araujo2009.pdf

Journal of Chromatography B, 877 (2009) 22242234

Contents lists available at ScienceDirect

Journal of Chromatography B

journa l homepage: www.e lsev ier .com

Key asp d l

Pedro ArNational Institu orway

a r t i c l

Article history:Received 2 JulyAccepted 29 SAvailable onlin

Keywords:ValidationTerminologySelectivitySpecicityAccuracyPrecisionLinear function analysisRangeLimit of detectionLimit of quantitationRuggednessRobustness

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1. Introduc

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d validation originates from the Latin validus meaningsuggests that something has been proved to be true,

of an acceptable standard. The International Organiza-ndardization denes validation as the conrmation byn and provision of objective evidence that the particu-

ents for a specied intended use are fullled [1]. Thisrimarily implies that a detailed investigation has beenand gives evidence that an analytical method, when cor-ed, produces results that are t for purpose as well asthe effectiveness of the analytical method with a highcuracy.ortance of method validation has been emphasised

te 40s when the American Chemical Society and Merckd the issue of how mathematics and statistics areprerequisite to successful development and adapta-analytical methods [2,3]. By that time a survey of

development of analytical methods revealed that no

is part of a special issue entitled Method Validation, Comparisonguest edited by Serge Rudaz and Philippe Hubert.5285039; fax: +47 55905299.ress: [email protected].

comparisons were carried out with other or similar methodolo-gies in order to check for accuracy in the reviewed articles [4].In addition, it was pointed out that statistical data analysis was asubject neglected by chemists developing experimental methods[3]. In the early 70s a series of articles were published stress-ing the need of implementing a consistent set of denitions fordetermining the performance-characteristics of developed ana-lytical methods and comparing unambiguously the advantagesand disadvantages of the increasing volume of reported analyti-cal methods [58]. This paved the way for the implementation ofmethod validation in analytical laboratories since the late 70s andthe current worldwide recognition that method validation is animportant component in any laboratory engaged in the develop-ment and establishment of standard methods. Nowadays, there areseveral international renowned organisations offering guidelineson method validation and related topics. Basic references are theAssociation of Ofcial Analytical Chemists (AOAC), the AmericanSociety for Testing and Material (ASTM), the Codex Committee onMethods of Analysis and Sampling (CCMAS), the European Com-mittee for Normalization (CEN), the Cooperation on InternationalTraceability in Analytical Chemistry (CITAC), the European Cooper-ation for Accreditation (EA), the Food and Agricultural Organization(FAO), the United States Food and Drug Administration (FDA),the International Conference on Harmonization (ICH), the Inter-national Laboratory Accreditation Cooperation (ILAC), The World

see front matter 2008 Elsevier B.V. All rights reserved.chromb.2008.09.030ects of analytical method validation an

aujo

te of Nutrition and Seafood Research (NIFES), PO Box 2029, Nordnes, N-5817 Bergen, N

e i n f o

2008eptember 2008e 2 October 2008

a b s t r a c t

Method validation may be regarded areected in the substantial number oyear. However, some of the relevant pachangeably and incorrectly or are mias well as wrong application of the mThese mistakes have led to misinterpto wrong scientic conclusions. In thissuch as selectivity, specicity, accuracyruggedness, and robustness are criticensure scientic correctness and cons/ locate /chromb

inearity evaluation

of the most well-known areas in analytical chemistry as iscles submitted and published in peer review journals everyters recommended by regulatory bodies are often used inter-lated, due to few references to evaluate some of the termsmatical and statistical approaches used in their estimation.on and ambiguity in the terminology and in some instancesle, the denitions of various relevant performance indicatorsision, linearity, range, limit of detection, limit of quantitation,iscussed with a view to prevent their erroneous usage andy among publications.

2008 Elsevier B.V. All rights reserved.

P. Araujo / J. Chromatogr. B 877 (2009) 22242234 2225

Health Organization (WHO), the International Organization forStandardization (ISO), the International Union of Pure and AppliedChemistry (IUPAC), the United States Pharmacopeia (USP), The ana-lytical chemistry group EURACHEM, etc.

Articlesing the detenforced byever, in spimisinterpreprevailing aparametersmost importical tools in

This artsidered whconcerninginformationsions about

Althouganalytical mto certain aels bioassayshould be c

2. The gen

In a gensists of at lsampling, s

2.1. System

A generathat the insrials (reagenetc) are suihave the protation suchpre-establiseral qualicsource of th

2.2. Sampli

The samfraction of ttigation. Thimportanceis truly reprmeaningfulthere is a sever the relevaluated in

2.3. Sample

Sample pdation. It ha6080% oflaboratory [well documselection oflytes, the ansize and the

2.4. Analysis

The analysis is related to the instrument used to extract qual-itative or q

abled sents, n

tputcent

of a pchem

theand c

ta ev

masighcal aationst im

idati

he eteriste difernaique, Japaterxteny cris andcal mty, rabustn

lectiv

termve cthey[12

ch aixture [16icitmeaunatevealeuthoesebe crd ecity (hod v

ed aropr

efersrence

xpering tboutare submitted for publication every year highlight-ermination of the parameters for method validationany of the above-mentioned regulatory bodies. How-

te of the volume of articles submitted and publishedtation and miscalculation still persists due to somembiguity in the denitions of some of the validation

