# Is there a way to convert beta regression coefficient in odds ratios?

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?

• 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?
– whuber
Sep 27, 2022 at 16:18
• 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. Sep 27, 2022 at 21:00
• 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)? Feb 21 at 15:09

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.
• @kjetilbhalvorsen in many fields $\beta$ is the usual notation for untransformed regression coefficients Sep 27, 2022 at 15:15