[R-meta] Question about Meta analysis

In study 3, there is just a single row. Just to be clear: You are referring to a 'test-retest r = 0.9' but this has no bearing on the sampling variance in V. If it is a within-study design, the computation of its sampling variance already should have been done in such a way that any pre-post correlation is accounted for.

I am trying to understand your coding for study 4 ("Within-study with one control and two intervention conditions"), which you coded as follows:
  studyid esid design subgroup type time1 time2 grp1 grp2  ne nc  yi   vi
5        4    5      2        1    1     1     2    e    c  40 40 0.5 0.05
6        4    6      2        1    1     1     3    e    c  40 40 0.6 0.05
But this coding implies that there are two independent groups, e and c, where e was measured at time point 1 and c at time points 2 and 3. I am not sure if I really understand this design.

For study 6, your coding is:
  studyid esid design subgroup type time1 time2 grp1 grp2  ne nc  yi   vi
11       6   11      2        1    1     1     2    c    c  90 90 1.1 0.05
12       6   12      2        1    2     1     2    c    c  90 90 1.2 0.05

But I think the coding should be:
  studyid esid design subgroup type time1 time2 grp1 grp2  ne nc  yi   vi
11       6   11      2        1    1     1     2    e    e  90 90 1.1 0.05
12       6   12      2        1    2     1     2    e    e  90 90 1.2 0.05

In study 5, there are two subgroups. Since there is (presumably) no overlap of subjects across subgroups, the sampling errors across subgroups are independent, so we just have two cases of what we have in study 2.

I recently added measure "SMCRP" to escalc(). This uses the pooled SD from pre and post to standardize the difference.

Am 06.05.2024 um 13:53 schrieb Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>:

Dear Max,

Please see below for my responses.

Best,
Wolfgang

-----Original Message-----
From: Maximilian Steininger <maximilian.steininger at univie.ac.at>
Sent: Friday, April 26, 2024 16:05
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-
project.org>; Viechtbauer, Wolfgang (NP)
<wolfgang.viechtbauer at maastrichtuniversity.nl>
Subject: Re: [R-meta] Question about Meta analysis

Dear Wolfgang,

Thank you very much for your detailed reply. I also wanted to take the
opportunity to thank you for your extremely well-documented resources. They are
enormously helpful.

Thanks for the kind feedback.

Indeed, creating the V matrix is not trivial, but your examples are a great
guide. If it's not too much to ask (if it is, nevermind!) I would appreciate
feedback on my approach. Here is an exemplary structure from my data, which
captures all of the dependencies that I have in my real dataset.

Study 1: Between-study with one intervention and one control group.
Study 2: Between-study with two interventions and one control group.
Study 3: Within-study with one control and one intervention condition (assumed
test-retest r = 0.9).
Study 4: Within-study with one control and two intervention conditions (assumed
test-retest r = 0.9).
Study 5: Between-study with two experiments, each containing two interventions
and one control group.
Study 6: Within-study in which two different (low correlation, r= .1) dependent
variables were used (assumed test-retest r = 0.9).

This is the (made-up) data set:

studyid = c(1,rep(2,2),3,rep(4,2),rep(5,4),rep(6,2))
esid = c(1:12)
design = c(rep(1,3), rep(2,3), rep(1,4), rep(2,2))
subgroup = c(rep(1,8), rep(2,2), rep(1,2))
type = c(rep(1,11),2)
time1 = rep(1,12)
time2 = c(rep(1,3), rep(2,2), 3, rep(1,4), rep(2,2))
grp1 = c("e","e1","e2","e","e","e","e1","e2","e1","e2","e","e")
grp2 = rep("c",12)
ne = c(10,15,20,30,40,40,45,50,80,100,90,90)
nc = c(11,16,16,30,40,40,46,46,61,61,90,90)
yi = seq(0.1, 1.2, by = 0.1)
vi = rep(0.05, 12)
dat = cbind.data.frame(studyid, esid, design, subgroup, type, time1, time2,
grp1, grp2, ne, nc, yi, vi)

This would be my V matrix:

V = vcalc(vi=vi, cluster = studyid, subgroup = subgroup, type = type, time1 =
time1, time2 = time2, grp1 = grp1, grp2 = grp2, w1 = nc, w2 = ne, rho = 0.1, phi
= 0.9, data = dat)

Thanks for the reproducible example. I had a look:

blsplit(V, dat$studyid)
blsplit(V, dat$studyid, cov2cor)

So, study 1 is just a single row and its sampling variance is as given (0.05).

In study 2 the correlation between the two effects should be around 0.5ish (it would be exactly 0.5 if you had not specified w1 and w2) due to a shared control group.

In study 3, there is just a single row. Just to be clear: You are referring to a 'test-retest r = 0.9' but this has no bearing on the sampling variance in V. If it is a within-study design, the computation of its sampling variance already should have been done in such a way that any pre-post correlation is accounted for.

