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AnalysisofrecentpharmaceuticalregulatorydocumentsonanalyticalmethodvalidationARTICLEinJOURNALOFCHROMATOGRAPHYAAUGUST2007ImpactFactor:4.17DOI:10.1016/j.chroma.2007.03.111Source:PubMed

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Availablefrom:AttilioCeccatoRetrievedon:10February2016

Journal of Chromatography A, 1158 (2007) 111125

Analysis of recent pharmaceutical reva

, ErPh

y Res0 Lie`g48 Mof Mepocaol of Pwitze007

Abstract

All analysts face the same situations as method validation is the process of proving that an analytical method is acceptable for its intendedpurpose. In order to resolve this problem, the analyst refers to regulatory or guidance documents, and therefore the validity of the analyticalmethods is dependent on the guidance, terminology and methodology, proposed in these documents. It is therefore of prime importance to haveclear definitions of the different validation criteria used to assess this validity. It is also necessary to have methodologies in accordance with thesedefinitions athe analyticaprocedures ptogether wit 2007 Else

Keywords: V

1. Introdu

The demquantify isefficacy ofcal methodbe validatepurpose. Wproceduresgenerally nthe validatistill three mregulatorythe specific

CorresponE-mail ad

0021-9673/$doi:10.1016/jnd consequently to use statistical methods which are relevant with these definitions, the objective of the validation and the objective ofl method. The main purpose of this paper is to outline the inconsistencies between some definitions of the criteria and the experimentalroposed to evaluate those criteria in recent documents dedicated to the validation of analytical methods in the pharmaceutical field,

h the risks and problems when trying to cope with contradictory, and sometimes scientifically irrelevant, requirements and definitions.vier B.V. All rights reserved.

alidation; Guidelines; Terminology; Methodology; Accuracy profile

ction

onstration of the ability of an analytical method toof great importance to ensure quality, safety andpharmaceuticals. Consequently, before an analyti-can be implemented for routine use, it must first

d to demonstrate that it is suitable for its intendedhile the need to validate methods is obvious, thefor performing a rigorous validation program are

ot defined. If regulatory documents allow selectingon parameters that should be established, there areain questions remaining: (a) How to interpret the

definitions of the parameters? (b) What should beprocedure to follow to evaluate a particular parame-

ding author. Tel.: +32 4 366 43 16; fax: +32 4 366 43 17.dress: Ph.hubert@ulg.ac.be (P. Hubert).

ter? (c) What is the appropriate acceptance criterion for a givenparameter? Furthermore, method validation is not specific topharmaceutical industry, but to most industrial fields involvingeither biology or chemistry. Even though each field of work hasits own characteristics and issues, the main criteria to fulfil aresimilar or should be similar since the validation of an analyti-cal method is independent of the industrial sector, matrix of thesamples or analytical technology employed. A harmonized val-idation terminology should be adopted to allow discussions andcomparisons of validation issues between scientists of differentfields. This consensus on terminology is not yet available evenif an attempt was made [1,2]. However, if it is desirable to havea harmonization between the different fields interested in ana-lytical validation, it is interesting to note that, even within thepharmaceutical field, all the laboratories are not using the sameterminology while they should use similar definitions to describevalidation criteria. The terminology used between different offi-cial documents such as the Food and Drug Administration (FDA)

see front matter 2007 Elsevier B.V. All rights reserved..chroma.2007.03.111on analytical methodEric Rozet a, Attilio Ceccato b, Cedric Hubert a

Serge Rudaz d, Bruno Boulanger b,a Laboratory of Analytical Chemistry, Bioanalytical Chemistr

University of Lie`ge, CHU, B36, B-400b Lilly Development Centre, rue Granbompre 11, B-13

c Analytical Chemistry Department, Faculty of Pharmacy, University13 Emil Isac Street, RO-3400 Cluj-Na

d Laboratory of Pharmaceutical Analytical Chemistry, Scho20 Bd. dYvoy, 1211 Geneva 4, S

Available online 1 April 2gulatory documentslidationic Ziemons a, Radu Oprean c,ilippe Hubert a,earch Unit, Institute of Pharmacy,e, Belgiumont-Saint-Guibert, Belgiumdicine and Pharmacy Iuliu Hatieganu,, Romaniaharmacy, University of Geneva,

rland

112 E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125

guide on validation of bioanalytical methods [3], ICHQ2R1[4], ISO [5,6], IUPAC [7], AOAC [8] is different. Further-more, in some cases inhomogeneous terminology can be foundthroughout the same document depending on the section whereit is mentioned. Therefore, the knowledge and understanding ofthese significant differences in terminology and definitions areessential since the methodologies proposed to fulfil the definitioncriteria can lead to confusion when preparing the validation pro-tocol and the experimental design. Furthermore the subsequentstatistical interpretation of the results obtained and the final deci-sion about the validity of the analytical procedure depends onthe consistent and adequate definition of the criteria assessed.This leads to highly critical consequences since the validatedanalytical method will be daily used in routine analysis (batchrelease, stability assessment, establishment of shelf life, phar-macokinetic or bioequivalence studies, etc.) to make decision ofthe utmost business and public health consequences. Therefore,the main objective of this review is to reveal the inconsisten-cies between the definitions of the validation criteria and theproposed experimental procedures to perform those criteria aswell as the statistical tools mandatory to help the decision aboutthe validity of the analytical procedure. The main points dis-cussed in this review are: (a) the distinction that can be madeconcerning specificity and selectivity; (b) the clarification of thelinearity concept and the difference with the response function;(c) the definition of precision, trueness and accuracy; (d) thediscussion about the decision rules to adopt from a statisticalpoint of view; (e) the definition of the dosing range in whichthe analytical method may be used and, last but not least, (f)the determ

the risks and problems when trying to cope with inconsistent,sometimes scientifically irrelevant, requirements and definitionsare highlighted.

2. Specicity or selectivity

The first criterion for an analyst when evaluating an ana-lytical method consists in its capability of delivering signalsor responses that are free from interferences and give trueresults. This ability to discriminate the analyte from interfer-ing components has been confusedly expressed for many yearsas selectivity or specificity of a method, depending on areaof expertise of the authors.

The terms selectivity and specificity are often usedinterchangeably while their significances are different. Thisconcept was extensively discussed by Vessman in differentpapers [913]. He particularly pointed out that organizationssuch as IUPAC, WELAC or ICH are defining specificity and/orselectivity in different manners (Table 1). However, a cleardistinction should be made as proposed by Christian [14], Aspecific reaction or test is one that occurs only with the substanceof interest, while a selective reaction or test is one that can occurwith other substances but exhibits a degree of preference forthe substance of interest. Few reaction are specific, but manyexhibits selectivity. This is consistent with the concept thatselectivity is something that can be graded while specificity isan absolute characteristic. Some tentative to quantify selectivitycan be found in the literature [1519]. For many analyticalchemists, it is commonly accepted that specificity is something

iona

Table 1Definitions of

Organization

IUPACterfer

er subacteri

h othre. Sppose

WELAC deterents inid to b

ISO

ICH e in thde imay be

AOAC ities, ud at uation

olved.

