Network Meta-Analysis Using R

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Network Meta-Analysis Using R

Network Meta-Analysis Using R

RESEARCHARTICLE

NetworkUsingAReviewofCurrentlyPackages

BinodNeupane1,DanielleRicher1,AshleyJoelBonner1,TaddeleKibret2,JosephBeyene1,2*

1.DepartmentofClinicalEpidemiologyandBiostatistics,McMasterUniversity,MDCL3200,1280MainStreetWest,Hamilton,Ontario,Canada,L8S4K1,2.DepartmentofMathematicsandStatistics,McMasterUniversity,HH218,1280MainStreetWest,Hamilton,Ontario,Canada,L8S4K1*beyene@mcmaster.ca

Abstract

Network(NMA)–astatisticaltechniquethatallowscomparisonofmultipleinthesamemeta-analysissimultaneously–hasbecomeincreasinglypopularinthemedicalliteratureinrecentyears.Thestatistical

methodologyunderpinningthistechniqueandsoftwaretoolsforimplementingthemethodsareevolving.BothcommercialandfreelyavailablestatisticalsoftwarepackageshavebeendevelopedfacilitatethestatisticalusingNMAwithvaryingdegreesoffunctionalityandeaseofuse.ThispaperaimstointroducethereadertothreeRpackages,gemtc,,,whicharefreelyavailablesoftwaretoolsimplementedinR.EachautomatestheprocessofperformingNMAsothatuserscanperformtheanalysiswithminimalcomputationaleffort.Wepresent,compareandcontrasttheavailabilityandfunctionalityofdifferentimportantfeaturesofNMAinthesethreepackagessothatclinicalinvestigatorsandresearcherscanwhichRpackagestoontheiranalysisneeds.Foursummarytablesdetailingdatainputandnetworkplotting,(ii)modeling(iii)assumptioncheckinganddiagnosticand(iv)inferenceandreportingareprovided,alongwithananalysisofapreviouslypublisheddatasettoillustratetheoutputsavailablefromeach

package.Wedemonstratethateachofthethreepackagesausefuloftools,andcombinedprovideuserswithnearlyallfunctionalitythatmightbedesiredwhenconductinga

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NMA.OPENACCESSCitation:NeupaneB,RicherD,BonnerAJ,KibretT,BeyeneJ(2014)NetworkMeta-AnalysisUsingR:AReviewofCurrentlyAvailableAutomatedPackages.PLoSONE9(12):e115065.doi:10.1371/journal.pone.0115065Editor:CynthiaGibas,UniversityofNorthCarolinaatCharlotte,UnitedStatesofAmericaReceived:September19,2014Accepted:November18,2014Published:December26,2014Copyright:ß2014Neupaneetal.Thisisanopen-accessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense,whichpermitsunrestricteduse,distribution,andrepro-ductioninanymedium,providedtheoriginalauthorandsourcearecredited.DataAvailability:Theauthorsconfirmthatalldataunderlyingthefindingsarefullyavailablewithout

restriction.Allrelevantdataarewithinthepaper.

Funding:FundingforthisworkcameformNSERC

andCIHR.Thefundershadnoroleinstudy

design,datacollectionandanalysis,decisionto

publish,orpreparationofthemanuscript.

CompetingInterests:Theauthorshavedeclared

thatnocompetinginterests

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exist.

PLOSONE|DOI:10.1371/journal.pone.0115065December26,20141/17

Network Meta-Analysis Using R

NetworkMeta-AnalysisUsingR

Introduction

Network(NMA),alsoknownasmultipletreatmentcomparison(MTC)ormultipletreatment(MTM),hasbeenincreasinglyusedinrecentyears[1–3]tosimultaneouslycomparetheeffectsofmultipletreatmentsonahealthoutcome.NMAisbeingrapidlyadoptedacrossawiderangeofhealthresearchareas[].ResearcherslookingtoundertakeaNMAintheirfieldwillfindfamiliarityinthesystematicprocessesofselectingandgradingcontributingstudies,asisrequiredforstandardmeta-analysis[].However,theadditionalanalysiscomplexitiesinvolvedwithaNMArequirestheusertobeawareofconsiderations,diagnostictools,andreportingstyles.

