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I'm currently working on a meta analysis and half of the included papers only reported the beta coefficient. I wanna pool the odds ratios and am now wondering if there is a way to convert beta coefficient in Odds Ratios or any other way how I would get the odds ratios from these papers (the raw data is not complete to calculate the odds ratios from there).

Any Ideas?

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    $\begingroup$ Are you asking about "Beta regression" or perhaps about a standardized regression coefficient in a logistic regression? Or maybe something else? Exactly what statistics do these papers report? $\endgroup$
    – whuber
    Sep 27, 2022 at 16:18
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    $\begingroup$ As you can see in the comments on my answer, we don't know what you mean. I have made a guess about what you could mean, kjetil made a different guess. It would be good if you clarify this by answering whuber's questions. The best way to do so is to edit your question. $\endgroup$ Sep 27, 2022 at 21:00
  • $\begingroup$ Do you mean to join odds ratios and log odds ratios, or odds ratios with coefficients from an OLS regression (thus, binary and continuous outcomes)? $\endgroup$ Feb 21 at 15:09

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That depends on where those coefficients come from. If they are from a logistic regression, you can just do $e^\beta$. In most computer programs (and hand calculators) the function for that would be called exp().

Since you are doing a meta analysis you probably also want the standard error of that odds ratio. For that you would typically use the delta method. In this case it would be $e^\beta \mathrm{se}_\beta$, so the odds ratio you computed times the standard error of the raw beta coefficient.

If those studies used some other model than a logistic regression model, then things will get a lot harder.

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  • $\begingroup$ How does this answer the question? The OP specifically asks about beta regression ... $\endgroup$ Sep 27, 2022 at 14:37
  • $\begingroup$ @kjetilbhalvorsen in many fields $\beta$ is the usual notation for untransformed regression coefficients $\endgroup$
    – wzbillings
    Sep 27, 2022 at 15:15
  • $\begingroup$ Wzbillings' interpretation is also mine. I interpret the OP's question to refer to the raw coefficients of a logit regression. Though if the logit link function is used for the beta regression, and that is common, then my answer also applies to beta regression. $\endgroup$ Sep 27, 2022 at 20:40
  • $\begingroup$ The question makes more sense if we parse the "beta regression coefficients" in the title as (beta) (regression coefficients), where beta refers to the raw or untransformed coefficients, instead of (beta regression) (coefficients), i.e. the coefficients of a beta regression for a compositional dependent variable. $\endgroup$ Sep 27, 2022 at 20:50
  • $\begingroup$ the papers mostly conducted logistic regressions $\endgroup$
    – Léonie
    Oct 2, 2022 at 14:28

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