Gestion du risque associé au cycle de vie des méthodes ...bictel.ulg.ac.be/ETD-db/collection/available/ULgetd-09302015-14010… · HPLC High Performance Liquid Chromatography –

UNIVERSITE DE LIEGE LABORATOIRE

FACULTE DE MEDECINE DE CHIMIE ANALYTIQUE

DEPARTEMENT DE PHARMACIE Professeur Philippe HUBERT

Thèse présentée en vue de l’obtention du grade de Docteur en Sciences

Biomédicales et Pharmaceutiques Année académique 2014-2015

Gestion du risque associé au cycle de vie

des méthodes analytiques

Cédric HUBERT Licencié en Sciences Chimiques

Diplômé d’études approfondies en Sciences Pharmaceutiques

UNIVERSITE DE LIEGE LABORATOIRE

FACULTE DE MEDECINE DE CHIMIE ANALYTIQUE

DEPARTEMENT DE PHARMACIE Professeur Philippe HUBERT

Thèse présentée en vue de l’obtention du grade de Docteur en Sciences

Biomédicales et Pharmaceutiques Année académique 2014-2015

Gestion du risque associé au cycle de vie

des méthodes analytiques

Applications aux molécules de faibles poids moléculaires analysées par Spectrométrie de Masse

Cédric HUBERT Licencié en Sciences Chimiques

Diplômé d’études approfondies en Sciences Pharmaceutiques

« Un problème sans solution est un problème mal posé »

Albert Einstein

Au terme de cette thèse, j’aimerais exprimer une profonde gratitude envers toutes les

personnes qui, de par leur soutien, mais également leurs conseils m’ont permis de mener à bien

cette expérience de vie inoubliable. Le chemin parcouru fut long et, par moments, parsemé

d’embûches, mais leur présence a rendu celui-ci extrêmement enrichissant.

Je désire remercier tout particulièrement Monsieur le Professeur Philippe Hubert.

« Philippe, je tiens tout d’abord à te remercier de m’avoir accueilli au sein de ton

laboratoire, mais également pour avoir sans cesse mis en œuvre tout ce qui était en ton

pouvoir pour me donner les moyens et les ressources nécessaires à l’aboutissement de cette

thèse. Tes conseils, ta compétence et tes idées ainsi que ton soutien m’ont été très précieux.

De plus, la confiance que tu m’accordes est une réelle motivation pour moi. Pour tout cela

et pour bien plus encore, je tiens à te témoigner ma plus sincère gratitude ».

Je désire également remercier Madame le Professeur Marianne Fillet, co-promotrice de

cette thèse, non seulement pour ses conseils judicieux prodigués au cours de nos échanges, mais

également pour son aide précieuse lors de la préparation et de la rédaction de cette thèse.

Je souhaite également exprimer ma gratitude à Monsieur Eric Ziémons, Docteur en

Sciences Pharmaceutiques, pour m’avoir fait bénéficier de son expérience et de sa compétence.

Ses idées et son avis éclairé dans le domaine des Sciences Pharmaceutiques ont été pour moi

d’une aide précieuse et inestimable. Mais plus encore que cela, l’écoute dont il m’a fait bénéficier

ainsi que son soutien constant, mais également son amitié ont été un réel moteur durant ce

parcours de longue haleine.

« Eric, même si ces quelques mots ne sauraient représenter fidèlement ma profonde

reconnaissance, MERCI ! ».

Mes sincères remerciements s’adressent également à tous les membres du Laboratoire de

Chimie Analytique, pour leur bonne humeur et les moments agréables passés en leur compagnie.

Nos « temps de midi » endiablés font partie intégrante de cette aventure et furent des instants de

détente inoubliables. Un remerciement particulier s’adresse à Monsieur Frédéric Lecomte pour

tous ces moments passés ensemble, mais également pour ses remarques et ses conseils avisés. Je

tiens également à associer à ces remerciements, Monsieur Pierre Lebrun, Docteur en Sciences

Mathématiques, et Monsieur Eric Rozet, Docteur en Sciences Pharmaceutiques, de m’avoir

consacré du temps afin de partager leurs connaissances et leur expertise considérables, en

statistiques. Une partie de cette thèse n’aurait pu être menée à bien sans leur aide.

J’aimerais également remercier Madame Joëlle Widart pour ses conseils et ses

connaissances en spectrométrie de masse. Je tiens également à lui adresser de sincères

remerciements pour m’avoir fait profiter de son expertise dans le domaine réglementaire ainsi

que pour nos débats animés, mais ô combien intéressants et fructueux.

Mes remerciements s’adressent à Mesdames et Messieurs les Membres du Comité de thèse

pour leur disponibilité et leurs précieux conseils, ainsi qu’à Mesdames et Messieurs les Membres

du Jury qui me font l’honneur de juger ce travail.

Je tiens également à remercier mes amis et ma famille pour leur soutien et leurs

encouragements, mais également pour leur compréhension dans les moments un peu plus

difficiles. Sans ce soutien, il m’aurait été bien plus compliqué et pénible d’arriver au bout de ce

travail.

Enfin, je tiens tout particulièrement à dédier cette thèse à mon épouse.

« Mour, ta gentillesse et ton écoute de tous les instants sont des soutiens indispensables.

Mais plus encore, la compréhension et la patience dont tu fais preuve à mon égard, sont

pour moi un réel réconfort. C’est, sans conteste, cet ensemble qui nous a permis d’atteindre

un équilibre indispensable à la réussite de cette aventure. Pour toutes ces raisons, mais

également pour ton aide essentielle lors de la rédaction de cette thèse, il m’est agréable de

dire que ce travail est le nôtre ».

Abbreviation

Les abréviations utilisées dans cette thèse sont listées ci-dessous.

A

AAPS American Association of Pharmaceutical Scientists

ACN Acétonitrile

AQbD Analytical Quality-by-Design

APCI Atmospheric Pressure Chemical Ionisation – Ionisation Chimique à Pression

Atmosphérique

API Active Principal Ingredient – Principe Actif

ATP Analytical Target Profile

B

B-term Difussion longitudinal (terme de l’équation de Van Deemter)

BEH Ethylene Bridged Hybrid

C

CBER Center for Biologics Evaluation and Research

CC Change Control

CDER Center for Drug Evaluation and Research

cGxP current Good “x” Practices - Bonnes pratiques de “x” en vigueurs

CMP Critical Method Parameter – Paramètre Critique de la Méthode

COST Changing One Separate factor a Time

CPP Critical Process Parameter – Paramètre Critique du Procédé

CQA Critical Quality Attribute – Attribut Qualité Critique

CS Calibration Standard – Standard de Calibration

CSM Calibration Standard within Matrix– Standard de Calibration dans la matrice

D

DEC Disposable Extractive Cartridge – Cartouche d’Extraction

DoE Design of Experiments – Plan d'expériences

DS Design Space – Espace de conception

E

EFPIA European Federation of Pharmaceutical Industries and Associations

ESI Electrospray Ionisation – Ionisation par électronébulisation

F

FDA Food and Drug Administration

G

GalN Galactosamine

GluN Glucosamine

GluN-13C6 Glucosamine isotopique

GMP Good Manufacturing Practices – Bonnes pratiques de fabrication

GxP Good “x” Practices – Bonnes pratiques de “x”

H

HILIC Hydrophilic Interaction Liquid Chromatography - Chromatographie Liquide

d’Interactions Hydrophiles

HMF Hydroxymethylfurfural

HPLC High Performance Liquid Chromatography – Chromatographie Liquide Haute

Performance

I

ICH International Conference on Harmonisation of Technical Requirements for

Registration of Pharmaceuticals for Human Use

I.D. (i.d.) Internal Diameter – Diamètre Interne

IDE Integrated Development Environment

IS Internal Standard – Standard Interne

ISO International Organization for Standardization

K

KG Ketoglutarate

L

LC Liquid Chromatography – Chromatographie Liquide

LLOQ Lower Limit of Quantification – Limite Inférieure de Quantification

LOD Limit of Detection – Limite de Détection

LOQ Limit of Quantification – Limite de Quantification

M

ME Matrix Effect – Effet de matrice

MeOH Méthanol

MS Mass Spectrometry (Spectromètre simple quadripôle)

MS-MS Mass Spectrometry (Spectromètre triple quadripôle)

MUX (MXI) Multiplexing Interface

M.W. Molecular Weight – Masse Moléculaire

N

NP Normal Phase – Phase Normale

O

OCDE Organisation for Economic Co-operation and Development

OFAT One-Factor-at-A-Time

OOS Out of Specification – Hors Spécification

OOT Out of Trend – Hors Tendance

P

PF Pharmaceutical Form – Forme pharmaceutique

PP Protein Precipitation – Précipitation de protéine

Q

QbD Quality-by-Design

QbT Quality-by-Testing

QC Quality Control - Contrôle de Qualité

R

RP Reversed Phase – Phase Inverse

RSD Relative Standard Deviation – Ecart-type relatif

S

SD Standard Deviation – Ecart-type

SIM Selected Ion Monitoring

SIR Single Ion Reaction

SPE Solid Phase Extraction – Extraction sur Phase Solide

SS Stability Study – Etude de Stabilité

SSS Standard Stock Solution – Solution-mère

T

TCA Trichloroacetic acid – Acide Trichloroacétique

TFA Trifluoroacetic acid – Acide Trifluoroacétique

TIC Total Ion Current

U

USP United States Pharamcopeia – Pharmacopée américaine

UV Ultraviolet

V

VS Validation Standard – Standard de Validation

Symboles

Les symboles et unités utilisés dans cette thèse sont listés ci-dessous.

^ Représentation de l’estimateur

atom% Pourcentage de pureté isotopique du composé

α Niveau de risque fixé (étape de validation)

bar Unité de pression

β Pourcentage défini de valeurs (probabilité)

βx Coefficient de l’équation de modélisation

Da Unité de masse atomique (Dalton)

δ Erreur systématique

eV Unité de mesure d’énergie (électron-volt)

ε Erreur associée au modèle

F Effets modélisés

θ Paramètres du modèle

in. Hg Unité de pression

k Facteur de tolérance

k’ Facteur de capacité (chromatographie liquide)

Λ Spécifications associées au modèle

λ Limite d’acceptation prédéfinie

µT Vraie valeur inconnue

M Réponses modélisées

m/z Rapport masse sur charge (spectrométrie de masse)

m Nombre de niveaux (étape de validation)

mρ Mélange de la phase mobile (chromatographie liquide)

N Nombre d’expériences

n Nombre de répétitions (étape de développement et de validation)

ν Degrés de liberté

π Niveau de qualité

p Nombre de série (étape de validation)

R2 Coefficient de détermination

S Critère de séparation

σ Erreur aléatoire

T Température

t0 Temps « mort » du système chromatographique

tA Temps de rétention au sommet du pic

tB Temps de rétention au début du pic

tE Temps de rétention à la fin du pic

v/v/v Proportion en volume de la phase mobile (chromatographie liquide)

X% Concentration nominale d’un composé « X » exprimée en pourcent

X.ACN Pourcentage d’acétonitrile dans la phase mobile (chromatographie liquide)

X Observation

x0 Nouvelle condition opératoire du domaine expérimental

χ Domaine expérimental

Z Variable aléatoire Normale

Table des matières

I. INTRODUCTION 17

I.1 Cycle de vie des méthodes analytiques 19

I.2 Analyse et contrôle du risque : Contexte réglementaire 23

I.3 Approche intégrée 28

I.4 Evaluation et gestion du risque analytique 38

II. OBJECTIFS 45

III. RESULTATS ET DISCUSSIONS 49

Préambule 51

III.1 Accord entre prédiction et validation 53

III.2 « Quality-by-Testing » 79

III.3 « Quality-by-Design » versus « Quality-by-Testing » 101

III.4 Validation de l’espace opérationnel : de l’optimisation à la validation en une seule étape 129

IV. CONCLUSIONS ET PERSPECTIVES 161

V. RESUME DE LA THESE 169

VI. LISTE DES PUBLICATIONS 175

Chapitre I

Introduction

Chapitre I : Introduction

19

I.1 Cycle de vie des méthodes analytiques

La chimiométrie, initiée dans les années 1970, revêt à l’heure actuelle une importance

capitale dans le domaine de la chimie analytique [1]. Cette discipline a connu un essor

considérable dès les années 1980 avec la parution de plusieurs journaux scientifiques tels que

« Journal of Chemometrics » ou encore « Chemometrics and Intelligent Laboratory Systems ».

Dans le même temps, plusieurs ouvrages scientifiques [2,3] ont également été publiés dont

notamment « Chemometrics: A textbook » rédigé par le Professeur D.L. Massart [4], reconnu

comme l’un des pères fondateurs de la discipline. Suivant une définition générale, cette

branche de la chimie analytique en constante évolution se décline en trois thèmes principaux :

- proposer des méthodes mathématiques et statistiques pour mieux exploiter les

résultats collectés chaque jour dans les laboratoires d’analyse en extrayant une

information plus pertinente,

- améliorer la qualité des mesures en optimisant les conditions de leur collecte,

- acquérir une connaissance accrue des processus analytiques.

Il ressort de cette définition que la chimiométrie est de nos jours un outil indissociable de

l’activité de l’analyste. Les objectifs décrits dans cette définition ne diffèrent d’ailleurs guère

des objectifs d’un système d’Assurance de Qualité. Il apparaît à travers cette description

succincte de la chimiométrie que cette discipline introduit la notion de gestion des activités

liées aux méthodes analytiques. Il convient donc de se pencher sur la description même de la

méthode analytique au travers des résultats qu’elle engendre. Ceux-ci sont le fruit d’un grand

nombre d’étapes pouvant être perçues, dans leur ensemble, comme un processus analytique.

Comme tout processus, celui-ci naît et évolue et peut éventuellement être appelé à disparaître

au gré des progrès technologiques. La notion du cycle de vie des méthodes analytiques

s’inscrit donc parfaitement dans cette évolution naturelle d’un processus. Dans un premier

temps, nous pouvons définir le cycle de vie des méthodes analytiques en 4 étapes distinctes,

tel qu’illustré à la Figure 1 [5].

La sélection de la méthode est l’étape initiale du cycle de vie des méthodes analytiques

et est inévitablement liée à la problématique. Ce terme regroupe non seulement la question

posée à l’analyste, mais également le niveau de qualité donné que celui-ci devra atteindre. En

effet, c’est la problématique qui guide l’analyste à choisir une technique analytique répondant

a priori aux besoins. Celle-ci doit permettre l’analyse, au sens large, du ou des analyte(s) dans

une gamme de concentration donnée. Ce choix est essentiellement basé sur l’expérience et la

connaissance de l’analyste, mais est cependant également orienté par les référentiels en

vigueur. En effet, la norme ISO 17025:2005 précise à ce sujet dans son chapitre 5.4.2 que : « le

laboratoire doit utiliser des méthodes d’essai et/ou d’étalonnage, y compris des méthodes

d’échantillonnage, qui répondent aux besoins du client et qui conviennent aux essais et/ou

étalonnages qu’il effectue, de préférence les méthodes publiées comme normes internationales,


20

régionales ou nationales » [6]. Bien que cette directive propose l’utilisation de méthodes

normées, il est cependant admis que, dans le cas où les méthodes officielles ne peuvent

répondre à la problématique, le laboratoire peut se tourner vers de nouvelles méthodes. Les

performances de ces dernières doivent alors être avérées ou démontrées. Dès lors, le

laboratoire rentre de plein pied dans le cycle de vie de la méthode analytique. Le choix de

cette nouvelle méthode doit être un compromis entre les techniques et expertises maîtrisées

au sein du laboratoire et les performances requises posées lors de la définition de la

problématique.

Développement

Validation INTRA-laboratoire

INTER-laboratoires Robustesse

Routine

Problématique Sélection

Re-validation

Fig. 1. Cycle de vie des méthodes analytiques suivant une approche conventionnelle [7].

Le développement de cette nouvelle méthode doit être confié à du personnel qualifié et

sa mise au point doit être largement documentée. L’analyste doit aussi définir le domaine

d’application de la méthode. En fonction de la technique choisie, il doit définir les différentes

étapes du mode opératoire et notamment adapter celles-ci à la matrice dans laquelle se

trouve les analytes. Il doit également considérer la gamme de concentration ciblée et ainsi

adapter les conditions opératoires permettant la détermination de ceux-ci avec un niveau de

qualité déterminé. Habituellement, le développement de la méthode analytique est envisagé

par l’intermédiaire d’étapes successives réalisées quasiment aléatoirement dans une

démarche pas à pas. Nous verrons, dans la suite de notre introduction, l’évolution de cette

démarche au cours des années jusqu’à l’utilisation et l’intégration des plans d’expériences

dans cette étape fondamentale du cycle de vie.

Dès l’instant où les performances qualitatives de la méthode rencontrent les attentes

de l’analyste, celle-ci est considérée comme aboutie. La phase de développement est donc

clôturée et la phase de validation débute. Comme le montre la Figure 1, cette étape est

envisagée après la mise au point complète de la méthode. La norme ISO 17025:2005 définit

que l’étape de validation doit être considérée comme une « étape ultime » avant la mise en

exploitation de la méthode analytique. Elle permet de démontrer son aptitude à atteindre des

objectifs définis a priori et donc de donner des garanties quant à ses performances


21

quantitatives lors de son utilisation en routine. La clause 5.4.5.1 l’énonce d’ailleurs comme

suit : « La validation est la confirmation par examen et l’apport de preuves objectives du fait que

les exigences particulières en vue d’une utilisation prévue déterminée sont remplies ». Dans ce

contexte, il est également important de préciser que deux types de validation peuvent être

envisagés. Tout d’abord, la validation intra-laboratoire. Elle est absolument requise lors du

développement d’une nouvelle méthode et ce, même lors de l’adaptation d’une méthode

dérivée d’un protocole normalisé. Cette étape majeure dans le cycle de vie des méthodes

analytiques fera l’objet d’un point spécifique de cette introduction. L’autre type de validation

est la validation inter-laboratoires. Celle-ci est extrêmement lourde à mettre en œuvre. Elle ne

doit être considérée que dans le cas où plusieurs laboratoires doivent utiliser la même

méthode ou lorsque cette méthode doit servir à des fins officielles comme, par exemple, les

méthodes normalisées.

De plus, une étape supplémentaire est généralement considérée au terme de la

validation. Cette étape consiste en l’évaluation de la robustesse de la méthode. Elle permet de

démontrer que des modifications mineures de paramètres critiques de la méthode

n’influencent pas ses performances qualitatives. A titre d’exemple, dans le cadre de

l’utilisation d’une technique séparative, l’analyste doit vérifier l’influence de ces modifications

sur la sélectivité de la méthode. A ce stade, il est important de noter que la tendance actuelle

est d’étendre la robustesse non seulement aux paramètres qualitatifs, mais également

quantitatifs. [8].

Finalement, suite à l’utilisation de la méthode en routine, il s’avère quelquefois

nécessaire d’y apporter des modifications. En fonction de l’importance des modifications

apportées, une nouvelle optimisation, une revalidation partielle, ou même une validation

complète de la méthode optimisée doit être envisagée. Dans d’autre cas, une comparaison

entre les performances de la méthode initiale et celles de la méthode optimisée peut s’avérer

suffisante et ainsi permettre d’éviter la réalisation d’une nouvelle validation, qu’elle soit

partielle ou complète. Ces comparaisons se basent sur une démonstration statistique de

l’équivalence entre deux méthodes [9,10]. Une fois les performances de la méthode optimisée

démontrées, celle-ci peut alors perdurer et son utilisation en routine peut, dès lors, reprendre

jusqu’à ce que l’analyste soit éventuellement obligé d’abandonner cette méthode pour, par

exemple, intégrer une autre technique permettant de répondre à des problématiques toujours

plus complexes et des niveaux d’exigences toujours plus grands.

L’approche décrite ci-dessus, qualifiée de conventionnelle, est essentiellement basée

sur une succession d’étapes toutes plus ou moins indépendantes les unes des autres. Cette

approche ne procure qu’une maîtrise modérée et une connaissance limitée de la méthode

développée. Bien que la succession des différentes étapes du cycle de vie des méthodes

analytiques reste semblable, depuis la fin des années 2000, une vision différente de

l’approche à adopter commence à s’imposer [11]. En effet, dès 2007, des organisations telles

que la « Pharmaceutical Research and Manufacturers of America » et l’« European Federation of


22

Pharmaceutical Industries and Associations (EFPIA) » ont mis en place des groupes de travail

afin de progresser sur l’intégration de la démarche « Quality-by-Design » dans le cadre du

cycle de vie des méthodes analytiques.

Cette démarche était initialement associée aux processus de fabrication, mais ses

atouts en terme de maîtrise du risque associé à l’activité considérée sont très clairement en

accord avec les attentes de l’analyste. En 2010, ces groupes de travail ont d’ailleurs publié un

« white paper » [12] définissant les éléments clés et les avantages de cette méthodologie

lorsqu’elle est appliquée en vue d’une intégration accrue des différentes étapes du cycle de vie

des méthodes analytiques. Ce document s’inscrit dans le respect des normes définies par les

organismes internationaux tel que l’« International Conference on Harmonisation of Technical

Requirements for Registration of Pharmaceuticals for Human Use » (ICH) [13-16]. Les éléments

clés sont la transposition des principes de l’approche « QbD » et des définitions qui y sont

associées, à partir du domaine de la production vers celui du contrôle de qualité.

Cette évolution est notamment liée à l’utilisation accrue des plans d’expériences lors

des différentes étapes du cycle de vie des méthodes analytiques. La Figure 2 illustre

clairement les deux aspects principaux de cette approche que sont la connaissance en

profondeur de la méthode et l’amélioration continue de celle-ci tout au long de son cycle de

vie.

Fig. 2. Cycle de vie des méthodes analytiques suivant l’approche « QbD » [12].


23

I.2 Analyse et contrôle du risque : Contexte réglementaire

A la lumière du chapitre précédent, il apparaît clairement que la notion de cycle de vie

des méthodes analytiques est étroitement liée aux aspects réglementaires. Il semble d’ailleurs,

de nos jours, impossible d’ignorer ceux-ci lorsque l’on évolue dans le domaine de l’industrie

pharmaceutique. Comme bien souvent, ce sont des événements dramatiques qui conduisent à

la création de normes, de directives ou d’organismes de référence ou de contrôle. L’industrie

pharmaceutique n’y échappe pas. En effet, le cadre réglementaire auquel sont soumises

actuellement les industries pharmaceutiques s’est créé et a évolué au gré des mises sur le

marché de médicaments ou de produits de santé dont la qualité n’était pas maîtrisée.

L’objectif d’une réglementation harmonisée est non seulement d’éviter que se reproduisent

de tels événements, mais aussi de favoriser l’efficacité et la qualité des produits de santé

délivrés aux patients. En 1901, le « Center for Biologics Evaluation and Research (CBER) » fut

créé dans ce but. L’évaluation et le contrôle du risque associé à la qualité du médicament ou

du produit de santé ont alors dirigé l’évolution du cadre réglementaire au fil du temps.

De nos jours, le cadre réglementaire imposé aux industries pharmaceutiques s’appuie

principalement sur deux grandes séries de directives que sont les « GxP » (l’acronyme de

« Good "x" Practices ») et les documents ICH. Le terme « GxP » se définit en français comme les

bonnes pratiques à adopter dans le cadre "x" (fabrication, essais cliniques, essais de

laboratoire,…) lié au domaine de la santé. Cet ensemble de directives rassemblé sous le terme

« GxP » a été initié en 1978 par la création des « Good Manufacturing Practices (GMP) » à

l’initiative de l’agence fédérale américaine « Food and Drug Administration (FDA) » [17,18].

Dans la foulée, au début des années 1980, les états qui composent à l’heure actuelle une partie

de l’union européenne ont également créé un cadre réglementaire. En 1990, à l’initiative de

ces états, du Japon [19] et des Etats-Unis d’Amérique, l’ICH a vu le jour lors d’une assemblée

tenue à Bruxelles. Les directives de l’ICH visent à rendre plus efficaces les processus liés aux

étapes de recherche, de développement et de fabrication tout en maintenant des garanties sur

la qualité, la sécurité et l’efficacité, ainsi que sur les obligations réglementaires pour protéger

la santé publique. D’autres organismes tels que l’« Organisation for Economic Co-operation and

Development (OCDE) » [20] ont également joué un rôle dans l’évolution du cadre

réglementaire tel qu’il est connu actuellement. Dans ce contexte de gestion de la qualité, des

méthodes permettant l’évaluation des risques ont également vu le jour au cours des années.

C’est le cas, par exemple, de la méthode des « 5 M » (Matière, Matériel, Méthode,

Main-d’œuvre, Milieu) dont une variante est connue sous le nom de diagramme de Ishikawa,

du nom de son inventeur.