NMAcanbeperformedeitherunderfrequentistorBayesianandseveralmodelshavebeenproposedunderbothframeworks[–].Networkmeta-analystsmustselectamodelingapproachandareadvisedtoexplorethedifferencesbetweenthefrequentistandBayesianapproaches[10].TheBayesianapproachismorefrequentlyused[1,3]asitcanproduceestimatesofrank

probabilities(theprobabilitythateachtreatmenttobethebest,secondbest,andsoon).Aftermakingseveralmodel-basedchoices,mustbeundertakentoverifyifthemodelwasappropriate.TheseapproachesmustassessheterogeneityandtwoassumptionsunderlyinganyNMAthatarehighlyinfluentialtotheresults.MethodsofidentifyinganddealingwiththeseissuesareexploredextensivelyintheNMAliterature[11–16].ItisimportanttopublishNMAresultsclearlyandcompletely.forreportingNMAresultsarediscussedatlengthinBafetaetal[].Displayingthenetwork,presentingrelativeeffectsandrankprobabilitiesareanimportantpartofreportingNMAresults.

ThereareseveralstatisticalprogramsavailablethatcanimplementthevariousstepsrequiredtocarryoutaNMA.FrequentistmodelscanbeimplementedusingcommercialprogramssuchasSASandFreelyavailablesoftwareprogramssuchasWinBUGS,orJAGScanbeusedtoconduct

BayesianNMA,buttheyrequiredevelopingaprogramcode(ormodifyingpre-existingcodes)thatcanbequiteinvolved.Inaddition,someoftheplottingtoolsofinteresttoNMAresearchersarenotincorporatedintotheseprograms.ThestatisticalsoftwareRisfreelyavailableandpopularamongstatisticiansbecauseitisopensource,allowingfortheimplementationofnewstatisticalmethodsalmostinstantaneouslythroughthecreationofpackages.RinterfaceswithallthreeBayesiansoftwareprogramsmentionedabovetoconductnetworkmeta-analyseswiththeuseofappropriatepackages.TheuserisnotrequiredtoprograminOpenBUGS,WinBUGSorJAGSinordertoimplementthese

packages,minimizingtheprogrammingrequiredoftheuser.Bycombiningthefunctionalityofafewpackages,almostalldesiredoutputscanbeobtainedinR.Recently,threepackages,gemtc(http://wendang.chazidian.com/web/packages/gemtc/index.html),pcnetmeta(http://wendang.chazidian.com/web/packages/pcnetmeta/index.),netmeta(),havebeendevelopedspecificallyfornetworkmeta-analysisintheR

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environment,

PLOSONE|DOI:10.1371/journal.pone.0115065December26,20142/17

Network Meta-Analysis Using R

NetworkMeta-AnalysisUsingR

allowinguserstoperformNMAwithminimalprogramming.Atthetimeofwriting(July2014),thesearetheonlypackagesdevelopedspecificallyfor

performingNMAthatweidentified.Eachcanautomaticallygenerateandruntheanalysismodelwithminimalprogrammingrequiredbyusers.ThetwopackagesperformtheanalysisundertheBayesianframeworkandthethirdperformsunderthefrequentistThepurposeofthispaperistopresentaofthreeR

packages,namely,gemtc,pcnetmeta,andnetmetawithrespecttoandeaseofuse.ThisguideisdesignedtoinformnewusersofNMAwhoarefamiliarwiththeRenvironmentandwouldliketofindoutwhichpackagesmightsuittheirneeds.Ifresearchersknowthestatisticalchoicestheywanttomake,thispaperwillhelpthemtodeterminehowtodoitinR.Thispaperisorganizedasfollows.Thebelowdescribestheapproachwefollowedtoidentifyandexplorethethreepackages.TheResultssectionsummarizesourfindings,includingananalysisofrealdatausingeachpackage.Thelastsectionprovidesconclusionsaboutourinvestigation.

