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In my book the example for interpreting a hazard ratio < 1 includes just a single example with a hazard ratio of 0.5. It is very confusing. If you have a hazard ratio of 0.2, does that mean the risk of hazard is reduced by (0.2) 20% or (1-.8) 80%?

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It is a ratio, so a hazard ratio of 0.2 means a relative reduction of 80%.

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