24

Gestion du risque associé à la qualité (« Quality Risk Management »)

La directive ICH Q9 [14] en particulier aborde, dans le cadre général du cycle de vie du

médicament ou du produit de santé, le concept de « Quality Risk Management ». Cette

directive s’appuie sur un concept visant à gérer le risque lié à la qualité tout au long du cycle

de vie du produit pharmaceutique. Ce concept se définit comme le processus à mettre en

œuvre afin d’évaluer, de contrôler et de documenter les risques associés à la qualité des

produits pharmaceutiques. Les deux principes fondateurs du concept de « Quality Risk

Management » reposent sur :

- l’évaluation du risque lié à la qualité qui doit être basée sur la connaissance

scientifique et être intimement liée à la protection du patient,

- les processus mis en œuvre pour la gestion du risque lié à la qualité qui doivent être en

rapport avec le niveau du risque encouru.

Il est également important d’insister sur le fait que ce cadre réglementaire est en constante

évolution. Ceci afin de garantir une amélioration continue de la maîtrise des risques toujours

plus présents et diversifiés. Au niveau producteur, nous pouvons, par exemple, mentionner

les risques liés à l’utilisation de peptides comme agents thérapeutiques. Du point de vue du

patient, la problématique croissante de la contrefaçon des médicaments en est l’illustration.

Approche « Quality-by-Design »

A partir de cette description historique du cadre réglementaire lié au cycle de vie des

produits pharmaceutiques, il est aisé se rendre compte de l’importance que revêtent

également l’évaluation et la gestion du risque au sein même du cycle de vie des méthodes

analytiques mises en œuvre lors des contrôles de qualité. Les stratégies mises en place à cette

occasion pour maîtriser le développement et l’utilisation des méthodes analytiques sont

également en constante évolution. Dans ce contexte, il nous semble important d’introduire les

notions réglementaires liées aux concepts de « Quality-by-Design » et de « Design Space (DS) »

qui sont au centre des travaux présentés dans cette thèse. Les aspects théoriques liés à ces

concepts sont quant à eux discutés dans le point suivant de cette introduction.

L’approche « QbD » apparaît dans le document ICH Q8(R2) [21] et peut être définie

comme une approche systématique du processus à mettre en œuvre. Cette directive définit les

concepts et les outils permettant de renforcer un cadre réglementaire sur base d’une

approche ciblant l’évaluation et la gestion du risque ainsi que la connaissance scientifique

accrue d’un processus, quel qu’il soit. A l’instar des processus de fabrication, la méthode

analytique peut elle-même être définie comme un processus. Dès lors, la façon d’obtenir des

garanties sur la qualité du processus analytique est la même comme le suggère P. Borman et

al. [22] (Figure 3).


25

Fig. 3. Comparaison entre l’application du concept « QdD » pour un processus de fabrication (gauche) et

l’application à un processus analytique (droite).

Dans le cas des processus analytiques, le terme « AQbD », pour « Analytical

Quality-by-Design » est employé. Comme le montre la figure 3, l’approche « AQbD » reprend

dès lors les étapes clés du cycle de vie des méthodes analytiques. La problématique se situe en

premier lieu et conduit de ce fait à la définition, par l’analyste, des performances attendues de

la méthode analytique. Il s’agit dans ce cas de l’« Analytical Target Profil (ATP) ». Dans le cadre

de la mise au point d’une méthode de dosage par exemple, l’« ATP » peut être défini comme

suit [23] : « La procédure doit être capable de quantifier un analyte en présence d’autres

composés dans une gamme de concentration définie et centrée sur une valeur nominale avec une

exactitude et une incertitude de telle sorte que le résultat obtenu soit compris dans des limites

fixées a priori autour de la vraie valeur avec une probabilité minimum définie et déterminée

avec un niveau de confiance fixé ». A cette fin, l’analyste doit identifier les « Critical Method

Parameters (CMP) » pouvant influencer les performances de la méthode analytique tel que

défini via l’« ATP » (l’objectif de la méthode). Ces paramètres sont dépendants de la technique

et de la méthode sélectionnées par l‘analyste. Une fois ceux-ci sélectionnés, ils sont assortis

d’une performance minimale à atteindre. Il s’agit ici des « Critical Quality Attribute (CQA) ». La

phase de développement de la méthode devient alors la définition d’un espace opérationnel

où la qualité est garantie, le « Design Space (DS) ». Les performances de la méthode doivent

ensuite être vérifiées et sont assorties d’une stratégie de contrôle permettant leur vérification

continue lors de l’utilisation du processus analytique en routine.


26

Concept du « Design Space »

Une étape du développement de la méthode consiste en la gestion des risques qui y

sont associés. Dans l’optique d’une stratégie « QbD » telle que définie par l’ICH Q8(R2),

l’accent doit être porté sur le « produit » (dans notre cas, la méthode), sa connaissance et le

contrôle des processus liés à sa « fabrication » par l’intermédiaire d’une base scientifique

solide tout en contrôlant le risque lié à la qualité. A cette fin, un autre concept est abordé dans

cette directive, le concept de « Design Space (DS) » ou espace de conception en français. Le

« DS » est défini comme un sous-ensemble de l’espace de travail (le domaine expérimental) à

l’intérieur duquel les critères de qualité associés aux paramètres critiques du processus sont

rencontrés tout en considérant l’incertitude associée à leur prédiction. Il ressort donc que, par

ce concept de « DS », le risque associé au développement d’une méthode analytique est évalué.

La directive définit d’ailleurs que, même si des changements de conditions opératoires à

l’intérieur de cet espace de conception interviennent, cela ne doit pas être considéré comme

une déviation par rapport au mode opératoire. Suivant cette définition et celle de la

robustesse évoquée dans la directive ICH Q2(R1) [24], le « DS » peut donc être considéré

comme une zone où la robustesse de la méthode analytique est définie. Par ce concept, on voit

que l’étape d’évaluation de la robustesse de la méthode, conventionnellement entreprise à la

suite de la validation de la méthode, est directement comprise dans la phase de

développement de la méthode. Comme nous l’aborderons par la suite, l’utilisation de la

planification expérimentale est donc bel et bien requise pour mettre en œuvre ce concept.

Consécutivement au développement de la méthode analytique centré sur des aspects

qualitatifs, l’évaluation des performances quantitatives doit également être faite. Cette

évaluation fait bien évidemment partie de la gestion des risques associés au développement

de la méthode analytique et doit idéalement faire partie des objectifs du processus analytique

(« ATP »). Cette étape correspond à la phase de validation de la méthode analytique qui peut

se traduire dans un contexte d’Assurance Qualité comme la qualification de fonctionnement

(« OQ »).

L’étape suivante dans la stratégie « AQbD », telle que présentée à la Figure 3, est la mise

en place d’une stratégie de contrôle. Celle-ci prend place au cours de l’utilisation en routine de

la méthode. Elle vise au suivi des performances tant qualitatives (maintien d’une séparation

minimale entre une paire critique en chromatographie liquide, par exemple) que

quantitatives (analyse d’échantillons de contrôle de qualité, « QC ») de la méthode analytique.

Ces stratégies de contrôle sont primordiales dans le cadre d’une approche

« Quality-by-Design ». En effet, elles vont permettre d’évaluer la méthode et de comparer ses

performances avec celles prédites tout au long de sa mise au point. La gestion des résultats

obtenus à partir d’échantillons « QC » en est un exemple abordé la Section III.1 de cette thèse.

Dans un contexte d’Assurance Qualité cette étape s’apparente à la qualification des

performances (« PQ »).


27

Un autre concept fondamental de l’approche « AQbD » est l’amélioration continue. En

effet, comme nous l’avons déjà évoqué, un des bénéfices du concept « AQbD » est la maîtrise et

la connaissance que l’analyste acquiert tout au long de la mise au point de la méthode

analytique. Ces connaissances et cette maîtrise vont lui permettre de faire face aux imprévus

liés à l’utilisation de la méthode en routine tels que, par exemple, l’apparition d’une éventuelle

impureté en fin d’étude de stabilité ou même un changement de spécification dicté par le

cadre réglementaire. Une application concrète de ce concept en terme d’Assurance de Qualité,

est la proposition d’amélioration de la procédure de « Change Control (CC) », faite en 2012 par

un groupe de travail de l’« EFPIA » [11]. La proposition de ce groupe est d’établir une

procédure de « CC » catégorisée par niveau qui prendrait en compte les risques associés aux

changements effectués dans la procédure analytique. Cette évaluation catégorisée considère

les éléments suivants :

- la maturité et la connaissance de la méthode analytique,

- l’aptitude générale de la méthode analytique,

- la criticité des attributs de qualité (« CQA »),

- la criticité de l’analyte,

- la capacité du système de qualité considéré par rapport à sa gestion des changements.

De par cette description réglementaire du concept « AQbD », il est aisé d’appréhender

que la gestion et l’évaluation du risque sont bien le cœur de cette approche. Dans ce contexte,

un des éléments clé est dès lors l’estimation de l’incertitude associée aux résultats. Cette

incertitude n’est rien d’autre qu’une estimation de l’erreur sur le résultat assortie du risque

que l’analyste est prêt à prendre. En d’autres termes, c’est l’erreur analytique affectée d’un

risque qui, le plus souvent, correspond à un facteur d’élargissement de 2 pour un risque

« alpha » de 5%. L’estimation de l’incertitude est d’ailleurs une obligation récurrente dans

plusieurs normes. A titre d’exemple, dans le norme ISO 17025:2005 au point 5.4.6 [6], il est

clairement mentionné que tout laboratoire doit être en mesure d’estimer l’incertitude

associée à ses résultats. Comme nous le verrons dans le point suivant, les outils et les

méthodologies récemment développés permettent à l’analyste d’améliorer la maîtrise du

risque associé aux processus analytiques.


28

I.3 Approche intégrée

Comme nous venons de l’évoquer, l’évaluation et la gestion du risque associé aux

méthodes analytiques passent par l’évaluation de l’incertitude sur le résultat. En effet, celle-ci

est la résultante de l’erreur analytique et du risque consenti. Elle s’exprime dans la même

dimension que le résultat. A la lumière de la littérature, trois outils intégrés sont

communément utilisés dans le cadre de la gestion du risque associé au cycle de vie des

méthodes analytiques. Les cartes de contrôle en sont un. Cet outil permet une surveillance du

risque encouru lors de l‘utilisation de la méthode en routine. Etant donné que cette étape du

cycle de vie des méthodes n’a pas fait l’objet d’une étude approfondie dans nos travaux, nous

n’aborderons pas les aspects liés à la gestion du risque par l’intermédiaire des cartes de

contrôle au cours de cette introduction.

Les autres stratégies intégrées ont trait à l’étape d’optimisation et à la phase de

validation. Elles sont centrées sur l’évaluation et la gestion du risque préalablement à

l’utilisation de la méthode en routine. Les outils envisagés pour aborder ces étapes du cycle de

vie ont bien évidemment évolué au cours du temps pour aboutir à des approches intégrées.

I.3.1 Optimisation

Approche conventionnelle [25,26]

Le développement ou l’optimisation d’une procédure analytique se fait sur base des

connaissances de l’analyste envers la technique envisagée et de ses connaissances préalables

sur la méthode elle-même. Il est néanmoins souvent nécessaire d’optimiser de nombreux

facteurs. L’analyste se base alors sur son expérience et entreprend des essais sur l’influence

de ces facteurs sur une réponse bien déterminée. Cette approche, dont les acronymes usuels

sont « COST » pour « Changing One Separate factor a Time » ou encore « OFAT » pour

« One-Factor-at-A-Time », est souvent considérée comme l’approche la moins efficace parmi

les différentes options car :

- elle nécessite un nombre d’expériences important pour acquérir une bonne précision

sur l’estimation des effets des facteurs analysés,

- elle ne permet pas d’estimer les interactions entre les effets des facteurs analysés.


29

Les conditions expérimentales sélectionnées par l’intermédiaire de cette approche ne sont

pas nécessairement (les plus) optimales. Cette méthodologie, qui est désignée au cours de

cette thèse comme la méthodologie « Quality-by-Testing (QbT) » (à l’instar de la méthodologie

« QbD » évoquée dans les points précédents) est encore néanmoins largement utilisée et peut

tout de même s’avérer « opportune » dans certains cas comme par exemple :

- Lorsque la connaissance préalable de la méthode permet à l’analyste de restreindre le

nombre de facteurs à étudier et d’éviter le recours à la planification expérimentale,

- lors d’une optimisation mineure de la méthode,

- lors d’une optimisation de facteurs peu prépondérants et dont leur interaction

mutuelle est faible,

- lorsqu’il est nécessaire de répondre à une problématique de manière urgente,…

Les exemples de méthodes analytiques développées ou optimisées suivant cette approche et

ayant fait leurs preuves en routine sont légion dans la littérature. Nous avons d’ailleurs utilisé

cette dernière au cours de nos travaux dont nous présentons les résultats dans la Section III.2

de cette thèse. Cependant, cette méthodologie ne permet pas d’appréhender le risque associé

à la méthode analytique, ni même de maîtriser complètement le processus analytique mis en

œuvre.

Planification expérimentale [27-29]

Depuis l’essor de la chimiométrie, la façon d’aborder l’étape de développement ou

d’optimisation des méthodes analytiques a singulièrement évolué. En effet, la chimiométrie

permet à l’analyste de s’appuyer sur des modèles mathématiques, pour la plupart statistiques,

lui permettant d’analyser plus finement l’information acquise lors de ces essais. Le Professeur

Massart définit d’ailleurs dans ce contexte la chimiométrie comme la discipline chimique qui

utilise les mathématiques, les statistiques et la logique formelle pour concevoir ou

sélectionner des procédures expérimentales optimales [30]. On parle alors de planification

expérimentale lorsque l’on considère la mise en œuvre d’un minimum de conditions

expérimentales réparties sur un domaine multidimensionnel dans le but d’extraire un

maximum d’informations pertinentes à propos du processus analysé au moyen de réponses

appropriées. Par l’intermédiaire de ces réponses, une équation mathématique modélisant au

mieux le processus soumis à l’étude peut être définie. Elle permet enfin de prédire le

comportement de ces réponses, et donc du processus soumis à l’étude, à l’intérieur de l’espace

multidimensionnel. Il existe une multitude de plans d’expériences à disposition de l’analyste.

Deux grandes catégories se dégagent tout de même : les plans de criblage et les plans

d’optimisation.


30

Les plans de criblage (ou plans de « screening ») sont souvent utilisés en première

intention afin de déterminer les facteurs ayant une influence significative sur la ou les

réponse(s) envisagée(s), l’étendue de leur influence, mais également dans certains cas, la ou

les réponse(s) réellement pertinente(s). Les plans de « screening » les plus souvent utilisés

sont les plans factoriels fractionnaires ou encore les plans de type Plackett-Burman [31].

Avant d’aller plus en avant dans la description des plans, il convient de s’attarder sur la

notion de l’étendue des facteurs considérés à travers les plans d’expériences. En effet, en

fonction du type de facteur considéré, son influence sur la réponse peut être drastiquement

différente. L’effet qu’a le facteur sur la réponse peut être linéaire, quadratique, cubique,… Un

facteur tel que la température aura dans la plupart des cas une influence linéaire et pourra

donc être estimée par l’intermédiaire de 2 niveaux. Il est par contre plus compliqué d’estimer

l’influence du pH dont la relation est polynomiale. Dans le cadre des plans de criblage, le

niveau des facteurs évalués est généralement fixé à 2, quelle que soit son influence.

Les plans factoriels complets se placent à la frontière entre les plans de criblages et les

plans d’optimisation. Ce sont les plus simples à appréhender. Ceux-ci sont uniquement à

considérer lorsque le nombre de facteurs et leur nombre de niveaux respectifs est réduit. En

effet, pour 3 facteurs, chacun comportant 3 niveaux (facteurs dont l’influence est considérée

comme quadratique), le nombre de conditions opératoires à tester avec ces plans est égal à

33 = 27. Il est également important de noter que la théorie de la planification expérimentale

préconise la répétition du point central du domaine expérimental (usuellement 2 répétitions

conduisant donc à 3 mesures) afin de pouvoir estimer la variabilité du processus soumis à

l’étude.

Deux plans d’optimisation sont les plus fréquemment envisagés : le plan central

composite et le plan de type Box-Behnken. Le plan central composite a d’ailleurs été envisagé

lors des travaux présentés à la Section III de la thèse. Ces plans contiennent des conditions

expérimentales organisées sous forme de plans factoriels complets ou factoriels

fractionnaires auxquels est ajoutée une répétition du point central et des conditions

expérimentales dans un nombre deux fois supérieur au nombre de facteurs étudiés. Cette

répartition des points dans le cas d’un plan central composite est particulièrement

intéressante. Nous y reviendrons d’ailleurs plus précisément au cours de la Section III. Les

plans de type Box-Behnken sont quant à eux utilisés lorsque l’analyste ne s’intéresse pas aux

conditions opératoires aux extrémités du domaine expérimental soumis à l’étude.

Dans le cadre des travaux présentés dans la thèse, un autre type de plan d’optimisation

a également été envisagé : le plan de mélanges. Ceux-ci sont spécifiquement conçus pour

optimiser l’étude des mélanges composés de plusieurs constituants tels que, par exemple, un

mélange ternaire de phase mobile en chromatographie liquide. La propriété de ces plans est

qu’ils font intervenir des facteurs dont il faut considérer les proportions de manière

dépendante des autres facteurs intervenant dans le mélange plutôt qu’une quantité variant de


31

manière indépendante. La valeur des facteurs est donc une proportion des autres facteurs

théoriquement comprise entre 0 et 1 (0% et 100%) et dont la somme de l’ensemble des

facteurs est égale à 1 (100%). Dans ce type de plan, il est impossible de faire varier un facteur

sans considérer l’impact sur les autres facteurs, ce qui influence profondément l’ensemble des

facteurs, les propriétés du plan, mais également l’interprétation des résultats. Sans entrer

dans les détails statistiques, lors des travaux présentés dans cette thèse, ces plans ont été

construits de sorte à ce que la géométrie des expériences soit rendue « D-optimal » afin de

minimiser la covariance des paramètres estimés dans le modèle du plan d’expériences

envisagé. Cela permet d’avoir une interprétation plus aisée des effets des facteurs. Cela

garantit également un rapport « nombre d’expériences / information » (autrement dit,

coût / bénéfice) optimal.

Modélisation d’une planification expérimentale

Par l’intermédiaire de la planification expérimentale, l’analyste va pouvoir explorer un

domaine expérimental. Celui-ci est défini sur base des facteurs ayant un effet prépondérant

sur le processus soumis à l’étude. L’analyste doit alors sélectionner la ou les réponse(s)

appropriée(s) qui lui permet(tent) d’obtenir une information pertinente à propos du

processus. Sur base des résultats obtenus lors de la réalisation d’un plan d’expériences,

l’analyste peut ensuite modéliser les résultats obtenus. À titre d’exemple, l’équation générique

ci-dessous (1) représente une relation mathématique modélisant les facteurs (Xi) sélectionnés

pour définir le domaine expérimental par rapport à une réponse Y. les βi représentent les

paramètres associés aux facteurs Xi et ε représente l’erreur associée au modèle.

Bien souvent, la modélisation du processus passe par la détermination d’un ou de

plusieurs critères représentatifs du processus. Dans le cas de la chromatographie liquide,

l’efficacité du processus est généralement évaluée par la résolution obtenue entre les deux

pics chromatographiques. Les travaux de Lebrun et Debrus [32-34] ont démontré que, dans le

cadre d’une modélisation, le critère de séparation (S) est plus approprié. Ce critère est défini

par la différence entre le temps de rétention du début du pic chromatographique élué en

second lieu et le temps de rétention à la fin du pic chromatographique élué en premier. Ce

critère a également l’avantage d’évoluer plus naturellement par rapport au comportement

chromatographique des pics, ce qui n’est pas le cas du critère habituel de résolution.

La modélisation des résultats obtenus par l’intermédiaire du plan d’expériences va

alors permettre l’établissement d’une surface de réponse. Cette méthodologie est largement

utilisée de nos jours dans le cadre des plans d’optimisation. C’est une approche multivariée

introduite par Box et Wilson dès les années 1950 [35]. Elle permet la modélisation de la

réponse en fonction des facteurs sélectionnés à travers le domaine expérimental étudié. Cette

relation permet ensuite de trouver un optimum en fonction de l’objectif fixé pour le processus


32

étudié. Généralement, ce sont la ou les réponse(s) moyennes qui sont utilisées pour

l’établissement de cette surface de réponse. Cependant, dans un contexte de modélisation,

porter son attention uniquement sur la moyenne peut être risqué. En effet, la moyenne peut

être trompeuse lorsque celle-ci est considérée sans tenir compte de l’incertitude associée aux

mesures [36]. Or, la méthodologie envisagée pour l’établissement des surfaces de réponse

tient uniquement compte de l’erreur globale du modèle et non de l’erreur de prédiction.

Autrement dit, cette méthodologie ne permet pas l’évaluation de l’incertitude associée aux

données modélisées. Cette méthodologie ne fournit donc aucun indice sur la fiabilité du

processus. De plus, aucune information par rapport au comportement futur du processus ne

peut être obtenue par cette méthodologie [37].

Afin de tenir compte de l’erreur de prédiction, Lebrun et al. ont mis au point une

méthodologie novatrice [34]. Celle-ci repose sur l’estimation de l’incertitude des futurs

résultats afin de définir une zone où les objectifs de la méthode sont atteints avec une

probabilité de succès définie. Cette zone appelée espace de conception, ou « Design Space (DS)

», représente un sous-ensemble du domaine expérimental soumis à l’étude où l’assurance

d’un niveau de qualité fixé est obtenue. Cette définition est par ailleurs en accord avec celle

fournie dans les directives ICH Q2(R1), ICH Q8(R2) et USP <1032> [21,24,38] où il est

clairement mentionné que la robustesse d’une procédure analytique est une mesure de sa

capacité à ne pas être affectée par de faibles changements délibérés des paramètres de la

méthode et ainsi fournir une indication sur la fiabilité de celle-ci lors d’une utilisation

normale. Cette méthodologie originale permet dès lors d’aborder le processus en terme de

risque et non en terme de réponse moyenne [37].

Par cette approche, faisant appel à la statistique Bayésienne, l’analyste peut obtenir

une distribution de la valeur estimée de tous les paramètres du modèle. Ce qui correspond

donc à l’incertitude liée à tous les paramètres du modèle. Il peut ensuite réaliser des

simulations sur l’ensemble du domaine expérimental, pour propager l’incertitude des

paramètres liés aux critères sélectionnés, afin de déduire la probabilité que ces derniers

rencontrent des spécifications bien définies [32,34,39-44]. Dans le cadre d’un processus

donné, l’analyste peut alors définir une zone de robustesse, le « DS », à l’intérieur du domaine

expérimental (χ), où la probabilité de succès par rapport à un ou plusieurs critère(s) (par

exemple : P(S > 0)) est rencontrée pour un niveau de qualité minimal (π) fixé, tel que

représenté sur la Figure 4 [34]. Il est important de remarquer sur cette figure que l’ordonnée

n’est pas le critère d’intérêt (critère S), comme pratiqué couramment avec les surfaces de

réponse, mais bien la probabilité que ce critère rencontre ses spécifications (P(S > 0)). Ce

concept représente donc bien une mesure prédictive de l’aptitude du procédé ou de la

méthode analytique étudié(e).


33

Fig. 4. Représentation schématique de la zone de conception (« DS ») à l’intérieur du domaine expérimental (χ)

définie à l’aide d’une probabilité de succès fixée (π) pour le critère S > 0 et ce, en fonction des paramètres X du

processus.

Cette approche récente est définie comme la stratégie « DoE-DS » combinant donc la

planification expérimentale et le concept de « Design Space ». Elle permet d’allier le bénéfice

d’une surface de réponse en tant qu’outil décisionnel avec la gestion du risque associée à la

prédiction grâce à l’évaluation de l’incertitude associée et ce, par rapport à des spécifications

qui doivent être rencontrées. Cette approche innovante sera dès lors au centre des

développements abordés lors des Sections III.3 et III.4.

I.3.2 Validation [45]

La démonstration du fait que la méthode développée est appropriée à son utilisation

en routine est une étape importante du cycle de vie des méthodes. En effet, elle est non

seulement requise par les autorités réglementaires, mais permet surtout à l’analyste d’évaluer

celle-ci et donc de disposer d’un outil décisionnel quant à son aptitude à quantifier. Cette

démonstration de la validité de la méthode devrait d’ailleurs être indépendante du secteur

industriel, de la technique utilisée ou même de la matrice à laquelle est confronté l’analyste. Il

semble donc intéressant de disposer d’un référentiel commun permettant de s’appuyer sur

des définitions et des terminologies communes pour cette étape importante du cycle de vie

des méthodes analytiques. Depuis le début des années 2000, des tentatives d’harmonisation

ont été initiées [46,47] car au sein même d’un secteur d’activités tel que l’industrie

pharmaceutique, la terminologie employée diffère [24,48-52]. A l’heure actuelle, il semble

qu’un consensus commence à se dégager [23]. Ce consensus préconise une approche basée

sur le principe de l’erreur totale. Suivant ce concept, chaque source d’erreur doit être évaluée

simultanément, avec un niveau de risque préalablement déterminé afin de construire un

intervalle de tolérance. Celui-ci doit être déterminé sur l’ensemble de la gamme de

concentration considérée. Au cours de cette introduction, nous présentons brièvement la

méthodologie et l’outil mis en œuvre lors de l’étape de validation d’une méthode analytique.

