Under what conditions is the log of RR (or OR) approximately Normally distributed? Sources would be very much appreciated - wikipedia for example just states the SE formula but provides no information on when it is true.
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asked Jan 6, 2020 at 12:14
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I'm reasonably confident this is just an assumption based on the CLT.
A distribution converges to a Normal whenever it's approximately a sum of a lot of fairly small, roughly independent values, positive or negative.
If a log-value is Normal, that indicates that it can be approximated as a product of a many such variables instead, as $\prod_0^ix_i = \exp(\sum_0^i\log(x_i))$.
Assuming the risk in both groups is >0 (even if it is very small), then $p(outcome)$ can often be modeled (especially in complicated systems, e.g. human body) as a conditional probability $p(outcome|v_1, v_2, ..., v_n)$, which satisfies that condition given enough variables if there are no strong correlations unaccounted for.
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1$\begingroup$ The question should be how useful normal approximations for these quantities are. Exact Bayesian uncertainty intervals are available, as well as fairly accurate profile likelihood confidence intervals. $\endgroup$ Commented Sep 9, 2023 at 11:16