[R-meta] Meta-analyzing ORs from GEEs

[Mark White]

Let's say I have 30 studies, where each study measures a dichotomous
outcome and has a dichotomous predictor. Some people have multiple
responses, so I use a GEE to model every one of the 30 studies. What I have
is a log-odds coefficient for each (via `coef(model)[2]` for each study),
as well as the variance for each of these coefficients (via
`diag(vcov(model))[2]` for each study). Note that no covariates are added
to the model. The only coefficients are the intercept and the one for the
dichotomous predictor.

Two questions for everyone:

1. Can I assign the coefficients (in logits—the log of the odds ratio) to
`yi` and the variances to `vi` from these GEE models and submit them
directly to `rma.uni()`? I am assuming here that the coefficients and
variances are all I need, and the `escalc` function says we should be
converting odds ratios to log-odds anyways. Note that there are no
dependencies *across *studies, so the robust variance estimates from the
GEE should capture all the dependencies.

2. If I can do that, what is the recommended way to present this to
non-statistical audiences? I can get a meta-analytic estimate for the log
of the odds ratio, but my clients are used to seeing risk differences
(e.g., "There was a +4 percentage point lift"). I could always convert
log-odds to odds ratios and then compute lifts from a variety of different
baselines (e.g., "If there was a 50% positive outcome in the control, then
we had a +3.5 percentage point lift"). Any other ideas?

Thanks,
Mark

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