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

[Simon Harmel]

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
>

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