Editing Meta-analysis (section)

==== Network meta-analysis methods ====
[[File:Indirekt jämförelse.jpg|thumb|300px|right|A network meta-analysis looks at indirect comparisons. In the image, A has been analyzed in relation to C and C has been analyzed in relation to B. However the relation between A and B is only known indirectly, and a network meta-analysis looks at such indirect evidence of differences between methods and interventions using statistical method.]]

Indirect comparison meta-analysis methods (also called network meta-analyses, in particular when multiple treatments are assessed simultaneously) generally use two main methodologies.<ref>{{Cite journal |last1=Rouse |first1=Benjamin |last2=Chaimani |first2=Anna |last3=Li |first3=Tianjing |date=2017 |title=Network meta-analysis: an introduction for clinicians |journal=Internal and Emergency Medicine |language=en |volume=12 |issue=1 |pages=103–111 |doi=10.1007/s11739-016-1583-7 |issn=1828-0447 |pmc=5247317 |pmid=27913917}}</ref><ref>{{Cite journal |last1=Phillips |first1=Mark R. |last2=Steel |first2=David H. |last3=Wykoff |first3=Charles C. |last4=Busse |first4=Jason W. |last5=Bannuru |first5=Raveendhara R. |last6=Thabane |first6=Lehana |last7=Bhandari |first7=Mohit |last8=Chaudhary |first8=Varun |last9=for the Retina Evidence Trials InterNational Alliance (R.E.T.I.N.A.) Study Group |last10=Sivaprasad |first10=Sobha |last11=Kaiser |first11=Peter |last12=Sarraf |first12=David |last13=Bakri |first13=Sophie J. |last14=Garg |first14=Sunir J. |last15=Singh |first15=Rishi P. |date=2022 |title=A clinician's guide to network meta-analysis |journal=Eye |language=en |volume=36 |issue=8 |pages=1523–1526 |doi=10.1038/s41433-022-01943-5 |issn=0950-222X |pmc=9307840 |pmid=35145277}}</ref> First, is the Bucher method<ref>{{cite journal | vauthors = Bucher HC, Guyatt GH, Griffith LE, Walter SD | title = The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials | journal = Journal of Clinical Epidemiology | volume = 50 | issue = 6 | pages = 683–691 | date = June 1997 | pmid = 9250266 | doi = 10.1016/s0895-4356(97)00049-8 }}</ref> which is a single or repeated comparison of a closed loop of three-treatments such that one of them is common to the two studies and forms the node where the loop begins and ends. Therefore, multiple two-by-two comparisons (3-treatment loops) are needed to compare multiple treatments. This methodology requires that trials with more than two arms have two arms only selected as independent pair-wise comparisons are required. The alternative methodology uses complex [[statistical model]]ling to include the multiple arm trials and comparisons simultaneously between all competing treatments. These have been executed using Bayesian methods, mixed linear models and meta-regression approaches.{{citation needed|date=June 2018}}

