FDA生物等效性统计方法

GuidanceforIndustry

StatisticalApproachestoEstablishingBioequivalence

U.S.DepartmentofHealthandHumanServicesFoodandDrugAdministration

CenterforDrugEvaluationandResearch(CDER)January2001

BP

GuidanceforIndustry

StatisticalApproachestoEstablishingBioequivalence

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OfficeofTrainingandCommunicationsDivisionofCommunicationsManagementDrugInformationBranch,HFD-210

5600FishersLane

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(Tel)301-827-4573

(Internet)

/cder/guidance/index.htm

U.S.DepartmentofHealthandHumanServicesFoodandDrugAdministration

CenterforDrugEvaluationandResearch(CDER)January2001

BP

TableofContents

INTRODUCTION 1

BACKGROUND 1

General 1

Statistical 2

STATISTICALMODEL 3

STATISTICALAPPROACHESFORBIOEQUIVALENCE 3

AverageBioequivalence 4

PopulationBioequivalence 5

IndividualBioequivalence 6

STUDYDESIGN 7

ExperimentalDesign 7

SampleSizeandDropouts 8

STATISTICALANALYSIS 9

LogarithmicTransformation 9

DataAnalysis 10

MISCELLANEOUSISSUES 13

StudiesinMultipleGroups 13

CarryoverEffects 13

OutlierConsiderations 14

Discontinuity 15

REFERENCES 16

APPENDIXA 21

APPENDIXB 25

APPENDIXC 28

APPENDIXD 32

APPENDIXE 34

APPENDIXF 35

APPENDIXG 40

APPENDIXH 45

GUIDANCEFORINDUSTRY1

StatisticalApproaches

toEstablishingBioequivalence

ThisguidancerepresentstheFoodandDrugAdministration'scurrentthinkingonthistopic.ItdoesnotcreateorconferanyrightsfororonanypersonanddoesnotoperatetobindFDAorthepublic.Analternativeapproachmaybeusedifsuchapproachsatisfiestherequirementsoftheapplicablestatutesandregulations.

INTRODUCTION

Thisguidanceprovidesrecommendationstosponsorsandapplicantswhointend,eitherbeforeorafterapproval,touseequivalencecriteriainanalyzinginvivoorinvitrobioequivalence(BE)studiesforinvestigationalnewdrugapplications(INDs),newdrugapplications(NDAs),abbreviatednewdrugapplications(ANDAs)andsupplementstotheseapplications.ThisguidancediscussesthreeapproachesforBEcomparisons:average,population,andindividual.Theguidancefocusesonhowtouseeachapproachonceaspecificapproachhasbeenchosen.ThisguidancereplacesapriorFDAguidanceentitledStatisticalProceduresforBioequivalenceStudiesUsingaStandardTwo-TreatmentCrossoverDesign,whichwasissuedinJuly1992.

BACKGROUND

General

Requirementsforsubmittingbioavailability(BA)andBEdatainNDAs,ANDAs,andsupplements,thedefinitionsofBAandBE,andthetypesofinvivostudiesthatareappropriatetomeasureBAandestablishBEaresetforthin21CFRpart320.Thisguidanceprovidesrecommendationsonhowtomeetprovisionsofpart320foralldrugproducts.

DefinedasrelativeBA,BEinvolvescomparisonbetweenatest(T)andreference(R)drugproduct,whereTandRcanvary,dependingonthecomparisontobeperformed(e.g.,to-be-marketeddosageformversusclinicaltrialmaterial,genericdrugversusreferencelisteddrug,

1ThisguidancehasbeenpreparedbythePopulationandIndividualBioequivalenceWorkingGroupoftheBiopharmaceuticsCoordinatingCommitteeintheOfficeofPharmaceuticalScience,CenterforDrugEvaluationandResearch(CDER)attheFoodandDrugAdministration(FDA).

