DesignSpacesforanalyticalmethods
E.Rozet,P.Lebrun,B.Debrus,B.Boulanger,P.Hubert
SincetheadoptionoftheICHQ8documentconcerningthedevelopmentofpharmaceuticalprocessesfollowingaQualitybyDesign(QbD)approach,therehavebeenmanydiscussionsontheopportunityforanalyticalmethoddevelopmentstofollowasimilarapproach.AkeycomponentoftheQbDparadigmisthedefinitionoftheDesignSpace(DS)ofanalyticalmethodswhereassuranceofqualityisprovided.SeveralDSsforanalyticalmethodshavebeenpublished,stressingtheimportanceofthisconcept.
ThisarticleaimstoexplainwhatananalyticalmethodDSis,whyitisusefulfortherobustdevelopmentandoptimizationofanalyticalmethodsandhowtobuildsuchaDS.Wedistinguishtheusualmeanresponsesurfaceapproach,overlappingmeanresponsesurfacesandthedesirabilityfunctionasonlytheycorrectlydefineaDS.WealsoreviewanddiscussrecentpublicationsassessingtheDSofanalyticalmethods.ª2012ElsevierLtd.Allrightsreserved.
Keywords:Analyticalmethoddevelopment;DesignofExperiments;DesignSpace(DS);Desirabilityfunction;Meanresponsesurface;Optimization;Probabilitymap;Qualityassurance;QualitybyDesign(QbD);Robustness
E.Rozet*,P.Lebrun,P.Hubert
AnalyticalChemistry
Laboratory,CIRM,Universityof
`ge,AvenuedelÕHoˆpital1,Lie
`ge,BelgiumB36,B-4000LieB.Debrus
SchoolofPharmaceuticalSciences,UniversityofGeneva,
SwitzerlandB.Boulanger`ge,BelgiumArlendas.a.,Lie
1.Introduction
Theconceptofqualitybydesign(QbD)has
beenrecentlyadoptedinthepharmaceuti-calindustrythroughseveralinitiatives{e.g.,FDAÕscGMPforthe21stCentury[1],ProcessAnalyticalTechnology(PAT)[2],andthenewregulatorydocuments,ICHQ8[3],Q9[4]andQ10[5]}.Thegeneralaimistoswitchfromthequalitybytesting(QbT)paradigmpreviouslyimplementedinthepharmaceuticalindustrytoadevelopmentaimedatimprovingtheunderstandingoftheprocessesandtheproductsandhenceimprovingproductquality,processefficiencyandregulatoryflexibility.
QbDisnotnewandinvolvesmanyqualityandstatisticaltoolsandmethods(e.g.,sta-tisticaldesignsofexperiments,multivariatestatistics,SixSigmamethodologies,andstatisticalqualitycontrol).Inordertoraisethequalityofpharmaceuticalproducts,ithasonlyrecentlybeenrecognizedthatincreasingthetestingoffinalproducts(i.e.QbT)isnotadequate[6].Instead,toincreasethequalityofpharmaceuticalproducts,qualitymustbebuiltintotheproducts(i.e.QbD),asalreadydoneinmanyotherindustries.Itrequiresunderstandingofhow
*Correspondingauthor.Tel.:+32436320;Fax:+32436317;
E-mail:eric.rozet@ulg.ac.be
variablesinvolvedinformulationandmanufacturingprocessesinfluencethequalityofthefinalproduct.ExamplesofapplicationsofQbDtopharmaceuticalpro-cessescanbefoundinnumerouscasestudiesintheliterature[e.g.,7–18].
Ithasbeenemphasizedthatanalyticalproceduresarealsoprocesses,andthatQbDcouldandshouldbeimplementedforthedevelopmentofanalyticalprocedures,astheyarenon-negligiblecomponentsoftheglobalpharmaceutical-productprocess[19].SeveralexamplesanddiscussionsaboutthedevelopmentofanalyticalmethodsfollowingtheQbDconceptareavailable,e.g.,[20–22].
AkeycomponentofthedevelopmentofanalyticalprocedureusingQbDiswhathasbeencalledtheDesignSpace(DS).TheaimofthisreviewarticleistofocusontheDSofanalyticalmethods.First,wesummarizethegeneralframeworkofQbDdevelopmentofanalyticalmethodstosituatethespecificplaceofDSinthisstrategy.Then,weprovideexplanationofwhatisDS,whyitisusefultodefinetheDSofanalyticalmethodsandhowtocorrectlycomputeandbuildtheDS.Toachievethis,wealsoreviewrecentpublica-tionsassessingtheDSofanalyticalmethods.
