[R-meta] robust variance estimator in meta-analyses of rare events (proportions)

[Pier-Alexandre Tardif]

Dear all,

I'm currently conducting a meta-analysis of proportions of rare events (including studies with zero event). Based on previous literature (see postscript below), it is generally suggested to avoid the following:
[1] continuity corrections;
[2] non-exact distributions;
[3] inverse variance methods to estimate the weights;
[4] fixed-effects models;
[5] not handling the correlation between the mean & variance.

Given the available packages in R (as far as I know), not all could be avoided ([3] remains). The following code is twofold. The lines preceded with �...� are recent additions made by Dr Pustejovksy based on this vignette: https://cran.r-project.org/web/packages/clubSandwich/vignettes/meta-analysis-with-CRVE.html. Lines without �...� are my previous 'standard' meta-analysis of proportions. Since there are a lot of steps following estimating the summary effect sizes + SE (e.g. assessing outliers, heterogeneity, small-study effect, etc.), I would have like to be able to use existing options to deal with these further steps. So here's my question: how could I obtain my back transformed effect size + confidence intervals after having used the robust variance estimator (coef_test)?

ies.da=escalc(xi=cases, ni=total, data=dat, measure="PFT", add=0)  #Solutions [1] and [5] by using a double-arcsine transformation without continuity correction
�...� ies.da$ES_id <- 1:nrow(ies.da) #Creates a unique ID for each effect size
pes.da=rma(yi, vi, data=ies.da, method="REML", level=95) #Solutions [4]
�...� coef_test(pes.da, vcov = "CR2", cluster = ies.da$ES_id) #Sandwich variance estimator is robust to model misspecification (solutions [2]).
pes=predict(pes.da, transf=transf.ipft.hm, targ=list(ni=dat$total)) #Backtransformation of the Freeman-Tukey double arcsine using the harmonic mean
print(pes, digits=5)

Thanks a lot,
Pier-Alex

P.S.
Stijnen (2010) Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data
B�hning (2010) Meta-analysis of clinical trials with rare events
Trikalinos (2013) Simulation-based comparison of methods for meta-analysis of proportions and rates
Kuss (2014) Statistical methods for meta-analysis including information from studies without any events-add nothing to nothing and succeed nevertheless
Ma (2016) Meta-analysis of proportions of rare events-a comparison of exact likelihood methods with robust variance estimation

Also in the Cochrane Handbook: �Methods that should be avoided with the rare events are the inverse-variance methods (including the DerSimonian and Laird random-effects method)�.

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