Intersubject Variability in Pharmacokinectics and Subject Characteristics in Phase I StudiesPeng Chai, Chun Feng, and Xiaopeng Li Celerion, Lincoln, NE

• Theprimaryfocusisonwhetherthe90%geometricconfidenceintervalfortheratiooftreatmentgeometricmeansisentirelycontainedwithinthe80.00–125.00%equivalencerange(Schuirmann’sTwoOne-SidedTests(TOST))asisinTable1.ThestatisticianwhoworkswiththepharmacokineticistshouldalsoexaminecloselyanothersetofstatisticaloutputsfromtheANOVA:

• Astatisticallysignificantsequenceeffectcouldindicatethecarryovereffect,treatment-by-periodinteraction,orfailureofrandomization.Thecauseofastatisticallysignificantperiodeffectisoftenunknown.Thisneverthelessshouldalertthestatisticiantofurtherinspectthedata.TheintrasubjectCVwhichindicateswithin-subjectvariabilityisderivedfromtheresidualerrorterm,i.e.,eintheaboveANOVAmodel,usingtheformula,intrasubjectCV(%)=100xsqrt[exp(residual)-1)].CorrespondingtointrasubjectCV,thereisintersubjectCVwhichisderivedfromsubject(sequence)asarandomeffectintheaboveANOVAmodel.

intersubjectCV(%)=100xsqrt[exp(subject(sequence))-1)]

• Here,intersubjectCVindicatesbetween-subjectvariabilityafteraccountingforthefixedeffectsoftreatment,sequence,andperiod.(IfSASProcMixedprocedureisused,residualandsubject(sequence)aswellastheirassociatedstatisticsareprovidedunderCovarianceParameterEstimates.)

• InTable1,theobjectiveofdemonstratingbioequivalenceusingTOSTapproachisattained.InTable2,theintrasubjectCVwhichdeterminesthestatisticalpowerandconfidenceintervalisnothigh(<30%).However,thehighintersubjectCVisquitenoticeableandshouldbecommunicatedtothepharmacokineticistforadditionalPKresearch.Thestatisticianshouldalsoexaminetheassumptionsofthestatisticalmodel.Normalprobabilityplotofstudentizedresidualscanbeusedtoassessnormalityofresidualerroraswellasidentifyoutlier(thereisoneprominentoutlier,Figure1).Residualplotcanassessmodelfittingandhomogeneityofvariance(Figure2).

Example2:

• ItisbeneficialtounderstandtherelationshipbetweensubjectcharacteristicsandvariabilityinPKamongsubjects,especiallywhenhighintersubjectCVisnoticed.Amultitudeofdemographic,physiological,andtherapeuticfactorscaninfluencethePKofadrug.Itisthennecessarytoexplorecollectedsubjectcovariatessuchasgender,age,weight,liverandrenalfunctionthatcanrelatetoPKbehavior.BoxplotwhichgraphicallysummarizesdistributionsofmultipledatasetscanbeusefultocomparedifferentlabtestsbytreatmentgroupsasinFigure3.Labvaluesofalanineaminotransferase(ALT),aspartateaminotransferase(AST),totalbilirubin(TBIL),andalkalinephosphatase(ALP)aredividedbytheupperlimitofnormalrange(ULN).Thepurposeistoscreenforsubjectswithatestvalueexceeding3xULNforALTorASTor2xULNforTBILandALP(Hy’sLawfordetectingpoten-tiallivertoxicity).InFigure3,nosubjectexceeds3xULNforALTorAST.However,forALTandAST,theactivetreatmentsAandBaredifferentfromplacebo.UsingsimplescatterplotsrelatingALTandASTtoPKparameters,Figure4furtherindicatesthat4activesubjectswhoshowedhighALT/ASTvaluesalsohadhighAUC0-tandCmaxvalues(however,thesubjectwhohadthehighestAUC0-tandCmaxvaluesdidnotexhibitthispattern).