IUPAC: Intern boratHarmonizatio Officiination of the limit of quantification (LOQ). Finally, except

selectivity and specificity in different international organizations

Definition

Selectivity (in analysis)1. (qualitative): The extent to which other substances in

substance according to a given procedure.2. (quantitative): A term used in conjunction with anoth

coefficient, index, factor, number) for the quantitative charSpecific (in analysis)

A term, which expresses qualitatively the extent to whicdetermination of a substance according to a given proceduultimate of selective, meaning that no interferences are supnot mentioned.Selectivity of a method refers to the extent to which it cancomplex mixture without interference from other componperfectly selective for an analyte or group of analytes is saNot defined.

Specificity is the ability to assess unequivocally the analytmay be expected to be present. Typically these might incluLack of specificity of an individual analytical procedure msupporting analytical procedure(s).Test for interferences (specificity): (a) Test effect of impuradditives, and other components expected to be present annonspecific effects of matrices. (c) Test effects of transformstability, and metabolic products, if tissue residues are inv

ational Union of Pure and Applied Chemistry; WELAC: Western European Lan; ISO: International Organization for Standardization; AOAC: Association ofl since there are, in fact, few methods that respond

Reference

[14]e with the determination of a

stantive (e.g. constant,zation of interferences.

er substances interfere with theecific is considered to be thed to occur. The term specicity is

mine particular analyte(s) in athe mixture. A method, which ise specific.

[20]

e presence of components, whichpurities, degradants, matrix, etc.compensated for by other

[4]

biquitous contaminants, flavours,nusual concentrations. (b) testproducts, if method is to indicate

[8]

ory Accreditation Cooperation; ICH: International Conference onal Analytical Chemists.

E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125 113

to only one analyte. Considering these elements, the IUPACdefinition stating that the specificity can be considered asthe ultimasituation inthat WELAselectivityfor an anaby the IUPpromoted itechniques

3. Respon

The resping relation(signal, e.gthe concencalibrationmonotoniction that gdiscussed t is widelyrion. The lthe quantitthe calibrarelationshipcentration.see laboratfunction issquared linauthors, tooften irrele(e.g. for bioing assays)working orand imprecthe inadeqution curve.the ICH doQ2A), the la given rantional to thBut later intioned thatof a plot oftent. The tthe result tconfounds,on the othethe text isresults shofor examplof least squambiguity,regressionusing apprthe fact tha

signal is paradoxically contained in the last sentence of thatsection devoted to linearity: In some cases, to obtain linearity

n asberessrma

makeverysectast-

transconc

argehoularopefA gu001 [calibthattraterthn re

in ths ind-line

ontintionthetomertBHowicalg moprope prover

se ise corall as mo

t is rether

ted ae pre ofin thto prd iminadrve.

tatisly in21,2cedtervwillte selectivity seems to be rational regarding thethe pharmaceutical industry [9]. It must be notedC provides probably the most clear definition of

by saying that a method which is perfectly selectivelyte is said to be specific [20]. As recommendedAC and WELAC, the term selectivity should be

n analytical chemistry and particularly in separationand the term specificity should be discouraged.

se function and linearity

onse function for an analytical procedure is the exist-ship, within a specified range, between the response. area under the curve, peak height, absorption) andtration (quantity) of the analyte in the sample. Thecurve should be described preferably by a simple(i.e. strictly increasing or decreasing) response func-ives reliable measurements, i.e. accurate results ashereafter. The response function or standard curveand frequently confounded with the linearity crite-

inearity criterion refers to the relationship betweeny introduced and the quantity back-calculated fromtion curve while the response function refers to the

between the instrumental response and the con-Because of this confusion, it is very common to

ory analysts trying to demonstrate that the responselinear in the classical sense, i.e. a conventional least-ear model is adapted. As demonstrated by severalsystematically force a linear function is not required,vant and may lead to large errors in measured resultsanalytical methods using LCMS/MS or ligand bind-where the linear range can be different from thedosing range [21,22]. A significant source of bias

ision in analytical measurements can be caused byate choice of the statistical model for the calibra-The confusion is even contained and maintained incument. In the terminology part of Q2R1 (formerlyinearity is correctly defined as the . . . ability (withinge) to obtain test results which are directly propor-e concentration (amount) of analyte in the sample.the methodology section (formerly Q2B) it is men-Linearity should be evaluated by visual inspectionsignals as a function of analyte concentration or con-ext indicates clearly that it is the signal and no morehat matters in the linearity. The document clearlyon one hand, linearity and calibration curve and,r hand, test results and signal. The continuation ofself-explicit: If there is a linear relationship, testuld be evaluated by appropriate statistical methods,e, by calculation of a regression line by the methodares. For an analyst, the test results are, withoutthe back-calculated measurements evaluated by theline that is in fact the calibration curve, established

opriate statistics methodologies. Last but not least,t no linearity is needed between the quantity and the

betweehave tothe regtransfonal tois theof thatsical leapplyversus

trick, ltrick sa linenal. Hthe FDMay 2only exceptconcen

Nevbetweefoundauthorsic nonthey ccalibra

IntrophoLambelinear.dynamloglomodeland thlinearresponthat than ove

remainall tha

Anoneglecpurpospurposmentsabilitybias anby thetion cuother sare on

assay [introduance inmodelsays and sample concentrations, the test data maysubjected to a mathematical transformation prior toion analysis. Indeed, if any kind of mathematicaltion can be applied to both concentration and/or sig-

their relationship looking like straight lines whatpurpose of requiring linearity? Clearly, the intend

ion was, confusedly, to suggest that to use the clas-square linear function it is sometimes convenient toformations to the data when the visual plot signalentration does not look straight. It is indeed a good

ly diffused to establish the standard curve, but thatd not be interpreted as a scientific necessity to haverelationship between the concentration and the sig-ully, since 1995 understanding has evolved so thatidance on Bioanalytical Method Validation issued in3] does not contain any more the word linearity butration/standard curve without particular restrictionThe simplest model that adequately describes the

ionresponse relationship should be used.eless, the same confusion in concept and wordingsponse function and linearity of results still can bee recent book by Ermer and Miller [23]. While thoseicate that some analytical procedures have intrin-ar response function, such as quantitative TLC . . .ue to use the linearity terminology to express thecurve.

same context, HPLC methods coupled to spec-tric detection (UV) are usually linear according toeers law while immunoassays are typically non-ever, even for HPLCUV methods covering a large

range, advanced models, such as quadratic models ordels, could be necessary. Indeed, it is important toerly the whole procedure, including all the handling

eparation of samples that do not obviously remaina large range of concentration even if the detector

, according to LambertBeers law. It has to be notedmplete analytical procedure should be modeled byppropriate response function. As long as the modelnotonic and allows an accurate measurement, that isquired.aspect that is very important and that has been largelynd ignored in the analytical literature is the fit-for-inciple [21]. The central idea is very logical: thean analytical procedure is to give accurate measure-e future; so a standard curve must be evaluated on itsovide accurate measurements. A significant source ofprecision in analytical measurements can be causedequate choice of the statistical model for the calibra-The statistical criteria such as R2, lack-of-fit or anytical test to demonstrated quality of fit of a modelformative and barely relevant for the objective of the427]. For that intend, several authors [1,2,28] havethe use of the accuracy profile based on the toler-als (or prediction intervals) to decide if a calibrationgive quality results. The models should be retained

