Hazard Ratio

When the outcome is the time until an event, such as death, relapse, or recovery, neither the risk ratio nor the odds ratio captures the timing. The hazard is the instantaneous rate of the event at a given moment, among those still at risk at that moment. The hazard ratio (HR) compares this rate between two groups across the whole follow-up period. An HR of 1 means equal event rates. An HR below 1 means the treatment slows events; HR 0.7 means a 30% lower rate of the event at any given time. An HR above 1 means faster events. The hazard ratio comes from survival analysis, namely Kaplan-Meier curves and especially Cox proportional hazards regression (covered later), which can also adjust for confounders. It uses all the timing information, including patients who are censored, meaning lost to follow-up or still event-free at the study's end, which makes it efficient for time-to-event data. Several cautions matter in interpretation. An HR is a rate ratio, not a risk ratio and not a statement about how much longer patients live; an HR of 0.7 does not mean 30% live longer or a 30% absolute benefit. The HR also assumes the ratio of hazards is roughly constant over time, the proportional hazards assumption; if the survival curves cross, a single HR is misleading and should not be reported alone. Good practice is to pair the hazard ratio with the actual Kaplan-Meier survival curves and the median survival times, so readers can see the clinical magnitude rather than only a ratio. Report the HR with its confidence interval, and an interval that includes 1 means the difference is not statistically significant. When the proportional-hazards assumption is doubtful, modern reports also give the restricted mean survival time, an absolute measure of average event-free time over the follow-up that clinicians often find easier to interpret than a hazard ratio.