# [R-meta] Implementation of the Inverse variance heterogeneity model

James Pustejovsky jepusto at gmail.com
Wed Nov 29 21:01:47 CET 2017

```I was just typing up an email saying the same thing (and using the same
example), but Wolfgang beat me to the punch! So count it as independently
replicated. I would add two things:

1. An alternative to the IVhet method is to use the FE model with robust
variance estimation (Sidik & Jonkman, 2006) to account for between-study
heterogeneity when estimating standard errors. This can be done with the
clubSandwich package (though you'll have to do the scale transformation as
a post-processing step):

### standard FE model
res <- rma(yi, vi, data=dat, method="FE")
library(clubSandwich)
coef_test(res, vcov = "CR2", cluster = dat\$id)

In this example, the robust standard error is *substantially* smaller than
the IVhet standard error. It also has very low degrees of freedom because
of the very unequal weighting of the studies.

2. In the conventional random effects model, the Knapp-Hartung method is
often recommended for testing the average treatment effect:

### standard RE model with Knapp-Hartung
res <- rma(yi, vi, data=dat, method="DL", test = "knha")
predict(res, transf=exp, digits=2)

I don't know if there is research into the relative performance of
Knapp-Hartung with inverse-sampling variance weights (anybody know of work
on this?), but on the face of it, it seems reasonable to generalize based
on its performance under conventional RE models:

### RE model with 1/vi weights ("IVhet")
res <- rma(yi, vi, data=dat, method="DL", weights=1/vi, test = "knha")
predict(res, transf=exp, digits=2)

James

On Wed, Nov 29, 2017 at 1:42 PM, Viechtbauer Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

> Dear Dirk,
>
> What Doi et al. describe are RE models with different weights than the
> default ones.
>
> "AMhet" uses unit weights. The possibility to fit this model was
> implemented in metafor since its first release in 2009. "IVhet" uses
> inverse sampling variance weights. The possibility to fit this model was
> implemented in version 1.9-3 in 2014.
>
> Using the example from Doi et al. (2015):
>
> ##############################
>
> library(metafor)
>
> dat <- get(data(dat.li2007))
> dat <- dat[order(dat\$study),]
> rownames(dat) <- 1:nrow(dat)
> dat <- escalc(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat,
> subset=-c(19,21,22))
>
> ### standard RE model
> res <- rma(yi, vi, data=dat, method="DL")
> predict(res, transf=exp, digits=2)
>
> ### RE model with 1/vi weights ("IVhet")
> res <- rma(yi, vi, data=dat, method="DL", weights=1/vi)
> predict(res, transf=exp, digits=2)
>
> ### RE model with unit weights ("AMhet")
> res <- rma(yi, vi, data=dat, method="DL", weights=1)
> predict(res, transf=exp, digits=2)
>
> ##############################
>
> The results are exactly those reported on 135: "When the meta-analytic
> estimates were computed using the three methods, they were most extreme
> with the AMhet estimator (OR 0.44; 95% CI 0.29-0.66), less extreme with the
> RE estimator (OR 0.71; 95% CI 0.57-0.89) and most conservative with the
> IVhet estimator (OR 1.01; 95% CI 0.71-1.46)."
>
> The idea to fit a RE model with inverse sampling variance weights was
>
> Henmi, M., & Copas, J. B. (2010). Confidence intervals for random effects
> meta-analysis and robustness to publication bias. Statistics in Medicine,
> 29(29), 2969-2983.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-
> bounces at r-project.org] On Behalf Of dirk.richter at upd.unibe.ch
> Sent: Wednesday, 29 November, 2017 17:22
> To: r-sig-meta-analysis at r-project.org
> Subject: [R-meta] Implementation of the Inverse variance heterogeneity
> model
>
> Dear R meta-analysis group,
>
> I was wondering whether there are any plans to implement the Inverse
> variance heterogeneity model (by Doi et al., see reference below) into R MA
> packages or whether this has been done recently (although I couldn't find
> anything on the Web). While the authors of this model have provided with
> MetaXL a free software that allows to run such an analysis, I would be
> happy to have it connected to or implemented into R to have the chance to
> run meta-regressions based on this approach. Currently, there is a only a
> connection to Stata for meta-regressions.
>
> Reference
>
> SA Doi et al. Advances in the meta-analysis of heterogeneous clinical
> trials I: The inverse variance heterogeneity model. Contemp Clin Trials.
> 2015 Nov;45(Pt A):130-8. doi: 10.1016/j.cct.2015.05.009
>
> Thanks,
> Dirk Richter
>
> UNIVERSITÄRE PSYCHIATRISCHE DIENSTE BERN (UPD) AG
> DIREKTION PSYCHIATRISCHE REHABILITATION
>
> Dirk Richter, Dr. phil. habil.
> Leiter Forschung und Entwicklung
> Murtenstrasse 46
> CH-3008 Bern
> Tel. +41 31 632 4707
> Mobil + 41 76 717 5220
> E-Mail: dirk.richter at upd.unibe.ch
> https://www.upd.ch/forschung/psychiatrische-rehabilitation/
>
> University of Bern Psychiatric Services
> Center for Psychiatric Rehabilitation
> Dirk Richter, Dr. phil., PhD
> Head of Research and Development
> Murtenstrasse 46
> CH-3008 Bern
> Switzerland
> Phone +41 31 632 4707
> Mobile Phone +41 76 717 5220
>
> _______________________________________________
> R-sig-meta-analysis mailing list
> R-sig-meta-analysis at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>

[[alternative HTML version deleted]]

```