114 E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125

Fig. 1. Accurweighted linerepresent thelimits, then th

or rejectedregardless obeen used bidation of aof loperam

As canthe weightbest accurathe 95% to95% of themodel, themation arethe ultimatthe future.are not as iselected mlooking at texhibited ain a way thdifferenceaccuracy pacy profiles of the LCMS/MS assay for the determination of loperamide in plasmar regression model with a weight equal to 1/X2, (C) linear regression model after logacceptance limits (15%, 15%); the dashed lines the 95% tolerance interval connece assay is able to quantify accurately, other wise not. The continuous line represents

based on the accuracy of the back-calculated resultsf the statistical properties. This approach has alreadyy several authors such as Streel et al. [29] for the val-LCMS/MS assay for the quantitative determinationide in plasma [29].be seen from Fig. 1 and indicated by the authors,ed linear regression provides for the procedure thecy profile as obtained by joining the extremes oflerance intervals, i.e. the interval that will containfuture individual results. Inversely, the simple linearquadratic or even a model with a loglog transfor-not adapted because they do not better contribute toe goal of the assay, i.e. providing accurate results inIndeed, the tolerance intervals for those three modelsncluded in the acceptance limits defined as with theodel. Nevertheless, as can be seen on Fig. 2, whenhe quality of fit as usually practiced, the four modelsR2 > 0.999 for all series. This figure, representinge quality of the linear fit [4], does not show any

from one model to the other. This contrast with therofile figure, where a major difference exists in the

quality of thcurve.

Anotherfunction, liobtained wassay (HPTassay (ELIusing a qua non-lineaeter logisti(Figs. 3.a.1function ofThe same athat clearlyis able to quwith the oththe fit of thmodels shodefinition.

The stanaccuracy oa (concentration pg/ml) using (A) linear regression model, (B)arithm transformation, (D) quadratic regression. The dotted linested. When the tolerance intervals are included in the acceptancethe estimated relative bias line.

e results depending on the model selected as standard

example to illustrate the difference between responsenearity and fit-for-purpose accuracy profile can beith a high-performance thin-layer chromatographicLC; Fig. 3) and an enzyme-linked immunosorbent

SA) published in [30] (Fig. 4). Indeed as can be seen,adratic response function for the HPTLC assay orr standard curve such as the weighted four param-c model for the ELISA, the graphic of the signaland 4.a.1) does not look linear, while the results as athe concentration are linear (Figs. 3.a.2. and 4.a.2.).pply with the accuracy profile (Fig. 3.a.3. and 4.a.3)shows that when using this standard curve, the assayantify over a large range. This property is not fulfileder linear models for both type of assay. In both cases,

e model is acceptable, but none of these two linearw acceptable linearity or accuracy according to ICH

dard curve model selection based on the obtainedf the results was difficult to envisage few years ago

E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125 115

Fig. 2. Respomodel (R2 = 0(R2 = 0.9997)

because itsition scenmodels befpower is nperfectly al

Havinglinearity, itrelative bution for whfrom a calition are thsignal or rassessed.

Statisticnon-linearindeed a quis a sum ocurved oof modelsof concentered, an unlarger rangnse functions for the LCMS/MS assay for the determination of loperamide in plasma.9991), (B) weighted linear regression model with a weight equal to 1/X2 (R2 = 0.9, (D) quadratic regression (R2 = 0.9991).

requires a lot of computing and is a post-data acqui-ario, e.g. evaluation of all the putative calibrationore making a choice. Currently, the computationalo more a limitation and the selection of a model isigned with the objective of the method.

stressed the difference between response function andallows to apply the concept of linearity not only to

t also to absolute analytical methods such as titra-ich the results are not obtained by back-calculationbration curve. Attempts to provide a response func-erefore of no use and impracticable as there is noesponse whereas the linearity of the results can be

al models for calibration curves can be either linear orin their parameter(s)as opposed to linear in shape,adratic model Y = + X + X2 is linear because it

f X even if its graphical representation may lookn a XY plot. The choice between these two familieswill depend on the type of method and/or the rangerations of interest. When a narrow range is consid-weighted linear model is usually adapted, while ae may require a more complex or weighted model.

Weightinganalytical mof the level

In caseconcentratithat weightparticularlynot weightothers hasthe curvewhere theis assumedindependenmany analpreparationshould noton either athe calibraof homogethe log scawith increais log-norm(concentration pg/ml) for series 2 only using (A) linear regression991), (C) linear regression model after logarithm transformation

may be important because a common feature for mostethods is that the variance of the signal is a functionor quantity to be measured.

of heterogeneous variances of the signal across theon range which is frequent it is natural to observeing improve significantly the accuracy of the results,at low concentration levels. When observations are

ed, an observation more distant to the curve thanmore influence on the curve fit. As a consequence,fit, and so the back-calculated may not be goodvariances are smaller. Regardless of model type, itthat all observations fit to a model are completelyt. In reality, replicates are often not independent for

ytical procedures because of the steps followed inand analysis of samples. In such cases, replicatesbe used separately. Models are typically appliedlinear scale or log scale of the assay signal and/or

tor concentrations. The linear scale is used in caseneous variance across the concentration range andle is usually recommended when variance increasessing response, because it suggests that the responseally distributed. Most commonly used types of

116 E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125

Fig. 3. Stand(left, a) a quadlimits (10%to quantify acthe continuou

polynomiawithout anmodel paralikelihoodsquare metard curves (top, 1), linearity profiles (middle, 2) and accuracy profiles (bottom, 3) oratic regression model, (right, b) a linear regression model. For the linearity profile a

, 10%); the dashed lines the 95% tolerance interval connected. When the tolerance incurately, other wise not. For the linearity profile, the continuous line represents the is line represents the estimated bias line.

l models include simple linear regression (with orintercept) and quadratic regression models. The

meters are estimated using the restricted maximummethod, which is equivalent to the ordinary leasthod when the data are normally distributed.

This beiimental deover the raresults or invide. As shbtained on a high-performance thin-layer chromatography usingnd the accuracy profiles, the dotted lines represent the acceptancetervals are included in the acceptance limits, then the assay is abledentity line (result = concentration) while for the accuracy profile

ng said, and because of fitting techniques, the exper-sign, i.e. the way to spread the concentration valuesnge may significantly impact the precisions of theverse predictions that the response function will pro-ow by Francois et al. [31], depending on the model

E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125 117

Fig. 4. Standalogistic modethe acceptancthe assay is abaccuracy profi

that will begive morerule of thuues, they shrd curves (top, 1), linearity profiles (middle, 2) and accuracy profiles (bottom, 3) obtl, (right, b) a linear regression on the most linear part of the response. For the linee limits (30%, 30%); the dashed lines the 95% tolerance interval connected. Whenle to quantify accurately, other wise not. For the linearity profile, the continuous linle the continuous line represents the estimated bias line.

used for the response function, there are designs thatprecise measurements than others. As general goodmb for optimally choosing the concentrations val-ow that for most models used in assays, from linear

to four-parextremes odard pointsgeneral, paained on an immuno-assay using (left, a) a weighted 4-parameterarity profile and the accuracy profiles, the dotted lines representthe tolerance intervals are included in the acceptance limits, then

e represents the identity line (result = concentration) while for the

ameter logistic models, having standard points at thef the range and equally spreading the replicated stan-over the range in between gives excellent results in

rticularly when the model has not yet been clearly

118 E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125

identified, which is the case during validation phase. They alsostress the importance of having replicates, particularly at theextremes bting. Whencan be envmeasureme

4. Accura

4.1. Truen

As can bin the ISO dand generaument on ttrueness is5725-Parttrueness (sthe averagand an accusually expto as accuIndeed it isa series ofconcept is

Bias = xi

Relative bi

Recovery (

The ISOness and hvalidation edent validatrue valueallows to cTherefore,predicted rtive bias oare daily cprocedure.analytical pacteristic oresult geneas we will

Howeveuments foproceduresreading boMethod vanonethelesof truenessexpresses tis accepted

reference value and the value found. This is sometimes termedtrueness. Whereas for the FDA Bioanalytical Method Vali-

docof ctrue

ermeexte

f theinol

ss.en cICHthee bevalu

distantialragebjecimpas ar

eutical stach u

y. Thution

indry wical ps incent t, espmmeortedt of aand tls.

