Lab 2 treeage tutorial 2 PDF

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RDS285–LAB2 TUTORIAL#2:MARKOVMODELANALYSISINTREEAGEPRO™   StartingTreeAgeProintheMicroLab FromSTART,selectProgramsÎTreeAgeProfromthemenuoptions,thenselectTreeAgePro SiteLicenseClient.Youwillseeapop‐upwindowaskingtocreateatabledirectoryatP:\ TreeAgePro.PressYEStocontinue.ThisactioncreatesafolderinyourP:driveandallthe “tables”usedinyourmodelwillbesavedthere(youwillcreatetablesintutorial#2).  Alternatively,atrialversionofTreeAgeProcanbedownloadedfromthewebsite: www.treeage.com(under“DownloadTrial”).  DecisionProblem Youwilldevelopa4‐stateMarkovmodeltoperformananalysisoftheexpectedoutcomesfora cohortof55‐year‐oldwomenwhohaveundergonetumorexcisionforlocalizedbreastcancer. Aftersurgery,allpatientsareinitiallytumor‐free(i.e.,willstartinthe“Local”Markovstate). Eachyear,patientsintheLocalstatefacea2%chancethattheywillexperiencearecurrence. Oftheserecurrences,75%willpresentasmetastaticdisease(andpatientswillenterthe“Mets” Markovstate),andtheremainderpresentaslocaldisease(andpatientswillenterthe“Recur” Markovstate).PatientsintheRecurstateundergorepeatresection.Followingthisoperation, theyfacea6%chanceofrecurrenceeachyear(assumethatalllocalrecurrences‐1st,2nd,3rd, etc.‐haveequivalentprognoses).Oftheserecurrences,90%willpresentasmetastaticdisease. Onlypatientswithmetastaticdiseasecandieofbreastcancer.Allwomenfaceaprobabilityof dyingfromothercausesbasedontheU.S.lifetables.Womenwhodie(eitherofbreastcancer orothercauses)willenterthe“Dead”Markovstate.  TheMarkovmodeldescribedaboverepresentsusualcareforwomenwithbreastcancer.Once youhaveconstructedthatMarkovmodelyouwillthenaddasecondstrategyofahypothetical newtreatment.Theeffectofthisnewtreatmentistoreducetheinitialriskofcancer recurrenceby50%;however,thetreatmentalsolowersthequalityoflifeofwomentakingthe medicationbecauseofsideeffects.Treatmentisonlytakenbywomenwhohavenot experiencedarecurrence(i.e.,thosewhoresideintheLocalstate).TheMarkovmodelforthe treatmentstrategywillbestructurallyidenticaltothatoftheusualcarestrategysoyouwilluse the“cloning”featureofTreeAgeProtoincorporatethisstrategy.  Aftercomparingthetwostrategiesbasedonquality‐adjustedlifeexpectancy,youwill incorporatecostsandcalculatetheincrementalcostperquality‐adjustedlifeyeargainedof treatmentcomparedwithusualcare.  MarkovStructure:UsualCare ThestructureoftheMarkovmodelforUsualCareisshowninFigure1(onpage2).TreeAgePro hasaspecialMarkovnode(representedbyapurple“M”withinacircle).Thebranchesthat leadoffofaMarkovnodedesignatealloftheMarkovstates(andonlyMarkovstates).Inthis 1

example,therearefourhealthstates:(1)Local,(2)Recur,(3)Mets,and(4)Dead.Deadisa terminalnodebecauseitisanabsorbingstate(i.e.,thereisnochanceofleavingthisstate). Thethreenonabsorbingstatesarechancenodes,offofwhichyoucancreateasubtree(also calledacycletree)thatreflectsthoseeventsthatcanoccurduringacycle.Thelastbranchat theendofeachpathwaywillbeaterminalnodeandthenametotherightofeachterminal nodemustbesettooneofthefourMarkovstatenames.These“jumpstates”specifywhat statetogotoforthenextcycle.(Notethatinaregulardecisiontree,these“payoff”variables representtheoutcomeoftheanalysis.InaMarkovmodel,outcomesaredefinedelsewhere– NOTattheterminalnode.)  TheprobabilitiesassignedtoeachbranchoffoftheMarkovnoderepresentstheprobabilityof beingineachofthefourMarkovstatesattime0.Inthisexample,youareassumingthatall womenarecancer‐freeimmediatelyfollowingtheirtumorexcision;thus,everyonestartsinthe Localstate.Theseprobabilitieswillonlybeevaluatedonce.Thecyclelengthforthisexampleis oneyear.Therefore,allprobabilitiesshowninthecycletrees(i.e.,thetreestructurestothe rightofeachMarkovstate)representone‐yearprobabilities,andwillgetevaluatedeachcycle.  Figure1:MarkovModelofUsualCare Die pDie

