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The hazards of Hazard Ratios

Posted Feb 24 2010 12:16pm

In reading the cancer chemotherapy clinical trial literature, the unsuspecting yet intrepid pathologist finds himself amongst herds of hazard ratios.  I have tried to make sense of this for myself as follows.

"Time-to-event" curves plot the occurrence of an event over time for treatment and control groups and Cox proportional hazards regression is commonly used to analyze time-to-event curves.  The goal of a treatment may be to decrease the duration of the disease (like with antibiotic therapy) or to increase the duration of being "disease-free" (like with cancer chemotherapy) or alive (could be with or without disease).  The hazard ratio describes the relative risk of the event developing (such as disease recurrence in the case of cancer) for a treatment group compared to a control group over the course of time.  While hazard ratios have been commonly used to describe the extent to which a treatment can affect the duration of the interval of time to the event, this use can be misleading at best.  In other words, the hazard ratio is not an expression of the relative speed to an endpoint.  The HR may indicate a beneficial treatment effect and implies that the time to the endpoint was reduced/prolonged by the treatment but it provides no information on the magnitude of that time difference.  It is important to remember here that the proportional hazards model includes an assumption that the hazard ratio is constant over time.  What the hazard ratio does do is express the likelihood of the event occurring at a time-point in comparison between the treatment and control groups.  In other words, if the hazard ratio (HR) is 1 at time t, then there is an equal likelihood of the event occurring between the two groups (that is, no difference or effect); if the HR is 0.5, there is a 50% less likelihood of the event occurring between the two groups; and if the HR is 2.0, there is twice the chance or 100% more likelihood of the event occurring between the two groups.  It does not say that the patient has half or twice the speed to the event compared to the control.

If I'm interested in comparing the change in time to the event between two groups, then I need to use a time-based parameter, such as the median endpoint ratio.  Commonly, this literature reports the length of time from study entry to an endpoint for treatment and control groups and these are illustrated by a Kaplan-Meier curve.  Here one can derive a median time in which 50% of cases in each group have reached the endpoint and a mean time in which an average time to endpoint for each group.  Time-to-event analysis also has the advantage of including patients who fail to complete the trial or do not reach the study endpoint because one can compare the number of patients in each group at multiple points in time.  By looking at time-based parameters, I can thus get an idea of how fast each group reached an endpoint within a specified time frame.

I've heard this explained more simply as the HR telling you the chances of winning a race and time-based parameters telling you the margin of victory.

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