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

[Angelo Franchini]

Dear Wolfgang,

Is there any way for rma to add random effects only to each treatment arm,
but not to the control one?

Many thanks,
Angelo


On Thu, August 5, 2010 6:21 pm, Viechtbauer Wolfgang (STAT) wrote:
> 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
>


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