[R-meta] DECOMPOSING RESIDUAL HETEROGENEITY

[Viechtbauer, Wolfgang (NP)]

So I figured out what netmeta() is doing to estimate tau^2 when using REML. It fits this model:

res9 <- rma.mv(yi, vi, mods = ~ acarbose + benfluorex + metformin + miglitol + pioglitazone +
                               rosiglitazone + sitagliptin + sulfonylurea + vildagliptin - 1,
               random = ~ comp | study, rho=1/2, data=dat)
res9$tau2

and then apparently uses the tau^2 value from this going forward (strictly speaking, it fits the model above, but uses 'random = ~ id | study', where 'id' is a unique value for every row in the dataset, but that ends up doing the same thing in this case).

However, the model above ignores the covariance between the sampling errors in the three-arm study. So, I would suggest that this isn't quite the right approach to estimate tau^2. I am cc-ing Gerta and Guido in the hopes that they can provide some feedback on this.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Viechtbauer, Wolfgang (NP)
>Sent: Friday, 20 January, 2023 15:55
>To: R meta
>Subject: Re: [R-meta] DECOMPOSING RESIDUAL HETEROGENEITY
>
>Dear Segun,
>
>To obtain these Q-statistics, you have to add the interaction between the study
>'design' variable and the treatment variables to the model (and use a model
>without random effects). Here is code to illustrate this.
>
>###################################################
>
>library(metafor)
>
>dat <- dat.senn2013
>
>dat <- dat[c(1,4:2,5:6)] # reorder variables first
>dat <- to.wide(dat, study="study", grp="treatment", ref="placebo", grpvars=4:6)
>dat
>
>### calculate mean difference and corresponding sampling variance for each
>treatment comparison
>dat <- escalc(measure="MD", m1i=mi.1, sd1i=sdi.1, n1i=ni.1,
>                            m2i=mi.2, sd2i=sdi.2, n2i=ni.2, data=dat)
>dat
>
>### note: pairwise() rounds the effect sizes to two decimal places, so do the
>same here
>dat$yi <- round(dat$yi, 2)
>
>### calculate the variance-covariance matrix of the mean differences for the
>multitreatment studies
>calc.v <- function(x) {
>   v <- matrix(x$sdi.2[1]^2 / x$ni.2[1], nrow=nrow(x), ncol=nrow(x))
>   diag(v) <- x$vi
>   v
>}
>V <- bldiag(lapply(split(dat, dat$study), calc.v))
>
>### add contrast matrix to dataset
>dat <- contrmat(dat, grp1="treatment.1", grp2="treatment.2")
>dat
>
>### network meta-analysis using a contrast-based random-effects model
>res1 <- rma.mv(yi, V, mods = ~ acarbose + benfluorex + metformin + miglitol +
>pioglitazone +
>                               rosiglitazone + sitagliptin + sulfonylurea +
>vildagliptin - 1,
>               random = ~ comp | study, rho=1/2, data=dat)
>res1
>
>### QE statistic is Q 'Total' from netmeta()
>
>res2 <- rma.mv(yi, V, mods = ~ acarbose + benfluorex + metformin + miglitol +
>pioglitazone +
>                               rosiglitazone + sitagliptin + sulfonylurea +
>vildagliptin +
>                               (acarbose + benfluorex + metformin + miglitol +
>pioglitazone +
>                               rosiglitazone + sitagliptin + sulfonylurea +
>vildagliptin):design - 1,
>                               data=dat)
>
>### QE statistic is Q 'Within designs' (Q.heterogeneity) from netmeta()
>res2
>
>### QM statistic is Q 'Between designs' (Q.inconsistency) from netmeta()
>anova(res2, btt="design")
>
>library(netmeta)
>
>dat <- dat.senn2013
>
>dat <- pairwise(treatment, sm="MD", mean=mi, sd=sdi, n=ni, studlab=study,
>data=dat)
>
>res3 <- netmeta(TE, seTE, treat1, treat2, studlab=study, data=dat,
>                reference.group="placebo", common=FALSE, method.tau="REML")
>res3
>
>###################################################
>
>Despite using REML in both rma.mv() and netmeta(), the estimate of tau^2 is just
>slightly different between res1 and res3 (and hence the estimated fixed effects
>are also just slightly different). It is not entirely clear to me why there is
>this discrepancy in the estimated value of tau^2 (when removing the three-arm
>study, Willms (1999), then results are exactly identical). I hope the netmeta
>authors could chime in here.
>
>Best,
>Wolfgang
>
>>I have been experimenting with the Senn2013 data in the Metafor package
>>and while trying to reproduce the results, I have been having difficulty
>>decomposing the residual heterogeneity ( QE( df=18) = 96.9841, Pval
>><0.0001) into within study and between study heterogeneity like I could
>>do with netmeta. At least to help me assess the inconsistency in the
>>network meta-analysis.
>>
>>I will really appreciate if you could advise me on how to go about it.
>>
>>Thank you so much for all your great work.
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