Sa spécificité est certainement le premier critère qu’un analyste doit aborder lors de l’étape

de validation. En effet, une méthode analytique doit être capable de délivrer une réponse qui

n’est pas ou peu affectée par des interférences (autres composés que celui d’intérêt, éléments


34

de la matrice,…). Cependant, dans le cadre d’une stratégie de développement « QbD », alliant

les plans d’expériences et le concept de « DS », ce critère doit être maîtrisé dès l’étape

d’optimisation de la méthode. Il n’est dès lors plus à tester lors de l’exercice de validation

formelle, mais simplement à confirmer.

Protocole de validation

Un plan d’expériences approprié est nécessaire lors de la réalisation de la validation

afin d’estimer correctement les sources d’erreurs. Ce protocole de validation est très

fortement lié à l’« ATP » défini dès le début du cycle de vie de la méthode analytique. Ces

expériences doivent couvrir la gamme de concentration envisagée pour les analytes. Les

échantillons intervenant dans la validation sont de deux types : les standards de calibration et

les standards de validation. Ces derniers sont des échantillons de concentrations connues

préparés de sorte à mimer les futurs échantillons qui seront rencontrés en routine. Il est dès

lors évident que ceux-ci doivent être préparés de sorte à intégrer au maximum la variabilité

inhérente à la mise en œuvre de la méthode. Ils doivent donc être préparés de manière

indépendante. Il convient également d’évaluer l’impact sur la méthode qu’auront des facteurs

tels que les équipements, les opérateurs et les séquences d’analyse en routine. Ces facteurs

sont évalués par l’intermédiaire de séries de validation où l’introduction du caractère

d’indépendance dans la préparation des standards de validation est essentielle. Le nombre de

ces séries est dépendant de la méthode validée et de la puissance statistique nécessaire. Au

cours de ces différentes séries de validation, l’analyste doit répéter le schéma de validation

préalablement défini. Dans le cadre de la thèse, les protocoles proposés dans le document de

référence de la Société Française de Sciences et Techniques Pharmaceutiques (SFSTP) [47]

ont été appliqués et adaptés au besoin.

Fonction de réponse [53,54]

La fonction de réponse est sans aucun doute un élément clef de l’étape de validation.

En effet, elle définit la relation qui existe, à l’intérieur d’une gamme de concentration

considérée, entre la réponse (par exemple, l’aire sous la courbe, l’absorbance,…) et la

concentration ou la quantité d’un analyte dans un échantillon. La fonction de réponse permet

donc d’obtenir les résultats servant à estimer les différentes sources d’erreurs. La courbe

d’étalonnage devra obligatoirement être une fonction de réponse monotone (strictement

croissante ou décroissante) qui permet d’obtenir des données fiables comme nous venons de

le préciser. Dans ce contexte, le choix du modèle est essentiel car son manque d’adéquation a

une influence directe sur les résultats et donc sur l’estimation des erreurs résultantes. Dans le

secteur pharmaceutique, il existe cependant une confusion entre la fonction de réponse et la

linéarité de la méthode sur laquelle nous reviendrons à la fin de ce chapitre.


35

Sources d’erreurs [54-65]

Indépendamment de la problématique de l’adéquation du modèle de régression, il

semble important de revenir sur les principales sources d’erreurs, à savoir :

- l’erreur systématique (ou justesse) représentant l’étroitesse de l’accord entre une

valeur de référence (acceptée comme telle) et la valeur déduite expérimentalement,

- l’erreur aléatoire (ou fidélité) directement liée à la dispersion des résultats et pouvant

être estimée à 2 niveaux,

- l’erreur totale (ou exactitude) qui n’est autre que la somme des deux précédentes et

qui se rapporte à un résultat individuel.

Ce concept d’erreur totale est extrêmement important et s’impose actuellement comme le

consensus attendu pour cette étape importante du cycle de vie des méthodes analytiques

qu’est la validation [23]. Suivant ce concept, un résultat acquis à partir de plusieurs mesures

(Xi) se compose de la vraie valeur de l’échantillon (μT), de l’écart entre la moyenne des

mesures (Xm) et la vraie valeur (Xm – μT) et, finalement, de la dispersion de ces mesures

autour de la moyenne (σ2 = Σ (Xi – μT)2 / N-1). Autrement dit, le résultat se compose de la

vraie valeur (μT) additionné des erreurs de mesures. Les erreurs de mesures n’étant rien

d’autre que la somme des erreurs, c’est-à-dire, la somme de l’erreur systématique (la justesse)

et de l’erreur aléatoire (la fidélité) tel que représenté à la Figure 5. En routine, il est

impossible de décomposer le résultat de la sorte étant donné que la vraie valeur de

l’échantillon est et restera inconnue. Il est donc indispensable d’estimer ces sources d’erreurs

lors de la phase de validation.

xi = µT + Justesse + Fidélité

µT

xi

xm

Justesse + Fidélité = Erreur Totale

xi = µT + erreur Totale

biais or Justesse

2 = (xi – xm)2/N-1

Erreur aléatoire =

xm - µT

Erreur systématique =

variabilité or Fidélité

Fig. 5. Représentation schématique des sources d’erreurs suivant le concept d’erreur totale.


36

Outil de décision : Profil d’exactitude [66-68]

À ce stade, il nous semble important de rappeler que la justesse et la fidélité sont des

notions associées à la méthode alors que l’exactitude est quant à elle associée au résultat.

L’intérêt fondamental du critère d’exactitude, quand il est bien compris, réside donc dans le

fait qu’il se rapporte à un résultat individuel. En routine, répéter un grand nombre de fois

l’analyse permettra de se rapprocher de la vraie valeur sans pour autant pouvoir estimer

l’écart (le biais) par rapport à cette dernière, mais ceci aura un coût considérable. Dès lors, un

outil se basant sur ce concept de l’erreur totale, lié aux futurs résultats, s’impose comme un

outil décisionnel adéquat dans le cadre de la validation et de la gestion du risque associé à

l’utilisation de la méthode.

Le profil d’exactitude est basé sur l’objectif même de toute méthode analytique, à

savoir sa capacité à quantifier de manière aussi exacte que possible chacun des échantillons

inconnus soumis au laboratoire. En d’autres termes, ce que l’analyste attend d’une procédure

analytique est que la différence entre le résultat (Xi) et la « vraie valeur » (μT) soit aussi petite

que possible et inférieure à une limite d’acceptation (λ) fixée a priori (Eq. 2). Cette limite

d’acceptation peut être différente en fonction du processus analytique envisagé.

Par conséquent, la validation doit donner des garanties que chaque future mesure

individuelle obtenue en routine soit suffisamment proche de la « vraie valeur ». L’analyste

souhaite donc connaître la probabilité que l’équation 2 soit rencontrée en fonction d’un

niveau de qualité minimum (πmin – Eq. 3 ).

Finalement, cette garantie sera donnée en fonction des performances de la méthode

dont les valeurs estimées ont été obtenues durant l’exercice de validation ( ). Le calcul

de l’intervalle de tolérance (Eq. 4) permettra ensuite de définir si la proportion attendue des

mesures qui seront comprises dans les limites d’acceptation fixées a priori sera, par la suite en

routine, supérieure à un niveau de qualité prédéfini. Par cette approche reposant sur un

intervalle de prédiction, il est évident que les attentes de l’analyste centrées sur l’exactitude

des futurs résultats et non sur les performances seules de la méthode analytique sont

correctement rencontrées. L’intervalle de tolérance est donc bien l’outil permettant de faire le

lien entre les résultats et la méthode.


37

Cette approche basée sur la prédiction postule implicitement qu’il y a une incertitude

sur les résultats fournis par la méthode évaluée en phase de validation (la justesse et la

fidélité) et qu’il faut donc en tenir compte. Plus cette incertitude est grande, plus l’intervalle

est grand. Cette notion implique donc une réflexion sur le nombre d’expérience envisagé, mais

insiste également tout particulièrement sur la nécessité d’un protocole de validation construit

de manière réfléchie et en accord avec l’objectif de la future méthode. Cet outil décisionnel

constitue le lien permettant d’être en accord avec la notion de l’« ATP » dont il est question

dés le début du cycle de vie des méthodes analytiques et donc, par conséquent, à la stratégie

« AQbD ».

Linéarité [53,54]

Dans cette introduction, il nous semble également important de rappeler le critère de

linéarité et la différence essentielle qu’il existe entre ce dernier et la fonction de réponse. La

linéarité est la relation entre la quantité introduite (définie grâce aux échantillons de

concentrations connues) et la quantité calculée a posteriori à partir de la courbe d’étalonnage

(la fonction de réponse). La linéarité de la méthode est donc sa capacité, à l’intérieur d’un

intervalle de dosage, d’obtenir des résultats directement proportionnels à la concentration en

analyte dans l’échantillon. La linéarité permet donc la démonstration de l’adéquation de la

méthode par rapport à son utilisation, mais n’est en aucun cas un outil décisionnel.


38

I.4 Evaluation et gestion du risque analytique

Ainsi que nous l’avons évoqué dans les chapitres précédents, les référentiels

réglementaires publiés au cours de ces dernières années étendent le concept d’assurance de

qualité à tout le cycle de vie du produit. Plus particulièrement dans le cadre qui nous occupe

dans nos travaux, ce concept s’étend, par conséquent, à l’intégralité du cycle de vie des

méthodes analytiques. Ce dernier doit être en permanence amélioré en fonction de l’évolution

de la connaissance impliquant dès lors une gestion de la connaissance acquise au cours de

chacune des étapes du cycle de vie. Cette gestion des sources de connaissance inclut donc

notamment la notion d’amélioration continue. Celle-ci est obtenue via l’identification et la

mise en œuvre de l’amélioration du processus analytique, la réduction de la variabilité de ce

dernier ou encore via son optimisation et son perfectionnement. Dans ce contexte,

l’évaluation et la gestion du risque associés au cycle de vie de la méthode analytique est

particulièrement utile pour identifier et prioriser les zones d’amélioration. Dans le contexte

du médicament au sens large, les référentiels tels que ceux proposés par ICH [14-16,21]

mettent l’accent sur la maîtrise scientifique du produit et donc, de facto, sur la maîtrise du

processus analytique. En d’autres termes, toute décision concernant le développement doit

être fondée, documentée, justifiée et permettre l’amélioration du processus sur la base de la

compréhension des variations envisagées. La garantie de respecter ces engagements passe

par l’établissement de « Design Space » capables d’appréhender valablement les impacts liés

aux variations proposées dans le processus analytique. Ceux-ci reposent sur l’identification

des « Critical Quality Attributes » ainsi que des « Critical Method Parameters » tels que nous les

avons précédemment définis. Dans le cas du développement de méthodes analytiques, cet

outil allié à la planification expérimentale est la base du concept d’« Analytical

Quality-by-Design ». A titre d’exemple, la gestion des risques consiste en la prise en compte de

l’erreur lors de la prédiction des « Critical Quality Attributes ». Le risque concerné correspond

alors à celui de ne pas observer une valeur prédite ou de prédire la possibilité de ne pas

atteindre un seuil sélectionné pour un « Critical Quality Attributes ». Comme cela a déjà

maintenant été démontré à de multiples reprises, le concept d’« Analytical Quality-by-Design »

permet d’augmenter très significativement la robustesse du processus analytique dès l’étape

de développement. Cette stratégie a également un impact positif sur l’étape de validation,

qu’elle soit initiale ou lors de tout changement ultérieur. Cette approche globale du

développement et de l’optimisation des méthodes permet de limiter le nombre de tests et de

vérifications requis. De plus, cette stratégie associée à une approche de la validation via le

concept de l’erreur totale devrait permettre de minimiser grandement le risque de rencontrer

des résultats hors spécification (« Results Out Of Specifications » ou « OOS ») au cours de la

phase de routine.


39

Prise individuellement, chacune de ces stratégies doit rendre possible l’évaluation et la

gestion des risques associés à chaque étape du cycle de vie des méthodes analytiques. Il

semble donc évident qu’une approche intégrée visant le cycle de vie dans son ensemble peut

maintenant être envisagée. Une telle approche devrait accroître significativement la confiance

des utilisateurs et des autorités lors de tout ajustement ultérieur de la procédure analytique

dans le domaine étudié. En effet, cette approche intégrée devrait permettre de définir le cadre

de la flexibilité opérationnelle et de proposer par la même occasion une réponse adéquate au

cadre réglementaire prôné par ces mêmes autorités.


40

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Chapitre II

Objectifs

Chapitre II : Objectifs

47

Au sein de l’industrie pharmaceutique, la qualité, au sens le plus large du terme, porte

la responsabilité de garantir la sécurité du patient. Depuis quelques années, les instances

réglementaires internationales ont entrepris une initiative appelée « International Conference

of Harmonisation (ICH) » visant à la mise en place d'un nouveau cadre pour stimuler les

évolutions et le progrès. Parmi les différents documents publiés, le référentiel ICH Q10 donne

la primauté à la maîtrise scientifique du produit et du procédé, et inscrit celle-ci dans une

dynamique nouvelle : celle de l’amélioration continue. A cette fin, la connaissance doit être

établie et exploitée ainsi que l’identification des facteurs de variabilité consolidés. C’est

pourquoi toute décision en termes de développement doit maintenant être fondée,

documentée, justifiée et améliorée sur la base de la compréhension des variations du procédé,

en ce inclus la maîtrise des processus analytiques inhérents au développement de tout

produit à visée thérapeutique.

Dès lors, les méthodes analytiques peuvent être perçues comme des processus à part

entière et être assorties de leur propre cycle de vie qui se décompose en une succession

d’étapes débutant toujours par la définition de la problématique. S’en suivront les étapes

d’optimisation et de validation de la méthode avant son utilisation en routine. Dans ce cadre

réglementé, il est donc devenu indispensable pour l’analyste de pouvoir évaluer et maîtriser

le risque de ne pas atteindre les objectifs fixés et ce, pour chacune des méthodes qu’il sera

amené à développer. La mise en œuvre de stratégies performantes pour l’identification, la

consolidation des facteurs de variabilité et la gestion du risque associé à l’utilisation des

méthodes analytiques constitue donc le principal objectif de notre travail.

A cette fin, nous nous attacherons tout d’abord à la phase de validation en tant

qu’étape critique avant l’implémentation du processus analytique en routine. En effet, nous

voulons être certains de disposer d’un outil incontestable permettant de prendre une décision

avec un risque maîtrisé avant d’aborder celui lié au développement des méthodes analytiques.

Nous tenterons donc de vérifier expérimentalement le caractère prédictif de l’intervalle de

tolérance et, par la même occasion, la puissance du profil d’exactitude. Pour ce faire, nous

tenterons de sélectionner différentes techniques analytiques avec ou sans préparation de

l’échantillon et ce, sur différentes matrices pharmaceutiques.

Ensuite, nous aborderons, dans un premier temps, l’étude du risque lié à l’étape

d’optimisation des méthodes analytiques par une approche itérative. Au travers d’un exemple

complexe, nous évaluerons au moyen du profil d’exactitude l’impact de cette stratégie

« Quality-by-Testing (QbT) » sur le risque lié à l’utilisation en routine de la méthode ainsi mise

en œuvre.

Chapitre II : Objectifs

48

Dans un second temps, nous nous intéresserons à une stratégie multivariée ou

« Quality-by-Design (QbD) », alliant la puissance de plans d’expériences à la définition d’un

« Design Space (DS) ». Au moyen d’un exemple pertinent, nous tenterons de démontrer que

cette dernière, contrairement à l’approche « QbT », permet d’acquérir une connaissance et

une maîtrise approfondie de tout le processus analytique. Au moyen de cette étude, nous

tenterons aussi de comparer ces deux stratégies d’optimisation mais aussi de mettre en

évidence les bénéfices de l’approche « QbD » en regard de sa capacité à évaluer le risque

associé aux aspects qualitatifs de la méthode analytique considérée.

Enfin, nous tenterons de terminer notre travail par l’intégration des phases

d’optimisation et de validation en une seule et même stratégie. Celle-ci devrait nous

permettre de donner une nouvelle dimension au « Design Space » qui ne sera plus simplement

un espace opérationnel où des performances qualitatives attendues seront rencontrées, mais

également un espace où l’on évaluera et maîtrisera les aspects quantitatifs de la méthode

analytique. Plus encore, cette stratégie globale devrait nous permettre d’envisager un niveau

d’intégration encore supérieur du risque analytique au travers du cycle de vie des méthodes

analytiques.

Chapitre III

Résultats et discussions

Chapitre III : Résultats et discussions

51

Préambule

Le cycle de vie des méthodes analytiques se définit conventionnellement comme une

succession d’étapes (Chapitre I : Introduction – Fig. 1.) qui débutent invariablement par une

question posée à l’analyste. Celle-ci s’énonce très souvent aussi simplement que : « Est-il

possible de doser les composés présents dans mon échantillon ? ». Cependant, cette

problématique initiale va très rapidement se complexifier en fonction du contexte de la

demande. En effet, la nature même des analytes, leur caractère acide/base, leur

hydrophobicité, la présence de chromophores vont avoir un impact direct sur le choix des

conditions opératoires. D’autres éléments tels que la présence d’une ou plusieurs substances

à doser, la nécessité de déterminer la teneur en produits de dégradations ou en impuretés,

mais également la nature de la matrice sont également des paramètres à considérer. Tous ces

éléments entrent dans l’anamnèse préalable à tout développement analytique.

Afin de guider le lecteur au travers des différentes sections abordées dans la partie

expérimentale, nous tenons à décrire en préambule le cheminement suivi lors de la réalisation

de notre travail de thèse. En effet, celui-ci pourrait, de prime abord, sembler avoir emprunté

le cycle de vie des méthodes de manière antéchronologique.

Dans un premier temps, nos travaux se sont concentrés sur l’étape de validation. Sur

base des recherches antérieures issues du laboratoire [1], nous avons très naturellement

abordé cette étape critique du cycle de vie en considérant le profil d’exactitude. Celui-ci

repose sur l’utilisation d’intervalles de tolérance dont l’intérêt à récemment été reconnu par

la Pharmacopée Américaine (« USP ») [2]. De plus, comme le montre la Figure 1 ci-dessous, le

nombre d’article utilisant le profil d’exactitude pour démontrer l’aptitude des méthodes à

quantifier n’a cessé de croître. Dès lors, nous nous sommes d’abord attachés (Section III.1) à

confirmer expérimentalement le caractère prédictif de l’intervalle de tolérance et, par

conséquent, à confirmer la puissance du profil d’exactitude en tant qu’outil décisionnel. En

effet, la validation est une étape importante dans le processus décisionnel lié à l’utilisation de

la méthode analytique. Il nous semblait dès lors essentiel de s’assurer de l’adéquation de cet

outil quant à sa capacité à évaluer une partie du risque associé au cycle de vie des méthodes

analytiques avant d’aborder l’étape relative à l’optimisation des méthodes.

[1] B. Boulanger, P. Chiap, W. Dewe, J. Crommen, Ph. Hubert, An analysis of the SFSTP guide on validation of chromatographic bioanalytical methods: progresses and limitations, J. Pharm. Biomed. Anal. 32 (2003) 753.

[2] R.K. Burdick, D.J. LeBlond, D. Sandell, H. Yang, H. Pappa, Statistical Methods for Validation of Procedure Accuracy and Precision, Pharmacopeial Forum 39 (2013).


52

Fig. 1. Fréquence du nombre d’articles traitant du développement d’une méthode analytique et dont la

validation a été réalisée par le biais des intervalles de tolérance au cours de ces dernières années (Sources :

« Scopus search » entre 2000 et mars 2015).

Dans un second temps, nos travaux se sont centrés sur l’étape d’optimisation.

Conventionnellement, cette étape du cycle de vie des méthodes est abordée en évaluant

chaque paramètre critique de manière individuelle. C’est pour cette raison que, dans la

Section III.2, nous avons tout d’abord considéré cette approche itérative, également appelée

stratégie « Quality-by-Testing ». Au travers d’un exemple complexe, nous avons confirmé que

cette approche ponctuée d’une validation sur base du profil d’exactitude peut déjà s’avérer

être adéquate en fonction de la problématique posée. Toutefois, cette approche ne nous

permet pas d’affirmer que les conditions sélectionnées sont optimales.

Par conséquent, nous nous sommes par la suite orientés vers une approche utilisant les

plans d’expériences. Cette dernière stratégie repose sur l’évaluation multivariée des

paramètres critiques de la méthode qui est désormais connue sous l’acronyme « AQbD » pour

« Analytical Quality-by-Design ». Au cours de la Section III.3, nous avons tout d’abord discuté

des bénéfices liés à cette approche en regard de sa capacité à évaluer le risque associé aux

aspects qualitatifs de la méthode analytique. Nous avons ensuite montré que cette approche

pouvait également être ponctuée d’une validation selon le même concept que précédemment

évoqué.

Finalement, nous avons voulu lier cette étape d’optimisation à celle de la validation.

Lors de nos travaux, nous nous sommes également attachés à démontrer que le coût en terme

de manipulation consenti lorsque l’on considère cette approche multivariée peut être mis à

profit afin d’en retirer les informations nécessaires à l’étape de validation. Dès lors, nous

avons montré dans cette dernière section que la stratégie novatrice que nous avons

développée peut donner à l’analyste les outils nécessaires à la gestion du risque tant qualitatif

que quantitatif et ce, dès l’étape d’optimisation.

A la lumière de ces explications traduisant notre cheminement, nous espérons que le

lecteur pourra plus aisément appréhender les différentes sections de ce chapitre décrivant les

résultats et les réflexions qui ont jalonné la réalisation de cette thèse.

C. Hubert, E. Rozet, A. Ceccato, W. Dewé, E. Ziemons, F. Moonen, K. Michail, R. Wintersteiger, B. Streel, B. Boulanger, Ph. Hubert, Using tolerance intervals in pre-study validation of analytical methods to predict in-study results. The fit-for-future-purpose concept, Journal of Chromatography A, 1158 (2007) 126.

Chapitre III

Accord entre prédiction et validation

Section III.1

Section III.1 : Accord entre prédiction et validation

55

Avant-propos

La validation des méthodes analytiques est un élément-clé du cycle de vie des

méthodes. Le but de la validation est de démontrer que la méthode est adaptée à l’utilisation

pour laquelle elle a été développée. C’est ce que l’on nomme en anglais : le

« Fit-for-future-purpose concept ». Dans le cas des méthodes quantitatives, l’objectif est donc

de quantifier les analytes avec une exactitude déterminée en fonction de spécifications fixées

a priori.

Dans ce contexte, l’approche la plus pertinente est indéniablement celle reposant sur le

concept de l’erreur totale. Chaque source d’erreur doit dès lors être évaluée simultanément.

Sur base d’un protocole de validation correctement élaboré, des données prédictives peuvent

être obtenues avec un risque α connu et ainsi mener à l’établissement d’un intervalle de

tolérance sur l’ensemble de la gamme de concentration considérée. Cette approche combinée

à des limites d’acceptation définies en fonction de l’objectif de la méthode fournit alors un

outil décisionnel prédictif : le profil d’exactitude. Cet outil décisionnel permet en théorie de

donner des garanties quant aux performances futures de la méthode et, par conséquent, de

gérer le risque associé aux résultats.

L’intervalle de tolérance étant par définition un outil prédictif, il était donc intéressant

de montrer que la pratique rencontrait bien la théorie. En d’autres termes, que les

performances quantitatives de la méthode analytique, définies lors de l’étape de validation,

étaient en accord avec celles de la routine. A cette fin, plusieurs méthodes appartenant à des

champs d’activités différents ont été considérées à travers le suivi de leurs « QC » obtenus lors

de leur utilisation.


56

Abstract

It is recognized that the purpose of validation of analytical methods is to demonstrate

that the method is suited for its intended purpose. Validation is not only required by

regulatory authorities, but is also a decisive phase before the routine use of the method. For a

quantitative analytical method the objective is to quantify the target analytes with a known

and suitable accuracy. For that purpose, first, a decision about the validity of the method

based on prediction is proposed: a method is declared proper for routine application if it is

considered that most of the future results generated will be accurate enough. This can be

achieved by using the “β-expectation tolerance interval” (accuracy profile) as the decision tool

to assess the validity of the analytical method. Moreover, the concept of “fit-for-purpose” is

also proposed here to select the most relevant response function as calibration curve,

i.e. choosing a response function based solely on the predicted results this model will allow to

obtain. This paper reports four case studies where the results obtained with quality control

samples in routine were compared to predictions made in the validation phase. Predictions

made using the “β-expectation tolerance interval” are shown to be accurate and trustful for

decision making. It is therefore suggested that an adequate way to conciliate both the

objectives of the analytical method in routine analysis and those of the validation step

consists in taking the decision about the validity of the analytical method based on prediction

of the future results using the most appropriate response function curve, i.e. the

fit-for-future-purpose concept.


