Point-Estimation-Odds-Ratios--Hazard-RatiosRates--Risk-点估计的比值比ratiosrates-危险-风险-精品PPT课件

3/20/2019,-,1,PointEstimation:OddsRatios,HazardRatios,RiskDifferences,Precision,ElizabethS.GOncologyBiostatisticsMarch20,2019,ClinicalTrialsin20Hours,3/20/2019,-,2,PointEstimation,Definition:A“pointestimate”isaone-numbersummaryofdata.Ifyouhadjustonenumbertosummarizetheinferencefromyourstudy.Examples:Dosefindingtrials:MTD(maximumtolerabledose)SafetyandEfficacyTrials:responserate,mediansurvivalComparativeTrials:Oddsratio,hazardratio,3/20/2019,-,3,TypesofVariables,Thepointestimateyouchoosedependsonthe“nature”oftheoutcomeofinterestContinuousVariablesExamples:changeintumorvolumeortumordiameterCommonlyusedpointestimates:mean,medianBinaryVariablesExamples:response,progression,50%reductionintumorsizeCommonlyusedpointestimate:proportion,relativerisk,oddsratioTime-to-Event(Survival)VariablesExamples:timetoprogression,timetodeath,timetorelapseCommonlyusedpointestimates:mediansurvival,k-yearsurvival,hazardratioOthertypesofvariables:nominalcategorical,ordinalcategorical,3/20/2019,-,4,Today,PointEstimatescommonlyseen(andmisunderstood)inclinicaloncologyoddsratioriskdifferencehazardratio/riskratio,3/20/2019,-,5,PointEstimates:OddsRatios,“Age,Sex,andRacialDifferencesintheUseofStandardAdjuvantTherapyforColorectalCancer”,Potosky,Harlan,Kaplan,Johnson,Lynch.JCO,vol.20(5),March2019,p.1192.Example:Isgenderassociatedwithuseofstandardadjuvanttherapy(SAT)forpatientswithnewlydiagnosedstageIIIcolonorstageII/IIIrectalcancer?53%ofmenreceivedSAT*62%ofwomenreceivedSAT*Howdowequantifythedifference?,*adjustedforothervariables,3/20/2019,-,6,OddsandOddsRatios,Odds=p/(1-p)TheoddsofamanreceivingSATis0.53/(1-0.53)=1.13.TheoddsofawomanreceivingSATis0.62/(1-0.62)=1.63.OddsRatio=1.63/1.13=1.44Interpretation:“Awomanis1.44timesmorelikelytoreceiveSATthanaman.”,3/20/2019,-,7,OddsRatio,OddsRatioforcomparingtwoproportionsOR1:increasedriskofgroup1comparedto2OR=1:nodifferenceinriskofgroup1comparedto2OR0:increasedrisklogOR=0:nodifferenceinrisklogOR0:decreasedrisk,3/20/2019,-,12,RelatedMeasuresofRisk,RelativeRisk:RR=p1/p2RR=0.62/0.53=1.17.Differentwayofdescribingasimilarideaofrisk.Generally,interpretation“inwords”isthesimilar:“Womenareat1.17timesaslikelyasmentoreceiveSAT”RRisappropriateintrialsoften.But,RRisnotappropriateinmanysettings(e.g.case-controlstudies)NeedtobeclearaboutRRversusOR:p1=0.50,p2=0.25.RR=0.5/0.25=2OR=(0.5/0.5)/(0.25/0.75)=3Sameresults,butORandRRgivequitedifferentmagnitude,3/20/2019,-,13,RelatedMeasuresofRisk,RiskDifference:p1-p2Insteadofcomparingriskviaaratio,wecomparerisksviaadifference.InmanyCTs,thegoalistoincreaseresponseratebyafixedpercentage.Example:thecurrentsuccess/responseratetoaparticulartreatmentis0.20.Thegoalfornewtherapyisaresponserateof0.40.Ifthisgoalisreached,thenthe“riskdifference”willbe0.20.,3/20/2019,-,14,WhydowesooftenseeORandnotothers?,(1)Logisticregression:Allowsustolookatassociationbetweentwovariables,adjustedforothervariables.“Output”isalogoddsratio.Example:InthegenderSATexample,theoddsratioswereevaluatedusinglogisticregression.Inreality,thegenderSAToddsratioisadjustedforage,race,yearofdx,region,maritalstatus,.