What is a hazard ratio and in what model is it commonly estimated?

• A. Hazard ratio is the ratio of cumulative incidences over the entire follow-up.
• B. Hazard ratio is the ratio of incidence rates over time with equal follow-up.
• C. Hazard ratio is the difference between hazard rates.
• D. Hazard ratio is the ratio of hazard rates between groups; estimated with Cox proportional hazards model.

Answer: (D)

Hazard in survival analysis is the instantaneous risk of the event occurring at a given moment, among those still at risk at that moment. A hazard ratio compares these instantaneous risks between two groups and is a ratio, not a difference. It reflects how much more (or less) likely an event is to happen at any moment in one group compared with the other.

The Cox proportional hazards model is the standard way to estimate this ratio because it expresses the hazard as h(t|X) = h0(t) exp(βX). The hazard ratio between groups is exp(β), and under the proportional hazards assumption it stays constant over time. So the correct description is the ratio of hazard rates between groups, estimated with the Cox proportional hazards model. The other options describe different concepts (cumulative risk, incidence rates, or a difference rather than a ratio) and don’t capture the idea of hazard ratio.