Emily,
I would offer a couple of suggestions for different ways to approach
this. I think the main question is whether, for the studies with
multiple intervention groups, do you really care (scientifically, with
respect to your research questions) about the distinction between
treatment conditions? If not---if they're really just a nuisance that
you need to find a way to smooth over---then two simple approaches to
handling them might be attractive:
1. Pick the single condition that best represents the treatment
construct of interest.
2. Average the treatment conditions together, and then take the
difference between the averaged treatment condition and the single
control condition. Say that you have treatment conditions q, r, s,
with sample means yq, yr, ys, sample standard deviations sq sr, ss,
and sample sizes nq, nr, ns. Calculate the average sample mean y_avg =
(nq * yq + nr * yr + ns * ys) / (nq + nr + ns). Say the control
condition has sample mean, sd, and size given by yc, sc, and nc. You
can then calculate a d statistic as
d = (y_avg - yc) / sp,
where sp^2 = ((nq - 1) * sq^2 + (nr - 1) * sr^2 + (ns - 1) * ss^2 +
(nc - 1) * sc^2) / (nq + nr + ns + nc - 4)). The variance of d is
(approximately)
Vd = 1 / nq + 1 / nr + 1 / ns + 1 / nc + d^2 / (nq + nr + ns + nc - 4).
You can also use a Hedges-g correction with J(nq + nr + ns + nc - 4),
where J(x) = 1 - 3 / (4 x - 1).
Option (2) will give more precise treatment effects (because of
increased sample size), but might muddy the water (or be harder to
explain in a paper) if the treatment conditions are really distinct.
But if the meta-regression model that you want to estimate does not
make any distinction between the treatment conditions, then option (2)
is actually very close or even identical to the more complex option
described below.
On the other hand, if you really care about the distinctions between
treatment conditions, as you would if the covariates you are examining
have variation within a given study depending on which treatment
condition you're looking at, then you would probably want to
3. Calculate the full sampling variance-covariance matrix of all
combinations of effects and feed this into metafor as part of the V
matrix.
Here's a blog post with the relevant formulas:
http://jepusto.github.io/Correlations-between-SMDs
<http://jepusto.github.io/Correlations-between-SMDs>
Cheers,
James
On Fri, Jun 16, 2017 at 7:46 AM, Emily Finne
<emily.finne at uni-bielefeld.de <mailto:emily.finne at uni-bielefeld.de>>
wrote:
Dear all,
as I am seemingly the first to post a question on this list, I hope my
question is not a silly one.
First of all I'd like to thank Wolfgang Viechtbauer for all the
examples, explanations, and loads of additional online-material
on how
to conduct different kinds of meta-analyses with metafor.
I've already learned a lot so far!
All these bits of code are really helpful and appreciated, since I am
relatively new to working with R (and in doing meta-analysis).
There is, however, one point I am still confused about. I try to
explain
my analysis first and then the question:
I have 30 RCTs matching our inclusion criteria and I use Hedges g as
effect size. The aim is to analyze different intervention techniques
(coded as present or absent) as potential moderators of effect sizes.
All studies included a self-report measure of the outcome, some
additionally reported results for an objective measure of the same
outcome. I would like to include both outcomes in a multivariate
model.
There are also a few studies with multiple treatment groups all
compared
to the same control condition. Since the groups differ in the
techniques
they used and are therefore of interest, information from all
intervention groups should be included.
Initially I wanted to compute two separate univariate models for
the two
outcome measures (subjective and objective), and because of the shared
control groups within some trials I split the sample size of the
controls (with two interventions compared to the same group of, say 40
people, I included two comparions with n=20 each) to avoid double
counting (that's what the Cochrane Handbook recommends in this case).
But after starting to work through the different options, I came
to the
conclusion that the multivariate model would be more appropriate for
this analysis.
So, the model I want to fit looks like this:
library(metafor)
MA1 <- rma.mv <http://rma.mv>(yi=Hedgesg, V, random = ~ Outcome |
trial, struct="UN",
data=datMA, test="t", mods=~Outcome)
or for one overall effect size (because both outcomes did not differ
significantly):
MA2 <- rma.mv <http://rma.mv>(yi=Hedgesg, V, random = ~ Outcome |
trial, struct="UN",
data=datMA, test="t")
for the overall effect and then for the meta-regression model:
MA3 <- rma.mv <http://rma.mv>(yi=Hedgesg, V, random = ~ Outcome |
trial, struct="UN",
data=datMA, test="t", mods=~ technique1)
My model is most similar to the example given here:
http://www.metafor-project.org/doku.php/analyses:berkey1998
<http://www.metafor-project.org/doku.php/analyses:berkey1998>
V is the variance-covariance matrix based on the variances and
estimated
covariances between the effects of both outcome measures within a
study
(as explained in the linked example above).
Trial is the study ID.
BUT besides these 2 outcomes I have these studies with multiple
intervention groups. There is one trial with even 6 effect sizes (2
outcomes * 3 interventions).
I wonder, what to do with the splitting up of control groups now. For
the two outcomes measured within the same persons, I am quite sure
that
I don't have to adjust any sample sizes (i.e., variances), because the
model 'knows' that these outcomes both are from the same persons .
But what about the multiple groups? They are of course also nested
within trials, but I didn't estimate a covariance between these effect
sizes and I did not tell the model anything specific about this
multilevel variant - or did I? (My idea is to additionally use the
robust estimation (with cluster = trial)).
Is it right then to use the original sample size/ variance from the
control groups although some were used in multiple comparisons? Or
should the affected CGs be splitted up within this model as in the
univariate model? Will metafor account for the nesting of different
interventions within a trial when computing an overall pooled effect
size with the specified multivariate model?
Which variant would yield the correct pooled effect size, whithout
'double counting'?
I think his is mainly a question on how the metafor 'rma.mv
<http://rma.mv>' weighs the
effect sizes to arrive at the pooled effect when using the random = ~
inner | outer factor argument.
I tried to find out by looking at the results of both variants but I
couldn't suss it out...
Any help would be appreciated. Many thanks!
Best,
Emily
--
Dr. Emily Finne, Dipl.-Psych.
Universit?t Bielefeld
Fakult?t f?r Gesundheitswissenschaften
AG 4: Pr?vention und Gesundheitsf?rderung
Postfach 10 01 31
D-33501 Bielefeld
Mail:emily.finne at uni-bielefeld.de
<mailto:Mail%3Aemily.finne at uni-bielefeld.de>
http://www.uni-bielefeld.de/gesundhw/ag4
<http://www.uni-bielefeld.de/gesundhw/ag4>
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