What to do with missing effect sizes in meta-analyses? I'm currently working on a meta-analysis but I'm unsure what to do with missing effect sizes. Effect sizes in my dataset may be missing for two reasons:

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*The effect size is non-significant and the authors do not report an exact estimate (nor respond to my request for additional information)

*The reported effect cannot be converted to the chosen effect size because information is missing (and corresponding authors do not respond)

I was advised not to exclude these missing effect sizes but to include them assuming them to be null. I'm wondering if this is indeed the right approach to take here and also if there are any papers on this topic that demonstrate this. Any other ideas on how to deal with these missing effect sizes are also welcome.

The problem of missing data in meta-analysis is a crucial one, and often goes hand in hand with small study effects, publication bias, and selective reporting.
A key problem is why data are missing. Indeed, some outcomes may not be reported because actually missing due to forgetfulness of the investigators. However, they could be lacking because they were non-significant or else (publication bias) or because the measurement tools were faulty (eg inappropriate imaging for surrogate outcomes), and so forth.
My personal take is to avoid assuming anything (even a null effect) and simply use a complete case analysis for the main analysis. Multiple data imputation can be performed, but also using several different approaches and varying assumptions, while remembering that the scope of inferential meta-analysis based on multiple data imputation is simply exploratory, at best.
Some useful references are the following:
Higgins et al, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2602608/
Jakobsen et al, https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-017-0442-1
Mavridis et al, https://onlinelibrary.wiley.com/doi/full/10.1002/jrsm.1349
