The hazard ratio is interpretable as an odds or a probability under the assumption of proportional hazards

TL;DR

This paper clarifies that under proportional hazards, the hazard ratio can be interpreted as an odds or probability, linking hazard ratios to more intuitive measures in survival analysis.

Contribution

It demonstrates that the hazard ratio is interpretable as an odds or probability when the proportional hazards assumption holds, unifying different statistical perspectives.

Findings

Hazard ratio equals odds under proportional hazards.

Supports interpretability of hazard ratios as probabilities.

Bridges gap between hazard ratios and intuitive measures.

Abstract

Three statistical studies, all published between 2004 and 2008 but without referring to one another, assert a useful equivalence involving the hazard ratio, a parameter estimated for time to event data by the frequently used proportional hazards model. Stated generally, when the assumption of proportional hazards is justified, the hazard ratio is equivalent to the odds that a randomly chosen person from the group whose hazard is represented in the ratio's numerator will experience the event of interest before a randomly chosen person from the group represented by the ratio's denominator.