57

1. Introduction

Consistent and efficient use of any analytical procedure requires the knowledge of its

reliability prior to its use. It is therefore necessary for each laboratory to validate their

analytical methods in order to demonstrate that it is suited for its intended purpose.

Validation is not only required by regulatory authorities [1,2] or in order to access

accreditation (e.g. ISO 17025 [3]), but is also the ultimate phase before the routine use of the

method. Analytical method validation must bring confidence for the laboratories in the results

that will be generated since they are used to make critical decision such as batch release of a

drug product, establishment and verification of shelf life, bioequivalence between two drugs,

pharmacokinetic studies or the diagnosis of a disease, etc.

Many regulatory documents have been released, primarily ICH and FDA documents in

the pharmaceutical industry to address that issue. Those documents related to analytical and

bioanalytical method validations suggest that all analytical methods have to comply with

specific acceptance criteria to be recognized as validated procedures. The primary aim of

these documents is to provide evidence that the analytical methods are suitable for their

intended use. Beyond the discrepancies and contradictions present in those documents [4],

very little is included about the process and rules for making a decision – i.e. to reject or to

accept an analytical method – with respect to its ability to achieve its objective.

For a quantitative analytical method the objective is to quantify the target analytes

with a known accuracy. For that purpose, an original strategy based on total or measurement

error and accuracy profiles as a decision tool has been proposed [5–7]. It is also an increasing

request of regulatory agencies to manage the risk associated with the use of these methods in

routine analysis [8,9].

The purpose of the present paper is to provide some theoretical background about

analytical validation concepts and to attempt to resolve some inconsistencies from a

statistical perspective by focusing on the real objectives of an analytical procedure and its

validation phase. The main idea being developed is that the decision to accept an analytical

procedure as valid for its use in routine should be based on the quality of the future results

that will be produced using the analytical procedure under investigation, i.e. based on the

prediction to obtain good results in the future according – or conditionally – to the amount

and quality of results obtained during the validation phase, also called pre-study validation

according to the FDA [2]. A methodology to achieve that is proposed and illustrated by four

different case studies. They result from the use in routine analysis of three analytical methods

developed for the determination of levonorgestrel in a polymeric matrix, loperamide in

plasma and ketoglutarate as well as hydroxymethylfurfural in plasma, respectively.


58

1.1. Objective of an analytical method

The objective of a quantitative analytical method is to be able to quantify as accurately

as possible each of the unknown quantities that the laboratory will have to determine [5–7].

In other terms, what all analysts expect from an analytical procedure is that the difference

between the measurement or observation (X) and the unknown “true value” μT of the test

sample be small or inferior to a predefined acceptance limit λ:

−λ < X − μT < λ ⇔ |X − μT | < λ (1)

The acceptance limit λ can be different depending on the objective of the analytical

procedure. This objective is linked to the requirements usually admitted by the practice

(e.g. 1 or 2% on bulk material, 5% on drug products, 15% for biological samples, L% for

clinical applications where “L” depends on factors such as the physiological variability and the

intent of use) [2].

An analytical method will be considered as valid or able to achieve its objective if for

each unknown sample to quantify it is very likely that the result obtained will fall within the

acceptance limits. This is formally express by:

π = P (|X − μT | < λ) ≥ πmin (2)

This probability π should ideally be larger than πmin, the quality level, e.g. 80%. When a

large number of samples are analyzed, then π can be seen as the proportion of results falling

within the acceptance limits.

Knowing the true bias (systematic error) δ, and the true precision (random error) σ,

under the classical assumption of normality for the measurement results, it is easy to

establish the relationship between the quality level π and the performance parameters. This is

obtained as follows:

where Z is a standard normal random variable. But this is purely theoretical because the true

performance parameters (δ, σ) are unknown.

1.2. Objective of the (pre-study) validation phase

Before an analytical method is used routinely on unknown samples, it is required to

perform a more or less extensive set of experiments to evaluate whether the method will be

able to meet the criteria described above. Those experiments are usually called “method

validation” or “pre-study validation” as opposed to the “in-study validation” or routine

analysis.


59

The aim of the pre-study validation phase is to generate enough information to have

guarantees that the analytical method will provide, in routine use, measurements close to the

true value without being affected by other elements present in the sample, assuming

everything else remains reasonably similar, i.e. the method and related handlings have not

been changed beyond the usual practices. In other words, the validation phase will contribute

to estimate the probability π described in Eq. (3).

The difference between the measurement (X) and its true value is composed of a

systematic error δ (bias or trueness) and a random error σ (standard deviation or precision)

[5,6]. The true values of these performance parameters are unknown but will be estimated

based on the validation experiments and the reliability of these estimates depends on the

adequacy of these experiments (design, size). Hence, the conditions used during the pre-study

validation must be representative of the future routine application of the analytical method,

for instance in terms of days, operator and equipments. Consequently, the objective of the

pre-study validation phase is to evaluate whether, given or conditionally to the estimates of

bias and variance, the expected proportion π̂ of measurements that will fall within the

acceptance limits is greater than a predefined level of proportion, say πmin. This is expressed

by:

π̂ = E δ̂,σ̂ {P [|X − μT | < λ]| δ̂ σ̂}≥ πmin (4)

The concept of expected proportion is very important and central to the idea

developed in this paper: it is about predicting, using consistent statistical methods, the

likelihood that each future result produced from a routine analytical procedure will be

accurate enough. If this future probability can be estimated, the decision of accepting or

rejecting an analytical method after the validation experiments should only be based on that

expected future probability π̂; probability that can be seen as a proportion when a large

number of samples is to be analyzed in routine. This value, in fact, intrinsically summarizes

and contains all the other important aspects known as validation criteria [5–7].

1.3. Decision rule based on prediction of future results

There exists no exact solution, in frequentist statistics, for estimating π from Eq. (4).

However, as it has already been proposed by other authors [5–7,10–14], a convenient

solution to this problem to make a reliable decision consists in computing the β-expectation

tolerance intervals [15]:

E δ̂,σ̂ {PX (δ̂ − kσ̂ < X − μT < δ̂ + k σ̂ | δ̂ ,σ̂)}= β (5)

where the k is determined so that the expected proportion of the population falling within the

interval is equal to β. If the β-expectation tolerance interval obtained in Eq. (5) is totally

included within the acceptance limits [−λ, +λ], i.e. if δ̂ − k σ̂ > −λ and δ̂ + k σ̂ < +λ then the


60

expected proportion of measurements within these acceptance limits is greater or equal to β.

For that reason, the tolerance intervals are also called predictions intervals. They represent

the location where β% of the future results are expected to lie. This information is particularly

valuable for making a decision about the capability of an analytical method.

Most of the time, an analytical procedure is intended to quantify over a range of

quantities or concentrations. Consequently, during the validation phase, samples are

prepared to adequately cover this range, and a β-expectation tolerance interval is calculated

at each level.

The “accuracy profile” is obtained, on one hand, by connecting the lower limits

together across the concentration levels and, on the other hand, by connecting the upper

limits. The inclusion of the measurement error profile within the acceptance limits [−λ, λ] at

key levels must be examined before declaring that the procedure is valid over a specific range

of values. This concept is illustrated in Fig. 1 that shows the six accuracy profiles obtained

using three response functions build either within or without the matrix of the studied

analyte and compared with the acceptance limits fixed at [−15%, 15%] over the whole range.

As long as the accuracy profile is included in the acceptance limits, the analytical method is

expected to provide accurate results for its intended purpose and therefore declared as valid.

Only the response functions used for the construction of the accuracy profile of Fig. 1d and f

achieve this objective.

The accuracy profile gives the analyst a sense of what a procedure will be able to

produce during routine analysis over the intended range. The interpretation of the accuracy

profile is that it shows where β% of the measurements provided by this analytical method will

lie. This is in direct connection with the objective of the analytical method, i.e to give

measurements close to the unknown true values.

The question probably most have at this stage is: does it work? So far it is a theoretical

demonstration based on well established statistical theories, but will it apply and permit such

a meaningful decision? The minimal values for β% that must be chosen a priori are usually

80%, 90% or 95%, that, symmetrically, implies that no more than 20%, 10% or 5%,

respectively, of future measurements will fall outside the predefined acceptance limits. That

way an appropriate risk management attitude is introduced through the use of tolerance

intervals that are easy to interpret and to give an analytical meaning.


61

Fig. 1. Accuracy profile obtained for the pre-study validation of the LC–UV analytical method for the

quantitation of levonorgestrel by considering (a) linear regression without matrix, (b) linear regression within

matrix, (c) linear regression after logarithmic transformation without matrix, (d) linear regression after

logarithmic transformation within matrix, (e) weighted 1/x linear regression without matrix, (f) weighted 1/x

linear regression within matrix; plain line: relative bias, dashed lines: β-expectation tolerance limits, dotted

curves: acceptance limit (%) and dots: relative back-calculated concentrations of the validation standards.


62

2. Materials and methods

2.1. Chemicals and reagents

2.1.1. Levonorgestrel method (LC–UV/polymeric matrix)

Levonorgestrel was supplied from Industriale Chimica (Saronno, Italy). The batch

number 040056 was used both in validation and routine phases. Acetonitrile gradient grade

was obtained from Merck (Darmstadt, Germany). Absolute ethanol (analytical-reagent grade)

was supplied by Fisher Scientific (Loughborough, UK). Water used for the HPLC mobile phase

and dilution was of Milli-Q quality (Millipore, Bedford, MA, USA). Aqua conservans (0.1%

parabens) was prepared using current Eur. Ph. quality methyl 4-hydroxybenzoate (0.8 g/l)

and propyl 4-hydroxybenzoate (0.2 g/l) both acquired from Fluka (Buchs, Switzerland).

Helium (alphagaz 1) was purchased from Air Liquide (Milmort, Belgium).

2.1.2. Loperamide method (SPE–LC–MS-MS/plasmatic matrix)

Loperamide hydrochloride was obtained from Welding (Hamburg, Germany)

and the internal standard (clonazepam-5-2(-chlorophenyl)-1,3-dihydro-7-nitro-2H-1,4-

benzodiazepin-2-one) was supplied by Sigma (Saint-Louis, MO, USA). Methanol and water

were of HPLC grade from Merck. Nitrogen was produced by an on-site nitrogen generator

from Air Liquide. Isolute DECs (1 ml capacity) filled with 50 mg ethylsilica encapped (C2EC)

were obtained from IST (International Sorbent Technology, Mid-Glamorgan, UK). Other

chemicals and reagents were fully described in a previous publication of Streel et al. [16].

2.1.3. Ketoglutarate and hydroxymethylfurfural method (SPE-SPE–LC–UV/plasmatic

matrix)

Ketoglutarate (KG) and hydroxymethylfurfural (HMF) were provided by Mayerhofer

Pharmazeutika (Linz, Austria). A 2-nitrophenylhydrazine (NPH) (Fluka) solution (0.08 M) was

prepared by dissolving the reagent in water at 40% 1 M HCl–ethanol (1:1, v/v). All solvents

used were of HPLC grade (Lichrosolv, Merck). A 100 mM buffer solution pH 6.8 was prepared

by dissolving the proper weights of anhydrous KH2PO4 (Merck), anhydrous K2HPO4 (Merck)

and NaCl in water. To extract the analytes from the biological matrix, a combined-cartridge

system consisting of vertically-connected SAX 100 mg / 1 ml (Varian, Baden, Switzerland)

cartridges with their polymeric Oasis hydrophilic lipophilic balance (HLB) 30 mg / 1 ml

(Waters, Dublin, Ireland) mates was used. Other information on chemicals and reagents are

available in [17].


63

2.2. Apparatus


Analysis in both validation and routine phases were carried out with LC 1100 series

system equipped with a binary pump, an autosampler, a thermostated column compartment

and a diode-array detector, from Agilent Technologies (Waldbronn, Germany). A LC

Chemstation (Agilent Technologies) was used for instrument control, data acquisition and

data handling. The separation was performed on a LiChrospher 100 RP-18 column

(250 × 4.0 mm I.D.; particle size: 5 μm) from Merck.


The automated sample preparation with extraction cartridges was performed by

means of an ASPEC system from Gilson (Villiers-le-Bel, France). The LC system consisted in a

Model 1100 Series liquid chromatograph from Agilent Technologies. Mass spectrometric

detection was carried out using an Applied Biosystems API 3000 Triple Quadrupole

instrument (Thornhill, Toronto, Canada) equipped with an APCI interface. The separation was

performed on a Zorbax SB-C18 Stable Bond (Agilent Technologies) analytical column

(150 × 4.6 mm I.D.) thermostatted at 35 °C. Full description of apparatus can be found in [16].


matrix)

The HPLC system was a Beckman Instrumentation (System Gold Nouveau, Beckman

Instruments, Fullerton, CA, USA) equipped with a Beckman 125/127 solvent delivery module

and a Beckman 166-UV Detector together with a Knauer-Y199, RP-8, 5 μm, 100 × 4 mm I.D.

(Knauer, Berlin, Germany) column. The corresponding guard column RP-8, 5 μm, 4 × 4 mm

(Merck) was replaced when necessary. Sample injections were made through a Rheodyne

injector (model 7725 i) outfit with a sample loop of 20 μl. Full description of apparatus can be

found in [17].

2.3. Chromatographic conditions


The chromatographic separation was achieved by an isocratic elution. The mobile

phase consisted of 60% of acetonitrile and 40% of water. Prior to use, mobile phase was

degassed for 10 min under helium flux. The chromatographic separation was performed at

30 °C using a constant flow rate of 1.0 ml/min. The injection volume was 100 μl. Ethanol was

used as washing solution. The UV detection was performed at 245 nm.


64


Chromatographic experiments were carried out in the isocratic mode. The mobile

phase consisted of a mixture of methanol and 5 mM ammonium acetate adjusted to pH 3.0

(25:75, v/v). The flow-rate was 1.0 ml/min and the volume injected was 50 μl. Full conditions

of separation and detection can be found in [16].


matrix)

The mobile phase was freshly prepared weekly and degassed with helium prior to

circulating into the system and was composed of (0.028% TFA–methanol–acetonitrile)

(58:32:10, v/v). The UV detection was performed at 330 nm. Separation was isocratically

achieved at a flow rate of 1.2 ml/min. Other chromatographic conditions are described in

[17].

2.4. Standard solutions

2.4.1. Solutions used for validation phase

Levonorgestrel method

Stock solutions were prepared by dissolving an appropriate amount of levonorgestrel

in ethanol in order to obtain a concentration of 0.2 mg/ml. Two independent stock solutions

were prepared for each series. Dilutions of the first stock solution were performed in the

mobile phase to reach final concentrations of 30, 500 and 1000 ng/ml. These solutions were

used as calibration standards (CSs) without matrix. The second stock solutions were diluted

in two steps. The first step was performed in mobile phase and the second in Aqua conservans

to reach final concentrations of 30, 500 and 1000 ng/ml. These solutions were used as

calibration standards within matrix. The validation standards (VSs) were prepared like the

calibration standards within matrix at the same concentration levels. They were obtained

with a third stock solution prepared by the second operator involved in the validation phase

(see Section 2.5). All solutions were extemporaneously prepared in amber volumetric flask

and stocked in darkness. Each calibration standard was prepared in duplicates (n = 2) from

their corresponding stock solutions whereas the validation standards were prepared in

quadruplets (n = 4).


65

Loperamide method

Six solutions of loperamide were prepared by diluting the stock solution, prepared in

methanol, with the mobile phase to reach concentrations ranging from 1.0 to 50.0 ng/ml.

These solutions were then used to spike plasma samples either for calibration curves at six

concentration levels (m = 6) ranging from 50 to 2500 pg/ml or for quality control during the

pharmacokinetic study. A stock solution of the internal standard clonazepam was prepared in

methanol. This solution was then diluted with the mobile phase to obtain a final concentration

of 5.0 ng/ml. During the validation phases, three calibration curves (k = 3) were prepared;

each by using new diluted solutions. Each calibration standard was injected in duplicate

(n = 2). The independent validation standards were prepared at final concentrations of 50,

100, 500, and 2500 pg/ml (n = 6). The same calibration scheme was used in routine analyses.

After thawing, plasma samples were first centrifuged at 3000 × g for 10 min and a 1.0 ml

volume was transferred manually to a sample vial on the appropriate rack of the ASPEC

system. A 1.0 ml volume of internal standard solution (5 ng/ml) was then automatically added

and mixed.

Ketoglutarate and hydroxymethylfurfural method

A single stock solution of each KG and HMF was prepared in water (5 mg/ml) and

stored at 4 ± 1 °C in amber glass vials. Mixture of working standard solutions was daily

prepared by appropriate dilutions with the same solvent. Aliquots not exceeding 40 μl of

these working solutions were added to blank plasma prior to solid-phase extraction (SPE) to

prepare calibration standards resulting in 0.02, 0.10, 0.50, 2.00, 10.00, 20.00 μg/ml. A total of

three calibration curves were prepared and analyzed independently by the method developer

during the validation phase. Once calibration validated, ensuing routine analyses were hence

built upon similar calibration models. The assay was corrected for blank human plasma KG

levels by deducting the response of endogenously occurring KG in each individual pool from

the corresponding total response (added + endogenous) of KG in the spiked plasma. A new

stock solution of each analyte was prepared at the same concentration as above. Likewise,

validation standards were prepared in human plasma from a new stock solution at the same

concentration as above so as to result, after processing, in the following concentrations: 0.02,

0.10, 2.00 and 20.00 μg/ml.


66

2.4.2. Solutions used for routine analysis

Levonorgestrel method

The calibration standards within matrix were prepared de novo for each series exactly

as described previously for the validation phase. The final concentrations reached were 30,

500 and 1000 ng/ml. Quality control (QC) samples at 30 and 500 ng/ml also prepared in Aqua

conservans were analysed in six replicates.

Loperamide method

The same calibration scheme as used in the validation phase was applied during

routine analyses. For the quality control samples, blank plasma samples were spiked with

solutions of loperamide in order to reach three concentration levels of 100, 500 and

1000 pg/ml, corresponding to low, middle and high QC levels, respectively. The QC samples

were stored at −80 ± 3 °C until analysis. Each QC was replicated six times [16].

Ketoglutarate and hydroxymethylfurfural method

Sets of QC samples were prepared in polypropylene vials by spiking 750 μl aliquots of

blank plasma with KG and HMF solutions freshly diluted from the corresponding stock

solutions to yield concentrations equal to 0.66 (low QC = 5 × LOQ), 13.33 (middle QC) and

133.33 (high QC) μg/ml. These QC samples were stored at −80 ± 3 °C until the day of

extraction. In each set, the aforementioned QC samples were analyzed in quadruplets [17].

2.5. Experimental design for validation phase

2.5.1. Levonorgestrel method

Two operators as well as two different equipments were involved during the validation

process in order to take into account possible sources of variability encountered during the

future routine use of the method. It was possible to perform a full validation with four series

in only two days including factors such as day, operator and equipment for between-series

variation. The design is presented in the Table 1.


67

Table 1 Experimental design applied for the pre-study validation of the LC–UV method for the

determination of levonorgestrel.

Day 1 Day 2

Operator 1 2 1 2

Equipment 1 2 2 1

Calibration standards without

matrix (CSs)

SSS1 SSS2 SSS3 SSS4

Calibration standards within

matrix (CSMs)

SSS5 SSS1 SSS4 SSS6

Validation standards (VSs) SSS2 SSS5 SSS6 SSS3

Series 1 2 3 4

Four series were executed in two days including equipment, operator and standard stock solution (SSS)

preparations as sources of variability.

The preparation of standard stock solutions (SSSs) can also be considered as another

variability source and was therefore included in the experimental design. Therefore, the same

SSS (i.e. prepared by one operator) was used by both operators to prepare two types of

standards, within and without matrix, as presented in Tables 1 and 2.

Table 2 Repartition of the preparation of each SSS between the two operators.

Standard Stock Solutions (SSSs) Prepared by (operator number)

SSS1 1

SSS2 2

SSS3 1

SSS4 2

SSS5 1

SSS6 2

2.5.2. Loperamide method

The validation phase was designed in three series each corresponding to a different

day in order to meet the most variable conditions encountered during the routine use of the

analytical method. Each of the four concentration levels of the validation standards was

analyzed in six replicates [16,18].


68

2.5.3. Ketoglutarate and hydroxymethylfurfural method

The validation phase was designed in three series each corresponding to a different

day in order to meet the most variable conditions encountered during the routine use of the

analytical method. Each of the four concentration levels of the validation standards was

analyzed in quadruplets [17,18].

2.6. Computations

The e.noval software (Arlenda, Liège, Belgium) was used to obtain the accuracy

profiles as well as validation results of all analytical methods. Whereas for the computation of

the routine phases results, the New-Daily software (Arlenda) was used in accordance to the

calibration model selected during the validation phase of each analytical procedure.


69

3. Results and discussion

3.1. Methods validation

Methods’ validation was assessed using the accuracy profiles approach based on

tolerance intervals for the total or measurement error, including both bias and standard

deviation for intermediate precision [5–7]. Such an approach reflects more directly the

performance of individual assays and will result in fewer rejected in-study runs than the

current procedure that compares point estimates of observed bias and precision. The concept

of accuracy profile was also used to select the most appropriate regression model for

calibration, to evaluate matrix effect, to determine the lower limit of quantitation (LLOQ) and

the range over which the method can be considered as valid. For this approach two

parameters must be set by the analyst, the acceptance limits on one hand and the risk of

having future measurements falling outside those acceptance limits on the other hand (1 − β).

3.1.1. Levonorgestrel method

Fit-for-purpose validation

Due to the objective of this method (drug release study from a polymeric matrix), the

present acceptance limits were set at ±15% and the risk (=1 − β%) of having future results

falling outside the acceptance limits was set at 5% maximum. Two sets of calibration curves

were prepared in order to evaluate a potential matrix effect. The calibration curves in matrix

were made by spiking Aqua conservans in order to reach three concentration levels of

levonorgestrel ranging form 30 to 1000 ng/ml, whereas the calibration curves out of matrix

were prepared in mobile phase at the same concentration levels. For each calibration curve

duplicates calibration standards were analyzed at each concentration level for 4 series or

runs. Several regression models were tested in order to look for the most appropriate

response function. This was achieved by preparing validation standard at the same three

concentration levels and analyzing them in quadruplets during 4 runs. The concentrations of

the validation standards were back-calculated using their respective response function in

order to determine, by concentration level, the mean relative bias, the standard deviation

intermediate precision as well as the upper and lower β-expectation tolerance limits at the

95% level and therefore draw their corresponding accuracy profiles [5–7]. The most suitable

regression model for the intended use of the analytical method was then selected on the basis

of these profiles [5–7] (cf. Fig. 1). This is the fit-for-purpose concept.

As shown in Fig. 1, from all the response functions tested, only the calibration curves

prepared in the matrix showed acceptable accuracy profiles, therefore demonstrating a strong

matrix effect. Among those acceptable profiles, the one obtained with the simplest response

function allowing to accurately quantify over the whole range studied was then selected,


70

namely the weighted 1/x linear regression model prepared within the matrix. The response

function obtained by applying this regression model is presented in Table 3.

Table 3 Pre-study validation results of the LC–UV analytical method for the quantitation of levonorgestrel.

Response function (p = 4; n = 2)

Weighted linear regression model (within matrix); calibration range (m = 3): 30 – 1000 ng/ml

Run 1 Run 2 Run 3 Run 4

Slope 0.2719 0.2786 0.2855 0.2748

Intercept -1.1170 -1.1420 -1.1310 -1.2350

Weight 1/x 1/x 1/x 1/x

r2 0.9999 0.9999 0.9999 0.9998

Trueness (p = 4; n = 4) (ng/ml) Relative bias (%)

30 1.5

500 0.1

1000 0.9

Precision (p = 4; n = 4) (ng/ml) Repeatability (RSD%) Intermediate precision (RSD%)

30 3.2 3.8

500 0.7 1.7

1000 0.6 1.1

Accuracy (p = 4; n = 4) (ng/ml) β-expectation tolerance limits (%)

30 [−7.5; 10.5]

500 [−5.2; 5.4]

1000 [−2.2; 4.0]

Linearity (p = 4; n = 4)

Range (ng/ml) [30; 1000]

Slope 1.009

Intercept -1.302

r2 0.9997

LOD (ng/ml) 4.82

LOQ (ng/ml) 30.0

p: number of runs (or series) of experiments; m: number of concentration levels; n: number of replicates per

concentration levels and per series.