, few existing guidelines to estimate some of them, andtantly lack of attention to the mathematical and statis-volved in their calculation.

icle discusses some key aspects that should be con-en validating analytical methods, especially thosechromatography methods, in order to derive usefulfrom experimental data and to draw robust conclu-

the validity of the method.h the aspects described in this article apply to all types of

ethods, in some instances they may not be applicablenalytical procedures. For instance, some animal mod-s or some immunoassays have unique features which

onsidered before submitting a validation report.

eral method validation steps

eral context, method validation is a process that con-east ve distinct steps, namely: system qualications,ample preparation, analysis and data evaluation.

qualications

l evaluation of system qualications allows to verifytrument is suitable for the intended analysis, the mate-ts, certied references, external and internal standards,

table for use in analytical determinations, the analystsper training and qualications and previous documen-

as analytical procedures, proper approved protocol withhed acceptance criteria has been reviewed. If the gen-ations of a system are ignored and a problem arises, thee problem will be difcult to identify [9].

ng

pling step assists in the selection of a representativehe material which is subsequently subjected to inves-e choice of an appropriate sampling method is of greatbecause it provides assurances that the sample selectedesentative of the material as a whole for the purpose ofstatistical inferences. Within the statistical literature,

ubstantial body of work on sampling strategies, how-ative costs and time involved in each strategy should be

advance.

preparation

reparation is a key element to successful method vali-s been pointed out that sample preparation represents

the work activity and operating costs in an analytical10]. The literature on sample preparation is ample andented. However, the analyst should remember that thea specic preparation procedure depends upon the ana-alytical concentrations, the sample matrix, the sampleinstrumental technique.

accepta broaelemenand outhe conchoiceas thetion ofspeed

2.5. Da

Thegain instatistiinformand mo

3. Val

In tcharacics werthe Intas a unEuropeing gresome eThe kemittesanalytilineariand ro

3.1. Se

Theintensiwhichidationto whiplex mmixturto specity; itUnforttion resome athat thshouldthe wospeciin metbe gradthe appcity rinterfe

3.1.1. EDur

cern auantitative information from the samples with anuncertainty level. The analysis could be visualised, inse, as a system possessing three interconnected basicamely input converter output. In general, the inputare designated by the letters x and y and they representration and the experimental response respectively. Thearticular analysis is based on many considerations, suchical properties of the analytical species, the concentra-analytes in the sample, the matrix of the sample, theost, etc.

aluation

in purpose of data evaluation is to summarise andt into a particular data set by using mathematical andpproaches. Data evaluation allows extracting usefuland drawing conclusions about the inputs and outputs,portantly about the validation process in general.

on method parameters

arly 80s, it was pointed out that the denition of theic parameters for method validation and related top-ferent between the existing organizations [11]. In 1990,tional Conference on Harmonization (ICH) was createdproject to bring together the regulatory authorities of

an and the United States with the objective of achiev-harmonization of parameters, requirements and, to

t, also methodology for analytical method validation.teria dened by the ICH and by other industrial com-

regulatory agencies around the world for evaluatingethods are: selectivity/specicity, accuracy, precision,

nge, limit of detection, limit of quantitation, ruggedness,ess.

ity and specicity

s selectivity and specicity have been the subject ofritical comments essentially focusing on the ways inare often dened by analysts working in method val-

15]. By denition the selectivity refers to the extentmethod can determine a particular analyte in a com-e without interference from other components in the]. This denition is often wrongly used as equivalenty, which is considered to be the ultimate in selectiv-

ns that no interferences are supposed to occur [12].ly, an inspection of the literature on method valida-d that both terms are still used without distinction byrs, even though by consulting the dictionary it is clear

terms should not be used interchangeably. Selectivityonnected with the word choose while specicity withxact. In this context, it is incorrectly to grade the termeither you have it or you do not). An analyst involvedalidation should always remember that selectivity cans low, high, bad, partial, good, etc., in order to chooseiate category for a particular purpose. The term speci-always to 100% selectivity [13,17,18] or, conversely, 0%s.

imental approaches to assess selectivityhe last decade, some researchers have expressed con-the lack of comprehensive recommendations from

2226 P. Araujo / J. Chromatogr. B 877 (2009) 22242234

ost-column infusion system.

accreditedthe selectivpapers on chical journalpopular app

1. Compariblank sam

2. Compariinjectioninterefer

3. Analysis

Other ap

1. Calculatiinating th

2. Compari3. Compari

the exter

In additigies, an inpost-columendogenouhas been pa HPLC systhrough a tdelivers a cthe HPLC dpossible toanalytical rdifferent saAn exampleof differentquently thean immunomass spectrpresents a ccomparisonFig. 2 whichsion is mainand that tharound theused.