Dead Metastatic

Local 1 Survive #

Get BCA pBCA1

# No BCA #

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pDieMets Survive #

Dead 0 Treat

2

pMets2 Local #

No BCA #

BCA

Recur

Local

Metastatic

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pMets1 Local

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BuildingtheTree YoushouldbefamiliarwithbuildingadecisiontreeinTreeAgePro(seetablebelowforkey tree‐buildingtools).UsingFigure1asaguide,enterthestructureoftheMarkovmodelfor UsualCareintoTreeAgePro.NotethatwhenyouchangethenodesattheendoftheMarkov cycletreestoterminalnodes,TreeAgeProwillpromptyoutoindicatewhichofthefour Markovstatesyouwanttouseasa“jumpstate.”DonotbuildbeyondtheMarkovnodeforthe Treatstrategyfornow.Notethatwhenyouenterprobabilitiesusingvariablesratherthan numbers,TreeAgeProwillalertyouthat,“thevariable‘_____’isnotdefined”andwillprompt youtocreateit.ClickYESfollowedbyOKtocreateeachvariable.Savethetree(youwillneed tosavetoamemorystick,totheC:drive,ortoyourP:drive).  OPTIONSmenu,ADDBRANCHESoption • Addabranch (ordoubleclickonnode,orCtrl+A) Clickonthebranchuntiltextinsertionbox • Labelabranch appears • Insertprobabilityvariable Clickdirectlybelowthebranch(orTabfrom branchlabel) OPTIONSmenu,CHANGENODETYPEoption • Changenodetype (orclickicononToolBar,orCtrl+T)  Utilities Youwillnowassignutilities.Inastandarddecisiontree,theutilityvalues(orpayoffvaluesin TreeAgePro)areassignedattheendofthetreeateachoftheterminalnodes.InaMarkov model,theterminalnodespecifieswhatstatetogotoforthenextcycle,ratherthanthe payoff.UtilitiesinaMarkovmodelareassignedatthefirstgenerationbranchesoffofthe Markovnode(i.e.,theMarkovstatebranches).  TherearethreetypesofutilitiesinaMarkovmodel: •

Theinitialutility(Init)ofastateistheutilitya“person”accruesbecauseofbeingina statewhenthemodelstarts(appliedonlyinthefirstcycle).

•

Theincrementalutility(Incr)ofastateistheutilitya“person”accrueseachtimeshe orhearrivesinthatstateasthemodelruns(appliedmanytimes).

•

Thefinalutility(Final)ofastateistheutilitya“person”accruesifsheorheisinthat stateatthetimethemodelfinishesrunning(appliedonlyinthefinalcycle).

 Youwilldefinetheseutilitiesusingutilityvariables(uLocal,uRecur,anduMets)inordertobe abletoquality‐adjustlifeexpectancy,andadiscountvariable(r)thatwillallowyoutodiscount lifeexpectancy(andquality‐adjustedlifeexpectancy).Thevariable“uLocal”istheutilityfor beingintheLocalstate.Thevariable“uRecur”istheutilityforbeingintheRecurstate.The variable“uMets”istheutilityforbeingintheMetsstate.Iftheseutilityvaluesareequalto1, thentheexpectedvaluerepresentslifeexpectancy(themodelgives“credit”of1fullyearfor spendingayearinany“non‐dead”state).Bysettingtheutilities≤1,onecancalculatequality‐ adjustedlifeexpectancy.Fordiscounting,youwilluseaTreeAgeProvariable(_stage)that 3

