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For the effect sizes there exist conventions as how big an effect size should be, for beeing considered low/medium/big - 0,2/0,5/0,8 - according to Cohen.

Is there something equivalent in respect to risk ratios?

In particular for the purpose of an evaluation of the efficiency of medical therapies. Comparing the new treatment to standard therapy, in a forest-plots of a metaanalysis.

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Although the convention exists that does not make it useful of course. Since it compares the shift in location with variability it means that two studies which achieve the same effect in absolute terms (say a reduction of 10 mm Hg in mean systolic blood pressure) would differ in their value of Cohen's d if the variability differed with the one which used a restricted group of people achieving a larger Cohen's d. Whether you think that is a good thing or not of course is a matter for debate.

You ask about relative risks and as far as I know there is no parallel set of conventional values which at least in my opinion is a good thing. If you want to know the practical effect of your therapy it is better to focus on absolute risk reduction and convert it to number needed to treat. You can then say to the clinicians that if they treat 100 people they will avert X cases of the bad outcome. A given value of relative risk can correspond to different numbers needed to treat depending on the baseline risk. So if the risk of the bad outcome is very low then a relative risk of 0.5 may be unimportant in practical terms (being struck by lightning) whereas if the risk is high (dying having contracted Ebola virus disease) then such a relative risk would be hugely important.

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