[R-meta] Need to specify meta analysis weights

[Emanuele F. Osimo]

Dear all,
I am conducting a random-effects meta-analysis of 4 longitudinal studies
measuring a blood inflammatory marker earlier on in life, and an unrelated
outcome (measured in an interview) years later.
The studies are not uniform in N (one is about 80k people, the 2 smallest
are about 2k people) and in time to follow up (ranging from 8 to 21 years).
I have odds ratios  and 95% confidence intervals for the outcome based on
cut-offs of the baseline marker (e.g. outcome for inflamed vs outcome for
non-inflamed).

I have 2 questions for you:
1- if I use weighting by N, as recommended by Cochrane, I am basically
reporting the findings of the larger study, which gets 88% of the weight.
The larger study is possibly qualitatively less good than the 2 smallest
studies. What do you suggest to use for weighting? Is there any compound
weighting methods that takes into account, say, study quality, N and
inverse variance?
2- time to follow-up: even if I am not measuring a difference in outcome
over time, but just the risk of an outcome after an exposure, do I need to
adjust for time to follow-up? And how?

Many thanks in advance for your time and thoughts on this.

Best wishes,

Emanuele

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