[R-meta] Multivariate meta-analysis when "some studies" are multi-outcome

I wouldn't think of dependence in sampling errors arising from 'levels'.
It arises whenever multiple estimates are computed with some kind of
overlap (or even total overlap) in the subjects being used for the
computations.

For example, the exact same n subjects are used to compute estimates 1 and
2 for two different response variables. Or the exact same n subjects are
used to compute estimates 1 and 2 for two different follow-up timepoints.
Or two estimates are computed, one contrasting treatment group 1 with the
control group and the other contrasting treatment group 2 with the control
group (then there is overlap due reuse of the control group). One can also
have all kinds of combinations of these things.

Of course, the degree of dependence depends on various things: How much
overlap is there in the subjects? How strongly are two different response
variables correlated? How much does the same response variable correlate
over time? Also, the source of the dependence leads to different equations
that can be used to estimate the correlation between the sampling errors of
non-independent estimates.

But the bottom line is: If at least one subject is involved in the
computation of two different estimates, then the sampling errors of the two
estimates are (probably) not independent.

Best,
Wolfgang

-----Original Message-----
From: Simon Harmel [mailto:sim.harmel at gmail.com]
Sent: Thursday, 18 March, 2021 13:26
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] Multivariate meta-analysis when "some studies" are

multi-

outcome

Sure, but imagine we have dependence due to the use of multiple

treatments from

the same study (esid), due to the use of multiple outcomes (outcomeid),

and

finally due to the heterogeneity among studies (studyid).

So, here dependence is arising "simultaneously" due to all three levels.

So how

should one define cluster id in 'impute_covariance_matrix()'?

Best,
Simon

On Thu, Mar 18, 2021, 7:12 AM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
Whether this makes sense or not depends on how we believe covariances

among the

sampling errors are arising. Two estimates from the same study based on

the same

sample of subjects (e.g., based on two different response variables)

probably have

correlated sampling errors. Two estimates from the same study, one for

female, the

other for male participants, not (the underlying true effects may still be
correlated). So, the 'cluster' variable should be specified accordingly

(i.e.,

same levels for the two estimates in the first case, different levels for

the two

estimates in the second case; i.e., 1, 1, 2, 3).

-----Original Message-----
From: Simon Harmel [mailto:sim.harmel at gmail.com]
Sent: Thursday, 18 March, 2021 12:53
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] Multivariate meta-analysis when "some studies" are

multi-

outcome

Dear Wolfgang,

Many thanks for your response. The reason I asked which level of

dependence does

V

matrix account for was that I realized (at least when using
'impute_covariance_matrix()' function) that always the highest cluster

level

(e.g., study_id rather than outcome_id or es_id) is used to construct

the V

matrix.

So, is there a reason for that?

Many thanks

On Thu, Mar 18, 2021, 6:38 AM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
Dear Simon,

Roughly, whatever you put into 'random' accounts for heterogeneity in

the true

effects (at possibly multiple levels) and can account for possible

dependencies

in

these true effects. Whatever you put into V accounts for the sampling

variances

in

the estimates or more precisely, their sampling errors, and can account

for

possible dependencies in these sampling errors.

I use the term 'dependencies' in a very vague/broad sense here, since

such

dependencies (in the true effects and/or the sampling errors) can arise

for all

kinds of different reasons.

Best,
Wolfgang

-----Original Message-----
From: Simon Harmel [mailto:sim.harmel at gmail.com]
Sent: Wednesday, 17 March, 2021 18:01
To: Viechtbauer, Wolfgang (SP)
Cc: Gladys Barragan-Jason; R meta
Subject: Re: [R-meta] Multivariate meta-analysis when "some studies"

are multi-

outcome

Dear Wolfgang,

I do want to quickly follow-up on the answer you linked
(

https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-July/000896.html).

In `rma.mv(y ~ x1 + x2, V, random = ~ 1 | study/outcome/id,

data=data)`, we

apparently take into account dependence among effect sizes due to

multiple

treatments (`id`), and multiple outcomes (`outcome`) by means of using

a level

for

each.

If so, what is the role of `V` when it comes to accounting for effect
size dependency? Does `V` simply determine the pair-wise structure of

effect

size

dependency? If yes, at what level?

Simon