Methods

RforNMA

WesearchedtheComprehensiveRArchiveNetwork(CRAN)foranycontributedRpackageswrittenprimarilyforNMA.ThreeRmetthisrequirement:gemtc,pcnetmeta,andnetmeta.AlthoughwefoundotherpackageswithsomeapplicationsforNMA,includingmetaphor,wedidnotconsiderthesepackagesastheyarewrittenforgeneralpurposemeta-analysis(univariateandmultivariate,respectively).Thegemtcpackagesynthesizesevidenceontherelativeeffectsofmultipletreatmentsbyfittinggeneralizedlinearmodel(GLM)underaBayesianframework.pcnetmetasynthesizesprobabilitiesofeventsintreatmentsfromanetworkoftrialsusingamultivariatemeta-analysisalsounderaBayesianframework.Thenetmetapackageisbasedongraphtheorymethodologytomodeltherelativetreatmenteffectsofmultipleunderaframework.

Inthenextsection,wepresentamoredetailedgeneralintroductiontonetworkmeta-analysis,especiallyconcerningtheofNMA,theinputdata,andthemethodology.Detailsaboutthespecificdatainputandanalysisoptions,statisticalmodels,methods,andformulationsusedinthethreepackagescanbefoundintherespectivereferencemanualsandoriginalarticles:etal[]forgemtc,Zhangetal[18]forpcnetmeta,andKonigetal[19]andKrahnetal[20]fornetmeta.

andaspectsofNMA

NMAenablesinvestigatorstotheeffectsofmultiplehealthcare

interventionsincludingtreatmentsthatwerenotpreviouslycomparedin

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head-to-

PLOSONE|DOI:10.1371/journal.pone.0115065December26,20143/17

Network Meta-Analysis Using R

NetworkMeta-AnalysisUsingR

headtrials.Additionally,combiningindirectanddirectevidencecansometimesprovidepreciseestimatesoftreatmenteffectstosupportdecision-making.Dependingonthetypeofoutcome(e.g.,count,theinputaggregatedatasetcanbeeither(e.g.,observednumberofeventsandnumberofpatientsrandomizedinatreatmentarmineachtrialforabinaryoutcomesuchasincidenceofdiabetes)or(e.g.,estimateoftherelativetreatmenteffectsuchaslog-oddsratioanditsstandarderrorforthe

binaryoutcomeforanytwotreatmentsinatrial).TherearetwobroadstatisticalinferenceframeworksthataretypicallyusedinNMA:aversusaapproach.TheBayesianframeworkisquiteflexibleandallows

incorporatingprioronmodelparametersandcomprehensively.Inaddition,onecouldmakedirectprobabilisticaboutparametersofinterest.

FortheresultsofNMAtovalid,thenetworkisassumedtomaintaintransitivity(potentialmodifiersoftreatmenteffectsaresimilarlydistributed

