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AHandbookofStatisticalAnalysesUsingRBrianS.EverittandTorstenHothornCHAPTER12Meta-Analysis:NicotineGumandSmokingCessationandtheEcacyofBCGVaccineintheTreatmentofTuberculosis12.1Introduction12.2SystematicReviewsandMeta-Analysis12.3AnalysisUsingRTheaimincollectingtheresultsfromtherandomisedtrialsofusingnicotinegumtohelpsmokersquitwastoestimatetheoveralloddsratio,theoddsofquittingsmokingforthosegiventhegum,dividedbytheoddsofquittingforthosenotreceivingthegum.Theoddsratiosandcorrespondingcon denceintervalsarecomputedbymeansofthemeta.MHfunctionfor xede ectsmeta-analysisasshownhereRlibrary(rmeta)Rdata(smoking,package=HSAUR)RsmokingOR-meta.MH(smoking[[tt]],smoking[[tc]],+smoking[[qt]],smoking[[qc]],+names=rownames(smoking))andtheresultscanbeinspectedviaasummarymethod{seeFigure12.1.Weshalluseboththe xede ectsandrandome ectsapproachesheresothatwecancompareresults.Forthe xede ectsmodel(seeFigure12.1)theestimatedoveralllog-oddsratiois0.513withastandarderrorof0.066.Thisleadstoanestimateoftheoveralloddsratioof1.67,witha95%con denceintervalasgivenabove.Fortherandome ectsmodelRsmokingDSL-meta.DSL(smoking[[tt]],smoking[[tc]],+smoking[[qt]],smoking[[qc]],+names=rownames(smoking))Rprint(smokingDSL)Randomeffects(DerSimonian-Laird)meta-analysisCall:meta.DSL(ntrt=smoking[[tt]],nctrl=smoking[[tc]],ptrt=smoking[[qt]],pctrl=smoking[[qc]],names=rownames(smoking))SummaryOR=1.7595%CI(1.48,2.07)Estimatedrandomeffectsvariance:0.0534META-ANALYSISRsummary(smokingOR)Fixedeffects(Mantel-Haenszel)meta-analysisCall:meta.MH(ntrt=smoking[[tt]],nctrl=smoking[[tc]],ptrt=smoking[[qt]],pctrl=smoking[[qc]],names=rownames(smoking))------------------------------------OR(lower95%upper)Blondal891.850.993.46Campbell910.980.501.92Fagerstrom821.760.803.89Fee821.530.773.05Garcia892.951.018.62Garvey002.491.434.34Gross952.621.036.71Hall852.030.785.29Hall872.821.335.99Hall960.870.461.64Hjalmarson842.171.104.28Huber886.002.5714.01Jarvis823.331.378.08Jensen911.430.842.44Killen841.330.434.15Killen901.230.931.64Malcolm803.520.8514.54McGovern921.170.701.94Nakamura903.821.1512.71Niaura941.340.355.19Pirie921.841.202.82Puska791.460.782.75Schneider851.710.525.62Tonnesen882.120.934.86Villa991.760.555.64Zelman921.460.683.14------------------------------------Mantel-HaenszelOR=1.6795%CI(1.47,1.9)Testforheterogeneity:X^2(25)=34.9(p-value0.09)Figure12.1RoutputofthesummarymethodforsmokingOR.thecorrespondingestimateis1.751.Bothmodelssuggestthatthereisclearevidencethatnicotinegumincreasestheoddsofquitting.Therandome ectscon denceintervalisconsiderablywiderthanthatfromthe xede ectsmodel;herethetestofhomogeneityofthestudiesisnotsigni cantimplyingthatwemightusethe xede ectsresults.Butthetestisnotparticularlypowerfulanditismoresensibletoassumeapriorithatheterogeneityispresentandsoweusetheresultsfromtherandome ectsmodel.ANALYSISUSINGR5Rplot(smokingOR,ylab=)OddsRatio0.401.002.516.3115.85Blondal89Campbell91Fagerstrom82Fee82Garcia89Garvey00Gross95Hall85Hall87Hall96Hjalmarson84Huber88Jarvis82Jensen91Killen84Killen90Malcolm80McGovern92Nakamura90Niaura94Pirie92Puska79Schneider85Tonnesen88Villa99Zelman92SummaryFigure12.2Forestplotofobservede ectsizesand95%con denceintervalsforthenicotinegumstudies.6META-ANALYSIS12.4Meta-RegressionTheexaminationofheterogeneityofthee ectsizesfromthestudiesinameta-analysisbeginswiththeformaltestforitspresence,althoughinmostmeta-analysessuchheterogeneitycanalmostbeassumedtobepresent.Therewillbemanypossiblesourcesofsuchheterogeneityandestimatinghowthesevariousfactorsa ecttheobservede ectsizesinthestudieschosenisoftenofconsiderableinterestandimportance,indeedusuallymoreimportantthantherelativelysimplisticuseofmeta-analysistodetermineasinglesummaryestimateofoveralle ectsize.WecanillustratetheprocessusingtheBCGvaccinedata.We rst ndtheestimateoftheoveralle ectsizefromapplyingthe xede ectsandtherandome ectsmodelsdescribedpreviously:Rdata(BCG,package=HSAUR)RBCG_OR-meta.MH(BCG[[BCGVacc]],BCG[[NoVacc]],+BCG[[BCGTB]],BCG[[NoVaccTB]],+names=BCG$Study)RBCG_DSL-meta.DSL(BCG[[BCGVacc]],BCG[[NoVacc]],+BCG[[BCGTB]],BCG[[NoVaccTB]],+names=BCG$Study)TheresultsareinspectedusingthesummarymethodasshowninFigures12.3and12.4.Rsummary(BCG_OR)Fixedeffects(Mantel-Haenszel)meta-analysisCall:meta.MH(ntrt=BCG[[BCGVacc]],nctrl=BCG[[NoVacc]],ptrt=BCG[[BCGTB]],pctrl=BCG[[NoVaccTB]],names=BCG$Study)------------------------------------OR(lower95%upper)10.390.121.2620.190.080.4630.250.070.9140.230.180.3150.800.511.2660.380.320.4770.200.080.5081.010.891.1590.620.391.00100.250.140.42110.710.570.89121.560.376.55130.980.581.66------------------------------------Mantel-HaenszelOR=0.6295%CI(0.57,0.68)Testforheterogeneity:X^2(12)=163.94(p-value0)Figure12.3RoutputofthesummarymethodforBCG_OR.PUBLICATIONBIAS7Rsummary(BCG_DSL)Randomeffects(DerSimonian-Laird)meta-analysisCall:meta.DSL(ntrt=BCG[[BCGVacc]],nctrl=BCG[[NoVacc]],ptrt=BCG[[BCGTB]],pctrl=BCG[[NoVaccTB]],names=BCG$Study)------------------------------------OR(lower95%upper)10.390.121.2620.190.080.4630.250.070.9140.230.180.3150.800.5