Measures of effect - hazard ratio

Definition

Hazard ratio compares the instantaneous rate (hazard) of an event occurring in one group versus another over the entire follow-up period of a time-to-event (survival) analysis - incorporating not just whether an event occurred but also when it occurred, distinguishing it from a simple relative risk which only considers whether an event occurred by a fixed endpoint
The standard effect measure reported from Cox proportional hazards regression, widely used in oncology and cardiovascular trials where time to an event (death, disease progression, cardiovascular event) is the outcome of primary interest

Because hazard ratio accounts for the timing of events throughout follow-up (not just the final cumulative count at a single endpoint), it makes more efficient use of the available data, including information from participants who are censored (lost to follow-up or study ends before they experience the event) partway through the study - this is a specific analytical advantage over simple relative risk when event timing varies and follow-up duration differs between participants

The proportional hazards assumption (that the ratio of hazards between groups remains constant over the entire follow-up period) underlies valid Cox regression/hazard ratio interpretation - this assumption should be checked, since a violated proportional hazards assumption (e.g. an early divergence in event rates that then converges later) undermines the validity of a single summary hazard ratio describing the whole follow-up period
Kaplan-Meier survival curves provide the visual complement to a reported hazard ratio, showing how the group differences actually evolved over the follow-up period

A single reported hazard ratio should be checked against the corresponding survival curve shape to confirm the proportional hazards assumption reasonably holds, rather than being interpreted in isolation as if event timing were necessarily consistent throughout follow-up
Hazard ratio interpretation follows a similar direction convention to relative risk (below 1 favouring the treatment/exposed group for a harmful outcome, above 1 favouring the comparison group)

Proportional hazards assumption and its violation risk, censoring and efficient data use in time-to-event analysis, Kaplan-Meier curve as the visual complement to a reported hazard ratio, common use in oncology/cardiovascular trial reporting

A single summary hazard ratio can be misleading if the proportional hazards assumption doesn't actually hold - e.g. if a treatment effect is concentrated early in follow-up and then converges with the control group later, a single overall hazard ratio may not accurately represent this changing pattern, which is why checking the underlying Kaplan-Meier curve shape alongside the reported hazard ratio is an important part of correctly interpreting time-to-event trial results

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