J:\!GUIDANC\3616fnl.doc01/31/01

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drugproductchangedafterapprovalversusdrugproductbeforethechange).AlthoughBAandBEarecloselyrelated,BEcomparisonsnormallyrelyon(1)acriterion,(2)aconfidenceintervalforthecriterion,and(3)apredeterminedBElimit.BEcomparisonscouldalsobeusedincertainpharmaceuticalproductlineextensions,suchasadditionalstrengths,newdosageforms(e.g.,changesfromimmediatereleasetoextendedrelease),andnewroutesofadministration.Inthesesettings,theapproachesdescribedinthisguidancecanbeusedtodetermineBE.Thegeneralapproachesdiscussedinthisguidancemayalsobeusefulwhenassessingpharmaceuticalequivalenceorperformingequivalencecomparisonsinclinicalpharmacologystudiesandotherareas.

Statistical

IntheJuly1992guidanceonStatisticalProceduresforBioequivalenceStudiesUsingaStandardTwo-TreatmentCrossoverDesign(the1992guidance),CDERrecommendedthatastandardinvivoBEstudydesignbebasedontheadministrationofeithersingleormultipledosesoftheTandRproductstohealthysubjectsonseparateoccasions,withrandomassignmenttothetwopossiblesequencesofdrugproductadministration.The1992guidancefurtherrecommendedthatstatisticalanalysisforpharmacokineticmeasures,suchasareaunderthecurve(AUC)andpeakconcentration(Cmax),bebasedonthetwoone-sidedtestsproceduretodeterminewhethertheaveragevaluesforthepharmacokineticmeasuresdeterminedafteradministrationoftheTandRproductswerecomparable.Thisapproachistermedaveragebioequivalenceandinvolvesthecalculationofa90%confidenceintervalfortheratiooftheaverages(populationgeometricmeans)ofthemeasuresfortheTandRproducts.ToestablishBE,thecalculatedconfidenceintervalshouldfallwithinaBElimit,usually80-125%fortheratiooftheproductaverages.2Inadditiontothisgeneralapproach,the1992guidanceprovidedspecificrecommendationsfor(1)logarithmictransformationofpharmacokineticdata,(2)methodstoevaluatesequenceeffects,and(3)methodstoevaluateoutlierdata.

AlthoughaverageBEisrecommendedforacomparisonofBAmeasuresinmostBEstudies,thisguidancedescribestwonewapproaches,termedpopulationandindividualbioequivalence.Thesenewapproachesmaybeuseful,insomeinstances,foranalyzing

invitroandinvivoBEstudies.3TheaverageBEapproachfocusesonlyonthecomparisonofpopulationaveragesofaBEmeasureofinterestandnotonthevariancesofthemeasureforthe

2Forabroadrangeofdrugs,aBElimitof80to125%fortheratiooftheproductaverageshasbeenadoptedforuseofanaverageBEcriterion.Generally,theBElimitof80to125%isbasedonaclinicaljudgmentthatatestproductwithBAmeasuresoutsidethisrangeshouldbedeniedmarketaccess.

3Foradditionalrecommendationsoninvivostudies,seetheFDAguidanceforindustryonBioavailabilityandBioequivalenceStudiesforOrallyAdministeredDrugProductsGeneralConsiderations.AdditionalrecommendationsoninvitrostudieswillbeprovidedinanFDAguidanceforindustryonBioavailabilityandBioequivalenceStudiesforNasalAerosolsandNasalSpraysforLocalAction,whenfinalized.

TandRproducts.TheaverageBEmethoddoesnotassessasubject-by-formulationinteractionvariance,thatis,thevariationintheaverageTandRdifferenceamongindividuals.

Incontrast,populationandindividualBEapproachesincludecomparisonsofbothaveragesandvariancesofthemeasure.ThepopulationBEapproachassessestotalvariabilityofthemeasureinthepopulation.TheindividualBEapproachassesseswithin-subjectvariabilityfortheTandRproducts,aswellasthesubject-by-formulationinteraction.

