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

[Viechtbauer, Wolfgang (SP)]

Then it would not make sense to compute different tau^2 values for the different levels of outcome and it would not make sense to compute different correlations for the pairs outcome1
outcome2, outcome1-outcome3, and so on, because what 1, 2, 3, ... stand for is essentially arbitrary and these are just numbers to dinstuish multiple outcomes.

Simpler structures would then be applicable. I would suggest to read:

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

And yes, one can also use autocorrelation structures then (not "HAR", but "AR" or "CAR" might be applicable).

Best,
Wolfgang

>-----Original Message-----
>From: Simon Harmel [mailto:sim.harmel using gmail.com]
>Sent: Tuesday, 16 March, 2021 13:46
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: [R-meta] Multivariate meta-analysis when "some studies" are multi-
>outcome
>
>Dear Wolfgang,
>
>Thank you very much. You mentioned that if "outcome '1' stands for the same thing
>across all studies), then one could also consider using an **unstructured** var-
>cov matrix with correlated random effects for outcomes within studies."
>
>So, what if outcome 1 does NOT stand for the same thing across studies? Can we
>still use some kind of autocorrelation structure?
>
>To be clear, what if all outcomes within a study are related, and by virtue of
>being a meta-analysis also relate across the studies, but their indecis may not
>represent the same thing across the studies (would this be a cross-classified
>case?)
>
>Many thanks,
>Simon
>
>On Tue, Mar 16, 2021, 5:23 AM Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>Dear Simon,
>
>At the very least, you should add random effects at the level of the studies and
>at the level of the estimates, so:
>
>dat$estid <- 1:nrow(dat)
>
>and then
>
>random = ~ 1 | id / estid
>
>For longitudinal data, one could also consider using some kind of autocorrelation
>structure for the estimates within studies. There are some examples here:
>
>https://wviechtb.github.io/metafor/reference/dat.ishak2007.html
>https://wviechtb.github.io/metafor/reference/dat.fine1993.html
>
>clubSandwich::impute_covariance_matrix() also allows for the construction of a V
>matrix with an autocorrelation structure.
>
>If the different outcomes are meaningfully related across studies (i.e., outcome
>'1' stands for the same thing across all studies), then one could also consider
>using an unstructured var-cov matrix with correlated random effects for outcomes
>within studies. This would be akin to:
>
>https://www.metafor-project.org/doku.php/analyses:berkey1998
>
>Best,
>Wolfgang
>
>>-----Original Message-----
>>From: Simon Harmel [mailto:sim.harmel using gmail.com]
>>Sent: Monday, 15 March, 2021 17:31
>>To: Viechtbauer, Wolfgang (SP)
>>Cc: R meta
>>Subject: Re: [R-meta] Multivariate meta-analysis when "some studies" are multi-
>>outcome
>>
>>Dear Prof. Viechtbauer,
>>
>>Many thanks for your response. I found the following particularly helpful
>>(https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2019-March/001484.html).
>>
>>So, I went from my initial model: `rma.mv(d, V = SE^2, mods = ~factor(outcome)-1,
>>random= ~1|id, data = dat)`
>>to now:
>>
>>`V <- clubSandwich::impute_covariance_matrix(vi = dat$SE^2, cluster = dat$id, r =
>>0.7)`
>>`rma.mv(d, V = V, mods = ~factor(outcome)-1, random= ~1|id, data = dat)`
>>
>>However, what type of dependence is accounted for by the multilevel part (i.e.,
>>`random= ~1|id`), and what type of dependence is accounted for by including the
>>imputed variance-covariance matrix?
>>
>>Specifically, in my data, all primary studies (n=52) are longitudinal, 15 of them
>>are multi-outcome, and almost all are multi-group treatments. Are all of these
>>types of dependence reasonably accounted for?
>>
>>Many thanks for your consideration,
>>Simon
>>
>>On Mon, Mar 15, 2021 at 6:54 AM Viechtbauer, Wolfgang (SP)
>><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>Hi Simon,
>>
>>I would suggest to search/browse the archives, as this kind of question has been
>>discussed at various points in the past. The archives can be found here:
>>
>>https://stat.ethz.ch/pipermail/r-sig-meta-analysis/
>>
>>There is no built-in search functionality for the archives, but one can restrict
>>search engines to conduct searches at particular sites. For example, if you do a
>>google search including
>>
>>site:https://stat.ethz.ch/pipermail/r-sig-meta-analysis/
>>
>>you should only get 'hits' from the mailing list archives. The same should work
>>with DuckDuckGo. Note sure about other engines.
>>
>>Note that search engines index the archives at semi-regular intervals, so the
>most
>>recent posts will not show up this way, but those can be searched manually.
>>
>>Best,
>>Wolfgang
>>
>>>-----Original Message-----
>>>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>>>Behalf Of Simon Harmel
>>>Sent: Saturday, 13 March, 2021 23:53
>>>To: R meta
>>>Subject: [R-meta] Multivariate meta-analysis when "some studies" are multi-
>>outcome
>>>
>>>Dear All,
>>>
>>>I'm conducting a meta-analysis where 15 out of 52 studies have used more
>>>than one outcome variable. In addition, almost all studies include multiple
>>>treatments.
>>>
>>>A shortened version (i.e., without moderators) of our dataset appears below
>>>(`*id`=study id; `d`=effect size; `SE` = standard error; `outcome`=outcome
>>>variable index*).
>>>
>>>I was wondering what would be the appropriate modeling options for such a
>>>situation?
>>>
>>>I appreciate your expertise and consideration,
>>>Simon
>>>
>>>*#-- R data and code:*
>>>dat <- read.csv("https://raw.githubusercontent.com/hkil/m/master/tst.csv")
>>>
>>>library(metafor)
>>>rma.mv(d, V = SE^2, mods = ~factor(outcome)-1, random= ~1|id, data = dat)
>>>## I'm assuming this would be an insufficient model