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

Two notes:

1) meta <- rma.uni(yi, sei) is not correct. It should be:

meta <- rma.uni(yi, sei=sei)

(assuming 'sei' is the name of the variable that contains the standard errors).

2) If you have the raw data, you can do an 'IPD' meta-analysis. Just combine the data from the 12 studies into one dataset. Then fit a multilevel (mixed-effects) model to these data that takes the clustering of observations within studies into consideration.

For a discussion/illustration of the IPD vs 2-stage (computing coefficients per study and then combining) approach, see:

http://www.metafor-project.org/doku.php/tips:two_stage_analysis

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Michael Dewey
Sent: Wednesday, 15 August, 2018 12:29
To: Creese, Byron; r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Meta-analysis dichotomous outcome/quantitative predictor and calculation of r2 or equivalent

Dear Byron

Comments in line

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.

Yes, that sounds reasonable to me.

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?

I am not sure why you would want to do that. You have the estimates and 
their standard errors so per study you have an estimate of the 
improvement in model fit by looking a the confidence interval and 
overall you have the same from the summary estimate and its confidence 
interval. If you try to summarise the R^2 what happens if you have 
identical standard errors but coefficients differing only in sign 
leading to the same R^2?

Many thanks,
Byron