STATISTICALMODEL

D

StatisticalanalysesofBEdataaretypicallybasedonastatisticalmodelforthelogarithmoftheBAmeasures(e.g.,AUCandCmax).Themodelisamixed-effectsortwo-stagelinearmodel.Eachsubject,j,theoreticallyprovidesameanforthelog-transformedBAmeasureforeachformulation,TjandRjfortheTandRformulations,respectively.Themodelassumesthatthesesubject-specificmeanscomefromadistributionwithpopulationmeansTandR,andbetween-subjectvariancesBT2andBR2,respectively.Themodelallowsforacorrelation,,betweenTjandRj.Thesubject-by-formulationinteractionvariancecomponent(SchallandLuus1993),2,isrelatedtotheseparametersasfollows:

D Tj Rj

2=varianceof(-)

=(BT-BR)2+2(1-)BTBR Equation1

Foragivensubject,theobserveddataforthelog-transformedBAmeasureareassumedtobeindependentobservationsfromdistributionswithmeansTjandRj,andwithin-subjectvariancesWT2andWR2.Thetotalvariancesforeachformulationaredefinedasthesumofthewithin-andbetween-

TR WR BR

subjectcomponents(i.e.,TT2=WT2+BT2and 2= 2+ 2).Foranalysisofcrossover

studies,themeansaregivenadditionalstructurebytheinclusionofperiodandsequenceeffectterms.

STATISTICALAPPROACHESFORBIOEQUIVALENCE

ThegeneralstructureofaBEcriterionisthatafunction()ofpopulationmeasuresshouldbedemonstratedtobenogreaterthanaspecifiedvalue().Usingtheterminologyofstatisticalhypothesistesting,thisisaccomplishedbytestingthehypothesisH0:>versusHA:#atadesiredlevelofsignificance,often5%.RejectionofthenullhypothesisH0(i.e.,demonstratingthattheestimateofisstatisticallysignificantlylessthanresultsinaconclusionofBE.Thechoiceofanddiffersinaverage,population,andindividualBEapproaches.

AgeneralobjectiveinassessingBEistocomparethelog-transformedBAmeasureafteradministrationoftheTandRproducts.AsdetailedinAppendixA,populationandindividualapproachesarebasedonthecomparisonofanexpectedsquareddistancebetweentheTandRformulationstotheexpected

squareddistancebetweentwoadministrationsoftheRformulation.AnacceptableTformulationisonewheretheT-RdistanceisnotsubstantiallygreaterthantheR-Rdistance.InbothpopulationandindividualBEapproaches,thiscomparisonappearsasacomparisontothereferencevariance,whichisreferredtoasscalingtothereferencevariability.

PopulationandindividualBEapproaches,butnottheaverageBEapproach,allowtwotypesofscaling:reference-scalingandconstant-scaling.Reference-scalingmeansthatthecriterionusedisscaledtothevariabilityoftheRproduct,whicheffectivelywidenstheBElimitformorevariablereferenceproducts.Althoughgenerallysufficient,useofreference-scalingalonecouldunnecessarilynarrowtheBElimitfordrugsand/ordrugproductsthathavelowvariabilitybutawidetherapeuticrange.Thisguidance,therefore,recommendsmixed-scalingforthepopulationandindividualBEapproaches(sectionIV.BandC).Withmixedscaling,thereference-scaledformofthecriterionshouldbeusedifthereferenceproductishighlyvariable;otherwise,theconstant-scaledformshouldbeused.

AverageBioequivalence

ThefollowingcriterionisrecommendedforaverageBE:

(T-R)2#A2 Equation2

where

T=populationaverageresponseofthelog-transformedmeasurefortheTformulation

R=populationaverageresponseofthelog-transformedmeasurefortheRformulation

asdefinedinsectionIIIabove.

Thiscriterionisequivalentto:

-A#(T-R)#A Equation3

and,usually,A=ln(1.25).

PopulationBioequivalence

Thefollowingmixed-scalingapproachisrecommendedforpopulationBE(i.e.,usethereference-scaledmethodiftheestimateofTR>T0andtheconstant-scaledmethodiftheestimateofTR#T0).

