The Hazard Ratio Is Equivalent to an Odds Under the Assumption of Proportional Hazards

Clinicians routinely interpret statistical findings from medical research to inform patients of treatment benefits. Studies that use the hazard ratio present special challenges. Clinicians should not equate hazard ratios with risk ratios, ie, relative risks. However, clinicians can provide patients with a straightforward interpretation of the hazard ratio as an odds, as long as the ratio was calculated in a study in which the assumption of proportional hazards is justified. In such a case, the hazard ratio is equivalent to the odds that a person, who is randomly chosen from the group represented in the ratio's numerator, experiences an event before a randomly chosen person from the group represented in the ratio's denominator. A mathematical derivation for the equivalence is provided to further clarify this idea for clinicians.