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I am conducting a meta-analysis and wish to convert odds ratios/log odds ratios to tetrachoric correlation coefficients. I have found equations for this conversion by Bonett et al and now need to convert standard errors of odds ratios to standard errors of tetrachoric correlation coefficients.

The escalc function in the metafor package will convert variances of odds ratios to variances of tetrachoric correlations, but this requires the sample sizes from a 2x2 contingency table. This information is not reported in some of the studies included in my meta-analysis, so I won't be able to use the function for some studies.

Is there an equation / function to convert the standard error or variance of the odds ratio to the standard error/variance of the tetrachoric correlation coefficient, which doesn't require information from the 2x2 table?

Thanks in advance for any help.

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I think you should do the meta-analysis without the studies that fail to report the base rates and sample sizes. These are not reproducible studies. It is to my mind an utter disgrace that epidemiology continues to use odds ratios. By analogy, when constructing a building one does not use a ruler made of elastic because it will fall down. Odds ratios are dependent on base rate and therefore the same OR can mean a different degree of association. Not suitable for science, IMO.

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