I am trying to understand your coding for study 4 ("Within-study with one control and two intervention conditions"), which you coded as follows:

  studyid esid design subgroup type time1 time2 grp1 grp2  ne nc  yi   vi
5        4    5      2        1    1     1     2    e    c  40 40 0.5 0.05
6        4    6      2        1    1     1     3    e    c  40 40 0.6 0.05

But this coding implies that there are two independent groups, e and c, where e was measured at time point 1 and c at time points 2 and 3. I am not sure if I really understand this design.

In study 5, there are two subgroups. Since there is (presumably) no overlap of subjects across subgroups, the sampling errors across subgroups are independent, so we just have two cases of what we have in study 2.

For study 6, your coding is:

  studyid esid design subgroup type time1 time2 grp1 grp2  ne nc  yi   vi
11       6   11      2        1    1     1     2    c    c  90 90 1.1 0.05
12       6   12      2        1    2     1     2    c    c  90 90 1.2 0.05

But I think the coding should be:

  studyid esid design subgroup type time1 time2 grp1 grp2  ne nc  yi   vi
11       6   11      2        1    1     1     2    e    e  90 90 1.1 0.05
12       6   12      2        1    2     1     2    e    e  90 90 1.2 0.05

although this makes no difference to V. Note that r = 0.9 is again irrelevant here, but for a different reason since it happens to cancel out in the computation of the covariance.

And this is how I would specify the meta-analytic model:

res <- rma.mv(yi, V, random = ~ 1 | studyid/esid, data=dat)

What still puzzles me about the V matrix is why no dependence for study 5
between experiment 1 and experiment 2 is modeled (which might be unnecessary
because this is taken care of by the random effect structure of three-level
model?) and why the correlation of the effects in study 4 is 0.95 and not equal
to my specification of phi = 0.9.

See above.

I also have a follow-up question regarding the use of SMD with raw score
standardization. Calculating SMD for within-designs based on the raw-score
metric, as suggested by Becker (1988), induces the problem that most within-
studies use a counterbalanced design, and therefore there is no clear SDpre. Can
this be ignored, or how should one best deal with it?

I recently added measure "SMCRP" to escalc(). This uses the pooled SD from pre and post to standardize the difference.

Thank you very much for your support. If it is too tedious to answer all my
questions, please just ignore them.

Best,
Max

Am 23.04.2024 um 11:11 schrieb Viechtbauer, Wolfgang (NP)

<wolfgang.viechtbauer at maastrichtuniversity.nl>:

Ah, now I get it. Then let me answer your other post here and maybe this will

be of use to all.

As noted in my answer to Sevilay, this part of the metafor documentation is

relevant:

https://wviechtb.github.io/metafor/reference/misc-recs.html#general-workflow-

for-meta-analyses-involving-complex-dependency-structures

This is in essence your Q1, and yes, this is good practice. Not sure if this

is 'best' practice. In general, how such complex cases should be handled depends
on many factors.

Not sure what distinction you are making between this approach and the use of

multivariate meta-analysis (combined with RVE), since the three-level model can
also be seen as a multivariate meta-analysis, as discussed in these examples:

https://www.metafor-project.org/doku.php/analyses:konstantopoulos2011
https://www.metafor-project.org/doku.php/analyses:crede2010

A major challenge in cases where there is sampling error dependency is the

construction of the V matrix. Many will not even attempt this and will rely on /
hope that RVE fixes up the standard errors of the fixed effects. Roughly, this
is at least asymptotically true as long as the cluster variable used in RVE
encompasses estimates that are potentially dependent (due to whatever reason).
In principle, the vcalc() function can handle quite a number of different types
of dependencies for constructing the V matrix, but I even struggle at times
trying to make it fit to a particular case. For example, this example shows this
so some extent:

https://wviechtb.github.io/metadat/reference/dat.knapp2017.html

The other challenge is the choice of the random effects. Often, people just

use a 'simple' three-level model, but more complex structures are certainly
possible and may provide a better reflection of the depedency structure. An
example where we did not use a V matrix (which would have been hopelessly
complex) but used a more complex random effects structure is this:

https://wviechtb.github.io/metadat/reference/dat.mccurdy2020.html

With respect to your other questions:

Q2) Yes, I would say the test-retest reliability can be a decent proxy for

estimating the correlation between estimates that are obtained at multiple time
points (assuming that the time lags are similar).

Q3) As you note, the pre-post correlation is needed to correctly compute the

sampling variance of a standardized mean change (with raw score
standardization). That's a different issue than using a correlation coefficient
to account for the dependency between two such effect sizes. So no, you are not
being overly conservatively in doing so.

Q4) You do not need to 'correct' the control / common comparator group sample

size when you account for the dependency via their covariance in the V matrix.

Q5) Hard to say without digging into the details of your data. But again, the

three-level model *is* already a particular type of multivariate model. This
aside, yes, these two ideas -- that there are multiple levels plus multiple
types of outcomes -- can certainly be combined.

In general, I would say you are asking the right questions and are on the

right track, but it is hard to say more without further details.

