Causal interpretation of the hazard ratio in randomized clinical trials

Abstract

Background: Although the hazard ratio has no straightforward causal interpretation, clinical trialists commonly use it as a measure of treatment effect. Methods: We review the definition and examples of causal estimands. We discuss the causal interpretation of the hazard ratio from a two-arm randomized clinical trial, and the implications of proportional hazards assumptions in the context of potential outcomes. We illustrate the application of these concepts in a synthetic model and in a model of the time-varying effects of COVID-19 vaccination. Results: We define causal estimands as having either an individual-level or population-level interpretation. Difference-in-expectation estimands are both individual-level and population-level estimands, whereas without strong untestable assumptions the causal rate ratio and hazard ratio have only population-level interpretations. We caution users against making an incorrect individual-level interpretation, emphasizing that in general a hazard ratio does not on average change each individual’s hazard by a factor. We discuss a potentially valid interpretation of the constant hazard ratio as a population-level causal effect under the proportional hazards assumption. Conclusion: We conclude that the population-level hazard ratio remains a useful estimand, but one must interpret it with appropriate attention to the underlying causal model. This is especially important for interpreting hazard ratios over time.