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

[Viechtbauer Wolfgang (STAT)]

Dear Angelo,

rma(yi=o, sei=se, mods=~s+t-1, method="REML")

is *a* way to run the arm-based pairwise meta-analysis. Whether it is the *correct* way is a question I cannot answer.

lme(o~s+t-1, random=~t-1 | s, weights=(~ se^2))

is a different model. First of all, it adds a random effect only to each treatment arm within each study, while the rma model above gives a random effect to each observation. Moreover, the lme model assumes that the sampling variances are only known up to a proportionality constant, while the rma model assumes that they are known exactly.

Similarly,

lm(formula = o ~ s + t - 1, weights = 1/se.o^2)

assumes that the sampling variances are only known up to a proportionality constant, while rma (with method="FE") assumes that they are known exactly.

For the same reason will

rma(yi=e, sei=se, method="REML")
lme(e~1, random=~1 | s, weights=(~ se.e^2))

and

rma(yi=e, sei=se.e, method="FE")
lm(e~1, weights = 1/se.e^2)

not give you the same results.

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: Angelo Franchini [mailto:Angelo.Franchini at bristol.ac.uk]
Sent: Wednesday, August 04, 2010 16:26
To: Viechtbauer Wolfgang (STAT)
Cc: 'Angelo Franchini'; r-help at r-project.org
Subject: RE: [R] metafor and meta-analysis at arm-level

> 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