(2)Canbemoregloballyapplied.Designofstudydoesnotrestrictusage.,3/20/2019,-,15,AnotherExample,“RandomizedControlledTrialofSingle-AgentPaclitaxelVersusCyclophosphamide,Doxorubicin,andCisplatininPatientswithRecurrentOvarianCancerWhoRespondedtoFirst-linePlatinum-BasedRegimens”,Cantu,Parma,Rossi,Floriani,Bonazzi,DellAnna,Torri,Colombo.JCO,vol.20(5),March2019,p.1232.Groups:paclitaxel(n=47)versusCAP(n=47)“14patientsintheCAPgroupand8patientsinthepaclitaxelgrouphadcompleteresponsesp1=14/47=0.30;p2=8/47=0.17OR=(0.30/0.70)/(0.17/0.83)=2.1,3/20/2019,-,16,OddsRatiovia2x2table,“14patientsintheCAPgroupand8patientsinthepaclitaxelgrouphadcompleteresponses“PatientsintheCAPgrouparetwiceaslikelytohaveaCRasthoseinthepaclitaxelgroup.”2x2Tableapproach:OR=ad/bc=(14*39)/(8*33)=2.1,3/20/2019,-,17,“RandomizedControlledTrialofSingle-AgentPaclitaxelVersusCyclophosphamide,Doxorubicin,andCisplatininPatientswithRecurrentOvarianCancerWhoRespondedtoFirst-linePlatinum-BasedRegimens”,Cantu,Parma,Rossi,Floriani,Bonazzi,DellAnna,Torri,Colombo.JCO,vol.20(5),March2019,p.1232.,PointEstimates:HazardRatios,“WhatistheeffectofCAPonoverallsurvivalascomparedtopaclitaxel?”MediansurvivalinCAPgroupwas34.7months.Mediansurvivalinpaclitaxelgroupwas25.8months.But,mediansurvivaldoesnttellthewholestory.,3/20/2019,-,18,HazardRatio,ComparesriskofeventintwopopulationsorsamplesRatioofriskingroup1toriskingroup2Firstthingsfirst.Kaplan-MeierCurves(product-limitestimate)Makesa“picture”ofsurvival,3/20/2019,-,19,HazardRatios,Assumption:“Proportionalhazards”Theriskdoesnotdependontime.Thatis,“riskisconstantovertime”Butthatisstillvague.HypotheticalExample:Assumehazardratiois2.Patientsinstandardtherapygroupareattwicetheriskofdeathasthoseinnewdrug,atanygivenpointintime.Hazardfunction=P(dieattimet|survivedtotimet),3/20/2019,-,20,HazardRatios,HazardRatio=hazardfunctionforStdhazardfunctionforNewMakestheassumptionthatthisratioisconstantovertime.,3/20/2019,-,21,HazardRatios,HazardRatio=hazardfunctionforPachazardfunctionforCAPMakestheassumptionthatthisratioisconstantovertime.,HR=2,3/20/2019,-,22,HazardRatios,HazardRatio=hazardfunctionforPachazardfunctionforCAPMakestheassumptionthatthisratioisconstantovertime.,HR=2,HR=2,3/20/2019,-,23,InterpretationAgain,Foranyfixedpointintime,individualsinthestandardtherapygroupareattwicetheriskofdeathasthenewdruggroup.,HR=2,HR=2,3/20/2019,-,24,Hazardratioisnotalwaysvalid.,HazardRatio=.71,3/20/2019,-,25,CAPvs.Paclitaxel,HazardRatioforProgressionFreeSurvival:0.60forCAPvs.Paclitaxel,3/20/2019,-,26,CAPvs.Paclitaxel,HazardRatioforOverallSurvival:0.58forCAPvs.Paclitaxel,3/20/2019,-,27,IntroductiontoPrecisionIssues,PrecisionVariabilityTwokindsofvariabilitywetendtodealwithvariationinthepopulation:howmuchdoindividualstendtodifferfromoneanother?varianceofstatistics:howcertainareweofourestimateoftheoddsratio?Theremightbegreatvariabilityinthepopulation,butwithalargesamplesize,wecanhaveverygoodprecisionforasamplestatistic.,3/20/2019,-,28,StandardDeviation,StandarddeviationmeasureshowmuchvariabilitythereisinavariableacrossindividualsinthepopulationCD20ExpressioninHodgkinandReed-SternbergCellsofClassicalHodgkinsDisease:AssociationswithPresentingFeaturesandClinicalOutcome,Rassidakis,Mederios,Viviani