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Simple question here. Suppose that I have 20 papers to be included in a meta-analysis, which compare the risk of death with 2 treatments, A vs. B. For 15 of them, I only have number of events and number of patients in both groups (A vs. B). For the other 5, I do not have the number of events/patients in group, but I have instead an adjusted HR/OR.

How can I pool together these two type of effect size (i.e., event count and HRs/ORs) into one meta-analysis with metafor?

My guess is that I can compute logOR and SE in the first place for those studies for which I have event count, and then pool together with the other pre-computed effect size (aOR, or aHR), but I am unsure whether this is suitable. Besides, I'm pretty aware that OR and HR are not interchangeable, so that caution should be use when pooling different effect measures.

Moreover, I was wondering if there is some straigthforward option/function to do this in the package.

Thank you in advance to anyone who want to make a guess.

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As you suggested, for the 2x2 tables, just compute the log odds ratios and corresponding sampling variances in the usual manner. For studies reporting odds ratios (and hopefully corresponding confidence intervals), you can just take the log of the odds ratios and the CIs can be converted to the corresponding standard errors as described in this answer. Squaring the standard errors gives you the sampling variances for these studies.

You can find an example illustrating this kind of workflow here:

https://www.metafor-project.org/doku.php/tips:assembling_data_or

In the example, just assume that the ORs are not the ones from the 2x2 table data but are adjusted estimates.

I would recommend to code for each study what kind of log odds ratio it is (i.e., unadjusted based on a 2x2 table or adjusted). Then you can examine via a meta-regression model if there is a systematic difference between these two types.

In principle, the same can be done with hazard ratios, but as you note, one should not combine them with ORs.

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  • $\begingroup$ Thanks! Exactly what I was looking for. The question is, since many studies report adj. HR, I may be forced to pool them together with the ORs. Is this a very strong violiation of principles of meta-analysis, or it can be sustainable, listing this as a limitation, and maybe performing sensitivity analysis to show the impact of the HR listed as ORs? $\endgroup$
    – user89547235
    May 10, 2021 at 9:55
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    $\begingroup$ ORs and HRs are really different measures and I think many would recommend against pooling them in the same analysis. I seem to remember the Cochrane handbook also discussing this, but can't find the section. A simple option is to just run two separate analyses. $\endgroup$
    – Wolfgang
    May 10, 2021 at 10:25

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