Clinical research & EBM · Reference
What is a hazard ratio?
A hazard ratio is a measure from survival analysis that compares how often an event occurs over time in one group relative to another. A hazard ratio of one means no difference; values above or below one indicate a higher or lower rate in the comparison group.
What the hazard ratio measures
The hazard is the instantaneous rate at which an event — such as relapse, recovery or another defined endpoint — occurs among those still at risk at a given moment. The hazard ratio compares this rate between two groups across follow-up. Unlike a simple proportion, it accounts for when events happen, not just whether they happen by the end of a study, which makes it well suited to time-to-event data. It is most commonly estimated from a Cox proportional hazards regression model, which can also adjust for other variables.
Interpreting the value
A hazard ratio is read relative to 1. An HR of 1 means the event rate is the same in both groups. An HR of 1.5 means the event occurs about 1.5 times as often in the comparison group over the period studied; an HR of 0.7 means it occurs about 30% less often. As with any estimate, an HR is reported with a confidence interval, and an interval that includes 1 indicates the difference is not statistically significant. A key assumption of the standard model is that the ratio stays roughly constant over time (proportional hazards).
Hazard ratio versus relative risk
The hazard ratio is related to, but distinct from, the relative risk and the odds ratio. Relative risk compares the cumulative probability of an event by a fixed point; the hazard ratio compares the rate of events continuously over time, using information from the whole follow-up period including censored observations. The two often have similar values when events are rare, but they answer subtly different questions. Hazard ratios are typically presented alongside a Kaplan–Meier curve that displays the underlying time-to-event patterns.
Key facts
At a glance
- Definition: Ratio of event rates between groups over time
- HR = 1: No difference between groups
- HR > 1: Higher event rate in the comparison group
- HR < 1: Lower event rate in the comparison group
- Estimated by: Cox proportional hazards regression
- Shown with: Kaplan–Meier survival curves
Common questions
FAQ
What does a hazard ratio of 0.7 mean?+
A hazard ratio of 0.7 means the event of interest occurs about 30% less often in the comparison group than in the reference group over the follow-up period. As a relative measure it is interpreted against a value of 1, which would mean no difference.
How is a hazard ratio different from relative risk?+
Relative risk compares the cumulative probability of an event by a fixed time point, while a hazard ratio compares the rate of events continuously across the whole follow-up, including censored observations. They often agree when events are rare but answer slightly different questions.
What is the proportional hazards assumption?+
The standard Cox model assumes the hazard ratio between groups stays roughly constant over time. If the relative effect changes substantially during follow-up, this assumption is violated and the single summary hazard ratio can be misleading.
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