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TrendsTrendsinAnalyticalChemistry,Vol.42,2013Figure1.TypicalstepsofQualitybyDesigndevelopmentofanalyticalmethodshighlightingtheplaceoftheconceptofanalyticalmethoddesignspace.ATP,AnalyticalTargetProfile;CQA,CriticalQualityAttribute;FMEA,FailureModeandEffectAnalysis;SST,SystemSuitabilityTests.2.PlaceofDesignSpaceinQbDanalyticalmethoddevelopment
TostartthedevelopmentofaQbDcompliantanalyticalmethodandfinallyreachthedefinitionofitsDS,several158
stepsillustratedinFig.1havetobeperformed.Thissectionsummarizesthemainstepsusuallyrequired.DeeperdetailscanbefoundintheexhaustivereviewofVogtandKord[19]aswellasinthefollowingdocu-ments[20–23].
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TrendsinAnalyticalChemistry,Vol.42,2013Thefirststepistodefinetheintendedpurposeoftheanalyticalmethod.ThishasbeencalledtheAnalyticalTargetProfile(ATP)[20–22,24]whichissimilartotheQualityTargetProductProfile(QTPP)forpharmaceutical-process.ThisATPwillbeasetofcri-teriathatdefineswhatwillbemeasured,inwhichmatrix,overwhatconcentrationrange,andthere-quiredperformancecriteriaofthemethod,togetherwithspecificationsfortheselastones.TheseperformancecriteriacanbecalledCriticalQualityAttributes(CQAs)oftheanalyticalmethodtokeepanomenclatureclosetotheoneusedinpharmaceutical-processdevelopment.ExamplesofATPfortheinterestedreadersareavailable[20–22,24].
Themethodunderdevelopmentwillthenfollowariskassessment[19].Theanalyticalmethodcanbedecom-posedinaflow-charthighlightingthemainstepsoftheprocedurefromsamplepreparationtodataanalysis.Thisallowsidentifyingparametersthatshouldbestudiedduringtheriskassessment.
Typically,thefirststepintheriskassessmentistobuildafishbonediagram(orIshikawadiagram)toidentifyfurtherpotentialfactorsandrelatethemtotherequire-mentincludedintheATP[25].Thisdiagramclassifiesrisksingroupsrelatedtoinstrumentation,materials,methods,chemicalsandreagents,measurements,humanfactors,environmentalissues(e.g.,laboratorytempera-ture,relativehumidity,andlight)[26,27].
Havingdefinedtheriskfactors,theycanberankedandprioritizedusingdedicatedapproaches{e.g.,FailureModeandEffectAnalysis(FMEA)[27–29]}.Thehighnoiseriskfactors(e.g.,analysts,equipment,daysofanalysis,bat-chesofreagentorofmaterials,andsamplebatches)cansubsequentlybeevaluatedexperimentallyusingMea-surementSystemAnalysisapproaches[30–32]tostudytheirimpactontherepeatabilityandthereproducibilityofthemethod,andeventuallycorrectivemeasuresmaybeimplementedtoreducetheirimpact.
High-riskinstrumentalparameterscanalsobeassessedexperimentallyusingstatisticalDesignofExperiments(DoE)methodology.Theseparametersarethecriticalprocessparameters(CPPs).FromtheDoEresultsandtheirinter-pretation,theDSoftheanalyticalmethodwillbeobtained.Weprovidefurtherinformationconcerningthecon-ceptofDSforanalyticalmethodsintheremainingsec-tionsofthisarticle,asitisitscoreaim.Formalanalyticalmethodvalidationisthenneeded[19,33-35].
Nonetheless,thedevelopmentofQbDanalyticalmeth-odsdoesnotendwiththeDS.Acontrolstrategyofthemethodhastobeimplementedtoassurethatthemethodwillperformasintendedonaroutinebasis.Herealso,elementsfromtheMSAand/orfromtheDScanbeusedtoselectresponsesthathavetobemonitoredateachana-lyticalrun.Theseresponsesthatwillbeimplementedinthecontrolstrategyareknownassystem-suitabilitytestsorvaliditytests.Theycanbethedefinitionofaminimum-
Trends
resolutionvaluebetweenacriticalpair,theacceptablevaluefortailingpeaks,themaximumacceptablevalueexpressedinRSDfortherepeatedanalysisofastandardsolution,theminimumvalueofthedeterminationcoeffi-cient(R2)ofastandardcurve,andsoon.WerecommendreadingthefollowingdocumentsasexamplesofhowtoobtainsuchinformationfromtheapplicationoftheDoEmethodologyandtheresultinganalyticalDS[36,37].AnothermethodologythatcanbeimplementedasacontrolstrategyforanalyticalmethodscontrolchartssuchasShewhartX
istousestatistical
ÀRones[32].Outofcontrolmethodscanbedetectedefficientlyandcorrectiveactionsrealizedbyfollowingthedailyperformanceofanalyticalmethodsonsuchcharts.
