is reported with a 95% CI and a log-rank p-value for the unadjusted curves. Before quoting any single HR, the authors should state that proportional hazards was checked (Schoenfeld residuals or log–log plots) — an HR is only as good as that assumption.
- Reporting one HR when proportional hazards is violated (crossing or converging curves).
- Misreading an HR as a risk ratio — it is a ratio of instantaneous event RATES, not cumulative risks.
- Overfitting — cramming too many covariates into the model for the number of events.
Quick check
What must you check before trusting a Cox hazard ratio?
Answer: The proportional-hazards assumption — that the hazard ratio stays roughly constant over time (e.g. curves that don’t cross, supported by Schoenfeld residuals or a log–log plot).
Ready to build your plan? EMF Premium gives you all 40,000+ questions, 20 mocks and 1,215 OSCE stations from £29/month — or a one-off 3- or 6-month pass.