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I would like to run a meta-regression in which the independent variable is composed of weighted reported odds ratios (ie, the number of events for a particular medication side effect divided by total events reported for that med) and the dependent variable is a set of effect sizes. However, I have an issue with the reported odds ratios in that some of them are based off a much greater number of events than others (eg, a reported odds ratio based off 10 total side effects for a med vs. a reported odds ratio based off 1000s of total side effects for a med) and I would like to account for this through weights. Does anyone know how to do this? Thank you for any help!

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  • $\begingroup$ Set the weights proportional to the variance of each estimate. $\endgroup$ Jul 27, 2022 at 21:40
  • $\begingroup$ Sorry, would you mind getting more specific? I have somewhat rudimentary stats knowledge. $\endgroup$
    – M BG
    Jul 27, 2022 at 22:40
  • $\begingroup$ (meant to say inversely proportional to variance). The idea of using weights for regression makes sense to you (I suspect upon reading this question, but lmk if im wrong). So you just need to calcluate the variance of each of your log-odds, using for example the ideas here: stats.stackexchange.com/questions/266098/… and then plug the inverse of that into the weights parameter of your regression package. $\endgroup$ Jul 28, 2022 at 14:17
  • $\begingroup$ Ah, okay. I understand what you mean. After calculating that weight, do you have any sense of how I might apply it to a meta-regression (ie apply weights to the independent variable in the meta-regression)? The meta-regression programs I am aware of only allow weights to be added to the dependent variable. $\endgroup$
    – M BG
    Aug 1, 2022 at 19:45
  • $\begingroup$ Oh I see it in the independent variables, the term to google there is Error in Variables regression. You should be able to use those as the variance of those ratios as the variance of independent variable. $\endgroup$ Aug 1, 2022 at 19:51

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