O dot I ofn truen ary, tht t-te

i i

ich aaceuesisacce

mesthan

wheted.nt frer wecause of the leverage of those points on the fit-the model has been identified, then optimal designs

isaged to improve again slightly the precision of thents.

cy, trueness and precision

ess

e seen from the following definition of trueness findocuments [5,6], the International vocabulary of basicl terms in metrology (VIM) [32] or Eurachem doc-he Fitness for Purpose of Analytical Methods [33],a concept that is related to systematic errors: ISO

1 (General Principles and Definitions) definition ofection 3.7) is: The closeness of agreement betweene value obtained from a large series of test resultsepted reference value. The measure of trueness isressed in terms of bias. Trueness has been referredracy of the mean. This usage is not recommended.expressed as the distance from the average value ofmeasurements (xi) and a reference value T. This

measured by a bias, relative bias or recovery:

T

as (%) = 100 (

xi TT

)

%) = 100 xiT

= 100 relative bias (%)

documents 5725 unambiguously affirm what is true-ow to measure it. Application of this concept to thexperiments is that measuring several times indepen-

tion standards, for instance i standards, for which theof analyte concentration or amount (T) is knownompute their predicted concentration or amount: xi.it is possible to compute the mean value of theseesults (xi) and consequently estimate the bias, rela-r recovery. Those values are well estimated as theyomputed during the validation step of an analyticalTrueness is related to the systematic errors of therocedures [2,5,6,34]. Trueness refers thus to a char-r a quality of the analytical procedure and not to arated by this procedure. This nuance is fundamental,see thereafter.r, when looking for trueness in the regulatory doc-r the validation of the pharmaceutical analytical, this concept is not per se defined. Conscientiouslyth the ICH Q2R1 [4] and the FDA Bioanalyticallidation [3] documents references to this concept ares made. When looking at ICH Q2R1 part 1 the useis made: The accuracy of an analytical procedurehe closeness of agreement between the value whicheither as a conventional true value or an accepted

dationdegreeknowntimes tand byracy oof termtruene

Whin thements,distancminedat theis essean ave

very oresultsampletherapologicthat eaquateldistribof eachrecove

analytThi

documumentRecobe repamoun

mean

intervathe ISof parbetwee

Whrecove

Studen

H0 : x

H1 : x

for whpharmhypothis, wein 5 tihigherlentlyis rejecdiffereAnothument this reference is made in the Glossary: Theloseness of the determined value to the nominal orvalue under prescribed conditions. This is some-

d trueness. Here can be seen a mix between truenessnsion accuracy of the mean (by opposition to accu-results). ISO documents also specify that this use

ogy of accuracy should be avoided and replaced by

omparing both of those two last quotes of truenesor FDA documents to the definition of ISO docu-

main difference is that both documents talk about thetween the true value and the value found or the deter-e whereas the trueness definition of ISO is lookingnce between the average value and the true value. Itto distinguish the difference between a result and

value. The results of an analytical procedure are itstive. When examining a quality control sample, thects the decision to release a batch. When unknown

e determined the results gives information about theeffect of a drug or about the pathological or physi-te of a patient and so on. What matters is to ensurenknown or known sample will be determined ade-is average value only gives the central location of theof results of the same true content, not the position

ividual result. By extension, the bias, relative bias orill locate the distribution of the results produce by therocedure relative to the accepted true value.oherence of definition is not only found from oneo another but also in different sections in a single doc-ecially in ICH Q2R1 document. In part II, Section 4.3.nded data relative to accuracy: accuracy shouldas percent recovery by the assay of known addednalyte in the sample or as the difference between thehe accepted true value together with the condenceThis is coherent with the definition of trueness formcuments and not with the corresponding definitionthe ICH document. In other documents confusioneness and accuracy is also observed [7,35].

ssessing the acceptability of the bias, relative bias ore methodology mostly used is to apply the followingst:

T = 0T = 0

signification level is set, generally at 0.05 in thetical field. This means that it is accepted that the nullH0 will be rejected wrongly 5 times out of 100. Thatpt to erroneously consider the bias different from 0out of 100. When the computed student quantile is

the corresponding theoretical quantile, or equiva-n the p-value is smaller than , the null hypothesisTherefore, there is a high confidence that the bias isom 0 as the significant level is fixed by the analyst.ay to interpret this test is to look if the 0% relative

E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125 119

bias or 100% recovery is included in the 1 confidence inter-val of the relative bias or recovery, respectively. If these valuesare outsidehypothesisbe made wbias, relativis that the tor recoveryin numerouprobabilityby the userclude thatcould be anconsider thof the procethis way isbias of myquestion thstep of theprocedurean equivaletypes of tesbias, relativbias, relativtrueness ofrecommendability of ais utopia. Fexperimentanalytical psis test, whanalytical qthe results acome back5, the connmethods.

4.2. Precis

Contrarcan be founICH Q2R1an analytic(degree offrom multipthe prescrisistent witValidation,

As statedard devia(RSD) or cerror linkethe resultsis independtrueness esprecision lecould be as

(1) Repeatability which expresses the precisionunder the sameoperating conditions over a short interval of time. Repeata-

lity iterms vauipmprodborardiza

repprocin tdet

s theion odocreci

le anr repvolves.

repilityurthriabi

vale labure itorye obanc

rin

rderan an

is ofs recumbst sq

owood

m thons:

=p

xij,cacentumb

1pn

i=their corresponding confidence interval then the nullis rejected. However, the only conclusion which canhen the null hypothesis is not rejected is not that thee bias or recovery is equal to 0, 0% or 100% but itest could not demonstrate that the bias, relative biasis different than 0 or 100. As clearly demonstrateds publications [27,3638], the risk, which is theto wrongly accept the null hypothesis, is not fixed

in this situation. Furthermore, this approach can con-the bias is significantly different from 0, whereas italytically acceptable [27,3638]. It will also alwaysat the bias is not different from 0 when the variabilitydure is relatively high. In fact, the Student t-test useda difference test which answers the question: Is theanalytical procedure different of 0? However, the

e analyst is wishing to answer during the validationanalytical procedure is: Is the bias of my analyticalacceptable? The test to answer this last question isnce or interval hypothesis test [27,3638]. In theset, the analyst has to select an acceptance limit for thee bias or recovery, that is limits in which if the truee bias or recovery of the analytical procedure lays thethis procedure is acceptable. Different authors haveed the use of this type of tests to assess the accept-bias [27,38]. Indeed a perfectly unbiased procedureurthermore the bias obtained during the validationis only an estimation of the true unknown bias of therocedure. Nevertheless, this latest interval hypothe-ile statistically correct, is not answering to the realuestion: the very purpose of validation is to validatemethod will produce, not the method itself. We will

to this objective and explain more in detail, in Sectionections existing between good results and good

ion

y to trueness, homogenous definitions for precisiond in the regulatory documentation. For instance, thePart 1 definition of precision is: The precision ofal procedure expresses the closeness of agreementscatter) between a series of measurements obtainedle sampling of the same homogeneous sample underbed conditions. This definition of precision is con-h its definition in the FDA Bioanalytical MethodISO, Eurachem, IUPAC, FAO and AMC documents.d in all documents, precision is expressed as stan-tion (s), variance (s2) or relative standard deviationoefficient of variation (CV). It measures the randomd to the analytical procedure, i.e. the dispersion ofaround their average value. The estimate of precisionent of the true or specified value and the mean or

timate. Each document makes reference to differentvels. For ICH Q2R1 and ISO documents, three levelssessed:

bi(2) In

rieeq

(3) Relada

Theentireportionmentallatter irepetit

Thebatch pa singsion omay inoratorinamelyvariablyst. Fthe vatory.

