[R] metafor and meta-analysis at arm-level

[Angelo Franchini]

Hello Wolfgang.

I'd appreciate if you could help me check whether I am doing the proper
thing to do an arm-level meta-analysis with metafor and what differences
there might be in trying to do the same with lme and lm.

I am following the arm based model described in section 3.2 of the
Salanti's paper that you mentioned in your previous e-mail, namely:

theta = B*eta + X*mu + W*beta

where:
theta = vector of parameter for outcomes in treatment arms (theta_ij for
study i, treat. arm j)
eta    = vector of parameter for outcomes in control arms (eta_i for study i)
mu     = vector of effects (treat. vs cont.) (mu_ij for study i, treat.
arm j)
beta   = vector of random effects (beta_ij for study i, treat. arm j)


In my specific case with a pairwise meta-analysis, I had my data arranged
as in columns for the following variables:
s t o se

with
s as study/trial identifier
t as 0/1 for control/treatment arm
o as observed outcome in control or treatment arm
se as standard error of that outcome measure

I then ran metafor as:
rma(yi=o, sei=se, mods=~s+t-1, method="REML")

for random effects, and REML replaced by FE for fixed effects.

Is that the correct way to run the arm-based pairwise meta-analysis?

Shouldn't I be able to obtain similar results with LME for random-effects
by using the command:
lme(o~s+t-1, random=~t-1 | s, weights=(~ se^2))

and for fixed-effects with:
lm(formula = o ~ s + t - 1, weights = 1/se.o^2)


For the trial-based pairwise meta-analysis I used:
data arranged as:
s e se

with:
s study
e effect
se standard error

and commands:
rma(yi=e, sei=se, method="REML")

or

lme(e~1, random=~1 | s, weights=(~ se.e^2))

for random-effects, while for fixed-effects:
rma(yi=e, sei=se.e, method="FE")
lm(e~1, weights = 1/se.e^2)

Does that make sense?


Many thanks for any comment/advice on this matter.
Best regards,
Angelo



On Fri, July 9, 2010 11:55 am, Viechtbauer Wolfgang (STAT) wrote:
> With "appropriate design matrix", I mean the X matrix in the
mixed-effects
> model y = Xb + u + e, where y is the vector of outcomes, u is a vector
of
> (possibly correlated) random effects, and e is a vector of (possibly)
random errors. The X matrix is specified via the 'mods' argument in the
rma() function. If y consists of arm-level outcomes, then you need
appropriate dummy variables in X to code what type of arm the outcome
corresponds to.
>
> Have you read, for example:
>
> Salanti, G., Higgins, J. P. T., Ades, A. E., & Ioannidis, J. P. A.
(2008).
> Evaluation of networks of randomized trials. Statistical Methods in
Medical Research, 17(3), 279-301.
>
> This article may be helpful.
>
> Best,
>
> --
> Wolfgang Viechtbauer                        http://www.wvbauer.com/
Department of Methodology and Statistics    Tel: +31 (0)43 388-2277
School for Public Health and Primary Care   Office Location:
> Maastricht University, P.O. Box 616         Room B2.01 (second floor)
6200 MD Maastricht, The Netherlands         Debyeplein 1 (Randwyck)
>
>
> ----Original Message----
> From: r-help-bounces at r-project.org
> [mailto:r-help-bounces at r-project.org] On Behalf Of Angelo Franchini
Sent: Tuesday, July 06, 2010 10:37 To: Wolfgang Viechtbauer
> Cc: r-help at r-project.org; Angelo Franchini
> Subject: Re: [R] metafor and meta-analysis at arm-level
>
>> Hello Wolfgang,
>> Thank you very much for your response.
>> When you mentionthe "appropriate design matrix", do you mean by that
the 'n1i, n2i, m1i, m2i, sd1i, sd2i' arguments of the rma function, or
am I missing something? I read the documentation on metafor
>> (introduction), rma/rma.uni and escalc, and that was the only way that
I could find for the package to use information at the arm-level rather
than the trial one.
>> As for the complexity of possible correlations between effects, that is
something to be considered for the network analysis case, correct? Many
thanks.
>> Best regards,
>> Angelo
>> On Sun, July 4, 2010 6:06 am, Wolfgang Viechtbauer wrote:
>>> Hello Angelo,
>>> You can either supply the arm-level outcomes and corresponding
sampling variances directly (via the yi and vi arguments) or supply
the necessary information so that the escalc() or rma() functions can
calculate an appropriate arm-level outcome (such as the log odds). See
the documentation of the escalc() function and in particular the part
about proportions and tranaformations thereof as possible outcome
measures.
>>> This is the easy part. Then you need to set up an appropriate design
matrix to code what arm each observed outcome corresponds to. And
finally comes the tricky/problematic part. The rma() function assumes
independent sampling errors and independent random effects for each
observed outcome. Independent sampling errors is (usually) ok when
using arm-level outcomes, but the independent random errors part may
not be appropriate. This is why I am working on functions that do not
make this independence assumption. With those functions, you can then
carry out multivariate and network-type meta-analyses. These
>>> functions will become part of the metafor package in the future. Best,
>>> --
>>> Wolfgang Viechtbauer
>>> http://www.wvbauer.com
>>> "Angelo Franchini" <Angelo.Franchini at bristol.ac.uk> wrote:
>>>> Hi,
>>>> I have been looking for an R package which allowed to do
>>>> meta-analysis (both pairwise and network/mixed-treatment) at
>>>> arm-level rather than at trial-level, the latter being the common way
in which meta-analysis is done. By arm-level meta-analysis I mean one
that accounts for data provided at the level of the
>>>> individual arms of each trial and that does not simply derive the
difference between arms and do the meta-analysis on that.
>>>> I am not sure metafor can do that, but hopefully someone more
experienced on it can clarify that to me. I can see that it can take
data in both forms, arm and trial level, but it looks as if the
arm-level information would be converted into trial one through
escalc and the latter then used for the meta-analysis. Is that right?
>>>> Many thanks.
>>>> Angelo
>>>> --
>>>> NIHR Research Methods Training Fellow,
>>>> Department of Community Based Medicine
>>>> University of Bristol
>>>> 25 Belgrave Road
>>>> Bristol BS8 2AA
>>>> Tel. 0779 265-6552
>>>> ______________________________________________
>>>> R-help at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
>>>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>


-- 
NIHR Research Methods Training Fellow,
Department of Community Based Medicine
University of Bristol
25 Belgrave Road
Bristol BS8 2AA

Tel. 0779 265-6552