representstheMarkovcyclenumber.NotethatTreeAgeProhasabuilt‐indiscounting function;forthepurposeofthistutorial,youwillmanuallyentertheformulasfordiscounting futurelifeyears.  Toenterutilityvalues,goone‐at‐a‐timetoeachofthefirstgenerationbranches(states)offof theUsualCareMarkovnode(Local,Recur,Mets,andDead),pulldowntheVALUESmenu,and chooseMARKOVSTATEINFORMATION.Aneditingboxwillappearwhichwillallowyoutoenterthe threeutilities.Alternatively,youcandoubleclickonthe‐‐‐Markov‐‐‐boxbeneatheachofthe firstgenerationbranchestogettheeditingbox.  Theutilityassignmentsaregiveninthefollowingtable.Youwillneedtocreatevariableswhen youenterunrecognizedvariables.Notethattheonlystatethathasaninitialutilityassignedis theLocalstate,whichistheonlystatethatapersoncanstartinattime0.   UtilityAssignments Branch Initial* Incremental Final Local 0.5*uLocal uLocal/(1+r)^_stage 0 Recur 0 uRecur/(1+r)^_stage 0 Mets 0 uMets/(1+r)^_stage 0 Dead 0 0 0 *Firstyeargetscreditforhalfayear‐knownasthe“half‐cyclecorrection.”  CreatingTablesinTreeAgePro Youwillinputatableofage‐specifichazardratesforwomen(fromtheUSlifetables)thatwill allowyoutoincorporatenon‐BCAcausesofdeathforwomenasafunctionofage.Youwill defineatablenamed“mufem”andenterthelifetablehazardratesfromanExcelspreadsheet. Selecttherootnode(“BCA”),pulldowntheVALUESmenu,andchooseVARIALBESANDTABLES.Click onTABLESLIST(buttonattop)followedbyNEWTABLE(buttononright).Youwillneedtogive thetableanamethatwillberecognizedbyyourtree(Name)andafilename(File)forthetable file.Type“mufem”forboththetableNameandFile.ClickOK.  Toentervaluesintothetable,clickon“mufem”intheTablesList.With“mufem”highlighted, youthenclickOPENTABLE,thenon,EDITTABLE.Thiswillputyouinablanktablewithapromptfor atableentry,ADDTABLEENTRY.ClickCANCEL.Atableconsistsoftwocolumns.The“Index”(first column)isthevaluethatyouwillusetorefertothecorrespondingnumberinthesecond column(“Value”).TreeAgeProinterpretstheterm“tablename[Index]”astheValueassociated withtheparticularIndex(notethattheIndexvaluehastobeenclosedin[brackets]).Youcould enterIndex/ValuepairsoneatatimebypullingdowntheTABLEmenuandselectingADDENTRY. FornowyouwillcopyandpastefromanExcelspreadsheet.  InExcel,openthefiletitled“rds285_2006lt.xls”,availableonthecoursewebpage(inAdditional Materialsfolder,clickonlink“Lifetables–AnnualMortalityRates”).Thisfilecontainsthree sheetswithage‐specifichazardrates,oneforthewholepopulation(ALL),oneformales,and oneforfemales;notethatthesearerates,notprobabilities.Copythetwocolumnsofdatafrom 4