acrosstrials)consistency(indirecteffectestimatesareconsistentwiththatofdirecteffects),whileinterpretationofthetreatmenteffectsismorestraightforwardiftheyarealsotrials[].Therefore,acarefulevaluationofclinicalandmethodologicalheterogeneityacrosstrialsisimportanttomakesurethatthenetworkmaintainstransitivity(i.e.,includestrialswithsimilarpatientsandtrialcharacteristicswithinandacrosstrials).presenceofheterogeneityandinconsistencyinthenetworkcanbequantifiedandassessedforwhichdifferentmethodshavebeenproposed[11–16].Ifthereisunexplainedheterogeneity–identifiedthroughclinicalorstatisticalinvestigations-arandom-effectsratherthanafixed-effectmodelispreferred.ItisacommonpracticeintheNMAliteraturetoassumeacommonheterogeneityforalltreatmentseffectsunderrandom-effectassumption.havebeenproposedtoaccountforinconsistencyifsuspected[].Assessmentofmayalsohelptoidentifymoreappropriatemodel(e.g.,fixedvs.random-effects)forthedata[].AkaikeinformationcriteriaandDevianceinformationcriteriaarewidelyusedcriteriatoassessgoodness-of-fitofthemodelsinfrequentistandBayesianframeworks,respectively.Detailedreviewsaboutassessinganddealing[,]and[]inanetworkandchoiceoffrequentistorBayesianframeworksforNMA[]areprovidedingreatdetailsinthefirstbookonnetworkmeta-analysis[].

OurreviewofthethreeRpackagesreflectsthemethodologicalandstatisticalaspectsofNMAdescribedabove.Tosummarize,ananalystbeginswithanexplorationofthenetworkandproceedswithproposingandamodelforthedata.Themodelassumptionsandfitareassesseddiagnosticprocedurestocomeupwitha‘‘final’’whichwillthenbeusedtogenerateandinterpretresults.

Withthisprocessinmind,wereviewedtheavailablefeaturesorcapabilitiesofthesepackageswithrespecttoconductingaNMA:importingandpreparingdata,creatingamodel,detectinganddealingwithheterogeneityandinconsistencyandassessingmodelfits,andobtainingestimatesofeffectsor

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PLOSONE|DOI:10.1371/journal.pone.0115065December26,20144/17

Network Meta-Analysis Using R

NetworkMeta-AnalysisUsingR

Table1.DatainputandnetworkplottingfunctionalityfromNMARpackagesgemtc,pcnetmetaandnetmeta.Tasks

Formsofinputdata

FeaturesArm-leveldataContrast-leveldata

Acceptsmulti-arm($3)trials

Typesofoutcomedatathatcanbeanalyzed

BinaryCountContinuousSurvival

Extractsdescriptivemeasures

Totalnumberofstudies

gemtc33333333

pcnetmeta3733777777733

3Usercanspecify,defaultby#studiesusingthetreatment3Numberofstudiesmakingthiscomparison

netmeta73333333373337

3Inversestandarderrorofaggre-gateddirecttreatmenteffects

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Totalnumberofmulti-armstudies3TotalnumberofparticipantsTotalnumberoftreatments

Networkplotandoptions

NetworkplotAddnodelabels

Nodesizereflectsnetworkchar-acteristic

Edgethicknessreflectsnetworkcharacteristic

doi:10.1371/journal.pone.0115065.t001

333377

probabilities.Theauthorsofthepackagesweretoverifytheaccuracyof–.Wealsousedeachpackagetoperformnetworkmeta-analysisofpubliclyavailabledataontheincidenceofdiabetes[27].Inparticular,thisdatasetwasselectedforillustrationbecauseitrepresentsatypicalnetworkconsistingofcomparisonoftheeffectsoftreatmentsin22closetothemediannumbersof6treatmentsand21trials,respectively,onabinaryoutcome,themostcommonoutcometype,intheNMAliterature[3].Thenetworkincludesmulti-armstudiesandthereisanevidenceofinconsistencyinthenetwork,thusprovidinganopportunitytoseehoweachofthepackagesidentifiesanddealswiththiscommonissue.Theoutputfromeachpackageisincludedtoprovidevisualsofthereportingtoolsavailable.

Results

tosummarizetheimportantofNMAthatareavailableinoneormoreofthelatestversionsofthegemtc(versionreleasedon2014-03-11)[28pcnetmeta(versionreleasedon2014-03-09)[29],andnetmeta0.5-0,released2014-06-24)[30]packages.

PLOSONE|DOI:10.1371/journal.pone.0115065December26,20145/17