Readersity are referelsewhere [

curacy

uracy is the degree of agreement between the experimentalobtained by replicate measurements, and the accepted ref-value. It has been pointed out that the accuracy is the mostaspect that any analytical method should address [23]. Theination of this parameter allows estimating the extent tosystematic errors affect a particular method. The preced-nition of accuracy is in accordance with several regulatoryFig. 1. Liquid chromatography mass spectrometry p

bodies, books and published articles on how to assessity of a method [14,19]. A non-exhaustive survey ofromatographic method validation published in analyt-

s during the last 10 years revealed that the three mostroaches used to measure selectivity are:

son of the chromatograms obtained after injection ofples with and without the analytes.

son of the chromatographic response obtained afterof analytical solutions with and without all the possible

ents.of certied reference materials.

proaches used in a lesser extend in the last 10 years are:

on of the chromatographic response factor by discrim-e analytical species from closely related structures.

son with certied methods.son of the slopes obtained by the standard addition andnal standard methods.

on to these previously well-known mentioned strate-teresting liquid chromatography mass spectrometryn infusion technique that enables detecting specics sample components that affect the target analytesroposed [20]. This approach uses a syringe pump andtem simultaneously coupled to a mass spectrometeree connector (Fig. 1). The ow from the syringe pumponstant amount of the analytes while the ow fromelivers a processed blank sample, in that way it isstudy dynamically the effect of the matrix on the

esponses over the entire chromatographic run, whenmple treatments, columns and mobile phases are used.

from the literature is the evaluation of the inuenceextraction techniques on matrix effects and conse-magnitude of these effects on the signal of sirolimus,

3.2. Ac

Accvalue,erencecrucialdetermwhiching desuppressant that under specic chromatographic andometry conditions elutes at approximately 6 min andharacteristics transition at m/z 931.6 864.6 [21]. Theof the various infusion chromatograms is showed inallows concluding that the observed signal suppres-

ly due to endogenous components in the whole bloode analytical signal is less prone to matrix interferenceselution time when the solid phase extraction method is

interested in analytical procedures to achieve selectiv-red to comprehensive articles on the subject published14,17,22].

Fig. 2. Compaprecipitation, acolumn infusioC. The solid liReprinted fromTandem-MS. CElsevier.rison of (A) mobile phase, (B) whole blood sample prepared by proteinnd (C) a whole sample prepared by solid phase extraction by the post-n method. The areas inuenced by matrix effects are shown in B and

nes indicate the regions of altered ionization due to matrix effects.P.J. Taylor, Matrix Effects: The Achiles Heel of Quantitative HPLC-ESI-

linical Biochemistry, 38 (4) (2005): 328334 with permission from


Table 1Requested conditions to measure the different precision components according to the ISO/DGuide 99999 [33].

bodies (ICHto mentionited organiscombinatioconcept ofin order tocal and lega[24,25]. InUSP and IUin scienticvalidation55 articlesdifference bwithout usi

Several aracy of a maccuracy ar

1. Measurincomparin

2. Measurinknown aage of re

3. Comparithose fro

4. Determinmeans of

The rstclosely resesample und

The secotage that thand the anadissimilaritpurposes thmonised GuTechnical Rin cases whliquid samplution [27].

A refereto a nationdifferent or

The fourples are una

therkingof abtaitheocitenceng thntrartestid.

guiICH

um oionanal

9 des suids, tr hisidaticy byed inls 5

ecisio

termf Ba*One or more conditions should be changed.

, FDA, and USP) and the IUPAC. However, it is importantthat this denition is acknowledged by other accred-ations as trueness or bias and the term accuracy as then of trueness and precision (ISO, EURACHEM, AMC). Thetrueness as is stated in ISO-5725-1 has been inventedaddress some philosophical objections among medi-l practitioners regarding the concept of statistical bias

this article, the term accuracy as dened by ICH, FAD,PAC is used because it seems to be the preferred term

journals. A ScienceDirect search using the keywordstrueness and validation accuracy showed that onlyused the former keywords while 3876 the latter. Theecomes more dramatic when the search is performedng the word validation.pproaches have been suggested to evaluate the accu-

ethod. The main strategies currently used to assess thee:

g the analyte in a particular reference material andg the result with the certied value.g the analyte in blank matrix samples spiked with

nalytical concentrations and determining the percent-covery.ng the results from the method under validation withm a reference method.ing the analytical concentration in the sample bythe standard addition technique.

strategy should be used as long as the reference material

Anobeen taresultsvalue onately,that prcompeassessiand cociencymetho

Theby theminimcentratwholelevel =ment imethoable fofor valaccuraprepar(3 leve

3.3. Pr

Theulary ombles the analytical concentration and the matrix of theer investigation.nd strategy, despite its popularity, it has the disadvan-e accuracy can be misestimated if the spiked analytelyte contained in the sample behave differently due toies in their chemical form and reactivity. For speciationis approach is not recommended [26]. The IUPAC Har-idelines for In-House Validation of Methods of Analysis

eport recommends the use of the second approach onlyere the method under validation is intended either forles or samples subjected to total destruction or disso-

nce method in the context of the third strategy refersally or an internationally fully validated method withsimilar measurement principles and sources of errors.th strategy is generally used in cases where blank sam-vailable.

closeness ocate measuThe determprocess ofvalidation.the randommeasuremethe coefcie

The reguaccuracy shlast decadeods are welthe review rreproducibiably. The rethe presentular properreported strategy to assess the accuracy of a method haspart in prociency test schemes in order to compare the

particular method under validation with the consensusned by the participating laboratories [28,29]. Unfortu-seconders of this proposal have not taken into accountency testing is aimed at monitoring performance and

of individual accredited laboratories [30] rather thane accuracy of newly developed methods. It is irrational,y to the general requirements for participating in pro-ng, to take part in such schemes without a fully validated

dance for validation of analytical procedures issuedrecommends checking the accuracy by performing af nine determinations over a minimum of three con-

levels (low, medium and high) corresponding to theytical range investigated (3 levels 3 replicates perterminations) [31]. Although, this minimum require-table in general for chromatographic or spectroscopyhe analyst should follow the recommendations suit-/her particular method. For instance, the FDA guidanceon of bioanalytical methods suggests evaluating the

measuring a minimum of three concentration levelspentaplicate in the range of expected concentrationsreplicates per level = 15 determinations) [32].