the“FEMALES”sheetontotheclipboardbypressingCTRL‐CorselectingCOPYfromtheEDIT menu,excludingtheheaders(i.e.,copyonlycellsA2throughB102)–notethatthemortality rateatage100is10000(i.e.,anyonewhosurvivestoage100dies).InTreeAgePro,pastethe tablebypressingCTRL‐VorselectingPASTEfromtheEDITmenu.Saveandclosethetable.  IntheMicroLab,TreeAgeProwillautomaticallysavethetablefile(“mufem.tbl”)inthe P:\TreeAgeProsubdirectory.Whenyoufinishthelab,youcancopythetableyoucreateontoa zipdrive,CD,orleaveitinyourownPdrive.WhenyouareusingTreeAgeProonyourown computer,TreeAgeProwillautomaticallysavetablefilesinthe“Tables”subdirectoryofyour “TreeAge”directory(Default:C:\ProgramFiles\TreeAgePro\Tables).Note,inorderforthe modeltorun,anyrelevanttablesmustresideinthe“Tables”folder.  Alternatively,toensurethatthetablesalwaysaccompanythetree,youcansavethetreeusing SAVEAS;under“Saveastype”,select“PackageFiles(*.pkg).Thispackagefilenowcontainsboth treeandallrelevanttables.  AssigningProbabilitiesandDefiningVariables Whereyouassignvaluestoprobabilitiesisimportant.Ingeneral,somevariableswillbe assignedglobally(affectingthewholetree);otherswillbeassignedlocally(affectingaportion ofthetree).Inthisexample,pBCA1(theannualprobabilityofrecurrenceafterfirstlocaltumor diagnosis)willbeassignedlocallyandpBCA2(theannualprobabilityofrecurrenceafter>1 localtumordiagnoses)willbeassignedglobally.However,ifpBCA1andpBCA2weregiventhe samename(e.g.,pBCA),youwouldhavetoassignseparatevaluestothematdifferentpointsin thecycletree.  Youwillfirstdefinethemortalityvariables,whichareeachsetequaltoanequationandnota singlevalue.Therearetwomortalityvariables,pDieandpDieMets.Thefirstvariable representstheannualprobabilityofdyingfromnon‐BCA‐relatedcausesandisafunctionof age.Thesecondvariablerepresentstheannualprobabilityofdyingofmetastaticcancerin additiontodyingfromothercauses.TheequationforpDie(shownbelow)convertstheannual ratesfromthelifetable(inmufem)toannualprobabilities.Thefirstcycle(year1)throughthe Markovmodel,_stageisequalto0.Hence,therateselectedfromthetableisthatassociated withthestartingageofthecohort(55).Thesecondcyclethroughthemodel,_stageisequalto 1andtheannualrateselectedfromthemufemtableisthatassociatedwith56‐year‐old women.Theoverallannualmortalityrateforwomenwithmetastaticdiseaseisequaltothe sumoftheratesofdyingfromothercausesandtheexcessdisease‐specificmortalityrate (definedasmuMets).TheequationforpDieMets(shownbelow)covertsthesumoftheserates toannualprobabilities.  pDie=1‐exp(‐mufem[Age+_stage])  pDieMets=1‐exp(‐mufem[Age+_stage]‐muMets) 

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Todefinethesevariables,selecttherootnode,pulldowntheVALUESmenuandchooseVARIABLES ANDTABLES(orclicktheV=buttonontheToolBar)thenclickonVARIABLESLIST.FirstselectpDie fromthevariablelistandthenselectpDieMetswhileholdingdowntheCtrlkey.ClickonDEFINE VARIABLE‐DEFAULTFORTREE.Definethesevariablesbytheaboveequations.Asbefore,whenyou enterthenamesofunrecognizedvariables,TreeAgeProwillaskyouifyouwanttocreatethe variable.ClickYESfollowedbyOK.  Theremainingvariableswillbedefinednumerically.Onceagain,selecttherootnode,pull downtheVALUESmenuandchooseVARIABLESANDTABLES(orclicktheV=buttonontheToolBar). FirstselectAgefromthevariablelist,thenselectthefollowingvariableswhileholdingdownthe Ctrlkey:muMets,pBCA2,pMets1,pMets2,r,uMets,anduRecur.Thesearethevariablesthat youwilldefinegloballyforthetree.NotethatpBCA1anduLocalwillbedifferentforthetwo strategiesandsoyouwilldefinethemlocally.HolddowntheDEFINEVARIABLEbuttonandthen selectDEFAULTFORTREE.EnterthefollowingvalueswhenpromptedandthenclickOK,orpress Enter.  Variable Value uRecur 0.80 uMets 0.40 r 0.03 pMets2 0.90 pMets1 0.75 pBCA2 0.06 muMets 0.50 Age 55  LocallyDefiningVariables SincethevalueofpBCA1anduLocalwillbedifferentdependingonthestrategy,youwilldefine thesetwovariableslocallyattheUsualCareandTreatbranches.FirstselecttheUsualCare branchandclicktheV=buttonontheToolBar.SimultaneouslyselectpBCA1anduLocal.Hold downtheDEFINEVARIABLEbuttonandthenselectATSELECTEDNODE(S).AssignuLocalthevalueof 0.95andpBCA1thevalueof0.02.NextselecttheTreatbranchandclicktheV=buttononthe ToolBar.SimultaneouslyselectpBCA1anduLocal.HolddowntheDEFINEVARIABLEbuttonand thenselectATSELECTEDNODE(S).AssignuLocalthevalueof0.90andpBCA1thevalueof0.01. Savethetree.  CreatingClones ThecloningfeatureofTreeAgeProallowsyoutomakeanexactduplicateofatreestructureto attachatotherlocationsinthetree.Thisisdifferentfromthecopyandpastefeatureinthat whenyoucopyandpasteatree,youcanthenmakechangestothepastedtreewithout affectingtheoriginaltree.Whenyoucreateaclone,youareonlyallowedtomakechangesto the“clonemaster”(andeachchangewillautomaticallybemadetoallcopiesofthatclone). SincetheMarkovmodelfortheTreatstrategyisidenticalinstructuretotheUsualCare strategy,youwillmaketheUsualCaremodelthatyoualreadybuiltaclonemasterandattacha