3.WhatisDesignSpaceofanalyticalmethodsAsstatedabove,themaininterestofthisworkistofocusontheconceptofDSappliedtoanalyticalmethods.InICHpharmaceutical-developmentguidelineQ8[3],theDSisdefinedas‘‘themultidimensionalcombinationandinteractionofinputvariables(e.g.,materialattributes)andprocessparametersthathavebeendemonstratedtoprovideassuranceofquality’’.Therefore,themultidimensionalcombinationandinteractionofinputvariablecorre-spondstoasubspace,so-calledtheDS,whereassuranceofqualityhasbeenproved.TheDSisnecessarilyencompassedwithintheexperimentaldomain,whichisthemultidimensionalspaceformedbythefactorrangesusedduringmethoddevelopment.ThemainconceptlyingbehindtheICHQ8definitionofDSisassuranceofquality(alsoknownasquality-riskmanagement).Thisdocumentalsostatesthat‘‘Workingwithinthedesignspaceisnotconsideredasachange’’.
Intheframeworkofmethoddevelopment,DScanbeconsideredasazoneoftheoreticalrobustnessasnodrasticchangesinthelevelsoftheCQAsofthemethodshouldbeobserved.Hence,todefineananalyticalDS,awiselyse-lectednumberoffactors,alsocalledcriticalprocessparameter(CPP)-operatingfactors(e.g.,gradienttimeinchromatography,andconcentrationofreagentsinimmunoassays)thatimpactontheanalyticaltechniqueunderdevelopmenthavetobestudiedsimultaneously.Usually,theCPPsareobtainedfromariskanalysisandaprioritizationstrategy,asexplainedinSection2.ThejuxtapositionofunivariatestudiesoftheinvolvedfactorscannotdetermineananalyticalDSproperly,aspotentialinteractionsofthefactorsinvolvedcannotbestudied.TheseinteractionsmayresultinsynergicorantagonisticeffectsontheresponsesmeasuredandthereforemodifythedelimitationoftheDS.
TheanalyticalDSisfinallyamultivariatedomainofinputfactorsensuringthatcriticallychosenresponsesareincludedwithinpredefinedlimitswithanacceptablelevelofprobability.Theanalyticalmethodisthereforenolongerdefinedbyasinglepointinthespaceofitsoperating
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Trendsparameters(e.g.,onevalueofwavelength,onevalueofproportionoforganicmodifier,oronevalueofpHofthemobilephase).TheanalyticalmethodisidentifiedbyarangeofoperatingconditionsthataredefinedbytheanalyticalDS.Severalauthorshaveproposedtocallana-lyticalDSthe‘‘MethodOperableDesignRegion’’(MODR;[20–23])inordertodistinguishitfromtheprocessDS.Thisname,MODR,clearlystatesthattheanalyticalpro-cedureisdefinedasamultivariaterangeofvaluesofoperatingparameterswheretheanalyticalmethodpro-videsqualityoutputswithadequateprobability.4.WhyDesignSpaceforanalyticalmethods?ThekeymeaningofQbDandhenceofanalyticalDSistoincreasetheunderstandingoftheanalyticalproceduresthemselvesandtounderstandbettertherelationshipbetweentheanalyticalproceduresandthecapabilityoftheprocessthatincludesthem[38].TheanalyticalDS,asdefinedintheICHQ8document,allowstheinclusionofthemeasurementuncertaintytoassesswhethertheanalyticalprocedureswillprovideassuranceofquality.TheDSobtainedforananalyticalprocedurewillensurethatitwillbeausefulanalyticalmethod,allowinguserstotakeadequatedecisionswiththeresultsgeneratedfromit.TheexerciseofdefiningaDSforanalyticalmethodsallowsuserstodeterminethecriticalanalyticalmethodparameters(correspondingtotheCPPsinprocessliterature)thatloadheavyweightsontheCQAsoftheanalyticalmethods.Controloverthemostimportantfactorscanhencebejudiciouslyimplemented.TherangesoverwhichthesemethodparameterscanbevariedareknownattheendofthedefinitionoftheanalyticalDS.ThisimpliesthattheDSofananalyticalmethodisameasureofitsrobustness.Inaddition,thecontrolstrat-egyoftheanalyticalprocedurecanbeimplementedbyselectingsystem-suitabilityteststhatarehighlycorre-latedtotheCQAsoftheanalyticalprocedure[20–22,37].AsmovingwithintheDSisnotconsideredchange,moreflexibilityfortheanalyticalmethodsduringitsroutineapplicationispossible.HencechangecontrolswillonlyberequiredwhensteppingoutsidetheDSlimits.Theparticularcaseofmethodtransferfromlaboratoriestolaboratoriesiseased[39].Thisispossiblesinceadap-tationoftheanalyticalprocedurebeingtransferredcanbeperformedwithinitsDSatthereceivingsite.
