Hazard & Hazard Rate

The hazard is the instantaneous rate at which an event occurs among patients still event-free and at risk at a given moment — events per unit of person-time. It can rise and fall over time, and it is the quantity that underlies survival analysis and the hazard ratio. It is not cumulative risk (the probability of the event over a whole period).

Two survival curves over time. At any instant the slope of a curve reflects the hazard — the rate at which events are happening among those still at risk. Steep stretches mean a high hazard; flat stretches mean a low one. The hazard here is high early and falls as time goes on.

Read the hazard locally, not as a single overall number: it is the event rate at that point in time. The cumulative risk, by contrast, is the total height the curve has fallen by a given time. Two treatments can share a cumulative risk yet have very different hazards along the way.

Survival analysis and the hazard ratio are built on the hazard, so misreading it as a probability corrupts interpretation. In EM, many conditions have a front-loaded hazard — danger is highest early — which justifies intensive early monitoring even when overall prognosis is good.

• Hazard = instantaneous event rate (per person-time)
• It can vary over time — not a single fixed figure
• Hazard (a rate) ≠ cumulative risk (a probability)

Time-varying hazard after critical illness — the hazard of death after out-of-hospital cardiac arrest or major trauma is highest in the first hours to days and falls steeply for survivors who stabilise. Plotted over time, the survival curve drops sharply early then flattens. This is qualitative: the shape (a front-loaded hazard), not a single rate, is the teaching point — which is exactly why a single “mortality” figure can mislead.

• Calling the hazard a risk — it is a rate, not a probability.
• Assuming the hazard is constant when it usually varies over time.
• Confusing the hazard (one group’s rate) with the hazard ratio (two groups compared).