[R-meta] Meta-analysis dichotomous outcome/quantitative predictor and calculation of r2 or equivalent

[Creese, Byron]

Hello all, I am planning to conduct a meta-analysis of some data using metafor but have a couple of questions before I start...

I have data from 12 studies and I have the raw data so I can conduct exactly the same primary analysis on all studies.

My outcome variable is dichotomous and my predictor is quantitative.  I am also controlling for a number of other variables which are common across all datasets.

My primary analysis will be to run a logistic regression on each study.  

Because my predictor is quantitative I do not have ai (treatment positive), bi (treatment neg), ci (control positive) and di (control negative) so I think my best option would be a random-effects meta-analysis of the regression coefficients and their standard error, as follows:

meta <- rma.uni(yi, sei)

My first question was to check if that sounds reasonable.

Secondly, if I were running this analysis in just one study I would assess the improvement in model fit associated with the predictor by following this calculation using the NagelkerkeR2 function in fmsb package:

NagelkerkeR2(model)$R2 - NagelkerkeR2(model.null)$R2

Is there an equivalent figure for meta-analysis or would it be appropriate to meta-analyse the r2 from the above calculated in each study?

Many thanks,
Byron