Thea singlprocedlaborawith thperformcalledrules.

In oity ofanalysgated isame n

the leaused. Hlikelih[2,30].

Froprecisifollow

MSMj

wherejth conn the n

j =s also termed intra-assay precision.ediate precision which expresses within-laborato-riations: different days, different analysts, differentent, etc.ucibility which expresses the precision betweentories (collaborative studies, usually applied to stan-tion of methodology).

eatability conditions involve the re-execution of theedure to the selection and preparation of the testhe laboratory sample and not only the replicate instru-erminations on a single prepared test sample. The

instrumental precision which does not include thef the whole analytical procedure.ument of the FDA, also distinguish within-run, intra-sion or repeatability, which assesses precision duringalytical run, and between-run, inter-batch preci-eatability, which measures precision with time, ande different analysts, equipment, reagents, and lab-As can be seen in this document the same word,eatability, is used twice for both component of

which is certainly not free of confusion for the ana-ermore this document considers at the same levellity in a single laboratory or in different labora-

idation of an analytical procedure is performed byoratory as it has to demonstrate that the analyticals suitable for its intended purpose. The evaluation ofto laboratory method adequacy is usually performedjective to standardize the procedure or to evaluate thee of several laboratories in a proficiency test, also

g test, and is regulated by specific documents and

to evaluate correctly the two components of variabil-alytical procedure during the validation phase, thevariance (ANOVA) by concentration level investi-

ommended. As long as the design is balanced, i.e. theers of replicates per series for a concentration level,uare estimations of the variance components can beever, when this condition is not met the maximumestimates of those components should be preferred

e ANOVA table, the repeatability or within-runand the between-run precision are obtained as

1 1

pi=1

n(xij,calc j)2

lc is the average of the calculated concentration of theration level of the ith series; p the number of series;er of replicates per series;p

1

nk=1

xijk,calc

120 E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125

with xijk, calc being the calculated concentration from the selectedresponse function.

MSEj =p

If MSEj < M

2W,j = MS

2B,j =MS

Else:

2W,j = pn

2B,j = 0The inte

2IP,j = 2Wwhere 2W,jis the betw

It is impance formuoverestima

As can bdifferencethe concepat least ofand/or diffwhich analremain conwill compoencountereIt is eviden1 day. So ithe analytiuse, will thtor, and/orof these quthat will beintroducedestimation

When texperimentof runs or swith a cosselected artwo levels,four runs or

Havingparameter

Rj =2B,j

2W,j

Table 2Experimental design of four runs taking into account days, operators and equip-ments as sources of variability

r 1ent 2

eed(or ruce. Ha proresu

reder ofa relhis ltedrdsvalided foive sa ru

the qare

to.finitiof aesulgreesmedce i

e thisdoma m

reallytand

%) =

2 is

en ans useteda ne

valivalucorresponding true value T. The RSD computed by

ay depends only on the estimated precision (estimatedces), regardless of the estimated trueness.s being said, the use of relative estimate is convenient

direct reading point de view but triggers neverthelesss of queries: what matters the most for the results, theute) variance or the relative standard deviation? Imagine1n p

pi=1

nk=1

(xijk,calc xij,calc)2

SMj then:

Ej

Mj MSEjn

1 1

pi=1

nk=1

(xijk,calc xj,calc)2

rmediate precision is computed as follows:

,j + 2B,jis the within-run or repeatability variance and 2B,jeen run variance.ortant to note that the misapplications of known vari-la are still widely used and can lead to dramatic

tion of the variance components [36,39].e seen in the regulatory documents what makes the

between repeatability and intermediate precision ist of series or runs. These series or runs are composeddifferent days with eventually different operators

erent equipments. A run or series is a period duringyses are executed under repeatability conditions thatstant. The rational to select the different factors whichse the runs/series is to mimic conditions that will bed during the routine use of the analytical procedure.t that the analytical procedure will not be used onlyncluding the variability from one day to another ofcal procedure is mandatory. Then during its routinee analytical procedure be used by only one opera-on only one equipment? Depending on the answersestions, different factors representing the procedureused during the routinely performed analysis will bein the validation protocol, leading to a representativeof the variability of the analytical procedure.he selection of the appropriate factors is made, anal design can be made in order to optimize the numbereries to account for the main effects of these factorst effective analysis time. For example if the factore days, operators and equipments, each of them atthen a fractional factorial design allows to executeseries in only 2 days. The design is shown in Table 2.

computed the variance components, one interestingto observe is the ratio Rj, with

.

Run 1

Day 1OperatoEquipm

Indseriesvarianeitherwhoseto thenumbeobtain

In tcorrelain regaof thesize useffectwithinjudgeresultsbelongthe detationif the rthe deperfortoleranincludof free and(series

Usuative S

RSD (

wherevalue.

Whance icompugivingcase oference

by itsthis wvarian

Thifrom aa serie(absolRun 2 Run 3 Run 4

Day 1 Day 2 Day 2Operator 2 Operator 1 Operator 2Equipment 1 Equipment 1 Equipment 2

this parameter shows how important is the series ton to run) variance in comparison to the repeatabilityigh values of Rj, e.g. greater than 4, could suggestblem with the variability of the analytical procedurelts may vary from one run to the other, and so leadingvelopment of the method, or either stress a lack ofseries (runs) used during the validation process toiable estimate of the between-series variance 2B,j .ast situation, all the results within a run are highlyto each others providing little effective informationto the run to run results. The effective sample sizeation is consequently smaller than the real sampler the design of the validation experiments. The termample size is used to indicate that when the resultsn a correlated, then there is in fact less information touality of results as compared to a situation where allfully independent and not dependent of the run theyThis is an important feature to take into account foron of the degrees of freedom to use for the compu-confidence interval or of a tolerance interval. Indeedts of repeated experiments are correlated computing

of freedom with the total number of experimentswill artificially reduce the confidence interval or thenterval. The Satterthwaite degrees of freedom [40]concept of effective sample by modeling the degreesbetween a minimum value the number of series

aximum value the total number of experimentsplicates) [41].

