[R-meta] Performing a multilevel meta-analysis

Fernando Klitzke Borszcz |ern@ndobor@zcz @end|ng |rom gm@||@com
Mon Aug 17 23:05:36 CEST 2020

Dear Tzlil,

The SEM is a standard deviation of the change between trials/tests. Two
previous meta-analyses analyzed this type of effect using the SAS software.
(see Hopkins WG, Schabort EJ, Hawley JA. Reliability of power in physical
performance tests. Sport Med. 2001;31:211–34. and Gore CJ, Hopkins WG,
Burge CM. Errors of measurement for blood volume parameters: a
meta-analysis. J Appl Physiol. 2005;99:1745–58).

As SEM is an SD, I suggest analyze it with a logarithmic transformation
(SDLN escalc function in metafor;
https://rdrr.io/cran/metafor/man/escalc.html) discussed in Nakagawa et al. (
equations 7 and 8.

Best regards.

Em seg., 17 de ago. de 2020 às 17:43, Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> escreveu:

> Dear Tzlil,
> Just to let you know (so you don't keep waiting for a response from me): I
> have no suggestions for how one would meta-analyze such values.
> Best,
> Wolfgang
> >-----Original Message-----
> >From: Tzlil Shushan [mailto:tzlil21092 using gmail.com]
> >Sent: Saturday, 15 August, 2020 5:10
> >To: Viechtbauer, Wolfgang (SP)
> >Cc: r-sig-meta-analysis using r-project.org
> >Subject: Re: [R-meta] Performing a multilevel meta-analysis
> >
> >Dear Wolfgang,
> >
> >First, thank you so much for the quick response and the time you dedicate
> to
> >my questions. And yes, I looked on the mailing list and have seen some
> >meaningful discussions around some of my questions. Based on the
> readings, I
> >assume that an extension of my multilevel model with robust variance
> >inference is a good idea.
> >
> >However, I still would like to give a chance to the second question I had
> >and I'll try to be more specific this time. I hope you (or others in this
> >group) can help me with that.
> >
> >One of the effect sizes in the meta-analysis is the 'standard error of
> >measurement' (SEM) of heart rate from a test-retest (reliability)
> >assessment. Simply described, this assessment was performed twice on a
> >matched group and I'm interested in the variability of this measure. This
> >effect size is derived from the pooled standard deviation (mean
> test-retest
> >SD) and intraclass correlation (ICC) of a test-retest. For example, if the
> >mean ± SD of test one is 80.0 ± 4.0 and test two is 80.5 ± 4.8, and
> >intraclass correlation is 0.95, the SEM will be 4.4*√(1-0.95)= 0.98.
> >Practically, this effect size is a form of SD value.
> >
> >I'm aware of the fact that the first thing that I probably should do if I
> >want to use metafor package is to convert these values into coefficient of
> >variation (CV%). However, because the outcome measure (heart rate) is
> >already calculated in percentages values (% of heart rate maximum), we'd
> >like to meta-analyse the SEM in the original raw values. Further, using
> this
> >effect size is important for having practical implications in the paper.
> >
> >I've seen some discussion in the mailing
> >list https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-
> >May/000828.html?fbclid=IwAR2dSpruCCqlk631VKBAflkibrD8Gke-
> >9sSGgMHxG4TtY_ocZX1IsZCPlI0 on CV% from matched groups
> >with escalc(measure="CVRC", y = logCV_1 - logCV_2). However, I'd like to
> >know if there is a way to fit the escalc equation to the SEM values (which
> >is only one value from each paired test)? or alternatively, if there are
> >other approaches I should consider?
> >
> >Kind regards,
> >
> >Tzlil Shushan | Sport Scientist, Physical Preparation Coach
> >
> >BEd Physical Education and Exercise Science
> >MSc Exercise Science - High Performance Sports: Strength &
> >Conditioning, CSCS
> >PhD Candidate Human Performance Science & Sports Analytics
> >
> >‫בתאריך יום ד׳, 12 באוג׳ 2020 ב-4:46 מאת ‪Viechtbauer, Wolfgang (SP)‬‏
> ><‪wolfgang.viechtbauer using maastrichtuniversity.nl‬‏>:‬
> >Dear Tzlil,
> >
> >Your questions are a bit too general for me to give meaningful answers.