=====Bayesian framework=====
Specifying a Bayesian network meta-analysis model involves writing a directed acyclic graph (DAG) model for general-purpose [[Markov chain Monte Carlo]] (MCMC) software such as WinBUGS.<ref name="Valkenhoef, G. 2012">{{cite journal | vauthors = van Valkenhoef G, Lu G, de Brock B, Hillege H, Ades AE, Welton NJ | title = Automating network meta-analysis | journal = Research Synthesis Methods | volume = 3 | issue = 4 | pages = 285–299 | date = December 2012 | pmid = 26053422 | doi = 10.1002/jrsm.1054 | s2cid = 33613631 }}</ref> In addition, prior distributions have to be specified for a number of the parameters, and the data have to be supplied in a specific format.<ref name="Valkenhoef, G. 2012"/> Together, the DAG, priors, and data form a Bayesian hierarchical model. To complicate matters further, because of the nature of MCMC estimation, overdispersed starting values have to be chosen for a number of independent chains so that convergence can be assessed.<ref>{{cite journal |vauthors=Brooks SP, Gelman A | year = 1998 | title = General methods for monitoring convergence of iterative simulations | url = http://www.stat.columbia.edu/~gelman/research/published/brooksgelman2.pdf| journal = Journal of Computational and Graphical Statistics | volume = 7 | issue = 4| pages = 434–455 | doi=10.1080/10618600.1998.10474787| s2cid = 7300890 }}</ref> Recently, multiple [[R (programming language)|R]] software packages were developed to simplify the model fitting (e.g., ''metaBMA''<ref>{{Cite web | vauthors = Heck DW, Gronau QF, Wagenmakers EJ, Patil I |title=metaBMA: Bayesian model averaging for random and fixed effects meta-analysis |url=https://CRAN.R-project.org/package=metaBMA |access-date=9 May 2022 |website=CRAN|date=17 March 2021 }}</ref> and ''RoBMA''<ref>{{Cite web | vauthors =  Bartoš F, Maier M, Wagenmakers EJ, Goosen J, Denwood M, Plummer M |title=RoBMA: An R Package for Robust Bayesian Meta-Analyses |date=20 April 2022 |url=https://CRAN.R-project.org/package=RoBMA |access-date=9 May 2022}}</ref>) and even implemented in statistical software with graphical user interface ([[Graphical user interface|GUI]]): [[JASP]]. Although the complexity of the Bayesian approach limits usage of this methodology, recent tutorial papers are trying to increase accessibility of the methods.<ref>{{Cite journal | vauthors = Gronau QF, Heck DW, Berkhout SW, Haaf JM, Wagenmakers EJ |date=July 2021 |title=A Primer on Bayesian Model-Averaged Meta-Analysis |journal=Advances in Methods and Practices in Psychological Science |language=en |volume=4 |issue=3 |pages= |doi=10.1177/25152459211031256 |s2cid=237699937 |issn=2515-2459|doi-access=free |hdl=11245.1/ec2c07d1-5ff0-431b-b53a-10f9c5d9541d |hdl-access=free }}</ref><ref>{{Cite journal | vauthors = Bartoš F, Maier M, Quintana D, Wagenmakers EJ |date=2020-10-16 |title=Adjusting for Publication Bias in JASP & R - Selection Models, PET-PEESE, and Robust Bayesian Meta-Analysis | journal = Advances in Methods and Practices in Psychological Science |url=https://osf.io/75bqn |doi=10.31234/osf.io/75bqn |s2cid=236826939 |doi-access=free |hdl=11245.1/5540e87c-0883-45e6-87de-48d2bf4c1e1d |hdl-access=free }}</ref> Methodology for automation of this method has been suggested<ref name="Valkenhoef, G. 2012" /> but requires that arm-level outcome data are available, and this is usually unavailable. Great claims are sometimes made for the inherent ability of the Bayesian framework to handle network meta-analysis and its greater flexibility. However, this choice of implementation of framework for inference, Bayesian or frequentist, may be less important than other choices regarding the modeling of effects<ref name="ReferenceC">{{cite journal | vauthors = Senn S, Gavini F, Magrez D, Scheen A | title = Issues in performing a network meta-analysis | journal = Statistical Methods in Medical Research | volume = 22 | issue = 2 | pages = 169–189 | date = April 2013 | pmid = 22218368 | doi = 10.1177/0962280211432220 | s2cid = 10860031 }}</ref> (see discussion on models above).

=====Frequentist multivariate framework=====
On the other hand, the frequentist multivariate methods involve approximations and assumptions that are not stated explicitly or verified when the methods are applied (see discussion on meta-analysis models above). For example, the mvmeta package for Stata enables network meta-analysis in a frequentist framework.<ref>{{cite journal | vauthors = White IR | year = 2011 | title = Multivariate random-effects meta-regression: updates to mvmeta | journal = The Stata Journal | volume = 11 | issue = 2| pages = 255–270| doi = 10.1177/1536867X1101100206 | doi-access = free }}</ref> However, if there is no common comparator in the network, then this has to be handled by augmenting the dataset with fictional arms with high variance, which is not very objective and requires a decision as to what constitutes a sufficiently high variance.<ref name="Valkenhoef, G. 2012" /> The other issue is use of the random effects model in both this frequentist framework and the Bayesian framework. Senn advises analysts to be cautious about interpreting the 'random effects' analysis since only one random effect is allowed for but one could envisage many.<ref name="ReferenceC"/> Senn goes on to say that it is rather naıve, even in the case where only two treatments are being compared to assume that random-effects analysis accounts for all uncertainty about the way effects can vary from trial to trial. Newer models of meta-analysis such as those discussed above would certainly help alleviate this situation and have been implemented in the next framework.

=====Generalized pairwise modelling framework=====
An approach that has been tried since the late 1990s is the implementation of the multiple three-treatment closed-loop analysis. This has not been popular because the process rapidly becomes overwhelming as network complexity increases. Development in this area was then abandoned in favor of the Bayesian and multivariate frequentist methods which emerged as alternatives. Very recently, automation of the three-treatment closed loop method has been developed for complex networks by some researchers<ref name="Manual" /> as a way to make this methodology available to the mainstream research community. This proposal does restrict each trial to two interventions, but also introduces a workaround for multiple arm trials: a different fixed control node can be selected in different runs. It also utilizes robust meta-analysis methods so that many of the problems highlighted above are avoided. Further research around this framework is required to determine if this is indeed superior to the Bayesian or multivariate frequentist frameworks. Researchers willing to try this out have access to this framework through a free software.<ref name="Epigear"/>