[R-meta] Meta-analysis of differences in variances from cross-over trials

Viechtbauer, Wolfgang (NP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Wed Feb 22 13:44:48 CET 2023

Dear Lorenzo,

There are two issues here:

1) The type of outcome measure

If you want to focus on the variances (and not CVs), then why not use the (log transformed) variability ratio (measure="VR" in escalc())? The pooled effect can then be back-transformed via exponentiation and then squaring (predict(..., transf=function(x) exp(x)^2)), yielding an estimate of the ratio of the variances under the two conditions.

2) Cross-over trials

The difficulty here is that the variance in condition 1 and the variance in condition 2 is obtained from the same individuals. For this, you could use measure="VRC" but then you need to supply the correlation between the measurements under the two conditions. If this is unknown (presumably), then you will have to use a guestimate thereof.

Search for "VRC" in:


for more details on this measure.


>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Lorenzo Lolli via R-sig-meta-analysis
>Sent: Tuesday, 21 February, 2023 18:23
>To: r-sig-meta-analysis using r-project.org
>Cc: Lorenzo Lolli
>Subject: [R-meta] Meta-analysis of differences in variances from cross-over
>Dear Wolfgang,
>I’m contacting you given your recent work relevant to formal systematic review
>and meta-analysis of cross-over trials.
>In particular, I'm interested in the meta-analysis of differences in variances
>from cross-over trials since the summary of these estimates can inform future
>sample size justifications relevant to future applied studies aiming to
>investigate the value of nutritional supplements to support recovery in elite
>Given your seminal work in this area, I’m contacting you with particular
>reference to your recent paper in this field “Senior AM, Viechtbauer W, Nakagawa
>S. Revisiting and expanding the meta-analysis of variation: The log coefficient
>of variation ratio. Res Synth Methods. 2020 Jul;11(4):553-567. doi:
>10.1002/jrsm.1423.”. While I’m aware of the procedures available in metafor, the
>details in the script you provided as a supplement of the full paper you co-
>authored, and your sensible points on the value of deriving the log coefficient
>of variation ratio, my colleagues and I would be interested in deriving
>differences in variances expressed in original units of measurements from the
>meta-analysis of cross-over trials.
>As an example, we refer to pursuing an approach similar to what illustrated in
>Figure 2 (mid-panel) in “Mills HL, Higgins JPT, Morris RW, Kessler D, Heron J,
>Wiles N, Davey Smith G, Tilling K. Detecting Heterogeneity of Intervention
>Effects Using Analysis and Meta-analysis of Differences in Variance Between Trial
>Arms. Epidemiology. 2021 Nov 1;32(6):846-854. doi: 10.1097
>EDE.0000000000001401.”. Of course, we’re aware what illustrated by Mills and
>colleagues is incorrect for the summary of effects from cross-over studies and
>applicable to conventional parallel-arm, randomised controlled trials only.
>Accordingly, what would be your advice for deriving differences in variances
>expressed in original units of measurements using, for example, procedures
>available in state-of-the-art packages such as metafor?
>Many thanks for taking your time in this exchange.

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