Finally,themainreasontodeterminetheDSofananalyticalprocedureisthatitprovidesinformationonhowoftentheanalyticalprocedurewillmeetitsrequirementinordertoprovidereliable,usefuldata.5.HowtodefinetheDesignSpaceofanalyticalmethods
InordertodefinetheDSofanalyticalmethods,severalstepshavetobeperformed.Thestartingpointistogather160
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andtoreviewallhistoricalinformationavailableontheanalyticalmethodunderdevelopment,previouslydevel-opedmethodsthatarecloselyrelated,andtheliteratureandscientificinformationavailableonthesubject.5.1.CriticalqualityattributesandmodeledresponsesThefirststepistodefinetheCQAsoftheanalyticalmethodthathavetobeincludedintotheATP.TheseCQAsaretheresponsesthataremeasuredtojudgethequalityofthedevelopedanalyticalmethods.CQAsaredefinedas‘‘aphysical,chemical,biologicalormicrobiologicalpropertyorcharacteristicthatshouldbewithinanappropriatelimit,range,ordistributiontoensurethedesiredproductquality’’[3].Forseparativeanalyticalmethods(e.g.,chromatography),theCQAscanberelatedtothemethodselectivity(e.g.,theresolution(RS)criteria).AdditionalCQAscanbetheruntimeoftheanalysis,theprecisionoftheanalyticalmethod,thelowerlimitofquantificationorthedosingrangeoftheanalyticalmethod.SometimestheseCQAscanbedirectlymodeledthroughamultivar-iate(non-)linearmodel.Howeverinsomesituations,themodeledresponsesmaydifferentfromtheCQAs.TheCQAsareobtainedafterthemodelingoftheseprimaryresponses.
Forchromatographicmethods,theusualkeyCQAisresolutionofthecriticalpair.However,resolutionde-pendsupontheretentionfactorofthetwochromato-graphicpeaksinvolved,soseveralauthors[40–43]haveproposedtomodeltheretentionfactorsinsteadoftheresolution.Theresolutioncansubsequentlybecom-putedfromthesemodeledresponses.Similarly,severalcommercialsoftwarepackagesusethesolvophobicthe-ory[44,45]orthelinearsolvent-strengththeory[46,47]tomodeltheretentionfactorsandthenderivetheoptimalresolution,dependingonseveralfactors.5.2.Experimentalfactors,rangesandlevels
ToobtaintheDSofanalyticalmethods,thechoiceoftheexperimentalfactorsandtheirrespectiverangeispri-mordial.Fromthewholeexperimentaldesignregion,thefactorsandtherangesthatwillaffecttheresponsesmosthavetobechosen[48].Onthisdomain,sometimescalledtheknowledgespace,formaldesignsofexperi-mentswillbeperformed.Thisinvestigatedknowledgespaceisamultidimensionalspacethatneedstobelargeenoughtocreateresponsevariations.ThesevariationsshouldallowuserstoreachtheminimumrequirementsoftheCQAs.AnexampleforchromatographicmethodsisRS>1.5.Thenumberoffactorlevelsdeterminesthepolynomialdegreeofthemulti-linearequationusedtomodeltheresponses.Forexample,iftwolevelsareselected,themodelingequationcanonlybelinear.Generally,ifnopriorinformationabouttheresponsevariationisknown,preliminaryexperimentsshouldbecarriedouttoestimatetherangeandthemagnitudeofvariationofeachfactor.
TrendsinAnalyticalChemistry,Vol.42,2013Trends
5.3.DesignofExperiments(DoEs)andresponsemodelingThenaı¨vewaytoperformexperimentstogainknowl-edgeaboutaprocessortooptimizeitistoperformone-factor-at-a-time(OFAT)designs.OFATwillgenerallyrequireahighernumberofexperimentstoestimatethefactorseffectwithgoodprecisionandtheirinteractionscanrarelybeestimated.DoEsprovideaneffective,efficientapproachtoeval-uatesimultaneouslytheeffectsoffactorsandtheirinteractions,andtomodelandtopredicttherelationshipbetweenthesefactorsandtheCQAsorresponses[49–51].TheselectedDoEneedstohavegoodstatisticalproperties(e.g.,orthogonalityand/orrotatability),andshouldmaintainthenumberofexperimentsaslowaspossible.Thepossibilityofexpandingthedesignisalsoaninterestingpropertyinordertoextendtherangeofvaluesofthefactors,addnewfactors,orincreasethemodelcomplexitywhenstartingtoacquireknowledgeaboutthemethodunderdevelopmentandoptimization.Itshouldalsoallowestimationoftheexperimentalerrorandassessmentofthevalidityofthemodeltested.
