[R-meta] Performing a multilevel meta-analysis

Tzlil Shushan tz|||21092 @end|ng |rom gm@||@com
Wed Aug 19 13:28:07 CEST 2020

Dear Wolfgang and Fernando,

Woflgang, thanks for letting me know..

Fernando, thanks for your answer, I wanted to have some time working with
"SDLN" function you suggested before commenting again.

I'm familiar with those papers that investigated SEM, thanks for sending
them over. Since you already mentioned the "SDLN" function I have two

1) If I want to proceed with log transformation of SEM effect sizes, Do I
need to specify log() for the yi value? *res <- escalc(measure = "SDLN", yi
= log(sem), vi , data = dat)*?

2) Because it is hard to obtain the sampling variance for each individual
study (some reported CI and some not), What function should I use to
compute the sampling variance? is 1/(n-3) works fine in this case?

If I be able to compute the estimated standard error from individual
studies based on their confidence intervals: (CI upper - CI lower)/3.92 for
95% CI, then specify sei within the escalc function to compute the
variance. Does this approach serve better estimation for the model?

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 ג׳, 18 באוג׳ 2020 ב-7:05 מאת ‪Fernando Klitzke Borszcz‬‏ <‪
fernandoborszcz using gmail.com‬‏>:‬

> 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. (
> https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/2041-210X.12309)
> equations 7 and 8.
> Best regards.
> Fernando
> 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
>> _______________________________________________
>> R-sig-meta-analysis mailing list
>> R-sig-meta-analysis using r-project.org
>> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis

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