Hazard Ratio Explained

A hazard ratio (HR) compares the instantaneous rate of an event (the hazard) in one group with that in another over follow-up. It is the usual effect measure from Cox proportional hazards models and is used for time-to-event outcomes such as survival or time to relapse.

Key ideas

• The hazard is the rate at which events occur at a given time among those still event-free.
• An HR of 0.70 means that, at any point in time, the event rate in the treated group is 70% of that in the control group (a 30% lower rate), assuming the hazards are proportional.
• HR = 1 means no difference; HR > 1 indicates a higher event rate.
• Censoring: participants who have not had the event by the end of follow-up, or who are lost, contribute information until they leave the study.

The proportional hazards assumption

The Cox model assumes the HR is constant over time. If effects change (for example a treatment is effective early but not later), a single HR may be misleading. Check the assumption with plots and tests, and consider alternatives with statistical advice.

HR versus risk ratio

A risk ratio compares cumulative risk over a fixed period; an HR compares rates over time. They are not the same, and a hazard ratio can be hard to interpret causally because the groups compared at later times differ in who remains at risk. Complement HRs with absolute measures, such as risk or median survival at fixed times and Kaplan–Meier curves.

Illustrative example

Invented for teaching. In a cohort study, anticoagulation versus no anticoagulation gives a hazard ratio for stroke of 0.60 (95% CI 0.45 to 0.80). The 5-year stroke risk is 8% in the treated group and 12% in the untreated group, which is clearer for patients than the HR alone.

Common pitfalls

• Treating an HR as a risk ratio.
• Ignoring non-proportional hazards.
• Reporting an HR without number of events and follow-up.

Key takeaways

• HR compares event rates over time.
• Check proportionality and report absolute effects.

This page is general educational information about research methods. It is not medical, legal or regulatory advice; follow your institution's ethics board and your target journal's instructions.