71

Trueness [4–6,19] expressed in terms of relative bias (%) was then assessed from the

validation standards at the three concentration levels. As can be seen in Table 3, the bias did

not exceed the value of 1.5%, irrespective of the concentration level.

The precision of the analytical method was determined by computing the relative

standard deviations (RSD) for repeatability and time-different intermediate precision at each

concentration level of the validation standards [1,2,4–6,18,19]. The RSD values presented in

Table 3 did not exceed 4%.

Accuracy takes into account the total error, i.e. the sum of systematic and random

errors, related to the test result [1,4–6,19]. As shown in Table 3, the relative upper and lower

β-expectation tolerance limits (%) did not exceed the acceptance limits settled at ±15% for

each concentration level.

Consequently, the method can be considered as able to produce accurate results over

the concentration range investigated [1,4–6,19]. Therefore, the lowest amount of the targeted

substance which can be quantitatively determined under the experimental conditions with a

well defined accuracy, i.e. the lower limit of quantitation, was equal to 30 ng/ml [4–7].

The most important conclusion that can be made at the end of this validation phase is

that, thanks to the predictive attribute of the β-expectation tolerance interval, it is expected

that during the routine use of the validated analytical method less than 5% of future results

will fall outside the tolerance limits.

Results obtained during in-study validation

The levonorgestrel method was then used in routine. Twenty-one runs of 60 samples

were performed whose in-study validation was made using 12 QC samples at 30 and

500 ng/ml evenly spread over time within a run (6 time points × 2 concentration values). As

stated in the previous section, the weighted 1/x linear regression model prepared within the

matrix was selected as response function because it was predicted to provide the most

accurate results. With the QC samples it is then possible to evaluate whether the prediction,

and so the response function selection, was adequate or not. Fig. 2 represents the observed

(dots) relative errors of the six QC samples at each concentration level (1 = 30 ng/ml,

2 = 500 ng/ml) obtained over the 21 runs of routine use that would have been obtained if the

selected response function had been the regular linear regression, the linear regression after

natural logarithmic transformation and the weighted 1/x linear regression. As previously

mentioned, the later was the selected model, but for the sake of the demonstration we rebuild

all results assuming that other choice could have been made. The continuous lines represent

the upper and lower β-expectation tolerance or prediction limits while the dotted horizontal

lines represent the [−15%, 15%] acceptance limits. As can been seen, most of the results

effectively fall within the prediction limits and number of this figure is summarized in Table 4.

Globally, when considering the three potential options, about 94% of the QC measured are


72

within the 95% prediction limits. Also, it was an appropriate choice not to retain the simple

linear model here based on the accuracy profile information obtained during pre-study

validation because too many measurements near 30 ng/ml were expected to fall outside the

acceptance limits. It is indeed the case as shown on Fig. 2. Therefore, selecting the weighted

1/x linear regression model, based on prediction, was proven effective in providing reliable

results in routine as demonstrated by QC samples. Indeed, 96% of QC samples are within the

tolerance limits and so within the acceptance limits. In addition, the number of run rejected

was minimal since only the run 17 was discarded.

Fig. 2. Levonorgestrel method. Observed relative errors (dots) of the six QC samples at each concentration level

(1 = 30 ng/ml, 2 = 500 ng/ml) obtained over the 21 runs of routine use that would have been obtained if the

response function had been the regular linear regression, the linear regression after base 10 logarithmic

transformation and the (selected) weighted 1/x linear regression. The continuous lines represent the 95% upper

and lower β-expectation tolerance prediction limits while the dotted horizontal lines represent the [−15%, 15%]

acceptance limits.


73

Table 4 Tolerance limits from pre-study validation and proportion of QC samples observed within those

prediction limits during routine analysis for the four analytical methods.

Analytical method Response function Concentration Lower tolerance

interval (%)

Upper tolerance

interval (%)

Proportion QC

samples within limits

Levonorgestrel (95%

tolerance interval)

Linear regression 30 ng/ml -19.1 25.2 85%

500 ng/ml -5.4 5.6 93%

Linear regression after

logarithmic transformation

30 ng/ml -7.2 10.4 98%

500 ng/ml -4.5 7.5 94%

Weighted linear regression 30 ng/ml -7.5 10.5 99%

500 ng/ml -5.2 5.4 93%

Average 94%

Loperamide (90%

tolerance interval)

Weighted 1/x2 linear

regression

100 pg/ml -19.8 20.2 100%

500 pg/ml -4.6 10.5 72%

1000 pg/ml -7.4 13.3 92%

Average 88%

Ketoglutarate (90%

tolerance interval)

Linear regression 0.67 μg/ml -204.3 170.7 100%

13.33 μg/ml -2.6 10.2 100%

133.33 μg/ml -2.2 4.2 65%

Linear 0 – 13.33 μg/ml 0.67 μg/ml 25.0 39.6 90%

13.33 μg/ml -6.8 8.5 100%

133.33 μg/ml -9.8 1.3 95%



0.67 μg/ml -5.2 14.4 100%

13.33 μg/ml -11.4 -0.4 100%

133.33 μg/ml -0.6 5.7 55%

Quadratic regression 0.67 μg/ml -133.5 -9.9 100%

13.33 μg/ml -10.0 22.4 100%

133.33 μg/ml -3.8 4.9 85%

Weighted 1/x linear

regression

0.67 μg/ml 14.0 27.0 90%

13.33 μg/ml 0.7 9.2 95%

133.33 μg/ml -2.3 3.3 60%

Average 89%

Hydroxymethyl-

furfural (90%

tolerance interval)

Linear regression 0.67 μg/ml -34.6 120.1 100%

13.33 μg/ml 5.0 11.6 80%

133.33 μg/ml -6.7 9.7 100%

Linear 0 – 13.33 μg/ml 0.67 μg/ml -3.3 3.3 80%

13.33 μg/ml -2.1 3.8 80%

133.33 μg/ml -11.9 3.8 100%



0.67 μg/ml -4.4 3.4 95%

13.33 μg/ml 1.0 7.0 75%

133.33 μg/ml -6.8 10.3 100%

Quadratic regression 0.67 μg/ml -180.3 -27.9 100%

13.33 μg/ml 7.7 22.5 90%

133.33 μg/ml -7.7 8.1 100%

Weighted 1/x linear

regression

0.67 μg/ml 14.0 27.0 80%

13.33 μg/ml 0.7 9.2 80%

133.33 μg/ml -2.3 3.3 100%

Average 91%

3.1.2. Loperamide method


The full validation results of this method have been published elsewhere [16].

However, some relevant information for the follow-up of this paper is presented hereafter. In

Table 4, the 90%-expectation tolerance limits are presented. This is equivalent to a 10% risk.


74

The tolerance limits, obtained via the weighted 1/x2 linear regression model as calibration

curve, were included inside the acceptance limits set accordingly to the regulatory

requirements (±20%) for all the concentration levels [2,20,21]. The SPE–LC–MS/MS analytical

method is thus valid.


The loperamide method was then used in routine for 18 runs, each run having six QC

samples at three concentration levels, (two replicates by concentration, levels are 100, 500

and 1000 pg/ml). Fig. 3 represents the observed (dots) relative errors of the six QC samples at

each concentration level obtained over the 18 runs of routine use that have been obtained

with the selected response function. In fact, as can be seen in Table 4, 94 out of 108 QC

samples or 88% of results were observed in routine within the 90% prediction or tolerance

interval, confirming the precision of those statistical prediction intervals estimated before

starting the routine analysis. Once again the decision based on the prediction was proven

effective in providing reliable results in routine as demonstrated by the analysis of the QC

samples. In addition, no run was rejected.

Fig. 3. Loperamide method. Observed relative errors (dots) of the six QC samples at each concentration level

(100, 500 and 1000 pg/ml) obtained over the 18 runs of routine use that would have been obtained with the

selected response function. The continuous lines represent the 90% upper and lower β-expectation tolerance

prediction limits while the dotted horizontal lines represent the [−20%, 20%] acceptance limits.


75

3.1.3. Ketoglutarate and hydroxymethylfurfural method


Here also, the full validation results of this method have already been published [17].

In Table 4, the 90%-expectation tolerance limits values are reported for both analytes

considering different response functions. The bioanalytical method was validated using a

linear regression after logarithmic (base 10) transformation of both X- and Y-axes for KG as

well as for HMF. This model was used as response function, using the fit-for-purpose principle

because it was, in pre-study validation, the model that gave the best prediction intervals

within the acceptance limits [−20%, 20%] for both analytes. The other response functions

used for comparison are the regular linear model, the no-intercept line using level

13.33 μg/ml only, the quadratic model and the selected logarithmic transformed model.


For both analytes, 12 QC samples at each concentration level (0.67, 13.33 and

133.33 μg/ml, four replicates by level) were obtained for each of the 5 runs of routine use,

totaling 60 measurements. Results are shown in Table 4 for ketoglutarate and

hydroxymethylfurfural. With this example again, as can be seen, the prediction or tolerance

interval were particularly accurate. Indeed, as reported in Table 4, considering all three

concentration levels, 85% (51/60) and 89.7% (54/60) of QC samples were dosed within the

90% tolerance limits, respectively, for the ketoglutarate and hydroxymethylfurfural analytes

using the linear model after logarithmic transformation. Since the response function selected

is based on the prediction of accuracy of future measurements, the tolerance limits are

comfortably within the acceptance limits then, a proportion greater than 90% is expected to

be accurate enough with respect to the objective ([−20%, 20%] acceptance limits).


76

4. Conclusions

Analytical method validation is a critical step before implementation of the method for

daily routine analysis in order to demonstrate results reliability. Indeed based on the

validation experiments, analysts have to make a decision about the capability of the method

for its future routine use. To achieve this, it has been shown that the validation procedure

using accuracy profiles build on basis of β-expectation tolerance intervals allows to reliably

predict a region where a predefined proportion of future measurements will be observed.

Making a decision to accept or reject a method based on the predictions obtained by the

β-expectation tolerance intervals allows to align correctly the objective of an analytical

method and the objective of the validation phase. In the four examples shown, the prediction

obtained by the tolerance interval has been shown as particularly reliable for making trustful

decisions. Indeed, the expected proportions of QC samples were included in the tolerance

intervals build during the validation phase for all examples.

In addition, for the same reason, we propose to identify and select a response function

based exclusively on the prediction of accurate results it may provide and not on the usual

considerations such as R2 or any other statistics that are not aligned with the objective of a

method. That way a model and consequently the analytical method is fitted for its purpose:

providing accurate results.

Acknowledgments

Thanks are due to the Walloon Region and the European Social Fund for a research

grant to E.R. (First Europe Objective 3 project no. 215269).


77

References

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registration of Pharmaceuticals for Human Use, Topic Q2 (R1): Validation of Analytical

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Chapitre III

« Quality-by-Testing »

Section III.2

Section III.2 : « Quality-by-Testing »

81

Avant-propos

Lors de l’étude précédente, nous avons pu démontrer que l’étape de validation,

conduite par l’intermédiaire du profil d’exactitude permet de s’assurer de l’adéquation de la

méthode quant à son objectif, à savoir délivrer des résultats exacts en routine. Par la même

occasion, nous avons démontré que cet outil puissant permet également de sélectionner le

modèle de calibration le plus adéquat.

Démontrer les performances quantitatives d’une méthode tout en gérant le risque

associé aux futurs résultats est essentiel, mais cette étape n’est qu’une partie du cycle de vie

des méthodes. Dans cette optique, nous nous sommes plus spécifiquement intéressés à l’étape

d’optimisation.

Les exemples sélectionnés lors de l’étude précédente sont relativement simples et il

s’avère souvent que la problématique à laquelle est confronté l’analyste est plus complexe.

L’exemple abordé dans cette section en est une illustration. Nous y exposons le cas d’une

molécule polaire à très faible poids moléculaire (moins de 200 Da) contenue dans une matrice

biologique et dont la concentration ciblée est très faible. Pour cette étude, nous avons retenu

l’approche de type « Quality-by-Testing ». En effet, cette approche itérative fréquemment

utilisée par de nombreux analystes peut s’avérer suffisante pour obtenir des performances

quantitatives maîtrisées.


82

Abstract

A sensitive and accurate LC/MS method was developed for the monitoring of

glucosamine (GLcN) dog plasmatic concentration. In this scope, relatively low plasmatic

concentrations of GLcN were expected, ranging from 50 to 1000 ng/mL. Liquid

chromatography coupled to simple quadrupole mass spectrometry detection (LC/MS) was

selected bringing the selectivity and the sensitivity needed for this application. Additionally, a

solid phase extraction (SPE) step was performed to reduce matrix and ion suppression effects.

Due to the ionisable character of the compound of interest, a mixed-mode strong cation

exchange (Plexa PCX) disposable extraction cartridge (DEC) was selected. The separation was

carried out on a Zorbax SB-CN column (5 µm, 4.6 mm i.d. x 250 mm), considering hydrophilic

interaction liquid Chromatography (HILIC). Indeed, the mobile phase was made of methanol

and 5 mM ammonium hydrogen carbonate buffer at pH=7.5 (95/5, v/v). The detection was

led at m/z ratios of 180.0 and 417.0, for GLcN and IS respectively. Reliability of the results was

demonstrated through the validation of the method using an approach based on the accuracy

profile allowing managing the risk associated to the use of these methods in routine analysis:

it is thus guaranteed that each future result will fall in the ±30% acceptance limits with a

probability of at least 90%. Successful application of the method to a preliminary

pharmacokinetic study illustrated the usefulness of the method for pre-clinical studies.


83

1. Introduction

Glucosamine (GLcN, Fig. 1), is naturally present in glycoproteins and this amino

monosaccharide is an essential constituent of glycosaminoglycans [1-5]. Several studies have

shown that glucosamine can be considered as drug in osteoarthritis disease. Chondrocytes

incorporate the administrated GLcN into the glycosaminoglycan chains in cartilage [6]. The

articular function is restored by the synthesis stimulation and protection of proteoglycans [7].

Other mechanisms also involve an inhibition of the proinflammatory mediators in

osteoarthritis chondrocytes [8].

Fig. 1. Structure of glucosamine.

Owing to the putative importance of GLcN in the understanding and healing of

osteoarthritis, it is essential to develop sensitive and accurate bioanalytical methods for bio-

chemical, pre-clinical and clinical studies. The main difficulties in developing a bioanalytical

method for the quantitative determination of GLcN in biofluids are its high polarity, low

concentration, and the numerous possible interferences due to endogenous structurally

related compounds (glucose, galactose, and so on). As GLcN has poor absorbance in UV/vis,

classical detectors such as UV/vis spectroscopic detection coupled to reversed phase liquid

chromatography require pre-analytical derivatization procedures. Such procedures were

developed for GLcN determination in human plasma [9-11] or in rat plasma [12], but these

approaches often lack selectivity and sensitivity. Futhermore, their practical implementation

is sometimes quiet complicate. Electrochemical detection improved GLcN determination [13-

15]. Similarly, fluorescence detectors were also proposed to increase the sensitivity as well as

the selectivity of methods dedicated to the assay of GLcN, they were coupled either to

electrophoresis [16] for the determination of GLcN in horse plasma, or to HPLC for its

determination in human plasma [17]. However these methods required complex and

sometimes long sample preparation and clean-up procedures and do not reach quantification

limits needed in complex matrices. High performance liquid chromatography methods with

mass spectrometry (MS) detection have also been developed [18-20]. They include


84

time-consuming pre-analytical derivatization followed by reversed phase chromatography.

HPLC-ESI-MS/MS methods for the direct determination of GLcN in human plasma have also

been developed. They were performed either with a polymer-based amino column [21], or

cyano groups bonded on silica [22]. They employed a one step preparation procedure through

protein precipitation using trichloroacetic acid [21] or a methanol-acetonitrile mixture [22].

However, hydrophilic interaction liquid chromatography (HILIC) could be an

alternative to conventional RP-HPLC (reversed phase HPLC) or NP-HPLC (normal phase

HPLC) for the analysis of very polar compounds [23]. In HILIC, analyte retention is believed to

be caused by the partitioning of the analyte between a water-enriched layer of stagnant eluent

on a hydrophilic stationary phase and a relatively hydrophobic bulk eluent, with the main

components usually being 5-40 % water in ACN or methanol [24,25]. In this framework, the

HILIC mode was also considered during the development of the present method. The

development and optimisation steps of the procedure lead to a fully new method where a

solid phase extraction step by mixed-mode strong cation exchange sorbant was required to

minimize ion suppression effects [28]. The developed method was then fully validated using a

total error approach based on tolerance intervals and accuracy profiles [32-34] for the

accurate determination of GLcN in dog plasma. Finally, the suitability of the method for

pre-clinical applications was illustrated with a preliminary pharmacokinetic study.


85

2. Materials and methods


Glucosamine hydrochloride (GLcN; purity > 98%) was obtained from Acros Organics

(Morris Plains, NJ, USA). Miconazole nitrate (purity > 98%) was obtained from Sigma (St.

Louis, MO, USA). Acetonitrile and water of LC/MS grade were purchased from Biosolve

(Valkenswaard, The Netherlands). Methanol of HPLC grade and trichloroacetic acid (TCA),

formic acid, acetic acid, ammonium acetate, ammonium bicarbonate, ammonium formiate and

ammoniac (5%), all of analytical grade, were purchased from VWR International (Darmstadt,

Germany).

2.2. Apparatus

The LC/MS detection was performed using a Waters (Milford, MA, USA). Sample

Manager 27777, and Waters binary HPLC pumps 1525µ. The MS detector consisted on a

single quadrupole (Waters, Quattro, Micromass, Ultima/ZQ) with an electrospray source set

in the positive ionisation mode.

2.3. Sample preparation

2.3.1. Conditions tested during the optimisation phase

Two protein precipitation (PP) protocols were tested during this phase, as presented

in the related works, an organic [22] and an acidic [21] precipitation.

Phenylboronic Bond Elut PBA, 100 mg, 1 mL (Varina, Palo Alto, CA, USA) Disposable

Extractive Cartridges (DEC) and mixed-mode silica based weak cation exchange ISOLUTE

HCX-Q, 25 mg, 1 mL (Biotage, Uppsala, Sweden) DEC were then tested for the sample

clean-up. In the case of cation exchange DEC, the dog plasma sample was acidified in a

proportion 1/1.5 by phosphoric acid 2% (m/v) before being loaded onto cartridges.

Zinc salting out pre-treatment of dog plasma sample was also envisaged. The protein

precipitation agent was constituted of a 50/50 (v/v) mixture of a zinc sulphate solution at

10% (v/v) and a sodium hydroxide solution at 500 mM [26,27]. All these protocols were

tested on blank dog plasma and were then injected in LC/ESI-MS system with a post-column

infusion of GLcN at 10,000 ng/mL in order to qualitatively determine matrix effect as

described by Bonfiglio et al. [28–30].


86

2.3.2. Optimal extraction conditions

Three hundred fifteen microlitres of dog plasma sample were mixed with 25 µL of

miconazole internal standard (IS) working solution as well as with 35 µL TCA 10% in water.

After brief stirring with a vortex mixer, the samples were centrifuged at 8200 × g (7000 rpm)

for 15 min and 325 µL of the supernatant was collected for further sample clean-up. The

supernatant was then loaded onto Bond Elut Plexa (Varian, Palo Alto, CA, USA) DEC packed

with mixed-mode strong cation exchange sorbent (PCX, 60 mg, 1 mL). The cartridges were

previously conditioned with 1 mL of acetonitrile and then with 500 µL of 20 mM formiate

buffer at pH 3.0. Washing step was performed using 500 µL acetonitrile and the elution phase

consisted in 1.0 mL of a 70/30 (v/v) mixture of acetonitrile and 5% ammoniac. The eluate

was then evaporated to dryness by nitrogen gas and the residue was reconstituted with

150 µL of 5 mM pH 7.5 ammonium hydrogen carbonate buffer.

2.4. LC/MS conditions

The analytic chromatographic column consisted in a Zorbax SB-CN column (5 µm,

4.6 mm i.d. × 250 mm) purchased from Agilent (Waldbronn, Germany). A SunFire guard

column (Waters, Milford, MA, USA) packed with C18 material (3.5 µm, 4.6 mm i.d. × 20 mm)

protecting the analytical column and only acting as a filter in order to additionally reduce the

harmful effect of endogenous compounds that could be introduced in the chromatographic

system was also used. The isocratic separation was performed under HILIC mode using a

mobile phase consisting in a mixture of methanol and 5 mM ammonium hydrogen carbonate

buffer at pH 7.5 (95/5, v/v). The flow rate was settled at 0.3 mL/min, and the samples

injection volume was of 20 µL. The temperature of the autosampler was set at 10 °C.

The MS source consisted in an electrospray ionisation used in positive ion mode at a

temperature of 400 °C. The electrospray source used nitrogen at a flow rate of 90 L/h as

nebulizer gas and at 890 L/h as desolvation gas. The capillary voltage was settled at 4.0 kV

and the cone voltage at 17 V. Single ion reaction (SIR) mode was used to monitor GLcN at

m/z: 180 and the internal standard at m/z: 417.


87

2.5. Standard solutions

Stock solutions of GLcN were prepared by dissolving an accurate amount of the analyte

in pH 7.5 ammonium formiate buffer. The stock solutions of GLcN were diluted with the same

buffer (pH 7.5) and used to spike aliquots of dog plasma to five concentration levels covering

a range from 50.5 to 1010 ng/mL. Two types of spiked dog plasma were prepared daily,

namely calibration standards and quality control samples (QCs), both having the same

concentrations. Each sample was also spiked with internal standard in order to obtain a

concentration of 66 ng/mL of miconazole. Each calibration standard was analysed once

whereas each QC was analysed independently in duplicates. Calibration standards and QCs

were prepared for 4 different days for the method validation.

2.6. Experimental protocol for the routine phase

During this routine phase, two stock solutions of GLcN were prepared as described in

Section 2.5. The first one was diluted in order to reach concentration levels from 50.5 to

1010 ng/mL of spiked dog plasma. These solutions were used for establishing the calibration

curve.

The second stock solution of GLcN was diluted to prepare a quality control solution at

250 ng/mL of spiked dog plasma always as described in Section 2.5. This solution was

analysed at the end of the analytical sequence.

2.7. Computations

The e.noval software v2.0 (Arlenda, Liège, Belgium) was used to compute the

validation results of the bioanalytical method as well as to obtain the accuracy profiles.


88


3.1. Method development

3.1.1. Selection of LC/MS conditions

Based on previous works [21], a first attempt was made using an YMC Pack Amino

column (3 µm, 2.1 mm i.d. × 150 mm; Waters Corp., Milford, MA, USA) with acetonitrile/water

(80/20) mixture as mobile phase. For aqueous spiked samples, one peak corresponding to

GLcN was observed with retention time of approximately 5.0 min. Unfortunately when

analyzing dog plasma samples with MS detection, methods sensitivity was far too weak

reaching only 250 ng/mL GLcN. Another column, packed with Cyano bonded material, was

then tested, as it was suitable for the analysis of GLcN in human plasma samples by other

authors [22]. Using the conditions described in this study, two co-eluted peaks were observed

after 4.5 min (k’ = 0.27). In order to highlight this phenomena, the mobile phase composition

was slightly changed compared to Zhong et al. work [22]. It consisted in a mixture of

acetonitrile and 5 mM ammoniac acetate buffer 30/70 (v/v) at a flow rate of 0.5 mL/min. In

these conditions, two distinct peaks for GLcN were observed as shown in Fig. 2, the first one

at 9.6 min (k’ = 1.47) and the second one at 11.2 min (k’ = 1.90). Several attempts using

various dissolution solutions for GLcN and mobile phase compositions were made in order to

obtain only one peak, but without success. These two peaks seem to be the α- and β-anomers

of glucosamine resulting to the mutarotation of this amino sugar within the column as

described by Skelley et al. [31]. Consequently, the optimisation of the LC/MS conditions was

oriented to maximize the separation of the two peaks leading to the reduction of the plateau

height representative of the equilibration state between the interconverting species.

Fig. 2. Chromatogram of an aqueous sample spiked with 1000 ng/mL of glucosamine obtained with the Zorbax

SB-CN column and mixture of acetonitrile and 5 mM ammoniac acetate buffer 30/70 (v/v). The two peaks of

GLcN corresponding to its two conformations are shown at RT = 9.61 min and RT = 11.22 min.


89

Considering the behaviour of this small polar molecule weakly retained, the

hydrophilic interaction liquid chromatography (HILIC) was investigated. For economical and

ionisation efficiency reasons, MeOH was chosen as organic modifier. The mobile phase was

thus composed of a high percentage of organic solvent with a small percentage of volatile

buffer (95/5). The water-enriched liquid layer established within the stationary phase, allows

the partitioning of hydrophilic solutes, such as GLcN, from the mobile phase into the

hydrophilic layer leading to a higher retention onto the Cyano bound packed column [23]. The

change of the organic modifier (ACN to MeOH) and its proportion (40–95%) lead to a better

separation between the two anomers of this amino sugar as well as a higher retention time

and an improvement of the sensitivity.