n

precision is dened by the ISO International Vocab-sic and General Terms in Metrology (ISO-VIM) as the

f agreement between quantity values obtained by repli-rements of a quantity under specied conditions [33].ination of this parameter is one of the basic steps in theachieving repeatability and reproducibility in methodAssessing the precision implies expressing numerically

error or the degree of dispersion of a set of individualnts by means of the standard deviation, the variance ornt of variation.latory bodies emphasize that the terms precision and

ould not be used as synonyms. A literature review of thedemonstrated that analysts engaged in validating meth-l aware of the difference between these terms. However,evealed that in many instances, the terms repeatability,lity and intermediate precision are used interchange-ader should keep in mind that the word repeatability incontext, refers to obtaining the magnitude of a partic-

ty of a sample more than once by keeping constant the


global factors (human, preparation, instrumental and geographi-cal) over a short period of time; the term reproducibility refers toreproduce the magnitude of an already measured property bychanging one or more of the global factors over a short or anextended peto obtaininmore thangeographicaences betwshowed in T

It is wronSuch a ter

The termdiate prec

The repearemains csuch as aries, and tthe result

The reprothe resultthe variatcantly to

For validommendedminimum oprepared inunder stud[30]. Howevthat minimprocedurescheck the prbe different

3.3.1. TotalTotal err

overall erroneous contrthe measur(Etotal) could

Etotal = Esystwhere the tatic and ranFrom the pdifferencestion of the p(Esystematic),mandatorydenition uing the speit is possiblconsequentthe followinliterature o

Etotal = Accu

Etotal = Trueor

Etotal = Accu

The importance of estimating a total error in validation studiesis that it provides a measure of quality that can be compared tothe intended analytical quality of a test, which can be described interms of an

totaIt is asay, t

addhavebaselsoryejectallow

arisemporive

cy) wsirabividuble b

Unceunceult oues tty bee thts contlesof mer, t

ithtionrivin

ends [33remeped

ical v

rtainethos ofncer

rtains. Thtic

nstanbookbinedA an

.

taskethoaspediesrecoato

r witert w

endouldhas

aintyriod of time; and the term intermediate precision refersg the magnitude of a particular property of a sampleonce by using the same preparation, instrumental andl condition over an extended period of time. The differ-

een the three above mentioned precision componentsable 1 allow to derive the following conclusions:

g to report a so-called inter-day repeatability term.m should never be used in method validation.inter-day variation should be connected with interme-ision or in some circumstances with reproducibility.tability always ensures that the variability of the resultsonstant under identical conditions and also that factorsnalyst, procedures, instrumental conditions, laborato-ime have a negligible contribution to the variability ofs.ducibility always makes certain that the variability ofs remains constant under different conditions and thation of one or more factors does not contribute signi-the variability of the results.

ation of chromatographic methods, it is generally rec-checking the precision component by measuring af three concentration levels (low, medium and high)

triplicate and covering the whole analytical rangey (3 levels 3 replicates per level = 9 determinations)er, as was mentioned before, the readers must consider

um criteria vary according to the nature of the analytical. For instance, the minimum number determinations toecision of a biological or a biotechnological method mayfrom the minimum established in the present article.

erroror, a concept introduced 34 years ago, describes ther that may occur in a test result due to the simulta-ibution of random and systematic error components ofement procedure [34]. In general terms, the total error

be dened by the expression:

ematic + Erandomerm E represents the error and the associated system-dom subscripts dene the individual error contribution.revious expression, it is evident that the mentionedbetween the regulatory bodies regarding the deni-arameter that allows to estimate the systematic errorstermed for instance accuracy or trueness, makethe use of appropriate documentation of the particularsed in the calculation of the total error. By document-cic denition used to express the systematic errorse to derive alternative expressions for total error andly avoid ambiguities between denitions. For instance,g alternative expressions can be found in the current

n validation:

racy + Precision (using ICH terminology);

ness + Precision

racy (using ISO terminology).

for theresult.ular asreportsassaysassayscompuerror. Rerror iserrors

An ieter deaccuraIt is deset indallowa

3.3.2.The

the resthe valquantito judgverify i

CoutaintyHowevalong westimamain drecommtaintiemeasube grounumer

Uncecal mmeanthis u

UncemeanscienFor ihand

ComTypetions

Thement mvariousited bo5725-3a chromfamiliaan exprecomm

It sharticleuncertallowable total error [35] which sets a nominal limitl error tolerable in a single measurement or single testdvisable, when determining the total error of a partic-

o follow the recommended criteria. For instance, recentressing the issue of best practices for ligand bindingestablished a nominal total error of 30% for this kind ofd on their inherent variability [36,37]. In addition, it isto include all assay runs in the calculation of the total

ion of particular assay runs in the calculation of the totaled only in cases, where obvious and well-documented

[36].rtant consideration is that total error is a quality param-d from two performance parameters (precision andhich contribute mutually to the quality of a test result.le to set goals for the allowable total error, rather thanal goals for the allowable standard deviation and the

ias.

