How to interpret hazard ratios

2026-01-14

AI Summary

The causal interpretability of the hazard ratio in randomized controlled trials has long been debated, even under the proportional hazards assumption. This study systematically examines critiques of its causal interpretation and, by integrating the Cox proportional hazards model with modern causal inference frameworks, clarifies the precise conditions under which the hazard ratio can be endowed with a valid causal meaning. The analysis demonstrates that, under specific assumptions, the hazard ratio remains a useful estimator of causal effects, while also highlighting scenarios in which alternative effect measures—such as risk differences or ratios of survival probabilities—may be more appropriate. These findings provide both theoretical grounding and practical guidance for the analysis of time-to-event data in causal settings.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• hazard ratio
• causal interpretation
• proportional hazards
• time-to-event data
• Cox model

Innovation

• hazard ratio
• causal interpretation
• proportional hazards model
• time-to-event data
• Cox regression