In the framework of the evaluation of the suitable LC conditions, MS parameters were

determined through Flow Injection Analysis (FIA) experiments using a solution of GLcN at a

concentration of 10,000 ng/mL. GLcN was monitored at m/z: 180 corresponding to [M+H]+

transition of GLcN and miconazole, the internal standard, at m/z: 417. During this LC/MS

optimisation, it was also important to find an adequate flow rate for the quantification and the

separation of the two GLcN peaks as well as for optimal ESI-MS conditions. Regarding to Van

Deemter theory and dimension of the analytical column, particularly particle size of 5 µm, the

optimal flow rate should be found near 0.7 mL/min. Despite of this and in order to maximize

the MS sensitivity, a flow rate of 0.3 mL/min was selected. This relatively non-adequate choice

has for consequence a lower efficiency of the chromatographic system probably because the

longitudinal diffusion (B-term) is important but has allowed improving detection sensitivity.

The electrospray ionisation source in positive mode was set at a temperature of 400 °C and

the capillary and cone voltages were set at 4.0 kV and 17 V, respectively.

Under these conditions, the prospect of a selective determination of each one of the

anomer of this amino sugar is conceivable.

3.1.2. Optimisation of the SPE/HILIC/MS for dog plasma samples

On the basis of Roda et al. [21] and Zhong et al. [22] studies, acidic and organic protein

precipitation procedures for plasma clean-up were tested but no peak could be detected in

these conditions. Using the method proposed by Bonfiglio et al. for the quantitative evaluation

of matrix effect [28–30], important ionisation suppression was detected with these clean-up

procedures. Indeed, as shown in Fig. 3, around the GLcN retention time a significant matrix

effect was observed at m/z: 203. This could be due to a sodic adduct of glucose: [glucose−Na]+.


90

Fig. 3. Ion mass spectra ranging from m/z: 150 to 250 obtained at the retention time of GLcN for blank dog

plasma. The ion at m/z: 203 is preponderant and corresponds to the sodic adduct of glucose: [glucose−Na]+.

Table 1 Extraction rate obtained with the tested sample clean-up procedures for dog plasma samples

spiked with 1000 ng/mL of glucosamine.

Sample clean-up method Number of replicates (n) Extraction rate ± SD (%)

Acidic protein precipitation 3 0

Organic protein precipitation 3 0

Phenylboromic DEC 3 0

Weak cation exchange (HCX-Q) DEC 3 5.2 ± 3.1

Salting out (Zn) and strong cation

exchange (PCX) DEC

3 15.1 ± 1.8

Strong cation exchange (PCX) DEC 3 28.1 ± 3.3

In order to reduce this interference problem [28], several other clean-up procedures were

tested and are summarized in Table 1. As can be seen in Table 1, post-column infusion

highlighted a weak extraction rate combined with a strong ion suppression, when

Phenylboronic DEC were used as sample clean-up method. Mixed-mode weak and strong

cation exchange sorbents (HCX-Q and PCX, respectively) were also selected due to the

ionisable character of the compound of interest. HCX-Q did not seem to be suitable in terms of

extraction rate but lead to a reduction of the ion suppression. Only a weak but acceptable

extraction rate (28.1 ± 3.3%) was obtained with PCX cartridges as well as a reduction of ion

suppression effect. A pre-treatment of the dog plasma sample using zinc salting out method

[26,27] before PCX cartridge lead to a lower mean extraction rate (15.1 ± 1.8%) and so, was

not relevant.


91

The final conditions used for the SPE–LC-ESI/MS method comprised, first a solid phase

extraction using a mixed-mode strong cation exchange cartridge. The cartridge was

conditioned with 1 mL acetonitrile and then 500 µL of 20 mM formiate buffer at pH 3.0. Three

hundred twenty five microlitres of plasma previously acidified by 35 µL TCA were loaded

onto the cartridges. The washing step was performed with 500 µL acetonitrile and elution

was obtained with a 70/30 (v/v) mixture of acetonitrile and 5% ammoniac. The eluate was

then evaporated to dryness by nitrogen gas and the residue was recovered with 150 µL of

5 mM pH 7.5 ammoniac buffer. Twenty microlitres of the resulting solution were then

analysed using a Zorbax SB-CN column (5 µm, 4.6 mm i.d. × 250 mm) as described above.

3.2. Method validation

An original approach using accuracy profiles based on tolerance intervals was applied

to evaluate the reliability of the results generated by the developed LC/MS method [32–34].

The tolerance interval used is a “β-expectation tolerance interval” defining an interval in

which it is expected that each future result will fall with a defined probability (β) [35]. It is

therefore a predictive methodology. This tolerance interval is computed for each validation

standard concentration level, using their estimated intermediate precision standard deviation

and bias. By joining the upper tolerance limits on one hand and the lower tolerance limits on

the other hand, it defines an accuracy profile. As long as this profile stays inside the

acceptance limits settled according to the need of the final user or to regulatory expectations

the method can be considered as valid. Indeed, it guarantees that each future result will be

included in the a priori set acceptance limits with at least a probability β (e.g. 0.90 or 90%).

Such an approach reflects more directly the performance of individual assays and will

result in fewer rejected in-study runs than the current procedure that compares point

estimates of observed bias and precision with the target acceptance criteria according to the

FDA document [36] or recent AAPS/FDA proposals [37]. The concept of accuracy profile was

also used to select the most appropriate regression model for calibration, to determine the

lower limit of quantitation (LLOQ) and the range over which the method can be considered as

valid. The acceptance limits were settled at ±30% according to the regulatory requirements

[36,37] and the probability β at 90%.

3.2.1. Selectivity

The absence of matrix interferences at the retention time of GLcN was demonstrated in

Fig. 4, which illustrates chromatograms obtained after analysis of a sample of blank plasma

from six different dogs spiked with the IS, and blank plasma sample spiked with 1000 ng/mL

GLcN and the IS, and a real sample from a healthy dog treated by oral administration of a

single dose of 60 mg/kg of GLcN and collected after 4 h.


92

Fig. 4. Chromatograms of a blank dog plasma sample spiked with the IS, and a blank plasma sample spiked with

1000 ng/mL GLcN and IS, and a real sample of a healthy dog after oral administration of 1.5 g GLcN in capsule.

Where (a) are the recorded chromatograms at m/z: 180 (GLcN) and (b) are the recorded chromatograms at

m/z: 417 (SI). Conditions of analysis are as described in Section 2.4 LC/MS conditions.

3.2.2. Process efficiency

The recoveries of the analyte were determined at three different concentrations

ranging from 50.5 to 1010 ng/mL [36,38]. The mean recoveries are shown in Table 2. Those

recoveries were calculated by comparing peak areas of GLcN obtained from freshly prepared

dog plasma samples treated according to the described procedure with those found after the

direct injection on the analytical column of standard solutions at the same concentrations as

required by regulatory guidance [36]. All the recoveries were constant all over the range

studied, demonstrating the overall extraction efficiency of the process following FDA guidance

[36].

Table 2 Extraction rate obtained for three different concentrations of GLcN ranging from 50.5 to

1010 ng/mL considering the optimal extraction conditions.

Concentration (ng/mL) Number of replicates (n) Extraction rate ± SD (%)

50.5 3 22.9 ± 5.6

252.5 3 30.9 ± 1.5

1010 3 30.3 ± 3.0


93

3.2.3. Analysis of the response functions

In order to find the most adequate standard curve, several response functions were

fitted, namely the quadratic and weighted (1/X) quadratic ones as well as the linear and

weighted (1/X) linear functions. From every response function obtained, the concentrations

of the validation standards were back-calculated in order to determine, by concentration

level, the mean relative bias as well as the upper and lower β-expectation tolerance limits at

90% level by introducing the estimation of the standard deviation for intermediate precision.

From these data, different accuracy profiles were plotted to select the most suitable

regression model for the intended use of the analytical method as shown in Fig. 5 [32–34,39].

The acceptance limits were set at ±30%. Only two response functions allowed demonstrating

the capability of the method to quantify glucosamine over the whole concentration range

considered, since the tolerance intervals were totally included inside the acceptance limits.

These functions are the weighted (1/X) linear and the weighted (1/X) quadratic ones. As

these two last functions have provided the least and similar bias and imprecision, the linear

one was selected as the final standard curve as it was the simplest response function. The

validation results obtained by applying this regression model are presented in Table 3 for

each day of analysis.

Fig. 5. Accuracy profiles for the quantification of GLcN in dog plasma using (a) a quadratic model,

(b) a weighted 1/X quadratic model, (c) a linear model and (d) a weighted 1/X linear regression model.

Relative bias (plain red line), ±30% acceptance limits (black dotted curves), 90% β-expectation

tolerance limits (blue dashed lines), and relative back-calculated concentrations (green dots).


94

Table 3 Results of the validation of the SPE–LC-ESI/MS method dedicated to the quantification of

glucosamine in dog plasma samples.


Weighted linear regression model; calibration range (m = 5): 50 – 1000 ng/ml

Run 1 Run 2 Run 3 Run 4

Slope 0.002395 0.016970 0.005305 0.023570

Intercept 0.0646 -0.1525 -0.2305 0.6589

Weight 1/x 1/x 1/x 1/x

r2 0.9974 0.9997 0.9995 0.9983


50 11.90

100 -1.92

250 -3.92

500 -1.61

1000 -1.31


50 5.64 6.54

100 9.02 9.02

250 4.87 7.95

500 8.33 10.73

1000 6.21 9.30


50 [−3.96; 27.50]

100 [−20.74; 16.89]

250 [−22.43; 14.58]

500 [−24.66; 21.45]

1000 [−22.56; 19.94]


Range (ng/ml) [50.25; 1005]

Slope 0.986

Intercept -0.394

r2 0.9819

LOD (ng/ml) 15.23

LOQ (ng/ml) 50.25

p: number of days of analysis; n: number of repetitions per day of analysis; m: number of GLcN concentration

levels.


95

3.2.4. Trueness and precision

Trueness [32,36,40,41] expressed in terms of relative bias (%) was assessed from the

validation standards at 5 concentration levels as can be seen in Table 3. According to the

regulatory requirements [36], trueness was acceptable for GLcN, since the bias did not exceed

the value of ±15%, irrespective of the concentration level. The precision of the bioanalytical

method was then determined by computing the relative standard deviations (RSD) for

repeatability and time-different intermediate precision at each concentration level of the

validation standards [32,36,40,41]. The RSD values presented in Table 3 were relatively high,

with a maximum intermediate precision RSD of 10.7% for the 502.5 ng/mL concentration

level. However, they all remained still acceptable with regard to regulatory expectations [36].

3.2.5. Accuracy, LOQ, range and LOD


errors, related to the test result [32,36,40,41]. As shown in Table 3, the upper and lower

β-expectation tolerance limits (%) did not exceed the acceptance limits settled at 30% for

each concentration level. Consequently, the method is able to provide accurate results over

the concentration range investigated [32–34,39,41]. For GLcN, the lower limit of quantitation

(LLOQ) was 50.25 ng/mL. As for the limit of detection (LOD), it was estimated using the mean

intercept of the calibration model and the residual variance of the regression. The LOD was

evaluated at 15.23 ng/mL.


96

3.3. Routine application

The developed and validated SPE/LC/MS bioanalytical method was then applied at a

first preliminary pharmacokinetic study to measure the plasma levels of glucosamine in

9 dogs. The glucosamine in capsules was administrated orally to the dogs in a single dose of

60 mg/kg. Fig. 6 illustrates the glucosamine plasma concentration versus times profile

obtained. After the administration of the capsules, the plasma concentrations rapidly

increased reaching a peak of 1158 ± 86 ng/mL after 2 h. From this initial study, it can be

deduced that the absorption and distribution phases are extremely rapid. The present

pharmacokinetic results seem to show a two-compartment model. However, to obtain more

reliable estimates of the pharmacokinetics parameters, more time points will be required for

further studies.

Fig. 6. Mean pharmacokinetic profile of dog plasma GLcN concentration measured in healthy dogs (n = 9) after

single oral dose administration of 1.5 g GLcN.


97

4. Conclusion

A new sensitive and selective SPE-LC-ESI/MS method for the determination of GLcN in

dog plasma was developed. A solid phase extraction using mixed-mode strong cation

exchange sorbent was necessary in order to minimize ionisation suppression effects mainly

due to glucose present in large amount in plasma. Furthermore this method was successfully

validated with the 50.5–1010 ng/mL range. This allowed the determination of low GLcN

plasma levels in healthy dogs receiving this drug in a preliminary pharmacokinetic study.

Acknowledgments

KitoZyme S.A. (Belgium) is acknowledged for financial support for this work. Research

grants from the Belgium National Fund for Scientific Research (FRS-FNRS) to M. Fillet and

E. Rozet are also gratefully acknowledged.


98

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Nivet, L. Valat, E. Rozet, J. Pharm. Biomed. Anal. 45 (2007) 70.

[34] Ph. Hubert, J.J. Nguyen-Huu, B. Boulanger, E. Chapuzet, N. Cohen, P-A. Compagnon, W.

Dewé, M. Feinberg, M. Laurentie, N. Mercier, G. Muzard, L. Valat, E. Rozet, J. Pharm.

Biomed. Anal. 45 (2007) 82.

[35] R. Mee, Technometrics 26 (1984) 251.

[36] Guidance for Industry: Bioanalytical Method Validation, US Department of Health and

Human Services, Food and Drug Administration, Center for Drug Evaluation and

Research (CDER), Center for Biologics Evaluation and Research (CBER), May 2001.

[37] C.T. Viswanathan, S. Bansal, B. Booth, A.J. DeStefano, M.J. Rose, J. Sailstad, V.P. Shah, J.P.

Skelly, P.G. Swann, R. Weiner, AAPS J. 9 (2007) E30.

[38] B.K. Matuszewski, M.L. Constanzer, C.M. Chavez-Eng, Anal. Chem. 75 (2003) 3019.

[39] E. Rozet, V. Wascotte, N. Lecouturier, V. Preat, W. Dewe, B. Boulanger, P. Hubert, Anal.

Chim. Acta 591 (2007) 239.


100

[40] ISO 5725-1, Application of the statistics-accuracy (trueness and precision) of the

results and methods of measurement-Part 1: general principles and definitions,

International Organization for Standardization (ISO), Geneva, Switzerland (1994).


Hubert, J. Chromatogr. A 1158 (2007) 111.

C. Hubert, P. Lebrun, S. Houari, E. Ziemons, E. Rozet, Ph. Hubert, Improvement of a stability-indicating method by Quality-by-Design versus Quality-by-Testing: A case of a learning process, Journal of Pharmaceutical and Biomedical Analysis, 88 (2014) 401.

Chapitre III

« Quality-by-Design » versus « Quality-by-Testing »

Section III.3

Section III.3 : « QbD » versus « QbT »

103

Avant-propos

L’exemple de la section précédente démontre bien que l’optimisation d’une méthode

analytique suivant la stratégie « QbT » peut s’avérer adéquate même dans des cas complexes.

La validation de celle-ci suivant le profil d’exactitude et son utilisation avec succès lors d’une

étude préliminaire de pharmacocinétique sur des échantillons plasmatiques en sont d’ailleurs

la démonstration.

Cette approche univariée en phase d’optimisation n’est cependant pas optimale

lorsqu’il s’agit d’évaluer le risque. En effet, suivant cette approche conventionnelle, une

évaluation du risque lié aux aspects qualitatifs de la méthode analytique ne peut s’obtenir que

par l’intermédiaire d’une étude de robustesse à la suite de la validation de la méthode.

Cependant, même si cette étude subséquente est conduite, l’analyste ne peut obtenir qu’une

maîtrise partielle des risques puisque celle-ci est exclusivement centrée sur les conditions

opératoires sélectionnées pour la routine. Dès lors, il semble plus adéquat de considérer une

méthodologie permettant la gestion du risque tout au long du processus de développement et

d’optimisation de la méthode.

Il est donc intéressant de pouvoir disposer d’une méthodologie permettant de réaliser

cette étude de robustesse en phase d’optimisation. C’est dans ce contexte qu’une stratégie

alliant l’utilisation des plans d’expériences à la définition d’un « Design Space » est présentée.

Cette approche permet non seulement de définir un domaine expérimental plutôt que de

choisir des conditions opératoires fixes, mais également de gérer le risque lié aux aspects

qualitatifs à l’intérieur de cet espace opérationnel. L’exemple donné au cours de cette section

porte sur l’optimisation d’une méthode de suivi des impuretés d’un principe actif contenu

dans une matrice médicamenteuse complexe. Il met en regard cette approche intégrée, le

« Quality-by-Design », avec l’approche conventionnelle, le « Quality-by-Testing ». De plus, la

notion d’amélioration continue de la méthode analytique est également abordée au cours de

cette section.

Chapitre 3 : Résultats et discussions

104

Abstract

The understanding of the method is a major concern when developing a

stability-indicating method and even more so when dealing with impurity assays from

complex matrices. In the presented case study, a Quality-by-Design approach was applied in

order to optimize a routinely used method. An analytical issue occurring at the last stage of a

long-term stability study involving unexpected impurities perturbing the monitoring of

characterized impurities needed to be resolved. A compliant Quality-by-Design (QbD)

methodology based on a Design of Experiments (DoE) approach was evaluated within the

framework of a Liquid Chromatography (LC) method. This approach allows the investigation

of Critical Process Parameters (CPPs), which have an impact on Critical Quality Attributes

(CQAs) and, consequently, on LC selectivity. Using polynomial regression response modeling

as well as Monte Carlo simulations for error propagation, Design Space (DS) was computed in

order to determine robust working conditions for the developed stability-indicating method.

This QbD compliant development was conducted in two phases allowing the use of the Design

Space knowledge acquired during the first phase to define the experimental domain of the

second phase, which constitutes a learning process. The selected working condition was then

fully validated using accuracy profiles based on statistical tolerance intervals in order to

evaluate the reliability of the results generated by this LC/ESI-MS stability-indicating method.

A comparison was made between the traditional Quality-by-Testing (QbT) approach and

the QbD strategy, highlighting the benefit of this QbD strategy in the case of an unexpected

impurities issue. On this basis, the advantages of a systematic use of the QbD methodology

were discussed.


105

1. Introduction

Development of a quantitative method for impurity assay in a pharmaceutical form

(PF) requires an in-depth understanding of the method. In this context, the analytical

procedure must take a stability-indicating approach in order to allow a selective

determination of related substances (i.e. intermediate and by-product impurities as well as

degradation products) as required by pharmaceutical guidelines [1-3]. Indeed, the

development of stability-indicating methods is a major concern in the pharmaceutical

industry [4]. Nowadays, development of chromatographic methods is largely performed by

the traditional Quality-by-Testing (QbT) methodology or the trial-and-error approach.

However, such development does not provide neither the ability opportunity to advisedly

assess the robustness throughout the development process, nor the possibility of carrying out

quality risk management. Both concepts are requirements stipulated in recent U.S.

Pharmacopeia (USP) recommendations [5] as well as in pharmaceutical guidelines [6-8].

As recently stated by Nethercote [9] and Orlandini [10], the Quality-by-Design (QbD)

concept allows a systematic and scientific approach to the development of analytical methods,

enabling an earlier understanding and identification of variables affecting method

performance [11-14]. This approach also allows for the implementation of a control strategy

based on the enhanced understanding acquired regarding the analytical method. According to

the ICH guideline Q8(R2) [6], the QbD approach can be defined as an optimization strategy

combining Design of Experiments (DoE) and Design Space (DS). Within the specific context of

Liquid Chromatography (LC), QbD is used to simultaneously optimize both the separation

process and the robustness of the method over the whole experimental domain (i.e. the

knowledge space). A key component of the QbD paradigm is the definition of the DS of

analytical methods where assurance of quality is provided [15,16]. In the ICH guideline

Q8(R2) [6], DS is defined as “the multidimensional combination and interaction of input

variables (e.g. material attributes) and process parameters that have been demonstrated to

provide assurance of quality”. This guideline also states that “working within the design space

is not considered as a change. Movement out of the design space is considered to be a change

and would normally initiate a regulatory post approval change process”. As already discussed

in the scientific literature [17-23], the DS consequently defines a zone of robustness, as no

significant changes in terms of separation quality should be observed in the resulting

chromatograms.


106

The goal of the present study is to demonstrate the usefulness of the QbD approach

within the framework of a real example illustrating an issue with unexpected impurities

appearing during the last stage of a long-term stability study of a controlled released drug

formulation (under confidential agreement). The QbT approach, used during the initial

development of this method, did not provide sufficient knowledge in order to facilitate

adjustments to the method and overcome this issue. The characterized impurities (referred to

as the impurities), involved in our case study, were determined from the knowledge of the

route of synthesis and from active pharmaceutical ingredient (API) stress-test experiments.

P4AX91 (Molecular Weight (M.W.): 102 g mol-1), P4FX98 (M.W.: 115 g mol-1), P4NX99 (M.W.:

116 g mol-1), P4SX95 (M.W.: 139 g mol-1) and P4SX92 (M.W.: 170 g mol-1) are all degradation

products of P4MX01 (M.W.: 250 g mol-1), the API of the pharmaceutical form. In the particular

case in this study, where specific detection at very low concentration was required for all

impurities, a Liquid Chromatography coupled to Mass Spectrometry (LC-MS) technique was

selected. However, the use of LC-MS for a quantitative analysis of multiple molecules with

(very) low molecular weight and extracted from complex matrices (i.e. controlled released

formulations) leads to some key issues. Principal among these are analyzer resolution and

accuracy, and signal noise and signal spikes in Total Ion Current (TIC) mode. Regarding small

molecules extracted from complex matrices, the possibility cannot be excluded that

unexpected compounds will appear with pharmaceutical form aging and lead to co-elution

and co-detection in a specific Selected Ion Monitoring (SIM) chromatogram when a simple

quadrupole mass detector is used. This is even more complex when targeted impurities are

structural analogs with a very similar molecular weight (i.e. separated by only one molecular

weight unit) and containing heteroatoms. Indeed, in this case study, P4FX98 is a structural

analog of P4NX99 and its M.W. is smaller by only one mass unit. Due to the presence of

nitrogen atoms within the structure of these two compounds, the specificity of a simple

quadrupole mass detector was found to be insufficient, resulting in an interference of P4FX98

in the P4NX99 SIM chromatogram. The advantage usually obtained through the use of a triple

quadrupole mass detector did not apply in this case, as ions obtained from the fragmentation

of pseudo-molecular ions of targeted impurities led to the production of daughter ions with

the same mass-to-charge ratio (m/z). Therefore, in the presented case study, it was necessary

to use a liquid chromatography procedure in order to attain selectivity. An overall

methodology was then proposed and discussed. Finally, the selected working condition was

fully validated.


107

2. Experimental


Methanol (HPLC gradient grade) was purchased from J.T. Baker (Deventer, the

Netherlands). Water (ULC/MS grade) and acetonitrile (HPLC supra-gradient grade) were

provided by Biosolve B.V. (Valkenswaard, the Netherlands). Formic acid (98-100%, analytical

grade) and ammonia solution (32%, extra pure) were acquired from Merck (Darmstadt,

Germany). Ultrapure water was obtained from a Milli-Q Plus 185 water purification system

from Millipore (Billerica, MA, USA). Impurities, the API and P4NX99-D, the P4NX99 molecule

labeled with deuterium employed as the internal standard (IS), were all kindly provided by

the supporting pharmaceutical company.


Preparations of stock solutions of each single impurity and the API were divided into

three groups. This was done in order to prevent any peak distortion such as a retention time

shift or peak fronting and/or tailing due to different elution strengths between the injected

solution and the tested mobile phase. Group 1 was prepared using methanol (MeOH) as the

organic modifier. Solutions in Group 2 were made using acetonitrile (ACN), while in Group 3

an equal proportion of methanol and acetonitrile (MeOH/ACN) was used. Therefore, stock

solutions were prepared three times (i.e. one for each Group) by dissolving an appropriate

quantity of analytes in the dissolving solvent, a mixture of formic acid 0.1% and organic

modifier in the proportion 80/20 (v/v). The organic modifier was selected accordingly with

the Group description made above. All stock solutions were prepared daily and were diluted

using a dissolving solvent containing the organic modifier in the proportion of the tested

mobile phase to reach a concentration of 5 μg mL-1 for each impurity and for the API. The

relatively high concentration of these solutions was selected to ensure detection despite the

large number of ions simultaneously being recorded during the whole run time (i.e. all

impurities and the API).


108

Aged tablets (the pharmaceutical form involved in this study) and aged placebo tablets

(i.e. tablets from completed long term stability studies (36 months) and completed

accelerated stability studies (12 months) [1]) were kindly provided by the supporting

pharmaceutical company. Preparation of the pharmaceutical form was performed by a

generic extraction protocol. A validation step was performed on the two compounds of the

critical pair of monitored impurities, P4NX99 and P4FX98 in the presence of all the other

impurities and the API (see Supplementary data document). During the validation phase, the

calibration standards within the matrix and the validation standards were both prepared

taking into account placebo tablets and an appropriate quantity of P4MX01 (i.e. the quantity

corresponding to the mass of API contained in four tablets) in order to mimic real samples.