DoEcanbesplitupintotwomaincategories:screen-ingdesignsandresponse-surfacedesigns
5.3.1.Screeningdesigns.Screeningdesignsestimatetheeffectsoffactorsonselectedresponses.Whentoomanyfactors(fourormore)seemtoaffecttheresponsesandhavebeenrevealedbytheFMEAprioritization,thesedesignscanbeusedtoselectthosehavingthelargesteffectsontheresponses.Theremainingsignificantfac-torswillbestudiedinasubsequentDoE[e.g.,methodoptimization(seebelow)].Inthescreeningcategoryofdesigns,wellknownarethePlackettandBurmandesignsthatstudyfactorsattwolevels.Inliquidchromatography(LC),PlackettandBurmandesignsarealsousedtoestimatetherobustnessofanoptimalseparation[48,52,53].Figure2.Meanresponsesurfaceforrun-timewithrespecttopHand%acetonitrileobtainedfromthecentralcompositedesignappliedtothehypotheticalanalyticalmethodexample.Thedesiredmaximumrun-timecannotexceed20min.Hatchedregion:experimentaldomainwheremaximumrun-timeisatmost20min.http://www.elsevier.com/locate/trac
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TrendsOthertypesofscreeningdesignsaretwo-levelfrac-tionalfactorialones,whichgenerallydonotallowunderstandingofaprocessunderinvestigationifitmayincludeinteractionsandhigherordereffectterms.Howevertheyareveryusefulinselectingthemostimportantfactorsthatinfluencetheselectedresponsesoftheanalyticalmethodunderinvestigation.
5.3.2.Response-surfacedesigns.ThesecondcategoryofDoEcorrespondstodesignsusedtopredictandtooptimizetheresponses[54,55].TheseDoEsarethree-level,fullfac-torialdesigns,centralcompositedesigns,andBox-Benkhen[56]andDoehlertdesigns[57].D-optimaldesignscanalsobeselectedinordertoanswerparticularrequirements(e.g.,constraintsonthelevelsoffactors,orspecificmodels)[58].Thesedesignsareaimedatunderstandingtheprocessunderinvestigation.Itinvolvesunderstandingtherela-tionshipbetweenthefactorstoassessthebehavioroftheresponse,andtheeffectsontheresponse.Thesedesignsareusedtofindthecombinationoffactorsthatpredicttheoptimalresponsewithgoodprecision.
Morethantwolevelsofeachfactorareusuallyre-quiredinordertofitquadraticorhigherorderterms{e.g.,whenpHisafactorinLC,itmayberequiredtostudypHuptothethird-orderterm:pH+pH2+pH3[59]}.Response-surfacedesignsarekeytoolstodefinetheDSofanalyticalmethods.Theystudyalargeexperimentaldomain,understandingthebehavioroftheresponsesandtheCQAswithrespecttothestudiedfactors,andtheyprovideamodeltopredictthevalueoftheCQAswithintherangeoftheselevelsoffactors.
5.3.3.Responsemodeling.Themodelingoftheresponsescanberealizedintwomainways.Thefirstinvolvesatheoreticalormechanisticmodelthatconnectssomeofthefactorstotheresponses{e.g.,realizedwithsoftwareavailabletooptimizechromatographicmethodsusingthesolvophobictheoryorlinearsolvent-strengththeory[44–47]}.
Table1.CentralcompositedesignusedasexamplefordefiningtheDesignSpaceExperimentpHAcetonitrile%Run-time(min.)10
0
20.152À0.7071068À0.707106815.9830020.6840À114.6850019.6260120.9470020.0381
0
22.1090.70710678À0.707106819.0310À0.70710680.7071067818.37110.707106780.7071067821.60120018.6713
À1
0
16.29
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However,mostofthetime,therearenotheoreticalmodelsthatincludeallthefactorsthatmayinfluencetheresponsesandtheanalyticalCQAs.Inthiscase,empir-icalmodelscanbefittedonthedataobtainedtolinktheresponsesandthefactorsstudied.Thisisusuallyper-formedbyfittingmultiplelinearequationsofadequatepolynomialdegree,relatedtothenumberoffactorsse-lected.Insomesituations,itmayalsoberequiredtofitnon-linearmodels.
5.4.AremeanresponsesurfacestheDesignSpace?Whentheexperimentshavebeenperformedusingaresponse-surfacedesign,theresultingmodelisgenerallyillustratedandinterpretedthroughameanresponsesurfaceorcontourplot,asshowninFig.2.Themeanresponsesurfacedepictsthebehavioroftheresponsemeasuredwithrespecttotherangeoffactorsassessedandtothemodelfitted.Fig.2showsthemeanresponsesurfaceforthemaximumrun-timeofahypotheticalchromatographicmethodusedtoillustratefurtherkeyissuesconcerninganalyticalDS.Forthisexample,thetruemodelthatlinkstheresponsemodeledrun-time(y)tothefactorsproportionofacetonitrileinthemobilephase(ACN)andpHoftheaqueousbuffer(pH)issup-posedknown:
y¼b0þb1ÂACNþb2ÂpHþb11ÂACN2þb22ÂpH2
ð1Þ
0
B
b0¼20
1
with
B¼BB
b1¼2CBC
BCB
b2¼3C@bC
11¼À1CbA22¼À1
Torepresenttherealityofmethodoptimization,arotatablecentralcompositedesignwasdefinedinvolving13experiments,asshowninTable1.Valuesofmaxi-mumrun-timewerethensampledfromthefollowingnormaldistribution:
N(y,r),withr=1attheexperimentalconditionsproposedbytheDoEinTable1.