rtaintyrtainty of measurement is a parameter, associated withf a measurement that characterises the dispersion ofhat could reasonably be attributed to measurand (theing measured) [33]. This parameter is estimated in ordere adequacy of a result for its intended purpose and tonsistency with other similar results.s studies have reported the determination of the uncer-easurement results by using different approaches.

he lack of consensus among the various approachesthe absence of a worldwide-accepted criterion for theand notation of measurement uncertainty were theg factors behind the development in 1980 of the generalation INC-1 for the expression of experimental uncer-

]. INC-1 states that the uncertainty in the results of ant generally consists of several components which mayinto two categories according to the way in which theiralue is estimated.

ty Type A is the evaluation of uncertainty by statisti-ds. The components of this category are determined bythe variances or standard deviations. The evaluation oftainty applies to random and systematic errors.ty Type B is the evaluation of uncertainty by othere components of this category are usually based on

judgement using all the relevant information available.ce, uncertainty assigned to reference data taken froms, reference standards certicates, etc.uncertainty is characterised by the summation of the

d Type B variances and expressed as standard devia-

of determining the uncertainty of a particular measure-d requires the participation of experts familiar with thects involved in the recommendations issued by accred-

. For instance, a laboratory interested in applying ISOmmendation [38] in the evaluation of the uncertainty ofgraphic method will require the assistance of an experth the measurement method and its application and alsoith experience in the implementation of the guidanceed fully nested design and its statistical analysis.be noted that even though the author of the present

reported several studies on the determination of thein linear calibration, central composite designs and


nested designs for prociency testing, it is not his intention topresent a detailed coverage of the subject. The interested readeris referred to the comprehensive work on uncertainty by Kimothi[39].

3.4. Linear

Linear fuin calibratito the introcalibrationdescribed inaccepted as

Linearitytem consistis the assumthe input (xically by ththe origin onot cross th

It is comcurve by incoefcientto concludeAlthough thanalytical vin the contaround theods on a soCountless pusing the r-discussions

This methwith a corrThe calibrgreater thaIt was clelation coef

The authous quotatirespect theyaddition, thto evaluate

The FDAwhich is baissued by tcient shouland that thtical methovalue of r calinearity. Hr-test to cr = 0.999 is mrecommendhave reportation. Thisout over haneglected stopic of contion by thosand by thosembarked ulytical chem

3.4.1. Linear calibration functionThe expression y = f(x) + can be rewritten as

i +

yi ane anael i.

is andcalibt the= 1, thhat aterexsuf

ear. Aon ste coliterpectm sh

Replsider

entent

strumtionthanes hratio

s thad notne sty anely e

ds Colevetrati

ited oA stu

berthaent

perimregi

ortanorteand cropovari

ty oftrati

Errotratiin a

quarure eum ong e

I

i=1

J

j=function analysis

nction analysis is an area familiar to everyone involvedon experiments and perhaps this familiarity has ledduction of some fatal aws when the linearity of a

is assessed. Nowadays, such erroneous procedures areoral presentations, laboratory reports and papers and

correct., in the context of the previously described analysis sys-ing of the basic elements input converter output,ption that there is a straight line relationship between

) and output (y) variables that can be written mathemat-e expression y = f(x) if the straight line crosses throughr by the expression y = f(x) + if the straight line doesrough the origin.mon practice to check the linearity of a calibration

spection of the correlation coefcient r. A correlationclose to unity (r = 1) is considered sufcient evidencethat the experimenter has a perfect linear calibration.e Analytical Methods Committee and some articles onalidation discouraged using the correlation coefcientext of testing for linearity [4043], many laboratoriesworld base the linearity of their instrumental meth--called (by the author of the present article) r-test.ublished papers reinforce the idea, perhaps indirectly, oftest to check for linearity by reporting in their abstracts,and conclusions statements such as

od has a linear calibration range of 1.001000 ng/mlelation coefcient of 0.9999.ation graphs were linear with correlation coefcientsn 0.999 for all compounds.

ar that the calibration was linear as a result of a corre-cient close to 1 (rexperimental = 0.9996).

or of the present article is not stating that the previ-ons are incorrect, however it must be said that in some

are misleading in the context of linearity evaluation. Iney fail to indicate which statistical methods were usedtheir linear relationship.guidance for validation of analytical procedures [31]

sed on the Text on Validation of Analytical Procedureshe ICH [44], recommends that the correlation coef-d be submitted when evaluating a linear relationshipe linearity should be evaluated by appropriate statis-ds. This guidance does not suggest that the numericaln be interpreted in terms of degrees of deviation from

ence, it is extremely important to emphasise that anheck for linearity does not exist. We cannot say thatore linear than r = 0.997. It is surprising that despite the

ations of the accredited bodies, few published articlesed the use of statistical methods for linearity evalu-observation seems to indicate that the issue, pointedlf a century ago, about statistical data analysis being aubject by practitioners validating methods [3] is still atemporary relevance that needs an imperative atten-e currently engaged in validation of analytical methodse responsible for educating and training people to bepon the various aspects of this important area of ana-istry.

yi = x

whereand thtion levanalys

Theto 1 buto if rshow ta counr = 1 itnot linbasedvariancin thetant asfreedo

3.4.1.1.be conexperimexperimand incalibrahigher26 timin calibimplietion anonly ostrategeffectivMethotrationconcenaccredlowed.the numstratedexperimthe exdictionan impthe repcationlevels pidationlineariconcen