Therecommendedcriteriaare:

Reference-Scaled:

)

TR

(T-R)2+(TT2- 2

#p Equation4

2

TR

or

Constant-Scaled:

)

TR

(T-R)2+(TT2- 2

#p Equation5

2

T0

where:

T =populationaverageresponseofthelog-transformedmeasurefortheTformulation

R =populationaverageresponseofthelog-transformedmeasure

fortheRformulation

TT2 =totalvariance(i.e.,sumofwithin-andbetween-subjectvariances)oftheTformulation

TR

2 =totalvariance(i.e.,sumofwithin-andbetween-subject

variances)oftheRformulation

T0

2 =specifiedconstanttotalvariance

p =BElimit

Equations4and5representanaggregateapproachwhereasinglecriterionontheleft-handsideoftheequationencompassestwomajorcomponents:(1)thedifferencebetweentheTandRpopulationaverages(T-R),and(2)thedifferencebetweentheTandRtotalvariances

TR

(TT2- 2).ThisaggregatemeasureisscaledtothetotalvarianceoftheRproductortoa

T0

constantvalue(greater.

2,astandardthatrelatestoalimitforthetotalvariance),whicheveris

ThespecificationofbothT0andPreliesontheestablishmentofstandards.ThegenerationofthesestandardsisdiscussedinAppendixA.WhenthepopulationBEapproachisused,inadditiontomeetingtheBElimitbasedonconfidencebounds,thepointestimateofthegeometrictest/referencemeanshouldfallwithin80-125%.

IndividualBioequivalence

Thefollowingmixed-scalingapproachisoneapproachforindividualBE(i.e.,usethereference-scaledmethodiftheestimateofWR>W0,andtheconstant-scaledmethodiftheestimateof

WR#W0).AlsoseesectionVII.D,Discontinuity,forfurtherdiscussion.Therecommendedcriteriaare:

Reference-Scaled:

D

(T-R)2+2+(WT2-WR2)

WR2

#I Equation6

or

Constant-Scaled:

D

(T-R)2+2+(WT2-WR2)

#I Equation7

2

W0

where:

T =populationaverageresponseofthelog-transformedmeasurefortheTformulation

R =populationaverageresponseofthelog-transformedmeasure

fortheRformulation

D2 =subject-by-formulationinteractionvariancecomponent

WT2 =within-subjectvarianceoftheTformulation

WR2 =within-subjectvarianceoftheRformulation

W0

2 =specifiedconstantwithin-subjectvariance

I =BElimit

D

Equations6and7representanaggregateapproachwhereasinglecriterionontheleft-handsideoftheequationencompassesthreemajorcomponents:(1)thedifferencebetweentheTandRpopulationaverages(T-R),(2)subject-by-formulationinteraction(2),and(3)thedifferencebetweentheTandRwithin-subjectvariances(WT2-WR2).Thisaggregate

,a

W0

measureisscaledtothewithin-subjectvarianceoftheRproductortoaconstantvalue( 2

standardthatrelatestoalimitforthewithin-subjectvariance),whicheverisgreater.

ThespecificationofbothW0andIreliesontheestablishmentofstandards.ThegenerationofthesestandardsisdiscussedinAppendixA.WhentheindividualBEapproachisused,inadditiontomeetingtheBElimitbasedonconfidencebounds,thepointestimateofthegeometrictest/referencemeanratioshouldfallwithin80-125%.

STUDYDESIGN

ExperimentalDesign

NonreplicatedDesigns

Aconventionalnonreplicateddesign,suchasthestandardtwo-formulation,two-period,two-sequencecrossoverdesign,canbeusedtogeneratedatawhereanaverageorpopulationapproachischosenforBEcomparisons.Undercertaincircumstances,paralleldesignscanalsobeused.

ReplicatedCrossoverDesigns

ReplicatedcrossoverdesignscanbeusedirrespectiveofwhichapproachisselectedtoestablishBE,althoughtheyarenotnecessarywhenanaverageorpopulationapproachisused.ReplicatedcrossoverdesignsarecriticalwhenanindividualBEapproachisusedtoallowestimationofwithin-subjectvariancesfortheTandRmeasuresandthesubject-by-formulationinteractionvariancecomponent.Thefollowingfour-period,two-sequence,two-formulationdesignisrecommendedforreplicatedBEstudies(seeAppendixBforfurtherdiscussionofreplicatedcrossoverdesigns).

