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I am conducting a meta-analysis and the effect sizes are mostly Cohen's d or log odds ratios. However, a few of the effect sizes are regression coefficients obtained from negative binomial regressions. I would like to convert these negative binomial regression coefficients to Cohen's d or log odds ratios.

I would very much appreciate some advice on how to do this. I came across this Shiny App: https://stefany.shinyapps.io/RcountD/ but it requires knowledge of the original regression intercept, standard error, and dispersion, which I don't have as I'm using summary statistics. The summary statistics I have are the negative binomial regression coefficients, their standard errors, and the sample size.

Thanks in advance for your help.

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  • $\begingroup$ Can edit your post to add the summary statistics you have? $\endgroup$ – dariober Oct 30 '20 at 17:55
  • $\begingroup$ dariober, I have edited it to add the summary statistics. $\endgroup$ – JRB Oct 30 '20 at 18:43
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I have been advised by the developer of the Shiny app that it is not possible to convert negative binomial regression coefficients to Cohen's d without knowledge of the original regression intercept, standard error, and dispersion.

The answer is copied below:

"Unfortunately, since the Poisson family models are non-linear, the magnitude of the effect depends on both the effect itself and where you start (i.e., the intercept). A 5 times increase from 1 to 5 is a 4 unit change while a 5 times increase from 10 to 50 is a 40 unit change – very different! Likewise, you can’t calculate the SD for the Cohen’s d effect without the dispersion parameter."

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