How to interpret hazard ratios

TL;DR

This paper reviews the interpretation of hazard ratios in survival analysis, addressing criticisms about their causal meaning, and argues that they can still be validly interpreted causally with some considerations.

Contribution

The paper clarifies the causal interpretation of hazard ratios and discusses when alternative measures might be more appropriate.

Findings

Hazard ratios can have a valid causal interpretation under certain conditions.

Criticisms of hazard ratios' causal interpretability are addressed and countered.

Alternative effect measures may sometimes be preferable.

Abstract

The hazard ratio, typically estimated using Cox's famous proportional hazards model, is the most common effect measure used to describe the association or effect of a covariate on a time-to-event outcome. In recent years the hazard ratio has been argued by some to lack a causal interpretation, even in randomised trials, and even if the proportional hazards assumption holds. This is concerning, not least due to the ubiquity of hazard ratios in analyses of time-to-event data. We review these criticisms, describe how we think hazard ratios should be interpreted, and argue that they retain a valid causal interpretation. Nevertheless, alternative measures may be preferable to describe effects of exposures or treatments on time-to-event outcomes.