# Meta-regression / multivariate analysis of trials with a binary outcme

I have a series of single-armed trials where the outcome is a binary response. Imagine a trial where you have no control arm; you merely give 100 patients a procedure (which can be done in many different ways) and see how many are 'well' (more later) at the end of the year. There are hundreds of these trials for me to look at.

I believe I can meta-analyse these as big group as follows, assuming x is the number well, n is n, and they're in df.

model <- rma(measure="PLO", xi=x, ni=n, data=df) #PLO = logit transformed proportion (log odds)
print(res, digits=3) #This will print the log odds
predict(model, transf=transf.ilogit, digits=3) #This will back-transform with the inverse logit transformation


I can plot this quite nicely with:

forest(model,transf=transf.ilogit)


The thing is, as alluded to, there are lots of different ways to do the procedure and lots of different classifications of whether the patient is 'well'.

I want to do meta-regression/MV analysis on these trials (I may have over 100) to see if the characteristics of the trial predict the outcomes significantly.

I've done a lot of reading e.g http://www.metafor-project.org/doku.php/tips:regression_with_rma but my problem is all the examples of meta-regression seem to treat each 'row' equally, when of course they should be weighted by n.

I was wondering if it would be valid to supply my predictors in question merely via the mods argument and otherwise performing the analysis as I did for the meta-analysis, e.g.:

model_2 <- rma(measure="PLO", xi=x, ni=n, data=df, mods=~predictor1 + predictor2 + predictor3)


If I do I end up with something like:

Mixed-Effects Model (k = 60; tau^2 estimator: REML)

tau^2 (estimated amount of residual heterogeneity):     0.3651 (SE = 0.0908)
tau (square root of estimated tau^2 value):             0.6042
I^2 (residual heterogeneity / unaccounted variability): 81.40%
H^2 (unaccounted variability / sampling variability):   5.38
R^2 (amount of heterogeneity accounted for):            0.00%

Test for Residual Heterogeneity:
QE(df = 57) = 311.1484, p-val < .0001

Test of Moderators (coefficient(s) 2,3):
QM(df = 2) = 0.2739, p-val = 0.8720

Model Results:

estimate      se     zval    pval    ci.lb   ci.ub
intrcpt                  1.1155  0.2997   3.7220  0.0002   0.5281  1.7030  ***
predictor1               0.0974  0.2763   0.3525  0.7244  -0.4441  0.6390
predictor2              -0.0818  0.2085  -0.3923  0.6949  -0.4905  0.3269


1) Is this the appropriate way of doing this?

2) Also, when I used to do patient-level multivariate regression, my practice was to include variables in the multivariate analysis if they were significant on univariate analysis; is this standard practice for my example, too? As in should I supply them individually as single mods=~predictor and look for significance before including them in a model?

Thank you