[R-meta] Performing a multilevel meta-analysis

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 ?s 17:43, Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer at 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 at gmail.com]
Sent: Saturday, 15 August, 2020 5:10
To: Viechtbauer, Wolfgang (SP)
Cc: r-sig-meta-analysis at 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

??????? ??? ??, 12 ????? 2020 ?-4:46 ??? ?Viechtbauer, Wolfgang (SP)??
<?wolfgang.viechtbauer at 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 at gmail.com]
Sent: Thursday, 06 August, 2020 16:05
To: Viechtbauer, Wolfgang (SP)
Cc: r-sig-meta-analysis at 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 at 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 at r-

project.org]

On Behalf Of Tzlil Shushan
Sent: Wednesday, 05 August, 2020 5:45
To: r-sig-meta-analysis at 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