, precision is commonly expressed as the percent Rel-ard Deviation (RSD). The classical formula is:

100

2

x

the estimated variance and x is the estimated average

RSD precision is expressed, the corresponding vari-d, e.g. repeatability or intermediate precision. The

RSD is therefore the ratio of two random variables,w parameter with high uncertainty. However, in thedation of analytical procedure, because the true or ref-e is known, then the denominator should be replaced

E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125 121

that a bioanalytical method is used for supporting a pharmacoki-netic study. In that case the results are used for fitting the PKnon-linearthe resultsnot the RSits intendedon acceptavariance ofof its use. Tdealing witby the truelower end snot becauscan be seenabsolute scdistance bethe intermeis the samethat on that(RSD) expclude that rclear that, fimproves aate precisiothe fact thabecause thraise questIndeed whyels while thresults at hquestion listability orto discard ttrations, buaccuratelyOnly the vacommon prexpressioncarefully codiscardingthe study.

4.3. Accur

In documthe closeneeither as a cand the valISO [5,6] dis: the cloaccepted renote is addedom error aby the Anaunderstoodto analyticaoutlines tha

Therefore, accuracy denotes the absence of error of a result. Sim-ilar definitions of accuracy are found in the Eurachem document

totacaln th

ed eivalu

ofinkedxpre

ndardreme

s ofpre

the in anatic

T +

T =

T =

eve

parumeed at ofan a

interruene va

accu

prevrors

O 57reme

tionsults) off thebylue sin tlyticiews

definmos

e vamodel and what matters only is either the variance ofor the variance of the logarithms of the results, butD at all. Remember that a procedure is validated for

use. So what is the relevance of making a decisionnce of a method based on the RSD when only the

its results are important with regard to the intendhis distinction becomes particularly important whenh the LOQ. Indeed, since the RSD is the SD dividedconcentration value, the RSD becomes large at theimply because the SD is divided by a small number,

e the method becomes less precise. A good exampleby comparing the same information on Fig. 3.a.2 in

ale and Fig. 3.a.3 in relative scale. On Fig. 3.a.2 thetween the two dashed lines represents a multiple ofdiate precision in absolute value while on Fig. 3.a.3 itvalue but expressed in relative value. While it appearslater figure (a.3) the relative intermediate precision

lode at the smallest concentration, leading to con-esults are not precise enough at that level, it is alsoor this example, the absolute intermediate precisiont the smallest concentration because the intermedi-n SD is smaller. The contradiction comes here fromt the SD has been divided by a small number, not

e measurements are less precise, on contrary. Thisions on the meaning and the definition of the LOQ.

ignoring or discarding the results at those low lev-ey are obtained with a variance much smaller thanigh concentrations? Once again, the answer to thises in the intended use of the results: for supportingpharmacokinetic studies, not only it is not relevant

hose very precise measurements at the small concen-t they also are very useful, for example, in estimatingthe half-life or the pharmacokinetic of metabolites.riance or the SD matters, not the RSD. So, while theactice evaluate a method with respect to the relativeof the precision, scientists in the laboratories shouldnsider the absolute and fundamental variance before

data and question if it serves or not the objectives of

acy

ent ICH Q2R1 part 1 [4], accuracy is defined as: . . .ss of agreement between the value which is acceptedonventional true value or an accepted reference valueue found. This definition corresponds to the one ofocuments or VIM [32] which states that accuracyseness of agreement between a test result and theference value. Furthermore, in the ISO definition ad specifying that accuracy is the combination of ran-nd systematic error or bias. From this and as specifiedlytical Methods Committee (AMC) [34], it is easilythat accuracy rigorously applies to results and notl methods, laboratories or operators. The AMC alsot accuracy should be used that way in formal writing.

[33].The

analytibetweeaccepterence

the sumerror lis the e(or stameasu

the biaand thecases,

betweesystemerror.

X =

X

X

X

X

Howracy into docreportamoun

the medenceto the taveragfor thestatedatic erand ISmeasu

Validatest retration15% odeviatetrue vationedthe analier revof the

Forthe trul measurement error of the results obtained from anprocedure is related to the closeness of agreemente value found, i.e. the result, and the value that isther as a conventional true value or an accepted ref-e. The closeness of agreement observed is based onthe systematic and random errors, namely the totalto the result. Consequently, the measurement error

ssion of the sum of trueness (or bias) and precisiondeviation), i.e. the total error. As shown below, each

nt X has three components: the true sample value T,the method (estimated by the mean of several results)cision (estimated by the standard deviation or, in mostntermediate precision). Equivalently, the differenceobservation X and the true value is the sum of the

and random errors, i.e. total error or measurement

bias + precision

bias + precision

T = total error

measurement error

T = accuracy

r, when looking at the section corresponding to accu-t 2 of ICH Q2R1 document, the recommended datant accuracy are presented as: accuracy should bes percent recovery by the assay of known addedanalyte in the sample or as the difference betweennd the accepted true value together with the con-vals. This refers not anymore to accuracy but insteadess definition of ISO 5725 document because it is thelue of several results as opposed to a single result asracy that is compared to the true value, as already

iously. This section refers consequently to system-whereas accuracy as defined in ICH Q2R1 part 125 part 1 corresponds to the evaluation of the totalnt error. In the document FDA Bioanalytical Method[3], accuracy is defined as . . . the closeness of meanobtained by the method to the true value (concen-the analyte. (. . .) The mean value should be withinactual value except at LLOQ, where it should not

more than 20%. The deviation of the mean from theerves as the measure of accuracy. As already men-

he previous sections, this definition corresponds toal method trueness. For bioanalytical methods, ear-have already stressed the problem of the difference

ition of accuracy relative to trueness [1,2,27,38].t uses it does not matter whether a deviation fromlue is due to random error (lack of precision) or to

122 E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125

systematic error (lack of trueness), as long as the total quantityof error remains acceptable. Thus, the concept of total analyt-ical error oerror is essthat the totinterpretatidecision [1ation of theOnly evaluaccount theratories anachieve its

5. Decisio

Most ofmendationwhen an athe confusibe examineposed aboujustify the d[3]. The onbioanalyticidation partheoreticalmore thannot exceednot exceedvalidation,At least 67%be within 1QC samplebe outsideacceptancetions relatisummarizetriggers maposed objemust be sufThats clea15% of thesection onprevious rumethods pethe precisio

The objable to quaquantitiesterms, whathat the difand the unkinferior to

< X The acc

requiremen

procedure. The objective is linked to the requirements usuallyadmitted by the practice (e.g. 1% or 2% on bulk, 5% on phar-

ticalpredrefo

oughd wi

ithople,

r wofulfi

alreaits trss) aof testime rele exsequhethnd s

res thgrea

[|Xeve

ed pakes [1,ls [5

M{PXthe fpopxpe

ed wfor bds ussure

o .st ofer a

thehis rt eacacc

er ln Figreme

els move

80%or s w

5) rur accuracy as a function of random and systematicential. Furthermore, every analyst wants to ensureal amount of error of the method will not affect theon of the test result and compromise the subsequent,2,21,4246]. Decision based on the separate evalu-trueness and precision criteria cannot achieve this.

ation of the accuracy of the results which takes intototal error concept, gives guarantees to both labo-

d regulatory bodies on the ability of the method topurpose.

n rule

the regulatory documents do not make any recom-on acceptance limits to help the analyst to decide

nalytical procedure is acceptable. They insist, withons already mentioned, about the criteria that need tod, estimated and reported, but only few rules are pro-t the way to decide. It is a laboratory competence toecision of accepting and using an analytical methodly exception found concerns the FDA document onal methods that clearly indicates in the pre-study val-t: The mean value should be within 15% of thevalue, except at LLOQ,where it should not deviate by20%. The precision around the mean value should15% of the CV, except for LLOQ, where it should20% of the CV. Later, when referring to in-studythe same document indicates: Acceptance criteria:

(4 out of 6) of quality control (QC) samples should5% of their respective nominal value, 33% of thes (not all replicates at the same concentration) may15% of nominal value. In certain situations, widercriteria may be justied. However, these two sec-

ng to pre-study and to in-study acceptance criterias very well the in-depth confusion that exists and thatny debates in conferences on validation. The pro-

ctive is that for bioanalytical methods, measurementsficiently close from their true valueless than 15%.rly indicated here: QC samples should be withinir respective nominal value. As suggested in theaccuracy, this objective is not aligned at all with thele for (pre-study) validation that impose limits onrformance not the results such as the mean andn that must be better than 15% (20% at the LLOQ).ective of a quantitative analytical method is to bentify as accurately as possible each of the unknownthat the laboratory will have to determine. In othert all analysts expect from an analytical procedure isference between the measurement or observation (X)nown true value T of the test sample be small or

an acceptance limit a priori defined:

T < |X T| < eptance limit can be different depending on thets of the analyst and the objective of the analytical

maceu

limitsThe

ate enmethovalue wthe samIn othewill be

AsX andtruenevaluescan beand thof thes

Conuate w(M) ameasu

tine, is

E,{PHow

expectand mauthorinterva

EM,

whereof thethe -einclud15%]methoof meaequal t

Motify ovduringcover tlated a

Thethe lowseen o

measu

key levis validabove80% fthe run461specialties, 15% for biological samples, or whateverefined according the intent of use of the results).re, the aim of the validation phase is to gener-information to have guarantees that the analytical

ll provide, in routine, measurements close to the trueut being affected by other elements of the present inassuming everything else remain reasonably similar.rds, the validation phase should demonstrate that thisled for a large proportion of the results.

dy mentioned, the difference between a measurementue value is composed of a systematic error (bias ornd a random error (variance or precision). The truehese performance parameters are unknown but they

ated based on the (pre-study) validation experimentsiability of these estimates depends on the adequacyperiments (design, size).ently, the objective of the validation phase is to eval-er, given or conditionally to the estimates of biastandard deviation (M), the expected proportion ofat will fall within the acceptance limits, later in rou-ter than a predefined level of proportion, say , i.e.:

T| < ]|M, M} r, there exists no exact solution to estimate thisroportion. An easy solution to circumvent this aspecta reliable decision, as already proposed by other

28,4749], is to compute the -expectation tolerance0]:

[M kM < X < M + kM|M, M]} = actor k is determined so that the expected proportionulation falling within the interval is equal to . Ifctation tolerance interval obtained that way is totallyithin the acceptance limits [, +] (e.g. [15%,ioanalytical methods or [5%, 5%] for analyticaled for a batch release) then the expected proportionments within the same acceptance limits is greater or

the time, an analytical procedure is intended to quan-range of quantities or concentrations. Consequently,validation phase, samples are prepared to adequatelyange, and a -expectation tolerance interval is calcu-h level.uracy error profile is simply obtained by connectingimits and by connecting the upper limits, as can be. 1 or in the bottom of Fig. 3. The inclusion of thent error profile within the acceptance limits [,] atust be examined before declaring that the procedure

r a specific range of values. will usually be chosenand as shown by Boulanger et al. [43,44], choosingduring pre-study validation guarantees that 90% ofill later be accepted in routine when the 46l (e.g.le is used in routine.

E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125 123

That way, the pre-study validation decision and the (in-study)routine decision rule for acceptance of runs becomes alignedwith their rthe FDA gu15% and atee at all thThere are tthat could bFirst, as pobetween thtematic errfor examplestimated pine that moand so moshappen in testimates oof observatIf the meanmeasureme

(operator, dthere is pooare in factinterval aptwo pitfallsgood resultity (size, deinterval apdata, it remthe experimdation reflesubtle diffebe stressedational aspein the expetine. The mlot, differe. . . in orderpractice analready indbe validate

6. Dosing

For anyrange of anthe methodthe rangethe upper asample (indemonstratof precisiocal Methodis the ranthat can bracy and prrelationshi

and ULOQ is the upper limit of quantitation. Thus, the above-mentioned definitions are quite similar because for both of

the rruene ranure.lishen ac

pplie exIUPich tspecran

d devaboinescur

Q2feren

r thet: nor cothe

nge,se ir disr thvel o

refol ove

ceptaover

efinireme

ss threcauAccted ed fo

it o

co

ntitaes, and/oitatioamo

ined(or

d inICHntifiOQespective risks which is not the case as proposed byide [3]. Indeed having a mean (trueness) smaller thanprecision (CV%) smaller than 15% does not guaran-at most future results will be within [15%, 15%].wo statistical errors behind this classical assumptione summarized as good methods give good results.inted out in the section on accuracy, the differencee result and its true value is composed by the sys-or (trueness) plus the random error (precision). So, ife, a method shows an estimated mean of 14% and anrecision of 14% as well, it is then obvious to imag-st results will likely fall outside the acceptance limitst runs will be rejected. Second, predicting what willhe future routine depend largely on the quality of thef the mean and precision, i.e. primarily of the numberions collected and the conditions of the experiments.

and the precision are estimated based on too fewnts during pre-study validation, or with conditionsays, etc. . . .) not representative from the routine use,r confidence that the true bias or the true precisionnot greater than acceptance criteria. The tolerance

proach, which is a prediction interval, avoids thoseand correctly estimates the expected proportion of

s depending on the performance criteria and the qual-sign) of the performed experiments. If the tolerance

proach can prevent making decision based on poorains the responsibility of the analyst to ensure thatental conditions used during the (pre-study) vali-cts what will be used and practice in routine. Therence between the method and the procedure shouldhere: in the validation experiments, the various oper-cts or potential sources of variance must be included

riments to anticipate what could happen later in rou-ost classical factors are the operators, the column

nt set-ups, independent preparation of samples, etc.to simulate or mimic as closely as possible the daily

d set of procedure around the use of the method. Asicated, it is the whole procedure or practice that mustd, not only the method in its most restrictive sense.

range

quantitative method, it is necessary to determine thealyte concentrations or property values over whichmay be applied. ICH Q2R1 part 1 document defines

of an analytical procedure as the interval betweennd lower concentration (amounts) of analyte in thecluding these concentrations) for which it has beened that the analytical procedure has a suitable leveln, accuracy and linearity. The FDA Bioanalyti-

validation definition of the quantication rangege of concentration, including ULOQ and LLOQ,e reliably and reproducibly quantied with accu-ecision through the use of a concentrationresponsep, where LLOQ is the lower limit of quantitation

them,racy (tthat thprocedestabvides awhen aor at thdure.for whwithin

Themethomationdetermbration

ICHfor dif

(i) fouc

(ii) foofra

do(iii) fo(iv) fo

le

Theinterva is acresultsthese dmeasu

to assewith prange.evaluatargete

7. Lim

ICHof quamatricrities aquantlowestdetermtitationare use

same.

the quaits: LLange is correlated with the linearity and the accu-ess + precision). Moreover, both documents specifyge is dependent on the specific application of theICH Q2R1 part 2 states that the specied range isd by conrming that the analytical procedure pro-ceptable degree of linearity, accuracy and precisioned to samples containing amounts of analyte withintremes of the specied range of the analytical proce-AC defines the range as a set of values of measuredhe error of a measuring instrument is intended to lieied limits.ge should be anticipated in the early stage of theelopment and its selection is based on previous infor-ut the sample, in a particular study. The chosen rangethe number of standards used in constructing a cali-

ve.