Period

1 2 3 4

Sequence

T R T R

R T R T

Forthisdesign,thesamelotsoftheTandRformulationsshouldbeusedforthereplicatedadministration.Eachperiodshouldbeseparatedbyanadequatewashoutperiod.

Otherreplicatedcrossoverdesignsarepossible.Forexample,athree-perioddesign,asshownbelow,couldbeused.

Period

1 2 3

Sequence

T R T

R T R

Agreaternumberofsubjectswouldbeencouragedforthethree-perioddesigncomparedtotherecommendedfour-perioddesigntoachievethesamestatisticalpowertoconcludeBE(seeAppendixC).

SampleSizeandDropouts

Aminimumnumberof12evaluablesubjectsshouldbeincludedinanyBEstudy.WhenanaverageBEapproachisselectedusingeithernonreplicatedorreplicateddesigns,methodsappropriatetothestudydesignshouldbeusedtoestimatesamplesizes.ThenumberofsubjectsforBEstudiesbasedoneitherthepopulationorindividualBEapproachcanbeestimatedbysimulationifanalyticalapproachesforestimationarenotavailable.FurtherinformationonsamplesizeisprovidedinAppendixC.

Sponsorsshouldenterasufficientnumberofsubjectsinthestudytoallowfordropouts.Becausereplacementofsubjectsduringthestudycouldcomplicatethestatisticalmodelandanalysis,dropoutsgenerallyshouldnotbereplaced.Sponsorswhowishtoreplacedropoutsduringthestudyshouldindicatethisintentionintheprotocol.Theprotocolshouldalsostate

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whethersamplesfromreplacementsubjects,ifnotused,willbeassayed.Ifthedropoutrateishighandsponsorswishtoaddmoresubjects,amodificationofthestatisticalanalysismayberecommended.Additionalsubjectsshouldnotbeincludedafterdataanalysisunlessthetrialwasdesignedfromthebeginningasasequentialorgroupsequentialdesign.

STATISTICALANALYSIS

Thefollowingsectionsproviderecommendationsonstatisticalmethodologyforassessmentofaverage,population,andindividualBE.

LogarithmicTransformation

GeneralProcedures

ThisguidancerecommendsthatBEmeasures(e.g.,AUCandCmax)belog-transformedusingeithercommonlogarithmstothebase10ornaturallogarithms(seeAppendixD).Thechoiceofcommonornaturallogsshouldbeconsistentandshouldbestatedinthestudyreport.ThelimitedsamplesizeinatypicalBEstudyprecludesareliabledeterminationofthedistributionofthedataset.Sponsorsand/orapplicantsarenotencouragedtotestfornormalityoferrordistributionafterlog-transformation,norshouldtheyusenormalityoferrordistributionasareasonforcarryingoutthestatisticalanalysisontheoriginalscale.JustificationshouldbeprovidedifsponsorsorapplicantsbelievethattheirBEstudydatashouldbestatisticallyanalyzedontheoriginalratherthanonthelogscale.

PresentationofData

Thedrugconcentrationinbiologicalfluiddeterminedateachsamplingtimepointshouldbefurnishedontheoriginalscaleforeachsubjectparticipatinginthestudy.Thepharmacokineticmeasuresofsystemicexposureshouldalsobefurnishedontheoriginalscale.Themean,standarddeviation,andcoefficientofvariationforeachvariableshouldbecomputedandtabulatedinthefinalreport.

Inadditiontothearithmeticmeanandassociatedstandarddeviation(orcoefficientofvariation)fortheTandRproducts,geometricmeans(antilogofthemeansofthelogs)shouldbecalculatedforselectedBEmeasures.TofacilitateBEcomparisons,themeasuresforeachindividualshouldbedisplayedinparallelfortheformulationstested.Inparticular,foreachBEmeasuretheratiooftheindividualgeometricmeanoftheTproducttotheindividualgeometricmeanoftheRproductshouldbetabulatedsidebysideforeachsubject.Thesummarytablesshouldindicateinwhichsequenceeach

subjectreceivedtheproduct.

