Hazard ratio (HR)

A hazard ratio is the ratio of the instantaneous event rate in one group to that in a reference group at any given moment during follow-up, derived from a Cox proportional-hazards regression model. An HR of 0.75 means the treated group experiences the event at 75% of the rate of controls throughout follow-up, not that overall risk is reduced by 25% at a fixed time point — a common misreading. The proportional-hazards assumption requires that this ratio remain constant over time; violations (e.g., time-varying drug effects) must be tested, and when present, time-restricted or parametric models are more appropriate. In longevity and survival studies the HR is the dominant effect measure, but its magnitude depends on baseline hazard and follow-up length, limiting direct comparisons across trials.