Hazard ratio

Calculate a hazard ratio from the hazard rates in the treatment and control groups.

What is this for?

A hazard ratio compares the instantaneous rate at which events occur in two groups over the course of follow-up. Unlike a relative risk, which compares cumulative proportions at a fixed point, a hazard ratio uses the timing of events and handles censored observations, which is why it is the standard measure in survival analysis.

How to use it

Enter the hazard rate for each group, in consistent units of events per unit of person-time.
The ratio is dimensionless, so the units cancel provided they are the same in both groups.
Interpret alongside the confidence interval from the source analysis; this calculator produces the point estimate only.

Worked example

A survival analysis reports a hazard rate of 0.08 events per person-year in the treatment arm and 0.12 in the control arm.

Answer: HR = 0.08 ÷ 0.12 = 0.667, a 33% relative reduction in the instantaneous rate of the event.

Clinical pearls & pitfalls

A hazard ratio of 0.67 does not mean patients live 33% longer, nor that 33% fewer events occur overall. It describes the instantaneous relative rate at any moment during follow-up.
The proportional hazards assumption — that the ratio stays constant over time — is frequently violated, most obviously with immunotherapies whose survival curves cross or separate late. Look at the Kaplan–Meier curves, not just the reported hazard ratio.
Hazard ratios and relative risks answer different questions and are not interchangeable, though for rare events over short follow-up they converge.
A statistically significant hazard ratio with a trivial absolute difference in median survival is common in oncology trials. Ask for the absolute numbers.

Assumptions & limitations

Requires hazard rates as input. Extracting them from a published paper usually needs the survival curves or the original analysis, not just the summary table.
Produces a point estimate only. Confidence intervals require the underlying event counts and person-time, which this calculator does not take.
Assumes proportional hazards. When that assumption fails the hazard ratio is a weighted average over follow-up and can be seriously misleading.

References

Spruance SL, Reid JE, Grace M, Samore M. Hazard ratio in clinical trials. Antimicrob Agents Chemother. 2004;48(8):2787-2792.
Hernán MA. The hazards of hazard ratios. Epidemiology. 2010;21(1):13-15.
Cox DR. Regression models and life-tables. J R Stat Soc B. 1972;34(2):187-220.