3.4.1.2.concenJ-timesthree s(SSr) perror sfollowi

SSr =(1)

d xi represent the estimated experimental responselytical concentration respectively, both at a concentra-The coefcients and represent the sensitivity of the

the intercept respectively.ration function described by Eq. (1) must have an r closecondition given by if linear, then r = 1 is not equivalenten linear. In logical analysis terms, the best strategy tocondition is not equivalent to its converse is to provideample to it. To nd a counterexample to if linear, thences to show that there is something that has r = 1 but it isppendix A provides a comprehensive counterexample

atistical analysis of the various error sum squares andmponents from a linear calibration data set reportedature [45]. Before studying Appendix A, some impor-s such as replication, error sum squares and degrees ofould be discussed in advance.

ication. Replication is an important aspect that musted when the experimenter wants to test if a particularal calibration model, for instance Eq. (1), is linear. Theer must have a reasonable number of standard solutionsental replicates. It has been pointed out that the best

strategies are those with standard solution replicatesinstrumental replicates [42,46]. A preparation error

igher than the instrumental error has been reportedn experiments of triacylglycerols by LCMS [47]. This

t the most serious problems are related to prepara-to instrumental stability. Calibration experiments with

andard per concentration level are a poor calibrationd must be avoided unless the standard solutions arerror-free. For the establishing of linearity the Analyticalmmittee suggests preparing a minimum of six concen-ls in duplicates [42]. Even though duplication at eachon level is considered an optimal design strategy by thisrganisation, it is a poor approach that should not be fol-dy of the behaviour of the uncertainty as a function ofof replicates for the model described by Eq. (1) demon-

t performing between four and six replicates at eachal level decreases the uncertainty signicantly alongental range and produces a uniform condence pre-

on around the centre of the calibration graph which ist feature for quantication experiments [48]. Based on

d behaviour of the uncertainty as a function of the repli-onsidering that the minimum number of concentrationsed by various guidelines and articles on analytical val-

es between ve and six, it is reasonable to measure thea calibration function by preparing a minimum of veon levels in triplicates [31,43].

r sum squares. After selecting a sensible number ofon levels (I) and replicating every concentration level

particular calibration experiment, the summation ofed differences, namely the residual error sum of squaresxperimental error sum of squares (SS) and lack-of-tf squares (SSlof), must be calculated according to the

quations:

i

1

(yij yi)2 (2)


SS =I

i=1

Ji

j=1(yij yi)2 (3)

SSlof = SSr SS =I

i=1(yi yi)2 (4)

The term yij represents the experimental response, yi is the esti-mated response obtained by using Eq. (1), and yi is the averageresponse at every concentration level.

3.4.1.3. Degrees of freedom. The degrees of freedom (DF) associatedto Eqs. (2)(4) are respectively:

DFr = (IJ 2) (5)

DF = (IJ I) (6)

DFlof = (I 2) (7)

The bracketed number 2 in Eqs. (5) and (7) and associated withEqs. (2) and (4) respectively, represents the number of parametersdescribed by Eq. (1) (the slope + the intercept = 2 parameters). Ifa model with a different number of parameters to those describedby Eq. (1) were studied, for instance:

yi = xi + 2

The degrbe (IJ 3) acase, repres

By usinglevels (I = 5)it is possibleand SSlof res

3.4.1.4. Acceperformedseveral articin chromatoedly that anaware that

Analytical Method Committee suggests using the F-test as a reli-able approach to check the linearity of any calibration function.The procedure is as follows:

The purely experimental variance and lack-of-t variance desig-nated by 2 and

2lof

are estimated by computing the quotientsSS/(IJ I) and SSlof/(I 2) respectively.

The calculated 2 and 2lof variance terms are used to calculatethe Fisher variance ratio or F-test by the expression:

F(I2)/(IJI) =2

lof

2(9)

The value of F(I2)/(IJI) calculated experimentally is comparedagainst the critical value of F found in statistical tables, generallyat the 95% condence level for I 2 and IJ J degrees of freedom inthe numerator and denominator respectively. If the experimentaldata set describes a genuine linear calibration of the form givenby Eq. (1) then the condition Ftabulated > F(I2)/(IJI) must be fullled.Otherwise there are grounds to suspect that a different model tothe described by Eq. (1) must be proposed.

The estimation of the various error sum squares and the Fisherratio for testing the acceptability of a linear model proposed in theliterature is discussed in Appendix A.

nge

enerinter

whistratges.dynad asmices thhesttratiearencedet

deterxi + (8)

ees of freedom associated with Eqs. (2) and (4) wouldnd (I 3) respectively. The bracketed number 3 in thisents the three parameters ( + + ) of Eq. (8).Eq. (1) and the minimum criteria of ve concentrationin triplicates (J = 3) established in the previous section,to estimate 13, 10 and 3 degrees of freedom for SSr, SS

pectively.

ptability of linearity data. A ScienceDirect search wasusing the keywords linearity test and revealed thatles used these two words as a true measure of linearitygraphy method validation. It has been reported repeat-analyst engaged in any analytical validation should be

there is no test for linearity as such [42,43,4951]. The

3.5. Ra

In gas thelyte fordemonent ranrange,mariseor dynadescribthe higconcenThe lindependusually

Scheme 1. Main approaches proposed in the literature foral, the range of an analytical procedure can be denedval between the upper and lower concentration of ana-ch suitable precision, accuracy and linearity have beened. The literature on method validation describes differ-For instance, linear range, analytical range, calibrationmic range, working range. However, they can be sum-working (or analytical) range and linear (or calibration,) range. The former range which is wider than the latter,e interval between the lowest (limit of detection) andconcentration where the signal can be related to the

on for the evaluation of random and systematic errors.range corresponds to the valid interval of functional

of the signal on concentration or mass [52] which isermined by using the method of least squares, which

mining the limit of detection.