Theresponse-surfacemodeldefinedinEquation(2)isthenfittedtothedataobtainedandthecorrespondingresponsesurfaceisbuilt,asillustratedinFig.2:^y
¼b0þb1ÂACNþb2ÂpHþb12ÂACNÂpHþb11ÂACN2þb22ÂpH2
ð2Þ
ItisgenerallythoughtthattheDScanbeobtainedbysearchingtherangeofvaluesofthefactorsthatshowthattheresponse(orCQA)meetsapre-definedcriteria(e.g.,Rs>1.5orruntime<20min).ThehatchedregionofFig.2showsthevaluesofthetwofactorshavingaruntimelessthan20min.Itwouldbetemptingtodefinethismulti-variateregionastheDSforthishypotheticalexample.
TrendsinAnalyticalChemistry,Vol.42,2013TrendsFigure3.Probabilitymapshowingthetrueprobabilityofhavingamaximumrun-timeofatmost20minappliedtothehypotheticalanalyticalmethodexample.Hatchedregion:experimentaldomainwherethetrueprobabilitytohavearun-timeofmaximum20minisatleast90%.However,themeanresponsesurfacesdonotgiveanyguaranteethattheresponses(orCQAs)willattainthedefinedcriteriawithhighprobability[60].Indeed,theyonlyrepresentaregionwheretheresponseisobservedonaverage.Inotherwords,thereisonechanceintwothattheresponsewillbeonthismeanresponsesurface.Fig.3showsthetrueprobabilitytomeetthecriteriarequiredfortheCQAmaximumrun-time<20min.Thistrueprobabilitycanbeobtainedonlybecausethetrueunderlyingmodelisknownhere.AscanbeseenonFig.3,theprobabilitytomeetthespecificationisonlyabout50%attheedgeofthesupposedDS,wherethemaximumrun-timeis<20min.Itmeansthat,whenobservingthemeanresponsesurfacecorrespondingto20minofrun-time,thereiseffectivelyonechanceintwotoreachtheobjective.ItcanbeseenfromFig.3thatthissupposedDSdoesnotgiveaguaranteethatthespecifi-cationisreached.Indeed,forthecontourcorrespondingto20minofruntime,manyconditionshavealessthan50%chancetoreachthismaximumrun-time.ThisisfarfromtheDSrequirementoftheICHQ8thatstatesthatDSisaregionwhereprocessparameters‘‘havebeendem-onstratedtoprovideassuranceofquality’’.
Bycontrast,thehatchedregionofFig.3showsthevaluesofthefactorspHandACNthatensurethatthetrueprobabilityofhavingamaximumrun-timeof20minisatleast90%,sousingmeanresponsesurfacesalonedoesnotprovideanyassuranceofquality.
Inaddition,whenseveralCQAsaremeasuredsimul-taneously,adesirabilityfunctionoroverlapinmeanresponsesurfacesisgenerallyusedtofindtheoptimalconditionstoreachsimultaneouslythepredefinedper-formancecriterionrequiredfortheseresponses(orCQAs)[61,62].Hereagain,usingsuchaclassicalmethodologydoesnotgiveanyguaranteeabouttheprobabilityofachievingthemjointlyatthemeanoptimalconditions[63].Forexample,whenusingtwooverlappingmeanresponsesurfacesthathaveeachonly50%probabilitytoattainthedesiredresponse(orCQA)level,theprobabilitytoreachsimultaneouslytherequiredlevelsofthetworesponses(orCQAs)isp=0.5·0.5=0.25=25sup-posingthattheyareindependent!Inthissituation,the
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TrendsTrendsinAnalyticalChemistry,Vol.42,2013Figure4.Probabilitymapgivingtheestimatedprobabilityofhavingarun-timeofatmost20minobtainedfromtheexperimentsdefinedbythecentralcompositedesignappliedtothehypotheticalanalyticalmethodexample.Hatchedregion:theDesignSpaceshowingthattheprobabilityofhavingarun-timeofmaximum20minisatleast90%.levelofquality,p,decreasesaccordingtothepowerofp,thenumberofresponsessimultaneouslystudied(i.e.p=0.5p).Similarpitfallsarepresentwhenusingmeanpredictedglobaldesirabilityfunctions,whichignorethecorrelationbetweenthevariousresponses,andneglectthepredictionuncertaintyandtheuncertaintyofmodel-parameterestimates[].
