# [R-meta] Meta-analysis in R when there is no sampling variances

Viechtbauer Wolfgang (SP) wolfgang.viechtbauer at maastrichtuniversity.nl
Fri Jun 30 17:54:41 CEST 2017

```Dear Resham,

What kind of outcome/effect size measure are you dealing with? I will venture a guess and assume you are dealing with (log-transformed) ratios of means. The actual sampling variance is then computed with:

vi = sd1i^2/(n1i*m1i^2) + sd2i^2/(n2i*m2i^2)

where m1i and m2i are the means of the first and second group, sd1i and sd2i are the SDs, and n1i and n2i are the group sizes. And the problem is that the SDs are not known (but you do know the means -- as otherwise you would not be able to compute the outcomes in the first place -- and you do know the group sizes).

Here are some thoughts:

Note that the sampling variance can also be written as:

vi = cv1i^2 / n1i + cv2i^2 / n2i

where cv1i and cv2i are the coefficient of variation for the first and second group. Maybe you could make an educated guess how large the CVs are and use that as a rough approximation to the actual sampling variances. Some people have used:

vi = 1 / n1i + 1 / n2i

which actually just implies that we assume that the CVs = 1 within each group.

Then fit the model as usual (e.g., rma(yi, vi) where yi are the log-transformed ratios of means and vi the approximate variances). Then you could follow this up with bootstrapping. Code for this can be found here: http://www.metafor-project.org/doku.php/tips:bootstrapping_with_ma

And/or you could consider using robust estimates of the standard errors for the fixed effects. That can be done using the robust() function (see help(robust) for details).

Best,
Wolfgang

--
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Thapa, Resham - ARS
Sent: Friday, June 30, 2017 17:10
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] Meta-analysis in R when there is no sampling variances

Dear All,

I am conducting a meta-analysis in environmental research. Most of the literatures in my search did not report sufficient information to calculate sampling variances.  I have also seen meta-analysis conducted in my area of research with similar issues; they performed non-parametric bootstrapping procedure to calculate bootstrapped CIs for the weighted effect size. In these papers, they used Metawin software to weight individual effect size following Adams et al., 1997. Resampling tests for meta-analysis for ecological data. Ecology 78(5):1277-1283; where weights (wi) is given as:

Wi=(Nt*Nc)/(Nt+Nc); where Nt and Nc are replicates for treatment and control groups.

I want to use R and perform meta-analysis by following similar approach. Any helps and suggestions will be highly appreciated.

Thanks'
Resham

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