The P4MX01 used in this section of the study was a pure chemical free of its degradation

products.

2.3. Experiments

Experiments were performed on LC/MS equipment composed of: for the

chromatographic part, a Waters (Milford, MA, USA) sample manager 2777, a CTC Analytics AG

(Zwingen, Switzerland) Stack Cooler DW with a CTC Analytics AG Peltier thermostat allowing

cooling of samples at 10 °C, four Waters binary HPLC pumps 1525μ, and a Waters

temperature control module controlling a columns oven. The MS detector consisted of a

Waters Micromass single quadrupole (Quattro, Ultima/ZQ) equipped with a Micromass 4-way

Multiplexing Interface (MUX) in order to allow a 4-way analysis if necessary (Fig. 1). LC/MS

parameters that were not investigated during the development process (apart from the

columns description) are described in Table 1.

Fig. 1. Schematic representation of MUX LC/MS configuration used during the method development.

Column 1a and Column 1b represent two XBridge columns, while Column 2a and Column 2b represent the two

Inertsil columns. The specific configuration described above was used during Phase I.


109

Table 1 LC/MS conditions used during QbD optimization.

Columns used during optimization phase

1a and 1b Waters XBridge C18 2.1x150 mm (3.5 μm) Waters XBridge C18 guard column 2.1x10 mm (3.5 μm)

2a and 2b GL Sciences Inc. Inertsil ODS-3 2.1x150 mm (5 μm) GL Sciences Inc. Inertsil ODS-3 guard column 1.5x10 mm (3 μm)

Flow rate (μL min-1) 125

Injection volume (μL) 10

Molecular ions followed P4AX91 P4FX98 P4NX99 P4SX95 P4SX92 P4MX01

(m/z) 103 116 117 140 171 250

MS sources 4-ways electrospray ionization in positive mode (ES+)

Cone temperature (°C) 150

Capillary temperature (°C)

400

Nebulizer gas (L h-1) 50 (nitrogen)

Desolvation gas (L h-1) 700 (nitrogen)

Cone voltage (V) 22.0

Capillary voltage (kV) 3.0

Dwell time (ms) 50 (all SIR)

2.4. Optimization study

The optimization study was designed in two phases: (i) optimization of the method for

the determination of impurities and the API, (ii) optimization of the method taking into

account the aged matrix, which can contain unexpected degradation products leading to

multiple peaks in a specific SIM chromatogram (i.e. SIM chromatograms of impurities). During

the optimization phase, the responses evaluated were the retention times when the principal

Critical Quality Attribute (CQA) selected was the separation criterion (S) [17-19]. Once the

parameters (i.e. the Critical Process Parameters (CPPs)) whose variability is known to have an

impact on the CQAs were identified by a science-based process [9,10], a mixture model was

established for both DoEs. Each DoE was a D-optimal mixture design.

The responses measured on each chromatogram were the retention times at the

beginning ( tB

i ), apex ( tA

i ) and end ( tE

i ) of each peak i ∈ 1,...,P{ } , and the modeled responses

were transformations of these responses as follows: log(tj

i - t0

t0

), where tj

i represent the

measured retention times ( j ∈ B,A,E{ }) for each peak i, and t0

is the column dead time.


110

Multivariate multiple linear regression was used to account for the correlations between the

responses. Subsequently, a multivariate multiple linear regression model was fitted jointly for

all the responses.

))log(),log(),log(),...,log(),log(),(log(0

0

0

0

0

0

0

0

0

0

0

0

t

tt

t

tt

t

tt

t

tt

t

tt

t

tt P

E

P

A

P

B

i

E

i

A

i

B Y

The following model was applied:

Y=XB+E (1)

with εn, the nth line of E , assumed to follow a multivariate Normal distribution, ,

n = 1,…, N , with N representing the number of experiments. X is then the (N x F) centered

and reduced design matrix and B is the (F x M) matrix containing the F effects for each of

the M = 3 x P responses. Σ is the covariance matrix of the residuals.

In order to account for the variability of the parameters B and ε, a predictive density

of new predicted responses can be obtained using a Bayesian framework, considering the

non-informative prior distribution p(B,∑)= ∑-(M+1)/2

[19,20]. In this context, the predictive

posterior density of a new predicted set of responses at a new operating

condition x0 ∈ χ , is identified as a multivariate Student’s t distribution, defined as follows

),~( datay 0xΧ ~ ),)(1ˆ( 0

1

00

xXXxA

B x ,TM , (2)

where B̂ is the least squares estimate of B , )ˆ()ˆ(;)(ˆ 1 BXYBXYAYXXXB is a scale

matrix and ν = N − (M + F) + 1 represents the degrees of freedom.

Finally, the design space is defined formally as:

In other words, we are looking for a region of an experimental domain χ (often called

the knowledge space) where the expected probability that the CQAs are within specifications

Λ, is higher than a specified quality level π, given the model parameters θ, which include the

uncertainty estimated by the statistical model. Predictive probability is central when dealing

with concepts such as design space, as it allows us to quantify the guarantees and risks that

specifications will be met in the future runs of the analytical procedure, given the information

at hand. Specifications express the minimal satisfying quality that the experimenters want to

obtain. It should be noted that the T factor was fixed at 25 °C during Phase II.


111

2.5. Quality-by-Design approach

In the specific case of liquid chromatography, in-depth understanding and

identification of parameters affecting method performance reached by the QbD approach

allowed optimization of the separation and estimation of the method robustness over the

whole experimental domain [9-11]. This experimental domain was investigated with a

multidimensional grid search method [17]. CQAs and their associated prediction errors (the

distribution of S obtained by propagating the error using Monte Carlo simulations) were then

computed for each of the experimental conditions defined by the grid leading to the Design

Space where robust and risk-based optimal conditions can be found [15-23]. The Design

Space knowledge acquired during the development in Phase I was used to define the

experimental domain of Phase II, which constitutes a learning process.

2.6. Selected operating conditions

The selected operating condition consisted of a mobile phase composed of a mixture of

methanol and formic acid 0.1% adjusted to pH 4.00 (16/84, v/v) with an Inertsil ODS-3

column (5 μm, 2.1 mm i.d. x 150 mm) and an Inertsil ODS-3 guard column (3 μm, 1.5 mm i.d. x

10 mm) at a temperature of 25 °C. Flow rate and injection volume were kept at 125 μL min-1

and 10 μL, respectively, as during the development process. The LC/MS equipment

configuration was changed to a conventional ESI source (one channel configuration) with

parameters set as described in Table 1. Impurities were individually recorded with a dwell

time of 250 ms during a short time window centered on their respective retention time.

2.7. Software

The software RStudio v0.96, a free and open source Integrated Development

Environment (IDE) for R, was used to perform the retention time modeling with stepwise

multiple linear regressions, error propagation and the grid search method. Coding was

carried out with R 2.15.1. The e.noval software v3.0 (Arlenda, Liège, Belgium) was used to

compute the validation results of the analytical method as well as to obtain accuracy profiles.


112


The case study presented in this paper focused on an unexpected issue with

unidentified impurities appearing and increasing during the last stage of a long-term stability

study (SS). Fig. 2, showing the QbT approach (left), illustrates the traditional strategy still

widely used in developing stability-indicating methods and the one that was applied in the

case of the analytical method used in this routine SS. Following this QbT strategy, conditions

allowing a selective and/or specific determination of all API impurities are determined by a

“trial-and-error” methodology. The developed method is then tested on the pharmaceutical

form (PF) in order to ensure specificity among all compounds but also among potential

compounds extracted during the preparation of the pharmaceutical form. If this has not

happened, adjustments of the method are performed. At this point, impurities found in low

concentration in the API, even after an extensive stress test, could become undetectable once

in PF and could result in a lack of information on the specificity of the developed method.

Moreover, stress tests on the PF are still rarely performed, which also leads to a lack of

information on potential degradation products from the matrix and/or from interaction

between the matrix and the API. When the specificity of the method for all the addressed

compounds is verified, the validation phase is conducted and a verification of the robustness

is then performed, with or without the help of DoE. It has to be noted that this step in the QbT

approach only allows verification of the fact that a small perturbation in operating conditions

does not alter analytical performance. Under no circumstances does this approach lead to a

robust development of the method.

Stability studies, monitored by the developed method, can nonetheless lead to results

Out Of Specification (OOS) or Out Of Trend (OOT). This may arise from two major causes.

First, drug product instability could be the issue. This would lead to a reduction in the drug’s

shelf life, specific storage directives or even a change in the drug formulation (illustrated by

the dotted line on the left of Fig. 2). The second cause could be the inadequacy of the

developed method, leading to the need for re-adjustments in the method. Indeed, in the

particular case study presented here, unidentified impurities appeared during the last stage of

a long-term stability study carried out on the PF (T24 months and T36 months at 25 °C and at

60 % of relative humidity). These impurities gave an additional peak in the P4FX98 and

P4NX99 SIM chromatograms. These peaks co-eluted with the corresponding peaks in these

two impurities, leading to problems in the impurity assays and even to OOS and OOT results.

Consequently, the analysts have to decide whether to continue to adjust the method by QbT or

to acquire an in-depth understanding of the method using a Quality-by-Design strategy.


113

Fig. 2. Quality-by-Testing (QbT) approach versus Quality-by-Design (QbD).

3.1. Phase I: Robust conditions for the determination of the API and of impurities

The principal obstacle with the Quality-by-Testing strategy is that the approach does

not grant the understanding necessary in order to facilitate further adjustments to the

method when such issues occur. On the other hand, the Quality-by-Design (QbD) strategy

allows for an in-depth understanding of the developed method. Indeed, as described by ICH

guideline Q8(R2) [6], the QbD strategy is an optimization strategy combining Design of

Experiments (DoE) and Design Space (DS). In other words, information acquired by

performing DoE on CPPs is dealt with in order to compute CQAs with their associated

prediction error, leading then to a set of robust and risk-based optimal experimental

conditions. Within this set of conditions, analytical performances are guaranteed to be within


114

specifications fixed a priori, while the verification of robustness is no longer required. In this

case study, without any substantial understanding of how CPPs affected the chromatographic

separation, a QbD strategy was then initiated directly on the API and the impurities in order

to develop a stability-indicating method, as schematically presented at the top of Fig. 3.

Fig. 3. Details of the QbD strategy applied to the development of a stability indicating method.

Prior scientific knowledge based on the chemical structure of these compounds led to

some initial choices. The value of the pH parameter for the buffer part of the mobile phase

was fixed at 4.00, as an acidic mobile phase is highly recommended when an atmospheric

pressure ionization source is used in positive mode. Indeed, the impurities involved in the

critical pair (i.e. P4FX98 and P4NX99) have no acid/base characteristics. Moreover, some of

the studied impurities are sensitive at a higher pH. Taking into account the log P values

(ranging from -1.64 to -0.27, at 25 °C, as found on SciFinder®) for the impurities and the API


115

as well as the LC conditions of the original method, two slightly different columns bonding

with octadecyl silane groups (C18) were considered. Indeed, the API and the most prevalent

impurities (i.e. P4FX98 and P4NX99) can be regarded as weakly polar. The choice of

chromatographic columns was justified by the chemistry of both sorbents (C18 bonded

materials) allowing good retention for most of the organic compounds such as the molecules

involved in this study. This choice was also influenced by the differences in both

chromatographic columns in terms of geometrical and stationary phase characteristics, thus

leading to different selectivity possibilities required for the separation of P4FX98 and

P4NX99. Thus, binary or ternary mixtures of the mobile phase (mp), where organic modifiers

ranged from 10% to 45%, were studied. The working temperature (T) was extended as much

as possible with the equipment (T varied between 22 and 44 °C). In this context, a D-optimal

mixture design was built, as shown in Fig. 4A, in order to predict the chromatographic

behavior of each impurity as well as the API in this first part of the optimization study

(i.e. Phase I). A total of 20 experimental conditions (n = 22) were defined by this mixture

design. The central point (i.e. T = 33 °C, mp (%) = 18.8/18.8/62.4 (MeOH/ACN/buffer, v/v/v))

was independently repeated twice (i.e. carried out in triplicate) with the preparation of a new

buffer and a fresh mobile phase during the three days of experiments. Each experimental

condition was tested simultaneously with the two stationary phases in duplicate

(2x2 columns) using the MUX interface (see Fig. 1). As no significant difference was observed

between the replicates, data from the two ways of using the same column were combined.

The model, described in Eq. (1), involving linear and quadratic contributions of mobile

phase composition and temperature as well as their interactions, was established and

adjusted by a stepwise regression in order to simplify it and to suppress statically

non-significant effects. This developed model was built with a log transformation of retention

times (i.e. retention times at the beginning (tB), apex (tA) and end (tE) of peaks). In both

columns, agreement between predicted and observed responses for all the impurities was

very good. Indeed, all the impurities presented an Radj2 higher than 0.95. P4SX95 presented the

lowest Radj2 owing to its greater retention. Fig. 4B presents results obtained for the ODS-3

column. Using Monte-Carlo simulations from the prediction errors, the joint predictive

probabilities were calculated for both columns for selected CQAs: (i) the separation criterion

of the critical pair (SP4FX98-P4NX99), which has to be greater than 0.2 minutes, (ii) the retention

time of the API, which has to be greater than all the other compounds

(tB(P4MX01) > tE(all compounds)). A visual examination of slices at various temperatures of these two

three-dimensional probability surfaces (i.e. the probability that the CQAs will be within the

described acceptance intervals (λ)) revealed a larger DS for the Inertsil ODS-3 column,

regardless of the T factor. The DS obtained with Inertsil ODS-3 showed a good quality

prediction, as evidenced by the quality level (π) ranging from 0.65 to 0.85 for all probability

surfaces when considering the two selected CQAs. A larger DS obtained with this column


116

allows many more possibilities in terms of selectivity when the drug formulation was

considered during Phase II (see Fig. 3). The Inertsil ODS-3 column was then selected. The

systematic visual evaluation of slices at various temperatures by incremental steps of 1 °C

also showed that a lower temperature (T varies between 22 and 30 °C) led to a larger DS for

this column and by extension greater selectivity capabilities thereafter. Consequently, a

temperature of 25 °C was chosen, also taking into account practical reasons. Fig. 4C shows the

probability surface of the mixture design for a temperature of 25 °C obtained with the Inertsil

ODS-3 column.

Due to the knowledge acquired during Phase I, a second DoE was performed with a

reduced experimental domain (see blue lines in Fig. 4C). As highlighted in Fig. 3, an

understanding was gained of the analytical procedure regarding the chromatographic

behaviors of the API and the impurities and further development of this procedure can be

supported on the basis of this knowledge, which thus constitutes a learning process.

Fig. 4. (A) Conditions tested during Phase I at 33 °C and carried out on both columns in duplicate

(2x2 columns). Black dots represent the tested conditions at 33 °C. Red circles represent conditions tested at

22 °C and 44 °C. (B) Modeling results and corresponding residuals for Inertsil column involving a log

transformation of all retention times. Top: predicted vs. experimental tB, tA, tE; bottom: corresponding residual

plots, where P4AX91, P4FX98, P4NX99, P4SX92 and P4SX95 are represented by the colors dark blue, dark green,

light green, purple and brown, respectively. (C) Probability surface (i.e. P(CQAs>λ)) of the mixture design at

25 °C with Inertsil column. The DS (π = 70%) is defined by a dark line. Red circles represent the experimental

conditions for Phase II and blue lines define the tested area.

3.2. Phase II: Compliant stability-indicating method

The developed method needs to consider not only the impurities from API degradation

(addressed in Phase I), but also those from the matrix component of the drug formulation

(i.e. irrelevant interfering compounds, degradation products from the matrix or from an

API – matrix interaction) [24]. Hence, verification of the API DS needs to be performed with

the PF. If this step is unsuccessful, as it was in the case study presented, a second DoE is then

performed with a reduced experimental domain within the DS obtained in Phase I, as

illustrated at the bottom of Fig. 3. Red circles within blue lines, as shown in Fig. 4C, represent

experimental conditions tested during Phase II. In the present study, aged tablets were


117

utilized to perform the Phase II DoE in order to mimic unidentified impurities emerging at the

last stage of a long-term stability study. Indeed, such samples led to two additional peaks

(namely, P1 and P2) in the SIM chromatogram of P4NX99 (i.e. m/z: 117, chromatogram not

shown) and one additional peak (called P3) in the SIM chromatogram of P4FX98

(i.e. m/z: 116, chromatogram not shown). The reduced experimental domain was also wisely

selected in order to allow an elution of all the impurities (i.e. from the API stress test) within a

maximum of 25 minutes. The DoE was built as a D-optimal mixture design with

9 experimental conditions (n = 11) performed with the API, the impurities and prepared

within aged matrix. The central point (i.e. mρ (%) = 15.6/4.0/80.4 (MeOH/ACN/buffer,

v/v/v)) was independently repeated twice during this one-day study. As a reminder, the pH of

the buffer part of the mobile phase was fixed at 4.00 and the working temperature was set at

25 °C. Each experimental condition was tested simultaneously on four Inertsil ODS-3 columns

using the MUX interface. As the equivalence of the four channels of the MUX interface was

observed during Phase I, data from each column were analyzed together. The model,

described in the generic Eq. (1) for the D-optimal design, involving, this time, only linear and

quadratic contributions of mobile phase composition factors and their interactions, was once

more applied and adjusted by a stepwise regression in order to simplify it and to suppress

non statistically significant effects. The developed model, built with log transformation of

retention time, showed a good agreement between the predicted and observed responses for

P4SX95 and the compounds involved in critical separations (i.e. P4NX99, P4FX98, P1, P2 and

P3 for SIM chromatograms at m/z: 116 and 117), as presented in Fig. 5A. The Radj2 of all the

compounds considered in Phase II was found never to be below 0.99. The residuals for all

compounds fell within a [-0.6; 0.7] min interval. Independently of the procedure used to fit the

retention model, the joint predictive probabilities were calculated using Monte-Carlo

simulations from the prediction errors of a set of CQAs for which acceptance limits were fixed

as described below:

- SP4FX98-P4NX99 > 0.2 min (already guaranteed by working into the DS of Phase I),

- tB(P4MX01) > tE(all compounds) (already guaranteed by working into the DS of Phase I),

- SP1-P4NX99 > 0.2 min,

- SP4NX99-P2 > 0.2 min,

- SP4FX98-P3 > 0.2 min,

- tE(P4SX95) < 22.0 min.


118

Fig. 5. (A) Modeling results and corresponding residuals for the DoE for Phase II involving a log transformation

of all retention times. Top: predicted vs. experimental tB, tA, tE; bottom: corresponding residual plots, where

P4FX98, P4NX99, P4SX95 and P1, P2 and P3 are represented by the colors dark green, light green, brown, blue,

orange and red, respectively. (B) Probability surface (i.e. P(CQAs>λ)) of the mixture design at 25 °C at pH = 4.00

with Inertsil column involving aged tablets. The blue dot is the selected condition.

3.3. Definition of the DS and selection of operating condition

The computed probability surface, resulting from Phase II, is shown in Fig. 5B and

outlines two types of refined DS. The first (π minimal of 30%), namely DS 1, is defined by an

external dark line presenting a mixture of a mobile phase consisting of ACN, MeOH and buffer

proportions whose sum is equal to one and where these proportions (v/v/v) can range from 0

to 3.5, 11 to 20 and 79.5 to 86, respectively. By analogy, mobile phase proportions (v/v/v) in

the second DS, namely DS 2, can range from 0.5 to 2, 13 to 15.5 and 82.5 to 85, respectively.

Taking into account multiple constraints (i.e. CQAs) fixed to ensure selectivity with all

compounds in each SIM chromatogram and the assessment of predictive uncertainty, this

relatively low quality level is acceptable. However, the experimental conditions within each

DS all represented robust conditions for the evaluated CPPs. In this case study, the selection

of the working condition was made inside the largest DS (i.e. DS 1). A binary mixture with

MeOH as the mobile phase (rather than a ternary mixture) was selected in order to have a

simpler and robust operating condition for routine assays. Moreover, the use in this study of

an electrospray MS source in positive mode meant that it is more appropriate to use the

protic solvent methanol than ACN. This selected condition (the blue dot in Fig. 5B) is

identified by a mobile phase composed of a mixture of methanol and formic acid 0.1%

adjusted to pH 4.00 (16/84, v/v) with an Inertsil ODS-3 column (5 μm, 2.1 mm i.d. x 150 mm)

and an Inertsil ODS-3 guard column (3 μm, 1.5 mm i.d. x 10 mm) at a temperature of 25 °C.

Verification of the selected condition was made by a comparison (Fig. 6) between the

predicted SIM chromatograms (blue) and the observed SIM chromatograms (red) in order to

ensure its separation capability before use in routine assays. This verification was performed

on the same LC/MS equipment but with a change in the MUX configuration being made using


119

a conventional ESI source (one channel configuration). The test solution contained all the

compounds at an individual concentration of 50 ng mL-1 and was prepared within aged tablets

in order to mimic a potential real sample. This test solution was freshly prepared and injected

twice over a period of three days, leading, each time, to the same results. Considering the

computed uncertainty of the prediction for each impurity (shaded gray on predicted

chromatograms, Fig. 6), the comparison between predicted and observed chromatograms

seems very good. A coefficient of determination (R2) was calculated for the linear relationship

between all the retention times (Tbegin, Tapex, Tend) of all the impurities in predicted versus

observed chromatograms. This coefficient of determination equal to 0.998 shows a good level

of agreement between predicted and observed chromatograms. Separations between

impurities P4FX98 and P4NX99 as well as between P4NX99 and unidentified compounds

from the drug formulation (namely, P1 and P2) were successfully obtained at a Single Ion

Reaction (SIR) of 117. Moreover, the separation between P4FX98 and the unidentified

compound (namely, P3) was also completed at a SIR of 116. The API and the IS were also

added into the test solution at a concentration of 250 ng mL-1 and 50 ng mL-1, respectively.

Fig. 6. Left-hand: Predicted SIM chromatograms with predictive uncertainty (shaded gray area) for the selected

condition (ODS-3 column, MeOH/buffer pH: 4.0, (16/84, v/v), T = 25 °C); right-hand: Observed SIM

chromatograms for the selected condition. Peaks: a: P4AX91, b: P4FX98, c: P4NX99, d: P4SX95, e: P4SX92 and P1,

P2, P3: compounds from aged tablets.

3.4. Control strategy

Subsequent steps of the QbD strategy are rather similar to the QbT approach except

that the verification of the robustness of the method is unnecessary (see right hand side of

Fig. 2). A Control Strategy (CS) is therefore recommended instead, as requested by

pharmaceutical guidelines [6]. A control strategy is defined in the ICH guideline Q10 [8] as “a

planned set of controls, derived from current product and process understanding, that assures

process performance and product quality”. Typically, a CS is employed during a routine

application such as a System Suitability Test (SST) in order to demonstrate that the analytical


120

procedure still meets the CQAs defined during QbD development [25,26]. A CS also allows a

continuous verification of the adequacy of the method. In this particular presented case, the

criterion S between P4FX98 and P4NX99 (or the resolution between both impurities) inside

the SIM chromatogram at m/z: 117 can be selected. The criterion S must be higher than

0 minute. It must be noted that more than one criterion may be necessary in order to assess

the control strategy for a complex situation. An interesting aspect of a CS is its capacity to

promptly highlight an issue with the analytical procedure that may occur during stability

studies even if the stability-indicating capabilities of the method has been extensively checked

during the development process. In this situation, the analyst will be able to easily optimize

the analytical procedure in the light of new information by adding a layer onto the actual

Design Space without losing the knowledge of the method previously acquired (see Fig. 3).

This clearly constitutes a learning process.

3.5. Method validation

As an example, an approach using accuracy profiles based on statistical tolerance

intervals was applied. The aim was to evaluate the reliability of the results generated by the

developed LC/ESI-MS method when applied to the selected working conditions for the

quantification of P4FX98 and P4NX99, the impurities involved in the critical pair [27,28].

Accuracy profiles obtained at the end of the validation phase for P4FX98 and P4NX99 are

shown in Fig. 7A and 7B, respectively. A detailed description of this validation, including both

the prepared solutions and all the validation results, is presented in the Supplementary data

document.

Fig. 7. (A) Accuracy profile obtained for P4FX98. The plain line is the relative bias, the dashed lines are the 95%

β-expectation tolerance limits and the dotted curves represent the acceptance limits (30% at LLOQ and 15%

elsewhere). (B) Accuracy profile obtained for P4NX99. The solid line is the relative bias, the dashed lines are the

95% β-expectation tolerance limits and the dotted curves represent the acceptance limits (30% at LLOQ and

15% elsewhere).