5.5.AreprobabilitymapstheDesignSpace?
Asthepreviousapproachesrelatedtomeanresponsesurfacesdonotprovideanyguaranteethattheanalyticalmethodcanmeetthespecificationswithre-specttotheinvestigatedCQAswithhighprobability,otherapproachesshouldbeimplemented.Theseap-proachesshouldtakeintoaccountthemodel-parameteruncertaintyandshouldprovideinformationabouthowoftenthespecificationswillbemet.Thisisessential,sinceICHQ8clearlyrequiresitforalevelofassuranceguaranteeingthatthespecificationswillbemet.Severaloptionscanbeimplementedtoreachthisrequirement.Bayesianmodeling[],Monte-Carlosimulations[65]orbootstrappingtechniques[66]canbeperformedtoincludeuncertaintyoftheparametersofthemodelsandtoestimatetheprobabilityofmeetingthespecificationsimposedontheCQAs.
Fig.4showstheDSobtainedusingaBayesianapproachasproposedbyPetersonetal.[63]orLebrunetal.[7].AscanbeseenbythehatchedregionofFig.4,ifitisrequiredthatthespecificationovertheCQAshouldbemetwithaproba-bilityofatleast90%,theDSisfarlessthantheoneobtainedwiththemeanresponsesurface.Thismeansthespecifica-tion‘‘run-timeofatmost20minutes’’willbemetin90%ofruns.Thismeasureoftheassuranceofqualityistheprob-abilityassociatedwiththeDS.WeshouldalsonotethattheDSobtainedonFig.4isveryclosetothetrueprobabilitymapofthishypotheticalexample,asshowninFig.3.
Hence,whendefiningananalyticalDS,themethod-ologythatisusedshouldtakeintoaccounttheuncer-
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Table2.DetailsoftheanalyticalDesignSpacespublishedinthescientificliteratureAnalyticalmethodAnalytes
Matrix
ModelingapproachDesignSpacetypeRef.UHPLC-UVImpuritiesanddegradationproductTablets
ChromatographictheoryMeanresponsesurface[70]ofethinylestradiol
UHPLC-UV
Dienogest,estradiol,ethinylestradiol,CleaningvalidationChromatographictheory
Meanresponsesurface
[70]
finasterid,gestodene,levonorgestrel,samples
norethisteroneacetate
UHPLC-UV1-naphtol,duloxetine,related
SpikedandstressedChromatographictheoryMeanresponsesurface[70]impuritiesanddegradationproductscapsulesamplesUHPLC-UVBicalutamideandrelatedimpuritiesTabletsChromatographictheoryMeanresponsesurface[70]HPLC-UV
Paracetamol,4-hydroxy-3-methoxyna
EmpiricallinearmodelandMeanresponsesurface
[71]
benzylalcohol,DL-mandelicacid,Chromatographictheory
phthalicacid,p-hydroxyphenylaceticacid,vanillicacid,m-hydrophenylaceticacid,isovanillicacid,benzylalcoholandimpuritiesHPLC-UVPhthalicacid,vanillicacid,
Syntheticmixture
EmpiricallinearmodelandMeanresponsesurface[72]
isovanillicacid,aspirin,furosemide,Chromatographictheory
doxepin,terbinafin,atorvastatin,clopidogrelandrelatedimpuritiesHPLC-UVPhthalicacid,vanillicacid,
SyntheticmixtureChromatographictheoryMeanresponsesurface[73]
isovanillicacid,anthranilicacid,vanillin,syringaldehyde,ferulicacid,orthovanillin,benzoicacid
UHPLC-UV2ActivePharmaceuticalIngredientsEyedropsolutionChromatographictheoryMeanresponsesurface[74]and9impurities
HPLC-UV19antimalarialdrugs
SyntheticmixtureEmpiricallinearmodelMonte-CarloProbabilitymap[59]HPLC-UVDiflunisal,Granisetron,Nifedipine,SyntheticmixtureEmpiricallinearmodelMonte-CarloProbabilitymap[75]Phenytoine,SulfinpyrazoneHPLC-UV
D9-tetrahydrocannabinol,D9-DifferentCannabisEmpiricallinearmodel
Monte-CarloProbabilitymap
[67]
tetrahydrocannabinolicacidA,products
cannabidiolicacid,cannabigerolicacid,cannabidiol,cannabigerol,cannabinol,D8-http://www.elsevier.com/locate/tractetrahydrocannabinolHPLC-UVTertiaryalkaloidsStrychnos
EmpiricallinearmodelMonte-CarloProbabilitymap[68]usambarensisleavesHPLC-UV
Aprophinealkaloids
Leavesof
Empiricallinearmodel
Monte-CarloProbabilitymap
[69]
SpirospermumpenduliflorumThouars
HPLC-UVSulfide,sulfone,sulindac,E-sulindacDrugsubstanceEmpiricallinearmodelMonte-CarloProbabilitymap[76]HPLC-UV9unknowncompoundsDrugproductEmpiricallinearmodelMonte-CarloProbabilitymap[77]HPLC
na
na
EmpiricallinearmodelBayesianProbabilitymap[,78]
na:nodataavailable.
