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

[Röver, Christian]

Hi Pier-Alex,

since exact Likelihood-based methods avoiding continuity corrections
and approximations often run into numerical problems with zero event-
counts (see e.g. https://arxiv.org/abs/1807.09037), another option may
be to switch to a Bayesian approach. There is software available (also
implementing "exact" binomial likelihoods instead of normal
approximations), and priors distributions may also be readily
motivated; see e.g. here: https://arxiv.org/abs/1809.04407.

Cheers,

Christian Röver


On Fri, 2018-09-28 at 13:48 +0000, Pier-Alexandre Tardif wrote:
> 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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> 
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