DISCUSSION AND CONCLUSION:• Crossoverdesignusesawithin-subjectcomparisonbetween

treatments(thesubjectservesashis/herowncontrol)byseparatingoutthebetween-subjectvariabilitycomponent.Forthisreason,thestatisticianwantstofocusonintrasubjectCVtoensuresufficientpowerandsamplesizebecausefailingbioequivalencecanbeduetohighwithin-subjectvariabilityresultingintoowideaconfidenceinterval.HerewesuggestthatthestatisticianshouldalsoinspectintersubjectCV.AhighintersubjectCVindicatesvariationinabsorption,distribution,oreliminationofthedrugacrosssubjects.HighintersubjectPKvariabilitycanespeciallybeproblematicfordrugwithnarrowtargetconcentrationwindow.Althoughunderstandingtheactualcausesofwithin-andbetween-subjectvariabilitybelongstotherealmofPK,it’sthestatisticalmodelingthatactuallyquantifiesthemagnitudeofthesetwotypesofvariabilityforthepharmacokineticist.

• MostPhaseIstudiesusehealthysubjectswithrestrictiveinclusionandexclusioncriteria.Thesamplesizeofsuchstudiesisalsosmall.Theresultsfromtheseexploratoryanalysesaresuggestivefordirectionoffutureresearchwork.Forexample,ahighintrasu-bjectCV(>30%)canleadtoreplicatedesigntobetterquantifywithin-subjectvariationsforthetestandreferenceproductswhereasahighintersubjectCVshouldpromptcloserexaminationsofsubjectcovariates.

Figure 1. Figure 3.

Figure 2.

Figure 4.

BACKGROUND:• Pharmacokinetic(PK)andsafetyresultsofPhaseIPKstudiesare

assessedbypharmacokineticistandmedicalwriterrespectivelywiththestatisticianplayingthesupportingrole,e.g.,PKstatisticalmodeling.Hereexamplesareusedtoshowavarietyofstatisticalanalysesandinputsthatthestatisticiancanprovidetothepharmacokineticistandmedicalwriter.

• Whenanindividualsubject’sPKresponsesarerepeatedlymeasured,mixedeffectsmodelingcanprovideestimationoffixed-effectsparameters,between-subjectvariability,andresidualrandomeffects(includingwithin-subjectvariability).Forexample,acommonlyusedstudydesigninPhaseIPKstudiesisacrossoverdesigninwhichthetreatmentsequenceisrandomlyassignedtostudysubjects,andsubjectsaredosedduringthecourseofthestudyaccordingtothetreatmentsequence.TheANOVAmodelforcrossoverdesignis

y=μ+treatment+sequence+period+subject(sequence)+e

whereμisoverallintercept;treatment,sequence,andperiodarefixedeffects;subject(sequence)istherandomeffect;andeistherandomerror.Thedependentvariableyislog-transformedPKparameter,AUCorCmax.

Thecrossoverdesigniswidelyusedinbioavailability/bioequivalencestudiesaswellasdrug-druginteractionandfed/fastedstudies.

METHODS AND RESULTS:Example1:

• ThestatisticalresultsfromANOVAmodelingoncrossoverdesignareoftensummarizedasfollows:

Table 1.

GeometricLSMeans

TreatmentA TreatmentB %Geometric ConfidenceIntervalsParameter Test Reference MeanRatio (90%Confidence)

AUC0-t (ng*hr/mL) 27.68 26.70 103.67 95.07 - 113.05

AUC0-inf (ng*hr/mL) 28.09 27.23 103.18 94.79 - 112.32

Cmax (ng/mL) 2.05 1.84 111.58 101.47 - 122.70

Parameters are ln-transformed prior to analysis.Geometric LS Means are the exponentiated least-squares (LS) mean from the ANOVA.Geometric Mean Ratio = 100*(test/reference)

Table 2.

lnAUC0-t lnAUC0-inf lnCmax (ng*hr/mL) (ng*hr/mL) (ng/mL)

Fixed Effects

Treatment (p-Value) 0.488 0.539 0.059

Sequence (p-Value) 0.622 0.625 0.667

Period (p-Value) 0.048 0.052 0.121

Random Effects

Intrasubject CV (%) 25.93 25.38 28.51

Intersubject CV (%) 119.12 117.26 109.56

ULN = upper limit of normal (/ULN = lab value divided by ULN); A and B = active treatments; P = placebo