> >Also, some of your questions (with regard to modeling dependent effects
> and
> >using cluster robust methods) have been extensively discussed on this
> >mailing list, so no need to repeat all of that. But yes, if you use
> cluster
> >robust inference methods, I would use them not just for the 'overall
> model'
> >but also for models including moderators.
> >
> >Best,
> >Wolfgang
> >
> >>-----Original Message-----
> >>From: Tzlil Shushan [mailto:tzlil21092 using gmail.com]
> >>Sent: Thursday, 06 August, 2020 16:05
> >>To: Viechtbauer, Wolfgang (SP)
> >>Cc: r-sig-meta-analysis using r-project.org
> >>Subject: Re: [R-meta] Performing a multilevel meta-analysis
> >>
> >>Dear Wolfgang,
> >>
> >>Thanks for your quick reply and sorry in advance for the long ‘assay’..
> >>
> >>It is probably be better if I give an overview on my analysis.
> Generally, I
> >>employ meta-analysis on the reliability and validity of heart rate
> response
> >>during sub-maximal assessments. We were able to compute three different
> >>effect sizes reflects reliability; mean differences, ICC and standard
> error
> >>of measurement of test-retest design, while for validity, we computer
> >>correlation coefficient between heart rate values and maximal aerobic
> >>fitness.
> >>
> >>Since both measurement properties (i.e reliability/validity) of heart
> rate
> >>can be analysed from different intensities during the assessment (for
> >>example, 70, 80 and 90% from heart rate maximum), different modalities of
> >>tests (e.g running, cycling), and multiple time points across the year
> >(e.g.
> >>before season, in-season), one sample can have more than one effect size.
> >>
> >>I decided to employ three level meta-analysis, while level two and three
> >>pertaining to within and between samples variance, respectively. Then,
> >>include moderators effect within and between samples).
> >>
> >>Regarding the weights, the only reason I wonder if I need to adjust them
> is
> >>because the wide range of effect sizes per sample (1-4 per sample) and
> >>thought to use the approach you discussed in your recent post here.
> >>http://www.metafor-project.org/doku.php/tips:weights_in_rma.mv_models
> >>
> >>However, as I understand the default W in rma.mv will work quite well?
> >>
> >>With regards to the above (i.e multiple effect sizes for samples), I
> >>consider to add robust cluster test to get more accurate standard error
> >>values. As I understand, it may be a good option to control for the
> natural
> >>(unknown) correlations between effect sizes from the same sample.
> >>First, do you think it is necessary? If so, would you apply cluster test
> >>just to the overall model or for additional models including moderators.
> >>Second, Is it reasonable to report the results obtained from the
> multilevel
> >>and cluster analyses in the paper?
> >>Of note, my dataset isn’t large and includes between 15-20 samples
> >>(clusters) while around 50-60% have multiple effect sizes.
> >>
> >>With regards to the second question in the original email, we computer
> the
> >>standard error of measurement (usually attained from pooled SD of test-
> >>retest multiply the square root of 1-icc). Practically, these effect
> sizes
> >>are sd values. I haven’t seen enough meta-analysis studies using standard
> >>error of measurement as effect size and I speculate if you can suggest me
> >>what would be a decent approach for this?
> >>
> >>Cheers,
> >>
> >>On Thu, 6 Aug 2020 at 22:30, Viechtbauer, Wolfgang (SP)
> >><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> >>Dear Tzlil,
> >>
> >>Unless you have good reasons to do so, do not use custom weights. rma.mv
> ()
> >>uses weights and the default ones are usually fine.
> >>
> >>weights(res, type="rowsum") will only (currently) work in the 'devel'
> >>version of metafor, which you can install as described here:
> >>
> >>https://wviechtb.github.io/metafor/#installation
> >>
> >>I can't really comment on the second question, because answering this
> would
