# Hazard ratio (HR)

A hazard ratio (HR) tells you how fast events happen in one group versus a reference group, at any given moment during follow-up. Formally, it is the ratio of the instant event rates, from a Cox proportional-hazards model. An HR of 0.75 means the treated group has the event at 75% of the rate of the controls, throughout follow-up. (It does not mean overall risk is cut 25% at a fixed time point, which is a common misreading.) The proportional-hazards assumption requires that this ratio stay constant over time. Violations (like a drug effect that changes over time) must be tested. When they happen, time-restricted or parametric models fit better. In longevity and survival studies, the HR is the dominant effect measure. But its size depends on the baseline hazard and the follow-up length, which limits comparing it directly across trials.

## Sources

- Cox DR. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B
- Stensrud MJ, Hernán MA. (2020). Why test for proportional hazards?. JAMA. https://doi.org/10.1001/jama.2020.1267

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_Canonical: https://longevity-switzerland.com/en/glossary/hazard-ratio · Part of Longevity Cities · Updated 2026-06-22_