Fig. 3. Visual d essively replicate solutions of PGE2 at an initial concentration of 0.4 ng/ml.

in turns asslinear range

To demogested to prof the targeto remembthe intendeommends pfrom 80 to 1analyst intethe guidelinrange of the

3.6. Limit o

The limiamount of anecessarilyago, the Inteuse the termas the conof analyte istatistical p

Differenof the mainliterature onation of thconcentratithe analyteraphy LODreplicate soThe replicawhere theFig. 3 the vPGE2. The grecommendsubmittingbased on athe LOD isthe assumppendency omethod valamong anarelationshipknown low

concentration that produces a signal equivalent to three ores the standard deviation of the blank sample (3 blank or

ank).implications of using the previous criteria are illustrated inhere a limit of decision derived from the blank distributionlished at +2 blank. This limit of decision, at the 95% con-

level of the blank distribution is a probability that indicateser ore bla

imategatncenr thae st

ible ta cocal pnimu) theprobetermination of the limit of detection for PGE2 determined visually by diluting succ

umes homoscedasticy of the measurements over the.nstrate an acceptable linear range, it is generally sug-epare ve different standard solutions from 50 to 150%t analytical concentration [43]. However, it is importanter that the specied ranges often differ depending ond application of the procedure. For instance, the ICH rec-reparing ve different standard solutions (plus a blank)20% for the assay of a drug or a nished product [31]. Anrested in validating a particular method should consultes to encompass the recommended minimum speciedintended method.

f detection

t of detection (LOD) is commonly dened as the lowestnalyte in a sample that can be reliably detected but notquantitated by a particular analytical method. A decadernational Organization for Standardization proposed to

minimum detectable net concentration [53] deneddence with which it is possible to detect an amount

n the sample larger than that in a blank sample with aower of (1 ).t criteria are used for evaluating the LOD. A summary

approaches proposed for determining the LOD in then validation is presented in Scheme 1. Visual determi-e LOD is performed by preparing samples with known

lyticaltwo tim2 bl

TheFig. 4 wis estabdencewhethor to thfor estfalse nthe cois large84%. This possis notstatistithe mi(Fig. 4Bto theons of the analyte and by establishing the level at whichcan be reliably detected. Fig. 3 shows the chromatog-for PGE2 determined visually by diluting successivelylutions of PGE2 at an initial concentration of 0.4 ng/ml.te solutions are diluted up to a concentration levelanalyte is not longer detected visually. According toisual LOD corresponds to a concentration of 0.1 ng/mluidelines for validation of analytical procedures [31]the presentation of relevant chromatograms when

a validation report where the LOD determination isvisual criteria. Another approach used for estimatingthe calculation of the signal/noise relationship undertion that data normality, homoscedasticity and inde-f residuals are met. An inspection of the literature onidation revealed that this is the most popular approachlysts performing validation studies. The signal to noise

is determined by comparing the analytical signals atconcentrations with those of blank sample up to an ana-

Fig. 4. Statistifor estimatingnot a signal could be due to the sample (>+2 blank)nk (


the minimum number of independent determinations required toestablish the LOD is 10, it is advisable to increase the number ofreplicates when the LOD is dened as 2 blank to avoid reachingwrong conclusions. Both LOD criteria (3 blank or 2 blank)should be justied by presenting the relevant chromatograms.

The nal approach described in Scheme 1 is based on the quo-tient of two analytical parameters, namely the standard deviation() and the slope of a regression curve ( as in Eq. (1)). The formerparameter could be expressed as the standard deviation of the blank(blank), as the residual standard deviation of the calibration curveor as standard deviation of the intercept of the calibration curve.The guidelines on method validation do not express any particularpreference for the approaches described in Scheme 1, however theyrecommend that when reporting the LOD the denition used in itsevaluation should be stated.

3.7. Limit of quantitation

The limicentration oacceptable lis evaluated

1. Visual evare prepaquantie

2. Signal/noconcentran analyt10 times

3. Standardand are

The secoture, couldamount ofLOD (LOQ =

Other ddescribed ain its evalua

It is impevaluation otration therapproachesin an articlein order totual denitiprole appand Boulanconcept.

3.8. Ruggedness

This parameter evaluates the constancy of the results whenexternal factors such as analyst, instruments, laboratories, reagents,days are varied deliberately. By considering these critical externalfactors and inspecting Table 1, it is evident that ruggedness is ameasure of reproducibility of test results under normal, expectedoperational conditions from laboratory to laboratory and from ana-lyst to analyst [58]. Ruggedness cannot be erroneously used as asynonymous of robustness as it is going to be explained in the nextsection.

