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1、PaperSP07®SASMarkovChainMonteCarlo(MCMC)SimulationinPracticeScottDPatterson,GlaxoSmithKline,KingofPrussia,PAShi-TaoYeh,GlaxoSmithKline,KingofPrussia,PAABSTRACTMarkovChainMonteCarlo(MCMC)isarandomsamplingmethodwithMonteCarlointegrationusingMarkovchains.MCMChasgainedpopularityinmanyapplicationsduetoth
2、eadvancementofcomputationalalgorithms®andpower.TheSASMIProcedureprovidesMCMCmethodforfillingarbitrarymissingdataandforsimulatingrandomsamplesbasedoncompletedatainformation.ExtensionsofthisprocedurearecurrentlyavailableinexperimentalformtoperformBayesianstatisticalanalysis.Thepurposeofthispaperistous
3、easimulatedhypotheticalclinicaltrialefficacydatasetandChallenger’sO-ringfailuredataasinputinordertoperformtheMCMCmethodformissingdataimputation,modelparametersimulation,andmodeldiagnostics,andtouseSAStoperformaBayesiananalysisofdatacommonlyencounteredinclinicaltrials.®®®®TheSASV9productsusedinthispa
4、perareSASBASE,SAS/STAT,andSAS/GRAPHonaPCWindowsplatform.INTRODUCTIONMonteCarlomethodsaresamplingtechniquesthatdrawpseudo-randomsamplesfromspecifiedprobabilitydistributions.Inotherwords,MonteCarlomethodsarenumericalmethodsthatutilizesequencenumbersofrandomnumberstoperformstatisticalsimulations.AMonte
5、Carloalgorithminvolvesthefollowingcomponents:1)probabilitydistributionfunctions(pdf’s)–thetargetdistributionmustbespecifiedbyasetofpdf’s,2)randomnumbergenerator–asourceofrandomnumbersuniformlydistributedontheunitinterval,3)samplingrule–aprescriptionforsamplingfromthespecifiedpdf’s,4)scoring–theoutco
6、mesmustbesummarizedintooverallscores,5)errorestimation–anestimateofthestatisticalerror(variance)asafunctionofthenumberoftrials,6)variancereductiontechniques–methodsforreducingthevarianceintheestimatedsolutiontoreducethecomputationaltime,7)parallelizationandvectorization–analgorithmtoallowMonteCarlom
7、ethodstobeimplementedefficientlyoncomputercomputation.Forindependentsamples,thesimulationoutcomescanapply‘LawofLargeNumbers’.ButindependentsamplingfromMonteCarlomethodsmaybedifficult.Theissueofindepen
