关于HR值——what-are-hazard-ratios

lHazardratiosarecommonlyusedwhenpresentingresultsinclinicaltrialsinvolvingsurvivaldata,andallowhypothesistesting.Theyshouldnotbeconsideredthesameasrelativeriskratios.lWhenhazardratiosareusedinsurvivalanalysis,thismayhavenothingtodowithdyingorprolonginglife,butreflectstheanalysisoftimesurvivedtoanevent(theeventmay,insomeinstances,includecure).lAhazardistherateatwhicheventshappen,sothattheprobabilityofaneventhappeninginashorttimeintervalisthelengthoftimemultipliedbythehazard.Althoughthehazardmayvarywithtime,theassumptioninproportionalhazardmodelsforsurvivalanalysisisthatthehazardinonegroupisaconstantproportionofthehazardintheothergroup.Thisproportionisthehazardratio.lWhenexpressingtheresultsofclinicaltrials,itisbesttoconsiderthehazardratioalongsideameasureoftime,suchasmediantimetotheeventunderscrutiny,comparingactivetreatmentandcontrolgroups(thepointsatwhichhalfthesubjectshaveexperiencedtheeventineacharmofthestudy).1Whatis...?seriesNewtitleStatisticsForfurthertitlesintheseries,visit::April2009NPR09/1107S(tj)=S(tj–1)1–djDefiningahazardratioThehazardratioisanexpressionofthehazardorchanceofeventsoccurringinthetreatmentarmasaratioofthehazardoftheeventsoccurringinthecontrolarm.Thetermhazardratioisoftenusedinterchangeablywiththetermrelativeriskratiotodescriberesultsinclinicaltrials.Thisisnotstrictlycorrectastherearesubtleandimportantdifferences.Itisusefultounderstandthemeaningofthetermandalsobeabletoidentifywhenitisusedappropriately.Hazardratiosareincreasinglyusedtoexpresseffectsinstudiescomparingtreatmentswhenstatisticswhichdescribetime-to-eventorsurvivalanalysesareused.Inmostrecenttrialpublicationsthesehavelargelyreplaceddirectcomparisonsofnumberofevents(or‘rates’)afteraspecificpointintime,orattheendofastudy,seenintestssuchasthet-test.Forthetechnicallyminded,thehazardisusuallydenotedbyh(t)andistheprobabilitythatanindividualwhoisunderobservationatatimethasaneventatthattime.Itrepresentstheinstantaneouseventrateforanindividualwhohasalreadysurvivedtotimet.Supposethatkpatientshaveeventsintheperiodoffollow-upatdistincttimes,t1t2t3t4t5…tk.Aseventsareassumedtooccurindependentlyofoneanother,theprobabilitiesofsurvivingfromoneintervaltothenextmaybemultipliedtogethertogivethecumulativesurvivalprobability.Theprobabilityofbeingaliveattimetj,S(tj),iscalculatedfromtheprobabilityofbeingaliveattj–1,S(tj–1),thenumberofpatientsalivejustbeforetj,nj,andthenumberofeventsattj,dj(Equation1).1Inthisequationt0=0andS(0)=1.1Equation1.1ThereisaclearlydefinedrelationshipbetweenS(t)andh(t),whichisgivenbythefollowingcalculusformula(Equation2).1Equation2.1Thehazardh(t)canbeusedforfurtherstatisticalanalysis,nowadaysnearlyalwaysusingcomputers.Thehazardratiocanbecalculatedtocomparegroupsand,strictlyspeaking,istheeffectonthehazardofdifferencesor‘covariates’(forexample,drugtreatmentorcontrol),asestimatedbyregressionmodelswhichtreatthelogarithmofthehazardrateasafunctionofabaselinehazard,h0(t).Onemethod,theCoxmodel,isthemostcommonlyusedmultivariateapproachforanalysingsurvivaltimedatainmedicalresearch.ItisbasedonanassumptionthatthehazardsremainproportionatelyconstantanditismorecorrectlycalledtheCoxproportionalhazardsmodel.Mathematically,theCoxmodelisexpressedbythefollowingequation(Equation3).2Equation3.2Inthisequation,thehazardfunctionh(t)isdependenton,ordeterminedby,asetofpcovariates(x1,x2,...,xp),whoseimpactismeasuredbythesizeoftherespectivecoefficients(b1,b2,...,bp).Hopefullythefollowingdialoguewillmaketheseconceptsmoreaccessibleformostofus,whohavemorerudimentarymathematicalskills.DistinctionfromrelativeriskIncontrasttothehazardratio,therelativeriskratioisameasureofhowmanyeventsWhatarehazardratios?2Whatarehazardratios?Dateofpreparation:April2009NPR09/1107nj()h(t)=–dtd[logS(t)].h(t)=h0(t)xexp{b1x1+b2x2+...+bpxp3Whatarehazardratios?Dateofpreparation:April2009NPR09/1107Box1.ExamplesofwhentousesurvivaldataA.BloodpressureInatrialcomparingbloodpressurereductionscausedbytwodrugs,itisassumedthatthechangesinbloodpressureofthesubjectscausedbythedifferentdrugsarenormallydistributed(thisis‘thesample’fromapopulation).Calculationstodeterminewhetherthedifferencesbetweentheinterventionsarestatisticallydifferent(theprobabilityofthedifferencehavingoccurredbychance)arebasedonstatisticalmethodswhichcanbeappliedtocontinuousvariables.Themeanofthebloodpressuredifferencesarecalculated,andthevariance(andstandarddeviation)orrangeofbloodpressurechangescanalsobededuced.UsingthesemeasuresastatisticaltestsuchasaStudent’st-testoranalysisofvariance(ANOVA)3canbecarriedouttodeterminetheprobabilityofthedifferencesobservedhavingoccurredbychance.Conventionallyitisacceptedthatifthisprobabilityislessthan0.05(p0.05)thenthedifferencesarestatisticallysignificantandthenullhypothesiscanberejected–thetre