> >>require knowing all details of what is being computed/reported.
> >>
> >>As for the last question ("is there a straightforward way in metafor to
> >>specify the analysis with Chi-square values"): No, chi-square values are
> >>test statistics, not an effect size / outcome measure, so they cannot be
> >>used for a meta-analysis (at least not with metafor).
> >>
> >>Best,
> >>Wolfgang
> >>
> >>>-----Original Message-----
> >>>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-
> >>project.org]
> >>>On Behalf Of Tzlil Shushan
> >>>Sent: Wednesday, 05 August, 2020 5:45
> >>>To: r-sig-meta-analysis using r-project.org
> >>>Subject: [R-meta] Performing a multilevel meta-analysis
> >>>
> >>>Hi R legends!
> >>>
> >>>My name is Tzlil and I'm a PhD candidate in Sport Science - Human
> >>>performance science and sports analytics
> >>>
> >>>I'm currently working on a  multilevel meta-analysis using the metafor
> >>>package.
> >>>
> >>>My first question is around the methods used to assign weights within
> >>rma.mv
> >>>models.
> >>>
> >>>I'd like to know if there is a conventional or 'most conservative'
> >approach
> >>>to continue with. Since I haven't found a consistent methodology within
> >the
> >>>multilevel meta-analyses papers I read, I originally applied a weight
> >which
> >>>pertains to variance (vi) and number of effect sizes from the same
> study.
> >I
> >>>found this method in a lecture by Joshua R. Polanin
> >>>https://www.youtube.com/watch?v=rJjeRRf23L8&t=1719s from 28:00.
> >>>
> >>>W = 1/vi, then divided by the number of ES for a study
> >>>for example, a study with vi = 0.0402 and 2 different ES will weight as
> >>>follow;
> >>>1/0.0402 = 24.88, then 24.88/2 = 12.44 (finally, converting into
> >>>percentages based on the overall weights in the analysis)
> >>>
> >>>After I've read some of the great posts provided in last threads here
> such
> >>>as;
> >>>http://www.metafor-project.org/doku.php/tips:weights_in_rma.mv_models
> and
> >>>https://www.jepusto.com/weighting-in-multivariate-meta-analysis/
> >>>I wonder if it is not correct and I need to modify the way I use weights
> >in
> >>>my model..
> >>>
> >>>For some reason, I tried to imitate the approach used in the first link
> >>>above. However, for some reason I get an error every time I tried to
> >>>specify weights(res, type="rowsum") *Error in match.arg(type,
> >c("diagonal",
> >>>"matrix")) : 'arg' should be one of “diagonal”, “matrix”*
> >>>
> >>>My second question is related to the way I meta-analyse a specific ES.
> My
> >>>meta-analysis involves the reliability and convergent validity of heart
> >>>rate during a specific task, which is measured in relative values (i.e.
> >>>percentages). Therefore, my meta-analysis includes four different ESs
> >>>parameters (mean difference; MD, interclass correlation; ICC, standard
> >>>error of measurement; SEM, and correlation coefficient; r).
> >>>
> >>>I wonder how I need to use SEM before starting the analysis. I've seen
> >some
> >>>papers which squared and log transformed the SEM before performing a
> >>>meta-analysis, while others converted the SEM into CV%. Due to the
> >original
> >>>scale of our ES (which is already in percentages) I'd like to perform
> the
> >>>analysis without converting it into CV% values. Should I use the SEM as
> >the
> >>>reported values? only log transformed it? Further, is there a
> >>>straightforward way  in metafor to specify the analysis with Chi-square
> >>>values (as "ZCOR" in correlations)?
> >>>
> >>>Thanks in advance!
> >>>
> >>>Kind regards,
> >>>
> >>>Tzlil Shushan | Sport Scientist, Physical Preparation Coach
> >>>
> >>>BEd Physical Education and Exercise Science
> >>>MSc Exercise Science - High Performance Sports: Strength &
> >>>Conditioning, CSCS
> >>>PhD Candidate Human Performance Science & Sports Analytics
> _______________________________________________
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> R-sig-meta-analysis using r-project.org
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