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See here: https://en.wikipedia.org/wiki/Relative_risk#Inference

The sampling distribution of the $\log(RR)$is closer to normal than the distribution of RR, with standard error

$$SE(\log(RR)) = \sqrt{\frac{IN}{IE(IE + IN)} + \frac{CN}{CE(CE + CN)}}$$

I checked the reference, but the reference is also not very clear

There was a prior discussion here, but it also doesn't quite answer the question..

Conditions when the log of Relative Risk is approximately Normal

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One simple point: a risk ratio by definition can't be negative. A true normal distribution has to allow for negative values. The log of a risk ratio, in contrast, can have any real value.

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  • $\begingroup$ Yes, but there are a lot of distributions that "skew with non-negative values" . Why can't it be Poisson, for example? $\endgroup$
    – Matt Frank
    Nov 25 '20 at 15:10
  • $\begingroup$ @MattFrank if the question is whether the distribution of the log(RR) is closer to normal than the distribution of the RR itself, then this answer gives one important reason. The distribution of the RR could take on some other potentially useful parametric form, but that form couldn't be close to normal unless the RR is highly positive. For closeness of the log(RR) to normal, the page you link provides some insight. $\endgroup$
    – EdM
    Nov 25 '20 at 15:29
  • $\begingroup$ That's actually a good point. The wiki didn't say the resulting distribution is normal. It just says it's close to normal $\endgroup$
    – Matt Frank
    Nov 26 '20 at 16:24

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