[R-meta] conversion of OR to tetrachoric corr and its var

[Viechtbauer, Wolfgang (NP)]

Hi Eran,

See:

https://wviechtb.github.io/metafor/reference/conv.delta.html

and especially the example at the very end, which directly covers your question. Briefly, after conv.wald(), you use conv.delta() to convert the log odds ratio and its sampling variance to the tetrachoric correlation with its sampling variance.

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Eran Barzilai via R-sig-meta-analysis
> Sent: Friday, March 15, 2024 16:05
> To: r-sig-meta-analysis using r-project.org
> Cc: Eran Barzilai <barze445 using newschool.edu>
> Subject: [R-meta] conversion of OR to tetrachoric corr and its var
>
> Hello,
> Thank you for this great resource!
>
> I am working on a meta-analysis in clinical psychology where I compare if
> different types of childhood adverse experiences have different
> associations with later in life psychopathology.
> To do that I combine effect size that comes from Pearson’s r correlation,
> (log) odd-ratios, and mean differences (Cohen’s D). Since all the measures
> are clinical, I assume all are continuous variables regardless of if they
> were artificially dichotomized or not.
>
> My question is mostly about conversions of OR to the tetrachoric
> correlation.
>
> Most of the studies report the 2X2 table, allowing me to calculate the
> tetrachoric correlation directly using metafor’s escalc() function.
> However, some only report the OR and its CI. For these studies use
> metafor’sconv.wald() to calculate the log odd-ratios and their sampling
> variance. Then I can metafor’s transf.lnortortet.pearson() to convert the
> log odd-ratios to tetrachoric correlation.
>
> However, does it make sense to also use this function directly on the
> log-odds variance to convert it to the variance of the tetrachoric
> correlation?
>
> Alternatively, I thought of converting the log odd-ratios I calculate from
> conv.wald() to d, and then to the biserial correlations. Will this method
> produce more reliable estimation of the effect-size and its variance?
>
> Thank you for your help,
> Eran
>
> --
> Eran Barzilai, Ph.D., New School for Social Research
> Clinical Psychologist Postdoc, Williamsburg Therapy Group
> https://williamsburgtherapygroup.com/
> Part-time Faculty, The New School, Schools of Public Engagement, Bachelor's
> Program for Adults and Transfer Students
> Pronouns: he, him, his