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copyofthatclonetotheTreatbranch.(ThedifferencesbetweenthesetwoMarkovmodelsare withthevariablespBCA1anduLocal,whichhavealreadybeenlocallyassignedtobedifferent.) SelecttheUsualCarebranch,pulldowntheOPTIONSmenuandchooseSELECTSUBTREE(the subtreenodeswillbecomesolidcolors).NowpulldowntheEDITmenuandchooseCREATE CLONE.TreeAgeProwillpromptyouforanameforyourclonemaster.TypeBCAandthenclick OK.TheUsualCarebranchisthickenedtoindicatethatitrepresentsaclonemaster.Now selecttheTreatbranch,pulldowntheEDITmenuandchooseATTACHCLONE.Theattachedclone willbeinshowngrayandnotinblackandyouwillnotbeabletodirectlyeditit.  SettingtheMarkovTerminationCriteriaandChangingPreferences AstoppingcriterionthatindicateswhentostoptheanalysismustbesetateachoftheMarkov nodesbeforetheprogramwillrun.TodothisselecttheUsualCarebranch,pulldownthe VALUESmenu,andselectMARKOVTERMINATION.ClickingOKwillacceptthedefault;otherwiseyou maychangeit.Thedefaultwillrunthecohortthroughthemodeluntilalmosttheentirecohort isintheDeadstate.NowsettheMarkovterminationcriterionfortheTreatMarkov.  Toseevariabledefinitionsdisplayedonthetree,pulldowntheEDITmenu,selectPREFERENCES andfromthelistontheleft,selectVARIABLES/MARKOVINFO.Inthetextboxthatappearsonthe right,clickSHOWDEFINTIONS,EXPANDNODETOFITVARIABLES,andSHOWMARKOVINFORMATION,andthen clickOK(seeFigure2attheendofthistutorial).Youcanalsochangethenumericalformatting oftheresultsbypullingdowntheEDITmenuandchoosingNUMERICFORMATTING.Fornow,assign “2”forthenumberofdecimalplacesinthewindowforPAYOFFS&EXPECTEDVALUESandusethe dropdownmenustoSHOWNUMBERS“Exactly”andhave“None”forUNITS.  MarkovAnalysis Savethetreefirst.Toobtainthediscountedquality‐adjustedlifeexpectanciesforUsualCare andTreatment,selecttherootnode,pullingdowntheANALYSISmenuandchooseRANKINGS (14.35quality‐adjustedyearsforUsualCare;14.93quality‐adjustedyearsforTreatment).Note thatthesevaluesareexpectedvaluesperperson.ClickOKtoreturntothetree.Tolookata Markovtrace,selectoneoftheMarkovnodes,pulldowntheANALYSISmenu,andchoose MARKOVCOHORT(FULLDETAIL).Awindowwillappearwithfouroptions:(1)SUMMARYREPORT,(2) EXPANDEDREPORT,(3)GRAPH,and(4)EXCELCHART.SelectSUMMARYREPORT.TreeAgeProwillcreate areportthatincludesthestagenumber,stagereward(aweightedaverageoftheutilitiesfor thatstage),totalreward(acumulativesumofthestagerewards),theprobabilitiesofbeingin eachstateduringeachstage,andtheutilitycontributionfromeachstatetothetotal.This reportcanbepastedtotheclipboard(fromwhereitcanbepastedintoaspreadsheetfile)by selectingEXPORTfollowedbyCOPYTOCLIPBOARD,ordirectlyEXPORTTOEXCEL.Notethatoncethe dataareinaspreadsheet,summinganyparticularcolumnofprobabilitieswillgivethetotal expectedtimeinthatstate.AMarkovtraceisaveryusefultoolfordebuggingpurposes.Click OKandCLOSEtoreturntothetree.  SensitivityAnalysis Toinvestigatetheimpactofchangesinparticularvariablesontheanalysis,youcanperfor...