R1 part 2 recommends the minimum specified rangest studies:

assay of a drug substance or a finished (drug) prod-rmally from 80 to 120% of the test concentration;

ntent uniformity, covering a minimum of 70130%test concentration, unless a wider more appropriatebased on the nature of the dosage form (e.g. metered

nhalers), is justified;solution testing: 20% over the specified range;

e determination of an impurity: from the reportingf an impurity to 120% of the specification.

re, the dosing range is the concentration or amountr which the total error of measurement or accuracyble. It is essential to demonstrate the accuracy of thethe entire range. Consequently, and in order to fulfil

tions, the proposition of ICH document to realize sixnts only at the 100% level of the test concentratione precision of the analytical method should be usedtions to be in accordance with the definition of the

uracy, and therefore trueness and precision should bexperimentally and acceptable over the whole ranger the application of the analytical procedure.

f quantitation

nsiders that the quantitation limit is a parametertive assays for low levels of compounds in samplend is used particularly for the determination of impu-r degradation products. ICH Q2R1 part 1 defines then limit of an individual analytical procedure as the

unt of analyte in a sample which can be quantitativelywith suitable precision and accuracy. Limit of quan-quantitation limit) is often called LOQ. Both termsregulatory documents, the meaning being exactly thedocument defines only one limit of quantitation. Butcation range of the analytical procedure has two lim-and ULOQ. In the definition of quantitation limit(s)

124 E. Rozet et al. / J. Chromatogr. A 1158 (2007) 111125

excerpted from IUPAC, Eurachem let us understand that there ismore than one limit of quantification: quantification limits areperformancmeasureme

Eurachemis discusse

The FDAguishes bequanticathat can band accuraest amountdetermineddocument,with high

ICH Q2estimate th

A first a(s/n) ratio ato be sufficnoise. Thenot the sigchromatogrepresentsquantitatiotitation limbut lowestcomplicatesidered as t

The othment are bathe Slopelimit compquantitatiomultiplier o

DL3.3S

where isslope of the

The samtion in chrQ2R1 partis not alwaare proposeand those alternativesassumptionunits for ththat LOQ r

Other prquantitatiowhich is noapproachesand dependtional set-utime consta

is extremely subjective [51,52] and is equipment dependant. Theapproaches using the standard deviation of the intercept should

efullf thetimarmorlowec astorietherpropt conrsus

the ctionms squippprois lahas

accu

ur o

(LLOch [1menand

able

nclu

ana

ana

n ordlatoints

ly dedolos ofethuentefinianalositn prory,ions

wled

nksFunct N

nce

. Hubhen, Pe characteristics that mark the ability of a chemicalnt process to adequately quantify an analyte. But, indocument, only LLOQ, called quantification limitd.

Bioanalytical Method Validation document distin-tween the two limits and defines the lower limit oftion (the lowest amount of an analyte in a samplee quantitatively determined with suitable precisioncy) and the upper limit of quantication (the high-of an analyte in a sample that can be quantitativelywith precision and accuracy). As can be seen in thisthe only difference is the substitution of lowest

est word.R1 part 2 proposes exactly the same approaches toe (lower) quantification limit as for the detection limit.pproach is based on the well known signal-to-noisepproach. A 10:1 s/n is considered by ICH documentient to discriminate the analyte from the backgroundmain problem appears when the measured signal isnal used to quantify the analyte. For example, inraphy with spectral detection, the measured signalthe absorption units, i.e. the signal height but for then the areas are generally used. Therefore, the quan-it is not expressing the lowest level of the analyte,quantified absorbance. The problem becomes mored in electrophoresis, where the signal is usually con-he ratio between the peak area and the migration time.er approaches proposed by ICH Q2R1 part 2 docu-sed on the Standard Deviation of the Response andand it is similar to the approach used for detection

utation. The computation ways for detection (DL) andn limit (QL) are similar, the only difference being thef the standard deviation of the response:

QL10S

the standard deviation of the response and S = thecalibration curve.

e problems explained previously arise for the detec-omatography or electrophoresis. On one hand, ICH2 document assumes that the calibration is linear, thatys true. On the other hand, two ways of measuring d: those based on Standard Deviation of the Blankbased on the Calibration Curve. Neither of theseoffers the adequate solution. The former because thethat the signal units are the same as the measured

e calibration and the latter because of the assumptionange is already known.oblems with those methods of estimation of limits ofn are that they assume that there is a measurable noise,t always the case. Furthermore, when possible, theseare dependant on the manner the noise is measuredfrom one instrument to another or internal opera-

p such as signal data acquisition rate or the detectornt. The LOQ estimated using the signal to noise ratio

be cardant owell esFurtheof thelematilabora

Anotion isRSD ated veWhencentraproblemore e

these awith thcedurewhole

In olimitsapproarequireknownaccept

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[1] PhCoy used as the estimation of this intercept is depen-range of the calibration curve: the intercept is onlyted if the concentrations used are sufficiently small.e each of these approaches provides different valuer limit of quantitations [51,52]. This is highly prob-it does not allow to compare the LOQ of differents using the same analytical procedure.

approach to estimate the lower limit of quantita-osed by Eurachem, based on a target RSD [33]. Thecentration levels close to the expected LOQ are plot-their concentration, and a curve is fitted to this plot.urve crosses the target RSD the corresponding con-

levels is the LOQ. This approach alleviates most thetressed to the previous approaches, as it is not anyment and operator dependant. Still however, none ofaches fulfil the definition of the LOQ. Indeed evenst approach, only the precision of the analytical pro-been assessed without trueness estimation and theracy (trueness + precision) as required.pinion, the best way to compute both quantitationQ and ULOQ) is the use of the accuracy profile

,2,29,30,4345,4749] which fulfil the LOQ criteriat by demonstrating that the total error of the result isacceptable at these concentration levels, i.e. both anlevel of systematic and random errors.

sion

lysts, method validation is the process of provinglytical method is acceptable for its intended pur-er to resolve this very important issue, analysts refer

ry or guidance documents which can differ in sev-. Therefore, the validity of the analytical method ispendant on the chosen guidance, terminology and

gy. It is therefore highly essential to have clear def-the validation criteria used to assess this validity, toodologies in accordance with these definitions andly to use statistical methods which are relevant withtions, the objective of the validation and the objectiveytical methods.ioning the definitions and the methodologies duringocesses of regulatory documents to eliminate con-sometimes scientifically irrelevant, requirements andshould be recommended and rapidly implemented.

gements

are due to the Walloon Region and the Europeand for a research grant to E.R. (First Europe Objectiveo. 215269).

s

ert, J.-J. Nguyen-Huu, B. Boulanger, E. Chapuzet, P. Chiap, N..-A. Compagnon, W. Dewe, M. Feinberg, M. Lallier, M. Laurentie,

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[3] Guidance for Industry: Bioanalytical Method Validation, US Departmentof Health and Human Services, Food and Drug Administration, Center forDrug Evaluation and Research (CDER), Center for Biologics Evaluationand Research (CBER), Rockville, May 2001.

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