3.9. Robustness

This parameter evaluates the constancy of the results wheninternal factors (no external factors as in ruggedness) such as owrate, column temperature, injection volume, mobile phase compo-sition or any other variable inherent to the method of analysis are

delibnes [oughity oces rce th

ingd diffstrusicaltimete bosiveis re

al rem

hodm berecoplo

er, dory

ancme rtionbe vion a

thaey, t

ous tlabot of quantication (LOQ) is dened as the lowest con-r amount of analyte that can be determined with an

evel of precision and accuracy [9]. Similarly to LOD, LOQby using different approaches, that is:

aluation: samples with known analytical concentrationred and the minimum level at which the analyte can bed with an acceptable level of uncertainty is established.ise ratio: the signals of samples with known analyticalations are compared with those of blank samples up toical concentration that produces a signal equivalent tothe standard deviation of the blank sample (10 blank).-deviation/slope ratio (LOQ = 10 /): the parameters

calculated in the same fashion as LOD.

nd approach, which is the most used in the litera-be dened in a more general context as the lowest

analyte that can be reproducibly quantied above then LOD).enitions to express the LOQ different from thosebove could be used, provided that the denition usedtion is stated.ortant to note that the discussed approaches for thef the LOQ do not demonstrate that at the LOQ concen-

e is an adequate accuracy and precision. The differentproposed in the literature have been critically revisedwhich advocates using the accuracy prole approach

estimate an LOQ more in accordance with its contex-on [55]. The reader interested in applying the accuracyroach is referred to the articles of Hubert et al. [56]ger et al. [57] who were the rst to introduce this

variedguideli

Althducibilinuenevidenperformties anmiscon

Clasat-theevaluaprehenreader

4. Fin

Mettury frowidelydure emHowevregulatperformtion, socalculashouldvalidatfurtherof monerroneability,erately. It is generally not considered in most validation46].

robustness and ruggedness aim at testing the repro-f the test results regardless of internal or externalespectively, the literature on method validation bearsat both terms are used interchangeably. The analysta method validation should distinguish the similari-

erences between these validation parameters and avoiding ruggedness as robustness.and multivariate methodologies such as the one-factor-approach or a factorial design have been proposed to

th ruggedness and robustness. However for more com-studies on robustness and ruggedness evaluation the

ferred to [5962].

arks

validation has evolved rapidly over the last half a cen-ing a neglected area of many scientic disciplines into a

gnized process used to conrm that an analytical proce-yed for a specic test is appropriate for its intended use.espite this rapid evolution and the efforts of differentbodies to reach greater harmonization of the relevante indicators commonly evaluated in method valida-elentless inconsistencies in relation to their denitions,and interpretation are repeatedly used. Practitioners

igilant over the herein described key aspects of methodnd bear in mind that their misapplication goes much

n a simple rejection of a submitted report or a wasteime and resources. The acceptance and application oferminology can have serious implications in results reli-ratory performance and institution credibility.


Appendix A. Demonstration that a correlation coefcient close to 1 is not a reliable indicator of linearity

The data printed in bold type have been reported elsewhere [45].

Comments

The amount oanalyte/inteaverage are

0.09

0.130.250.491.25

The calibration 1.69Proposed lineaReported squa

Testing the acc d in Sx 2

0.35 106

0.50 106

1.00 106

2.00 105

5.00 105

7.00 104Residual error

squares (Eq.

Pure error sum(Eq. (3))

Lack-of-t errosquares (Eq.

Results after aEqs. (2)(4)

.69

Degrees of free =12Associated var

(2 = SS/DF).91

Fisher ratio (F

calculated (iFcalculated < Fthen Linear)

grees

Conclusions ortedck of

References

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Dekker In[10] http://fsh

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Anal. Chem. 61 (1989) 951A.

[51] Analytical Methods Committee. AMC Technical Brief 3, 2000, 1. .

[52] O. Mathias, Chemometrics: Statistics and Computer Application in AnalyticalChemistry, WileyVCH, Weinheim, 1999.

[53] International Organization for Standarization. ISO 11843-1: Capability of Detec-tion. Part 1: Terms and Denitions. ISO, Geneva, 1997.

[54] P. Araujo, L. Fryland, J. Chromatogr. B 847 (2007) 305.[55] E. Rozet, A. Ceccato, C. Hubert, E. Ziemons, R. Oprean, S. Rudaz, B. Boulanger,

Ph. Hubert, J. Chromatogr. A 1158 (2007) 111.[56] Ph. Hubert, P. Chiap, J. Crommen, B. Boulanger, E. Chapuzet, N. Mercier, S.

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[58] http://www.labcompliance.com/tutorial/methods/default.aspx.[59] M. Mulholland, Trends Anal. Chem. 7 (1988) 383.[60] E. Aguilera, R. Lucena, S. Crdenas, M. Valcrcel, E. Trullols, I. Ruisnchez, Trends

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Key aspects of analytical method validation and linearity evaluationIntroductionThe general method validation stepsSystem qualificationsSamplingSample preparationAnalysisData evaluation

Validation method parametersSelectivity and specificityExperimental approaches to assess selectivity

AccuracyPrecisionTotal errorUncertainty

Linear function analysisLinear calibration functionReplicationError sum squaresDegrees of freedomAcceptability of linearity data

RangeLimit of detectionLimit of quantitationRuggednessRobustness

Final remarksDemonstration that a correlation coefficient close to 1 is not a reliable indicator of linearityReferences

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