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

2 messages · Lorenzo Lolli, Wolfgang Viechtbauer

Original
Lorenzo Lolli
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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 athletes.
 
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.

Lorenzo
Wolfgang Viechtbauer
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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:

https://wviechtb.github.io/metafor/reference/escalc.html

for more details on this measure.

Best,
Wolfgang