DataAnalysis

AverageBioequivalence

Overview

Parametric(normal-theory)methodsarerecommendedfortheanalysisoflog-transformedBEmeasures.ForaverageBEusingthecriterionstatedinequations2or3(sectionIII.A),thegeneralapproachistoconstructa90%confidenceintervalforthequantityT-RandtoreachaconclusionofaverageBEifthisconfidenceintervaliscontainedintheinterval[-A,A].Duetothenatureofnormal-theoryconfidenceintervals,thisisequivalenttocarryingouttwoone-sidedtestsofhypothesisatthe5%levelofsignificance(Schuirmann1987).

The90%confidenceintervalforthedifferenceinthemeansofthelog-transformeddatashouldbecalculatedusingmethodsappropriatetotheexperimentaldesign.Theantilogsoftheconfidencelimitsobtainedconstitutethe90%confidenceintervalfortheratioofthegeometricmeansbetweentheTandRproducts.

NonreplicatedCrossoverDesigns

Fornonreplicatedcrossoverdesigns,thisguidancerecommendsparametric(normal-theory)procedurestoanalyzelog-transformedBAmeasures.GenerallinearmodelproceduresavailableinPROCGLMinSASorequivalentsoftwarearepreferred,althoughlinearmixed-effectsmodelprocedurescanalsobeindicatedforanalysisofnonreplicatedcrossoverstudies.

Forexample,foraconventionaltwo-treatment,two-period,two-sequence(2x2)randomizedcrossoverdesign,thestatisticalmodeltypicallyincludesfactorsaccountingforthefollowingsourcesofvariation:sequence,subjectsnestedinsequences,period,andtreatment.TheEstimatestatementinSASPROCGLM,orequivalentstatementinothersoftware,shouldbeusedtoobtainestimatesfortheadjusteddifferencesbetweentreatmentmeansandthestandarderrorassociatedwiththesedifferences.

ReplicatedCrossoverDesigns

Linearmixed-effectsmodelprocedures,availableinPROCMIXEDinSASorequivalentsoftware,shouldbeusedfortheanalysisofreplicatedcrossoverstudiesforaverageBE.AppendixEincludesanexampleofSASprogramstatements.

ParallelDesigns

Forparalleldesigns,theconfidenceintervalforthedifferenceofmeansinthelogscalecanbecomputedusingthetotalbetween-subjectvariance.Asintheanalysisforreplicateddesigns(sectionVI.B.1.b),equalvariancesshouldnotbeassumed.

PopulationBioequivalence

Overview

AnalysisofBEdatausingthepopulationapproach(sectionIV.B)shouldfocusfirstonestimationofthemeandifferencebetweentheTandRforthelog-transformedBAmeasureandestimationofthetotalvarianceforeachofthetwoformulations.Thiscanbedoneusingrelativelysimpleunbiasedestimatorssuchasthemethodofmoments(MM)(Chinchilli1996,andChinchilliandEsinhart1996).Aftertheestimationofthemeandifferenceandthevarianceshasbeencompleted,a95%upperconfidenceboundforthepopulationBEcriterioncanbeobtained,orequivalentlya95%upperconfidenceboundforalinearizedformofthepopulationBEcriterioncanbeobtained.PopulationBEshouldbeconsideredtobeestablishedforaparticularlog-transformedBAmeasureifthe95%upperconfidenceboundforthecriterionislessthanorequaltotheBElimit,P,orequivalentlyifthe95%upperconfidenceboundforthelinearizedcriterionislessthanorequalto0.

Toobtainthe95%upperconfidenceboundofthecriterion,intervalsbasedonvalidatedapproachescanbeused.ValidationapproachesshouldbereviewedwithappropriatestaffinCDER.AppendixFincludesanexampleofupperconfidencebounddeterminationusingapopulationBEapproach.

NonreplicatedCrossoverDesigns

Fornonreplicatedcrossoverstudies,anyavailablemethod(e.g.,SASPROCGLMorequivalentsoftware)canbeusedtoobtainanunbiasedestimateofthemeandifferenceinlog-transformedBAmeasuresbetweentheTandRproducts.Thetotalvarianceforeachformulationshouldbeestimatedbythe

usualsamplevariance,computedseparatelyineachsequenceandthenpooledacrosssequences.

