Does relative risk reduction refer to both 1-RR and 1-HR?

In clinical trials, the Hazard Ratio (HR) is often calculated to provide a risk estimate between two groups, e.g. 0.75. In my understanding, 1-HR refers to the relative hazard reduction, in this case 25 %, whereas 1-Relative Risk (RR) is the relative risk reduction, and that the relative hazard reduction and relative risk reduction are two separate entities. Nevertheless, they are used interchangeably in a lot of the clinical literature, i.e. 1-HR is referred to as the relative risk reduction.

See e.g.

Does relative risk reduction refer to both 1-RR and 1-HR?


Less is more. Stay pure. Stay poor.
My instincts say, "No". The HR is more similar to OR in regards to calculation and you can't do the 1-OR.
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I think it is sort of word games a bit. Reporting HR as RR is just making it digestable to a wider audience. Presumably the same goes for 1 - HR.

In vaccine studies 1 - RR is Vaccine Efficacy. According to my references, 1 - HR is also 'Vaccine Efficacy', although a different subscript is added. So they are the same, but not really. The use of 1 - HR is widely accepted in that context at least. I rarely work on human data though so its RR or risk difference all day long.

These pages are from 'design and analysis of vaccine studies' by springer etc.



Less is more. Stay pure. Stay poor.
@fed2 - thanks for sharing that, people are definitely moving from epidemic curves to VE metrics in many discussions.

@AnkyrinB - I would still agree with you that the terms do get used interchangeably (risk and hazards), but hazards are time dependent and purest always try to use the term hazards when discussing time to event survival estimands. I would think of it like this, are you using the same model to get relative risks and hazard ratios, no. You could do both with a generalized linear model - but I am imagining different links and distributions are employed, as well as assumptions at times (proportionality). To try and ignore issues by readers in interpreting them, I would commit myself to qualifying with hazards when referencing results from something like Cox model, etc. - just like when trying to be a purest between rates and risk and prevalence, etc.
@fed2 and @hlsmith - thank you both. I agree that this is mostly about semantics. But although I also use the term risk reduction or risk difference for both RR and HR, I think that relative risk reduction should be reserved for 1-RR. Take the following example from Steg et al 2019, Circulation: They find a HR of 0.71 and absolute risks after 4 years of 9.6% and 5.8%. That gives a RR of 0.60, and 1-RR=0.40. So the relative risk reduction after 4 years here (40%) clearly differ from 1-HR, which is 29%. Still, 29% is referred to as relative risk reduction. This is also the case in many other papers.

But maybe I should stop concerning myself with that kind of details:)