Design of Experiments > Hazard Ratio

## What is a Hazard Ratio?

The hazard ratio is a comparison between the probability of events in a treatment group, compared to the probability of events in a control group. It’s used to see if patients receiving a treatment progress faster (or slower) than those not receiving treatment.**A hazard ratio of 3**means that three times the number of events are seen in the treatment group at any point in time. In other words, the treatment will cause the patient to progress three times as fast as patients in the control group. Any ratio above 1 generally means that the treatment group healed faster or had a slower time to an event.**A hazard ratio of 1**means that both groups (treatment and control) are experiencing an equal number of events at any point in time.**A hazard ratio of 0.333**tells you that the hazard rate in the treatment group is one third of that in the control group.

What the “event” is depends on the type of study. For example, it may be death, a cure, or another event — like a stroke.

Hazard ratios can be used to:

- Show the relative risk of a complication (like developing a side effect from a drug) in treatment group vs. control group.
- Show whether a treatment shortens an illness duration.
- Show which individuals are more likely to experience an event first.

While a hazard ratio is similar to a relative risk ratio, it isn’t exactly the same. Let’s say a clinical trial investigated survival rates for two drugs (A and B). The reported hazard ratios and relative risk ratios were both 3.

- The
**relative risk ratio**tells you that the risk of death is three times higher with drug A than with drug B over the entire period of the study (i.e. it’s cumulative). - The
**hazard ratio**tells you that the risk of death is three times higher with drug A than with drug B at any particular point in time.

When evaluating hazard ratios, it’s recommended that you also use another measure, like: median survival time, overall survival, or time to progression. These factors can provide insights about clear benefits (i.e. survival time is increased on average by 180 days).

**Reference:
**Spruance et. al. Haz. Ratio in Clinical Trials. Antimicrob Agents Chemother. 2004 Aug; 48(8): 2787–2792.Available online here.

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