ReplicatedCrossoverDesigns

Forreplicatedcrossoverstudies,theapproachshouldbethesameasfornonreplicatedcrossoverdesigns,butcareshouldbetakentoobtainproperestimatesofthetotalvariances.Oneapproachistoestimatethewithin-andbetween-subjectcomponentsseparately,asforindividualBE(seesectionVI.B.3),andthensumthemtoobtainthetotalvariance.Themethodfortheupperconfidenceboundshouldbeconsistentwiththemethodusedforestimatingthevariances.

ParallelDesigns

Theestimateofthemeansandvariancesfromparalleldesignsshouldbethesameasfornonreplicatedcrossoverdesigns.Themethodfortheupperconfidenceboundshouldbemodifiedtoreflectindependentratherthanpairedsamplesandtoallowforunequalvariances.

IndividualBioequivalence

AnalysisofBEdatausinganindividualBEapproach(sectionIV.C)shouldfocusonestimationofthemeandifferencebetweenTandRforthelog-transformedBAmeasure,thesubject-by-formulationinteractionvariance,andthewithin-subjectvarianceforeachofthetwoformulations.Forthispurpose,werecommendtheMMapproach.

Toobtainthe95%upperconfidenceboundofalinearizedformoftheindividualBEcriterion,intervalsbasedonvalidatedapproachescanbeused.AnexampleisdescribedinAppendixG.Aftertheestimationofthemeandifferenceandthevarianceshasbeencompleted,a95%upperconfidenceboundfortheindividualBEcriterioncanbeobtained,orequivalentlya95%upperconfidenceboundforalinearizedformoftheindividualBEcriterioncanbeobtained.IndividualBEshouldbeconsideredtobeestablishedforaparticularlog-transformedBAmeasureifthe95%upperconfidenceboundforthecriterionislessthanorequaltotheBElimit,I,orequivalentlyifthe95%upperconfidenceboundforthelinearizedcriterionislessthanorequalto0.

Therestrictedmaximumlikelihood(REML)methodmaybeusefultoestimatemeandifferencesandvarianceswhensubjectswithsomemissingdataareincludedinthestatisticalanalysis.AkeydistinctionbetweentheREMLandMMmethodsrelatesto

differencesinestimatingvariancetermsandisfurtherdiscussedinAppendixH.SponsorsconsideringalternativemethodstoREMLorMMareencouragedtodiscusstheirapproacheswithappropriateCDERreviewstaffpriortosubmittingtheirapplications.

MISCELLANEOUSISSUES

StudiesinMultipleGroups

Ifacrossoverstudyiscarriedoutintwoormoregroupsofsubjects(e.g.,ifforlogisticalreasonsonlyalimitednumberofsubjectscanbestudiedatonetime),thestatisticalmodelshouldbemodifiedtoreflectthemultigroupnatureofthestudy.Inparticular,themodelshouldreflectthefactthattheperiodsforthefirstgrouparedifferentfromtheperiodsforthesecondgroup.Thisappliestoalloftheapproaches(average,population,andindividualBE)describedinthisguidance.

Ifthestudyiscarriedoutintwoormoregroupsandthosegroupsarestudiedatdifferentclinicalsites,oratthesamesitebutgreatlyseparatedintime(monthsapart,forexample),questionsmayariseastowhethertheresultsfromtheseveralgroupsshouldbecombinedinasingleanalysis.SuchcasesshouldbediscussedwiththeappropriateCDERreviewdivision.

Asequentialdesign,inwhichthedecisiontostudyasecondgroupofsubjectsisbasedontheresultsfromthefirstgroup,callsfordifferentstatisticalmethodsandisoutsidethescopeofthisguidance.ThosewishingtouseasequentialdesignshouldconsulttheappropriateCDERreviewdivision.

CarryoverEffects

UseofcrossoverdesignsforBEstudiesallowseac