165TrendsinAnalyticalChemistry,Vol.42,2013TrendsTrendstaintyofthemodelparameters,thecorrelationoftheresponsesstudiedandameasureoftheassuranceofattainingthequalitytarget.
6.DesignSpaceofanalyticalmethods
ThereareseveralexamplesofDSofanalyticalmethodsintheliterature,ascanbeseeninTable2.Alltheexamplesinvolvedliquidchromatographicmethods.MostareconventionalHPLCandfourexamplesinvolveUHPLC.Thedomainsofapplicationarenonethelessnotlimitedtothepharmaceuticalindustry.
Ofthe16examplescollected,three[67–69]aimtodefinetheDSofanalyticalmethodsappliedtoanalysisinplantmaterials.TheDSswereobtainedbyusingthemeanresponse-surfacemethodologyineightcases[70–74],hencefailingtoprovidethedemonstrationof‘‘assuranceofquality’’requiredintheICHQ8definitionofDS.SevenothercasesusedMonte-Carlosimulations[59,75–77],andonlyoneDSappliedaBayesianap-proach[,78].
Asalltheexamplesreportedinvolvedchromato-graphicmethods,theCQAsmeasuredrelatedtotheabilityofthemethodstoseparatethevariouscomponentsofthesamplesanalyzed.Theresolutionwasusedmost[,70–74,78],whileanotheronereportedwassepara-tion(thedifferencebetweenthetimeofthebeginningofthesecondpeakminusthetimeoftheendofthepreviouspeak)[59,67–69,75–77].OtherCQAsthatwereusedtodeterminetheDSweretotalruntime[59,,78],signal-to-noiseratioandtailingfactor[,78].TheselastexamplesdefinedaDSthatcouldsimultaneouslycomplywithspecificationsassignedtoeachindividualCQA(e.g.,aresolutionofthecriticalpeakpairofatleast1.5andamaximumruntimeof15min).
AlltheseexamplesshowedthataDScanbebuiltforanalyticalmethods.Theyalsoshowthetwomainvi-sionsaboutDS:
(1)pseudo-DSbasedonmeanresponsesurfacethatonly
givesinformationonthemeanpredictedquality;and,(2)DSthataccountsforuncertaintyandcorrelation
andprovidesalevelofassuranceofquality,asdefinedbyICHQ8document.
ThefactthatonlyDSsconcerningchromatographicmethodswerefoundintheliteraturedoesnotimplythattheDSisrestrictedtosuchtechniques.DScanbeobtainedforimmunoassaysorotherbio-assays(e.g.,PCR).However,nonewasreportedinthescientificliterature.7.Conclusion
TheDSrequirementoftheICHQ8statesthattheDSisaregionwhereprocessparameters‘‘havebeendemon-stratedtoprovideassuranceofquality’’.AnadditionalopportunityfortheDSforanalyticalproceduresisthepossibilitytomoveinsidetheDSwithouttheneedto
166
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TrendsinAnalyticalChemistry,Vol.42,2013
initiatearegulatorypost-approvalchangeprocess.ItisthenofcoreimportancetodemonstratethatthelevelofqualityrequiredfortheCQAscanbemetwithhighprobability.Methodologiestoachievethisaimareavailableandcanalleviatethefalseimpressionthatriskhasbeenmitigatedbyusingmeanresponsesurfacesorsimilarapproaches.Indeed,assuranceofqualityrequiresametrictomeasurehowoftenqualitywillbeachieved.Evidently,obtainingtheDSofanalyticalmethodsisnottheendofthestory.Inparticular,acontrolstrategyoftheanalyticalmethodwillhavetobedefinedinordertoassureandtomonitoritsdailyperformance.Themeth-odologyimplementedtodefinetheanalyticalDSwillalsohelpindefininganadequatecontrolstrategy.Finally,theachievementofaDSismeaninglessinitselfiftheDSisnotcompletelyincludedinaqualitysystemthathasaglobalrisk-managementplan.
Acknowledgments
Theauthorsareverygratefultotheanonymousreviewersforprovidingimportantcommentsthatledtosignificantimprovementsofthisarticle.AresearchgrantfromtheBelgiumNationalFundforScientificResearch(FRS-FNRS)toE.Rozetisgratefullyacknowledged.References
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