hazardratios

Hazard ratio is a measure used in survival analysis to compare the hazard rates between two groups over time. The hazard in this context is the instantaneous risk of experiencing the event of interest at time t, given survival up to that time. The hazard ratio, denoted HR, is the ratio h1(t)/h0(t) of two hazards. In many studies, HR is estimated with a Cox proportional hazards model or other time-to-event models.

Interpretation: An HR of 1 indicates no difference in hazard between groups. An HR less than 1 indicates a lower hazard in the numerator group; greater than 1 indicates a higher hazard. For example, an HR of 0.70 implies a 30% reduction in the hazard of the event for the treated group relative to control, at any time point under the proportional hazards assumption. It is important to note that the hazard ratio reflects instantaneous risk and is not the same as a risk ratio over a fixed time interval.

Estimation and assumptions: The Cox model estimates log HRs and assumes proportional hazards, meaning HR is constant over time. If this assumption is violated, alternative models with time-varying coefficients or stratification may be used. Confidence intervals quantify precision, and p-values test the null hypothesis HR = 1. The baseline hazard function remains unspecified in many models; to obtain absolute risk measures, the HR must be combined with the baseline survival.

Applications and limitations: Hazard ratios are widely used in clinical trials and observational studies with time-to-event outcomes to compare treatments or prognostic factors. Limitations include sensitivity to censoring, dependence on the proportional hazards assumption, and the potential to misinterpretation as a cumulative risk without considering the baseline hazard and follow-up time.