[R-meta] Transitivity in a three-level contrast-based network meta-analysis

Nicky Welton N|cky@We|ton @end|ng |rom br|@to|@@c@uk
Tue May 5 11:01:12 CEST 2020

Note that if the only med1vsmed2 evidence that you have come from 3-arm trials, then you cannot assess (loop*) inconsistency of the evidence statistically, since 3-arm trials cannot be inconsistent with themselves. Although there is a line in the network plot for med1vmed2 these trials really provide estimates of 2 relative effects med1vplacebo and med2vplacebo. So for the purposes of inconsistency checking you can think of this as a evidence on a star network. If there were studies that compare med1 vs med2 without placebo, then you have loops of evidence and can run inconsistency checks. 

Either way you can (and should) always assess the potential for inconsistency by inspecting the patient characteristics in the different studies, looking for differences in factors that may modify the treatment effect. If these seem homogenous, then that gives some reassurance that the studies are similar and can be combined without an a priori reason to expect inconsistency. But you can never be sure, as there could be other effect modifiers that are not reported in the baseline characteristics tables. If you find imbalance in potential effect modifiers across studies then you should be cautious combining the evidence, and may with to run subgroup analyses excluding studies that are on different populations, or revisit your inclusion/exclusion criteria.

Best wishes,


*Note there is another concept of design inconsistency where the effects in 3-arm studies may be inconsistent with the effects in the 2-arm studies. You could probably fit these models if you thought that design might be causing treatment effects to differ (although it's hard to imagine that would be the case ... perhaps the 3-arm trials are conducted more rigorously than the 2-arm trials ??).

-----Original Message-----
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf Of Natan Gosmann
Sent: 05 May 2020 08:45
To: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Cc: r-sig-meta-analysis using r-project.org
Subject: Re: [R-meta] Transitivity in a three-level contrast-based network meta-analysis

Dear Wolfgang,

Thank you very much for your really helpful explanation! It certainly clarified our doubts.


Em ter, 5 de mai de 2020 04:17, Viechtbauer, Wolfgang (SP) < wolfgang.viechtbauer using maastrichtuniversity.nl> escreveu:

> Dear Natan,
> Based on your description, the network plot should have lines between 
> at least some of the medication nodes. It's not a matter of what 
> effects you actually computed within the studies (e.g., in a three-arm 
> trial, you computed med1 vs placebo and med2 vs placebo) but what arms 
> are actually present in trials (so there should be a line between med1 
> and med2). In fact, the information about the head-to-head comparison 
> of med1 vs med2 is contained in the two effects comparing med1 vs 
> placebo and med2 vs placebo (also computing med1 vs med2 would be 
> redundant). I hope this clarifies things.
> Best,
> Wolfgang
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org]
> >On Behalf Of Natan Gosmann
> >Sent: Tuesday, 05 May, 2020 9:02
> >To: r-sig-meta-analysis using r-project.org
> >Subject: [R-meta] Transitivity in a three-level contrast-based 
> >network
> meta-
> >analysis
> >
> >Hi everyone,
> >
> >We are performing three-level models assessing both placebo and 
> >medication effects on continuous outcomes, estimating effect sizes 
> >with differences
> in
> >standardized mean changes (i.e. we estimate pre-post standardized 
> >mean change of the placebo group and of the medication group. After 
> >that, we calculate the difference among them). These models are being 
> >used to perform a contrast-based (all effect sizes are estimated 
> >considering the placebo group) network meta-analysis and we are 
> >including both two-arms (placebo vs medication) and three-arms 
> >(placebo vs medication 1 vs medication 2) trials.
> >
> >I have two question concerning the network plot of our study:
> >
> >1) Considering that all effect sizes are estimated based on placebo 
> >groups and pairwise comparisons among are contrast-based, our network 
> >plot should be star-shaped centered on placebo without any lines 
> >between medication nodes? If so, how should we assess the 
> >transitivity assumption of our network?
> >
> >2) For three-arms trials, even if we are not estimating the effect 
> >sizes through the head-to-head comparisons, we consider that some 
> >degree of variance is related to the fact that these medication 
> >groups are in the same study. These comparisons should be considered 
> >direct effects (therefore being presented as direct comparisons in the network plot)?
> >
> >Thank you very much!
> >
> >Best,
> >Natan Gosmann

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