On Defense of the Hazard Ratio

TL;DR

This paper discusses the causal interpretability of the hazard function in time-to-event studies, showing it can have valid causal meanings across different frameworks and can be practically useful.

Contribution

It demonstrates mathematically that the hazard function has causal interpretations under multiple frameworks and advocates for its practical interpretability.

Findings

Hazard function has causal interpretations in Rubin, Robins, and Pearl frameworks.

The hazard ratio over time can be meaningfully interpreted in practice.

Mathematical validation using single-world intervention graphs.

Abstract

In this short communication, we describe the recent debate on whether the hazard function should be used for causal inference in time-to-event studies and consider three different potential outcomes frameworks (by Rubin, Robins, and Pearl, respectively) as well as use the single-world intervention graph to show mathematically that the hazard function has causal interpretations under all three frameworks. In addition, we argue that the hazard ratio over time can provide a useful interpretation in practical settings.