Best,
Wolfgang

-----Original Message-----
From: Maximilian Steininger <maximilian.steininger at univie.ac.at>
Sent: Tuesday, April 23, 2024 10:16
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-
project.org>
Cc: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Subject: Re: [R-meta] Question about Meta analysis

Dear Wolfgang, dear Selivay,

I think Selivay was referring to my longer message from a few days ago (see
below). However, as I am only just starting to familiarise myself with the
method, I am unfortunately unable to provide Selivay with any

conclusive/helpful

answers.

I had hoped that my open questions from back then might still be answered,

but

perhaps they are too obvious or uninformed (or simply too long) and can be
answered with more literature research by myself.

Many thanks in any case for the link Wolfgang.

@Selivay: You can write me a direct message via
maximilian.steininger at univie.ac.at , then I can share you a detailed list of

all

the resources I used.

Best,
Max

Am 16.04.2024 um 17:47 schrieb Maximilian Steininger via R-sig-meta-analysis

<r-sig-meta-analysis at r-project.org>:

Dear all,

First of all, thank you for this mailing list and the work that has gone

into

the responses and the materials linked so far.

I have tried to use the previous answers to solve my specific problem, but I

am unsure if my conclusion is correct and appropriate and would appreciate
further feedback.

I am a PhD student ? so relatively unexperienced ? currently running a

systematic review and meta-analysis for the first time. My meta-analysis
includes several studies (60 studies; with overall 99 effects), that all use

the

same dependent variable, but that have different designs and thus different
forms of dependencies. I have three types of studies:

a) Between-participant designs comparing one (or more) intervention group to

a

control group.

b) Within-participant designs comparing one (or more) condition to a control

condition.

c) Pre-Post control group designs comparing one (or more) intervention group

(tested pre- and post-intervention) to a control group (also tested pre- and
post-control).

As indicated above, there are studies that report more than one effect.

Hence,

there is effect-size dependency and/or sampling error dependency. Some

studies

have multiple intervention groups, some studies have multiple comparison

groups

and the within studies (b) have ?multiple follow-up times? meaning that each
participant is tested multiple times on the same outcome. I am a bit confused

on

how to best model these dependencies, since I came across several approaches.

Initially I wanted to run a multilevel (three-level) meta-analysis with

participants (level 1) nested within outcomes (level 2) nested within studies
(level 3). However, reading through the archives of this group I figured that
this model does not appropriately deal with sampling error dependency.

To deal with this I came across the solution to construct a "working"

variance-covariance matrix and input it into my three-level meta-analysis

model

(using e.g. this approach https://www.jepusto.com/imputing-covariance-

matrices-

for-multi-variate-meta-analysis/<https://www.jepusto.com/imputing-covariance-
matrices-for-multi-variate-meta-analysis/>). Then I would fit this ?working
model? using metafor and feed it into the clubSadwich package to perform

robust

variance estimation (RVE). Of course I would conduct sensitivity analysis to
check whether feeding different dependencies (i.e. correlation coefficients)
into my variance-covariance matrix makes a difference. Q1) Is this the ?best?
approach to deal with my dependencies?

Alternatively, I came across the approach to use multivariate meta-analysis,

again coupled with constructing a ?working? variance-covariance matrix.

However,

I am unsure whether this makes sense because I don?t have multiple dependent
variables.

Furthermore, I have a couple of questions regarding my dependencies:

Q2) To calculate a ?guestimate? for the variance-covariance matrix I need a

correlation coefficient. As (almost) always none is provided in the original
studies. Would it be a plausible approach to use the test-retest reliability

of

my dependent variable (which is reported in a number of other studies not
included in the analysis) to guess the correlation?

Q3) For my meta-analysis I use the yi and vi values (e.g. effect sizes and

their variance). I calculate these beforehand using the descriptive stats of

my

studies and formulas suggested by Morris & DeShon (2002). For my effect sizes

of

the within- (b) as well as pre-post control group designs (c), I already use

the

test-retest reliability of the dependent variable to estimate the variances

of

these effect sizes. If I now use these ?corrected? effect size variances and

run

the model, would I use this same correlation to compute my variance-

covariance

matrix? Am I not, overly conservatively, ?controlling? for this dependency

then

twice (once in the estimation of the individual variance of the effect sizes

and

once in the model)?

Q4) For between-studies it is suggested to correct the sample size of the

control group (by number of comparisons) if it is compared more than once to

an

intervention. Do I also have to do this if I calculate a variance-covariance
matrix (which should take care of these dependencies already)? Is it enough

to

calculate the variance-covariance matrix and then use a multilevel or
multivariate approach? If it is not enough, do I also have to correct the

sample

size for within-participant designs (b) as well (e.g., all participants

undergo

all conditions, so I must correct N by dividing overall sample size by number

of

conditions)?

Q5) Can I combine multivariate and multilevel models with each other and

would

that be appropriate in my case?

Or is all of this utter nonsense and a completely different approach would

be

the best way to go?

Thank you very much for your time and kindness in helping a newcomer to the

method.

Best and many thanks,
Max