Hazard ratio
In one sentence
A hazard ratio compares the event hazards of two specified groups over follow-up.
The intuition
A hazard concerns the rate at which an event happens among people still at risk. It is different from the fraction who have had an event by five years. A ratio compares those rates rather than directly giving someone’s chance of recurrence.
How it works
Always identify the event, reference group, population and analysis. A ratio below one means lower estimated hazard in the numerator group; above one means higher estimated hazard. Under a proportional-hazards interpretation, HR 0.70 represents a 30% relative hazard reduction. It does not mean 30 percentage points fewer patients recur.
The proportional-hazards assumption means the ratio is reasonably stable over time. Curves that cross or effects that change with time can complicate a single summary. A reported model may adjust for covariates, adding assumptions that should be retained with the estimate.
Absolute outcome differences require a time horizon and the actual survival estimates. If a hypothetical five-year event risk is 20% in one group and 14% in another, the absolute difference is six percentage points and the risk ratio is 0.70. That risk ratio need not equal a reported hazard ratio.
Confidence intervals describe uncertainty under the analysis. A wide interval warns that the estimate is imprecise. It does not rescue an inapplicable population. Multiplying unrelated hazard ratios for stage, Ki-67 and ctDNA (circulating tumor DNA) can double-count correlated features and does not create a validated personal model.
Why it matters in cancer
It prevents a relative event-rate comparison from being presented as a personal probability or an absolute treatment benefit.
Worked example
A small cohort reports HR 14.8 with a very wide confidence interval. It suggests a prognostic association under that comparison, rather than a personal 14.8-fold probability or a treatment effect. Keep assay, sampling time and endpoint attached to it.
Common confusions
- Hazard reduction differs from absolute risk reduction and fewer events by a fixed date.
- An adjusted association does not automatically establish causation.
- A subgroup hazard ratio is not a personal probability multiplier.
Related concepts
Kaplan–Meier and endpoints.
Sources and scope
General teaching, source-checked October 8, 2026. The examples are hypothetical unless a study is explicitly named. Expert and learner review remain pending.