Hazard Ratio
The relative instantaneous event rate between two groups across follow-up.
From the Cox model — the ratio of the hazard (the instantaneous event rate among those still at risk) in one group versus another, assumed constant over time (the proportional-hazards assumption). It is not an odds ratio and not a ratio of survival times.
Two Kaplan–Meier curves whose entire separation is summarised by a single HR 0.75 (with 95% CI) — a 25% lower instantaneous event rate in the treatment arm at any moment, if proportional hazards hold.
Two Kaplan–Meier curves. Their separation over the whole follow-up is compressed into one number — the hazard ratio, reported with a 95% confidence interval. The treatment curve (plum) sitting above control (grey) gives an HR below 1.
HR 0.75 = a 25% lower instantaneous risk in the treatment arm at any given moment (under proportional hazards). An HR <1 favours treatment; an HR >1 favours control. An HR whose 95% CI crosses 1 is not statistically significant, however far from 1 the point estimate sits.
Most time-to-event trial results — mortality, time to intubation, time to recurrence — are reported as an HR with a CI. Misreading it as cumulative risk over the whole period, or as how much longer patients live, is a classic appraisal error that the exam loves to test.
HR = ratio of hazard rates(instantaneous, among those still at risk)HR 0.75 → 25% lower instantaneous risk(if PH holds)- CI crossing 1 = not significant
ANDROMEDA-SHOCK (JAMA 2019) — 424 patients with early septic shock, capillary-refill (peripheral-perfusion)–targeted vs lactate-targeted resuscitation. 28-day mortality 34.9% (74/212) vs 43.4% (92/212) → HR 0.75 (95% CI 0.55–1.02), p = 0.06. An 8.5% absolute mortality difference and a striking HR of 0.75 — but the 95% CI crosses 1 and p = 0.06, so the result is not statistically significant. The point estimate alone never makes a finding significant.
- Reading the HR as cumulative risk over the whole period, or as an odds ratio.
- Ignoring the proportional-hazards assumption (the HR is assumed constant over time).
- Equating an HR <1 with patients living measurably longer (survival-time gain).
Quick check
HR 0.5 — does treatment halve a patient’s overall chance of dying?
Answer: No — it halves the instantaneous hazard at each moment (under proportional hazards). The absolute survival difference depends on the baseline risk and the length of follow-up.
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