Relative rates not relative risks: addressing a widespread misinterpretation of hazard ratios

The use of the Cox proportional hazards model is ubiquitous in modern medical research. Despite the widespread implementation of this model, the terminology and interpretation that is used to describe the estimate hazard ratio (HR) has become loose and, unfortunately, often incorrect. Although some journals offer guidelines that advise against reporting HRs as relative risks, these guidelines are frequently overlooked. Perhaps due to a lack of understanding, authors continue to interpret the resultant HR as a relative risk-such an interpretation is inappropriate and can be misleading. The HR should be described as a relative rate, not as a relative risk. This article demonstrates that although the direction of the HR can be used to explain the direction of the relative risk, the magnitude of the HR alone cannot be used to explain the magnitude of the relative risk. This article clarifies the relationship between HRs and relative risks in a way that may be better suited for the applied clinical researcher. We also provide a convenient table illustrating the magnitude of relative risk under various values of the HR; the table demonstrates that for a given constant HR, the magnitude of the relative risk can vary substantially. As a take-home message, authors should refrain from using the magnitude of the HR to describe the magnitude of the relative risk. Authors should be strongly encouraged to ascribe accurate interpretations to the statistics derived from fitted Cox proportional hazards regression models.