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I am conducting a meta-analysis of individual studies that report probabilities and their standard error as an effect size. I plan to convert the probabilities and standard errors to the natural logarithm of the odds, however, I am not sure how to convert the standard errors of the probabilities into SEs of the natural logarithm of the odds.

Is there a formula to convert these? Better yet, is there a way to do this in R-studio?

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Best to convert SE to n given that SE²=pq/n Then run a meta-analysis of np (cases) and n using MetaXL using the Freeman-Tukey transformed proportion. Also see these papers: FTT paper and JECH paper

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