In time-to-event analysis, what does a hazard ratio compare?

• A. The instantaneous risk of the event between two groups
• B. The total number of events over the study
• C. The odds of the event
• D. The rate of censoring

Answer: (A)

In time-to-event analysis, a hazard ratio summarizes how the instantaneous risk of the event compares between two groups. The hazard at time t is the immediate risk of the event occurring at that moment, given survival up to t. The hazard ratio is the ratio of these hazard functions for the two groups (h1(t) / h0(t)). If hazards are proportional, this ratio stays roughly constant over time and tells you how many times higher or lower the immediate risk is in one group compared with the other at any moment. It’s not about the total number of events, nor about odds, nor about the rate of censoring. For example, a hazard ratio of 0.7 means the instantaneous risk in the treatment group is 30% lower than in the control group at any time, assuming proportional hazards.