121

4. Conclusion

The understanding of the method is a major concern when developing a

stability-indicating method and even more so when dealing with impurity assays from

complex matrices. In the presented case study, a Quality-by-Design approach was applied in

order to optimize a method. Indeed, optimization of a routinely used method was found to be

necessary in order to resolve an analytical issue occurring at the last stage of a long-term

stability study whereby unexpected impurities perturbed the monitoring of characterized

impurities. In the first phase, robust chromatographic conditions were found, allowing the

determination of the API and its impurities revealed by stress testing. The design space

established during this phase was then explored in order to find the working conditions

under which the specificity between impurities and the pharmaceutical form could be

verified. This strategy led to the determination of a refined DS. Within this area of robustness,

LC selectivity between the API and all the degradation products, even impurities from the

aged PF, was guaranteed. Furthermore, this stability-indicating method was fully validated in

relation to the selected working condition. The developed method was also subsequently used

in routine analysis, demonstrating the usefulness of the QbD approach for the development of

a stability-indicating method. The QbD methodology followed in this paper could be

advantageously applied to the development and improvement of any stability-indicating

method.

Acknowledgments

Research grants from the Walloon Project PPP (Convention OPTIMAL DS N°917007) to

P. Lebrun and the Walloon Project CWALITY (Convention iGUARANTEE N°1217614) to

P. Lebrun and E. Rozet are gratefully acknowledged.


122

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124

Supplementary data

A. Method validation

A.1. Preparation of validation standard solutions

The two compounds of the critical pair of characterized impurities, P4NX99 and

P4FX98, were presented in order to demonstrate the reliability of the developed method in

the presence of all impurities. The validation step involved the use of aged placebo tablets to

prepare the validation standards within the matrix in order to mimic samples that could be

analyzed at the end of a stability study. Stock solutions were prepared as described for group

1 (MeOH), providing five concentration levels for P4NX99 and P4FX98 covering a range from

5 ng mL-1 to 100 ng mL-1 and from 10 ng mL-1 to 200 ng mL-1 (injected concentrations) in all

standards, respectively. Two types of calibration standard were prepared daily, one with pure

chemicals (referred to as the calibration standard without matrix) and one other with an aged

placebo matrix (referred to as the calibration standard within matrix). The third type of

standard, the validation standard, was also prepared daily. Each sample was spiked with the

internal standard in order to obtain a concentration of 25 ng mL-1 of P4NX99-D. Each

calibration standard (without and within matrix) and each validation standard were analyzed

independently in duplicate over a period of four validation days.

A.2. Validation results

Once robust working conditions had been selected for the quantification of P4FX98

and P4NX99 (the impurities constituting the critical pair), validation of the selected working

condition was undertaken. This involved applying an approach using accuracy profiles based

on statistical tolerance intervals in order to evaluate the reliability of the results generated by

the developed LC/ESI-MS method.

The tolerance interval used was a “β-expectation tolerance interval”. This is a

predictive methodology, as it defines an interval in which it is expected that each future result

will fall with a defined probability (β). In this approach, the tolerance interval is computed for

each validation standard concentration level, using their estimated intermediate precision,

standard deviation and bias. By joining the upper tolerance limits on the one hand and the

lower tolerance limits on the other, it defines an accuracy profile. As long as this profile stays

within the acceptance limits set according either to the needs of the final user or to regulatory

requirements, the method can be considered as valid. Indeed, this approach guarantees that

each future result will be included in the a priori set acceptance limits with at least a

probability β (e.g. 0.95 or 95%). The concept of accuracy profile was also used to select the

most appropriate regression model for calibration, in order to determine the lower limit of

quantitation (LLOQ) and the range over which the method can be considered as valid. The


125

acceptance limits were set at ± 15% over the whole validated range except at the LLOQ where

the acceptance limits were fixed at ± 30%. Probability β was set at 95%.

A.2.1. Selectivity

The selectivity and robustness of selectivity were assessed using the Quality by Design

concept during the development of the method.

A.2.2. Analysis of the response functions

In order to find the most appropriate standard curve, several response functions were

fitted, namely the weighted (1/X) and (1/X2) quadratic functions and the weighted (1/X) and

(1/X2) linear functions. Several transformations of linear functions such as the logarithm and

square root transformation were also tested. In addition, linear regression through 0 fitted

with a selected tested concentration was also investigated as a calibration model. The

concentrations of the validation standards were back-calculated from each response function.

These concentrations were obtained by means of calibration standards without and within

the matrix. The aim was to determine, by concentration level, the mean relative bias and the

upper and lower β-expectation tolerance limits at 95% level by introducing the estimation of

the standard deviation for intermediate precision. From these data, accuracy profiles were

plotted in order to select the most suitable regression model for the intended use of the

analytical method. The acceptance limits were set at ± 30% for the lower level of tested

concentrations (5 ng mL-1 and 10 ng mL-1 for P4NX99 and P4FX98, respectively) and at ± 15%

for the remainder of the range of concentrations.

Four response functions demonstrated the capability of the method to accurately

quantify P4FX98 over the whole concentration range considered for this impurity, since the

tolerance intervals were completely contained within the acceptance limits. These functions

were the linear regression after square root transformation, the weighted (1/X) and (1/X2)

linear regression, and the linear regression, all obtained from the calibration standard

prepared within the matrix. As the linear regression function provided the lowest level of bias

and imprecision, it was selected as the final calibration model. The results obtained by

applying this regression model are presented in Table S-1 for each day of analysis, while the

accuracy profile is shown in Figure 7A. In the case of P4NX99, only one response function

allowed the demonstration of the capability of the method to quantify this impurity over the

whole concentration range considered, since the tolerance intervals were completely

contained within the acceptance limits. The calibration model was the linear regression

obtained from the calibration standard prepared without the matrix and using only the

highest concentration level of P4NX99 (100 ng mL-1). As this function also provided a low

level of bias and imprecision, it was selected as the standard curve. The results obtained by

applying this regression model are presented in Table S-2 for each day of analysis, while the

accuracy profile in Figure 7B.


126

Table S-1 Results of the validation of the LC/ESI-MS method for the impurity P4FX98 in aged pharmaceuticals

formulation containing the API P4MX01.


Linear regression model (within matrix); calibration range (m = 5): 10 – 200 ng/ml


10 0.46

20 0.91

50 -0.65

100 -0.10

200 0.41


10 7.60 7.60

20 4.02 4.02

50 4.14 4.14

100 4.46 4.46

200 2.86 3.32


10 [−18.69; 19.61]

20 [−9.21; 11.03]

50 [−11.08; 9.79]

100 [−11.34; 11.13]

200 [−9.64; 10.45]


Range (ng/ml) [10.15; 202.90]

Slope 1.00

Intercept -0.16

r2 0.9976

LOD (ng/ml) 3.07

LOQ (ng/ml) 10.15

p: number of days of analysis; n: number of repetitions per day of analysis; m: number of P4FX98 concentration

levels.


127

Table S-2 Results of the validation of the LC/ESI-MS method for the impurity P4NX99 in aged

pharmaceuticals formulation containing the API P4MX01.


Linear regression through 0 with the level 5 only (without matrix); calibration range (m = 5):

5 – 100 ng/ml


5 7.28

10 -0.99

25 0.99

50 1.25

100 0.88


5 3.10 3.10

10 3.50 3.50

25 2.81 2.84

50 2.36 3.72

100 1.48 2.00


5 [−1.43; 15.98]

10 [−10.84; 8.86]

25 [−7.04; 9.03]

50 [−12.05; 14.55]

100 [−5.69; 7.44]


Range (ng/ml) [5.05; 101.00]

Slope 1.01

Intercept 0.04

r2 0.9990

LOD (ng/ml) 1.53

LOQ (ng/ml) 5.05

p: number of days of analysis; n: number of repetitions per day of analysis; m: number of P4NX99 concentration

levels.


128

A.2.3. Trueness & Precision

Trueness expressed in terms of relative bias (%) was assessed from the validation

standards at 5 concentration levels for P4FX98 and P4NX99, as can be seen in Table S-1 and

Table S-2, respectively. According to regulatory requirements, trueness was acceptable for

both impurities, since their recovery values all fell within the 98.0 – 102.0% interval,

corresponding to a relative bias lower than 2% for all concentration levels except at the LLOQ

for P4NX99. At the LLOQ of this impurity, the recovery was equal to 107.3%. Although, this

value was higher than for the other concentration levels, the method still provided accurate

and reliable results. The precision of the method was then determined by computing the

relative standard deviation (RSD) for repeatability and time-different intermediate precision

at each concentration level of the validation standards for each impurity. The RSD values

presented in Table S-1 (P4FX98) and Table S-2 (P4NX99) were acceptable with regard to

regulatory requirements, with a maximum intermediate precision RSD of 7.6% for the

10.15 ng mL-1 concentration level of P4FX98.

A.2.4. Accuracy, LOQ, Range and LOD


errors, related to the test result. As shown in Table S-1 (P4FX98) and Table S-2 (P4NX99), the

upper and lower β-expectation tolerance limits (%) did not exceed the acceptance limits set at

± 30% at the LLOQ and at ± 15% for the remainder of the validated range. Consequently, the

method can be considered as being accurate over the whole concentration range investigated.

For P4FX98 and P4NX99, respectively, the lower limit of quantitation (LLOQ) was

10.15 ng mL-1 and 5.05 ng mL-1. The limit of detection (LOD) was estimated using the mean

intercept of the calibration model and the residual variance of the regression. The LOD was

evaluated at 3.07 ng mL-1 and 1.53 ng mL-1.

A.2.5. Linearity of the method

The linearity of the method was also demonstrated for all the impurities. Both

presented impurities showed a slope very close to 1 and an intercept close to 0 with an

R2 of 0.9990 and 0.9976 for P4FX98 and P4NX99, respectively. These results illustrate the

good linearity of the results generated by the developed method.

C. Hubert, S. Houari, E. Rozet, P. Lebrun, Ph. Hubert, Towards a full integration of optimization and validation phases: An Analytical-Quality-by-Design approach, Journal of Chromatography A, 1395 (2015) 88.

Chapitre III

Validation de l’espace opérationnel : de l’optimisation à la validation en une seule étape

Section III.4

Section III.4 : « DoE-DS quantitatif »

131

Avant-propos

Ainsi que nous l’avons clairement montré, l’application de la stratégie « QbD » présente

deux avantages majeurs. Tout d’abord, une meilleure connaissance des paramètres

influençant la méthode. Ensuite, une bonne connaissance de cette dernière, permettant ainsi

d’envisager son amélioration continue au cours de son utilisation en routine. En effet, nous

disposons d’un espace de conception, le « DS », à l’intérieur duquel le risque lié aux aspects

qualitatifs de la méthode est maîtrisé. Par conséquent, la validation par l’intermédiaire du

profil d’exactitude pour chacune des conditions opératoires comprises dans ce « DS » est

envisageable. L’exemple abordé dans la section précédente nous a d’ailleurs permis d’en faire

la démonstration pour la condition opératoire sélectionnée pour la routine.

Cependant, les avantages qu’offre cette stratégie peuvent induire un coût non

négligeable. En effet, une méconnaissance des objectifs ou une mauvaise appréhension de la

complexité de la méthode à développer peuvent aboutir à l’établissement d’un plan

d’expériences peu ou pas optimal. L’absence d’une étude préliminaire telle qu’une étude de

screening peut, dans certains cas, s’avérer également préjudiciable dans le cadre d’une

approche « QbD ». Quoiqu’il en soit, il est tout de même important de souligner que ce coût

n’est pas forcément plus important que celui d’une approche de type « QbT ». Suivant ce

constat, il semble dès lors opportun de mettre à profit au maximum les informations obtenues

lors de l’étape d’optimisation. Il pourrait même être intéressant d’agrémenter les

informations qualitatives obtenues par des informations quantitatives. Considérant cette

réflexion, une question s’impose : Est-il possible de combiner les étapes d’optimisation et de

validation en une seule ?

C’est dans cette perspective que nous présentons dans cette section une stratégie

novatrice issue de la maturation du concept « QbD » permettant la combinaison de l’étape

d’optimisation et de l’étape de validation. Afin d’éprouver cette hypothèse, l’exemple

sélectionné reprend l’optimisation de la méthode développée par le concept « QbT » de la

Section III.2 de ce chapitre.


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Abstract

When using an analytical method, defining an analytical target profile (ATP) focused on

quantitative performance represents a key input, and this will drive the method development

process. In this context, two case studies were selected in order to demonstrate the potential

of a quality-by-design (QbD) strategy when applied to two specific phases of the method

lifecycle: the pre-validation study and the validation step. The first case study focused on the

improvement of a liquid chromatography (LC) coupled to mass spectrometry (MS)

stability-indicating method by the means of the QbD concept. The design of experiments

(DoE) conducted during the optimization step (i.e. determination of the qualitative design

space (DS)) was performed a posteriori. Additional experiments were performed in order to

simultaneously conduct the pre-validation study to assist in defining the DoE to be conducted

during the formal validation step. This predicted protocol was compared to the one used

during the formal validation. A second case study based on the LC/MS-MS determination of

glucosamine and galactosamine in human plasma was considered in order to illustrate an

innovative strategy allowing the QbD methodology to be incorporated during the validation

phase. An operational space, defined by the qualitative DS, was considered during the

validation process rather than a specific set of working conditions as conventionally

performed. Results of all the validation parameters conventionally studied were compared to

those obtained with this innovative approach for glucosamine and galactosamine. Using this

strategy, qualitative and quantitative information were obtained. Consequently, an analyst

using this approach would be able to select with great confidence several working conditions

within the operational space rather than a given condition for the routine use of the method.

This innovative strategy combines both a learning process and a thorough assessment of the

risk involved.


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1. Introduction

Numerous reference documents such as the International Conference on

Harmonisation (ICH) guidelines [1-4] and the U.S. Pharmacopeia (USP) recommendations [5-

7] deal with the method development process and the topic of validation. All of these

documents emphasize the need to manage risk during the entire method lifecycle. As already

widely discussed in the scientific literature [8-13], applying the quality-by-design (QbD)

concept to analytical methods ensures a controlled risk-based development of a method

where quality assurance will be guaranteed [1]. Nowadays, the QbD concept is mainly applied

to the development step of the method as an alternative approach to the quality-by-testing

methodology, as discussed by Hubert et al. [14]. However, the QbD strategy encompasses

more than this single step of the method lifecycle. For instance, the control strategy forms

part of this strategy, since this is recommended to ensure optimal method performance [4],

although the robustness of the method is assessed separately by the determination of the

analytical method design space (DS). This control strategy needs to be implemented in order

to consolidate the understanding of the method and to allow its continuous improvement

[15]. In the same way, the validation step must be part of the continuous evaluation of the

analytical method rather than being an isolated activity. A similar approach is recommended

by the FDA for process validation, and this has been illustrated by Katz and Campbell [16].

In this context, defining the objectives of the method by means of an analytical target

profile (ATP) [17] is the major first step of the QbD methodology. As established by a stimuli

article of the USP Statistics Expert Committee [18], an ATP for an analytical procedure may be

defined, for example, as follows: “The procedure should be able to quantify [analytes] in the

presence of [X, Y, Z] over a range of A% to B% of the nominal concentration with an accuracy

and uncertainty ensuring the reportable results fall within ±C% of the true value with quantified

guarantees”. Taking this definition into account, it therefore seems essential that the ATP be

established before starting to develop the procedure. This ensures the definition in advance of

the required level of performance given the user requirements. Consequently, the ATP should

remain the reference concept throughout the method lifecycle.

The goals of the present study are set within this context. The capability of the

procedure to meet the specifications needs to be continuously reconsidered throughout the

method lifecycle. As a first stage towards a full integration of the optimization and validation

phases, the power of the QbD step using the design of experiments (DoE) was enhanced by

performing additional experiments in order to obtain quantitative data leading to the

gathering of valuable pre-validation information. In order to illustrate the feasibility of this

innovative approach, a case study already presented elsewhere [14] is selected. This research

was centered on the optimization of a liquid chromatography (LC) coupled to mass

spectrometry (MS) stability-indicating method using a QbD methodology. The study was

undertaken in order to identify the operational conditions, i.e. the design space (DS), that


134

would ensure good results in the future in terms of the separation of the two analytes as well

as protection from interfering peaks caused by the presence of impurities and/or co-extracted

pharmaceutical matrix compounds. Using an a posteriori study, conducted as part of the DoE

implemented during the QbD optimization step, the demonstration is made that this

particular step of the method lifecycle could also be used to estimate the calibration model,

the accuracy, and the limits of detection/quantification, as well as assisting in defining the

DoE to be applied during the formal validation step.

From this quantitative information regarding the overall studied domain, a formal

validation of a single set of working conditions could be considered. However, when

considering the whole lifecycle of an analytical method, two major factors favor the

continuous improvement of the method. First, in-study results often highlight surprising

discoveries (whether “good” or “bad”) about the procedure. Second, the product itself is

generally subject to modification or alteration (i.e. minor modifications in the formulation of

the product, testing of the product following a new type of stress test, specification changes,

etc.). In these cases, a return to the procedure development stage should be encouraged, as

facilitated by the implementation of a QbD approach. However, any time that the procedure

changes, the need to partially or completely validate the adapted method should be

considered [7]. Otherwise, a statistical demonstration of the method equivalence should be

implemented. [19,20]. Taking this into account, the benefits of extending the QbD concept to

the validation stage of the method would seem to be highly relevant. Indeed, this new strategy

could allow the evaluation of the quantitative performance of the method within the

qualitative DS. Within this high quality operational space, the quantitative robustness of the

method would be evaluated for multiple operational conditions rather than for one single set

of conditions, as usually occurs during the validation step. The evaluation of the proposed

strategy forms the second part of the present study. For this purpose, a case study involving a

method previously developed by the quality-by-testing approach is selected. An optimization

of this method was required for two reasons. First, an improvement of the separation and

detection conditions was required in order to eliminate the on-column mutarotation

phenomenon observed with amino sugars [21]. Second, a change in the biological matrix used

(i.e. from dog plasma to human plasma) as well as a change of equipment was needed [22]


135

2. Experimental


Methanol (MeOH; HPLC gradient grade) was purchased from J.T. Baker (Deventer, the

Netherlands). Water (ULC/MS grade), acetonitrile (ACN; HPLC supra-gradient grade) and

formic acid (ULC/MS grade) were provided by Biosolve B.V. (Valkenswaard, the Netherlands).

Ammonia solution (32%, extra pure), ammonium acetate (AnalaR, Normapur) and

ammonium bicarbonate (Rectapur) were acquired from VWR International (Darmstadt,

Germany). Ultrapure water was obtained from a Milli-Q Plus 185 water purification system

from Millipore (Billerica, MA, USA).

Chemicals (under confidential agreement) and reagents involved in the pre-validation

study (i.e. Part I of the present study) were described in a previous study [14].

D-(+)-Glucosamine hydrochloride (99%+) and D-(+)-galactosamine hydrochloride

(99%+) were purchased from Sigma (St. Louis, MO, USA). D-(13C6)-Glucosamine

hydrochloride (99 atom-% 13C), used as the internal standard, was provided by Omicron

Biochemicals INC. (South Bend, IN, USA).

Pooled human plasma of mixed gender origin (50% male donors / 50% female donors)

was obtained from Sera Laboratories International Ltd. (Haywards Heath, United Kingdom).


Within the framework of a new predictive approach applied to the pre-validation study

phase of the method lifecycle (i.e. Part I of the present study), an a posteriori study was

conducted based on previous research where the qualitative performance of this method had

already been demonstrated [14]. Since the quantitative performance of the method can be

affected only by the presence of unexpected compounds from aged placebo tablets (the

pharmaceutical form involved in the study), which interfere with both major impurities

(P4NX99, P4FX98 and P4NX99-D, see [14] for details), samples were prepared using only

these compounds. Stock solutions were prepared by dissolving an appropriate quantity of

analytes in a mixture of formic acid 0.1% and MeOH in the proportions 80/20 (v/v). Two

kinds of standard were then prepared by making suitable simultaneous dilutions of both

stock solutions in the presence of the extracted placebo pharmaceutical form, in order to

mimic real samples. The first standard contained a high concentration of P4NX99 and a low

concentration of P4FX98 (100 and 50 ng mL-1 of injected concentrations, respectively), while

the second standard was prepared with the opposite levels of concentration (25 and

200 ng mL-1 of injected concentrations, respectively). These solutions were prepared

independently and in triplicate.


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Another previous study [22] was also selected as a case study in order to illustrate the

applicability of the QbD methodology throughout the method lifecycle and, in particular,

during the validation phase (i.e. Part II of the present study). The screening part of the QbD

development was conducted on a mixture of pure glucosamine and galactosamine chemicals

at a concentration of 1000 ng mL-1 in order to ensure detection despite the use of a multiplex

interface. During the subsequent phases of the QbD development, stock solutions were

prepared and mixed together in plasma at appropriate concentration levels (see below).

Prepared plasma samples were vortex-mixed for several seconds in order to achieve

homogenization. A 100 μL aliquot of the plasma sample was loaded onto a Phree phospholipid

removal cartridge acquired from Phenomenex (Torrance, CA, USA). A 300 μL of a mixture of

ACN with 1% formic acid were then added. Finally, vacuum was applied at 2-7 in. Hg until the

filtrate could be collected.

2.3. Experiments

Experiments were performed on two kinds of liquid chromatography (LC) coupled to

mass spectrometer (MS) systems. The first system involved a high performance liquid

chromatography (HPLC) system composed as follows: a Waters (Milford, MA, USA) sample

manager 2777, a CTC Analytics AG (Zwingen, Switzerland) Stack Cooler DW with a CTC

Analytics AG Peltier thermostat allowing samples to be cooled at 10 °C, four Waters binary

HPLC pumps 1525μ and a Waters temperature control module controlling a column oven.

This HPLC system was coupled to a Waters MicroMass single quadrupole mass spectrometer

(Quattro, Ultima/ZQ) equipped, when necessary, with a MicroMass 4-way multiplex interface

(MXI). The second system was composed of a Waters “I-Class” ultra high performance liquid

chromatograph (UPLC) coupled with a Waters XEVO TQ-S tandem mass spectrometer

(MS-MS). The HPLC/MS system was involved in the study of the new predictive approach for

the pre-validation study (Part I of the present study) and during the screening phase of the

QbD method development for the determination of glucosamine and galactosamine in human

plasma (Part II of the present study). The UPLC/MS-MS system, on the other hand, was used

during the optimization phase of Part II and during the quantitative design space

determination study.


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The LC-MS conditions used during the experiments of the pre-validation study,

described in the first part of this study, were fixed as defined under the QbD optimization

study described in [14]. Four columns were simultaneously tested, using LC/MXI-MS

equipment [14], throughout the screening study that took place during the second part of the

present study. These were:

- Grace Alltech (Columbia, MD, USA) Alltima HP HILIC 2.1x150 mm (3.0 μm).

- Waters XBridge Amide 2.1x150 mm (3.5 μm).

- Waters XBridge BEH HILIC 2.1x150 mm (3.5 μm).

- ThermoFisher Scientific (Waltham, MA, USA) Syncronis HILIC 2.1x150 mm (5.0 μm).

These columns were tested in order to select the best one for improving the

chromatographic performance for a selective determination of glucosamine and

galactosamine, in the shortest possible time, without causing the on-column mutarotation of

each epimer. Each column was also available in a UPLC geometry in order to conduct the

optimization phase of the QbD development with the selected column using the UPLC/MS-MS

equipment. The liquid chromatography and mass spectrometry conditions for the

experiments, either fixed a priori based on scientific knowledge or investigated during the

screening design as well as during the optimization phase and the quantitative design space

determination, are described in Table 1.

2.4. A predictive approach developed for the pre-validation study

The responses obtained from the performance of the adapted DoE for P4FX98 and

P4NX99 were modeled in relation to the experimental factors of methanol, acetonitrile, and

the buffer, as well as the concentrations of P4FX98 and of P4NX99, resulting in a multivariate

calibration function:

Y = β0 + β1 × MeOH + β2 × ACN + β3 × buffer + β4 × concentration + β5 × MeOH × ACN

+ β6 × concentration × MeOH + β7 × concentration × ACN + β8 × concentration × buffer + ε

From this model, on a fine grid covering the experimental domain, responses for

P4FX98 and P4NX99 were then simulated a large number of times (i.e. 10,000), for both the

simulated calibration standards and the simulated validation standards. Different numbers of

series (or runs) and replicates per series were tested to assess the predictive ability of the

analytical procedure to be validated. Simulated results were then computed over the grid of

the experimental domain for each combination of series and replicates per series. The

probability of obtaining results within ±15% of the nominal concentration was also

computed.


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Table 1 LC and MS conditions, a priori fixed or investigated, during the screening design as well as

during the optimization phase and quantitative Design Space determination.

Screening Design

(HPLC/MS)

Optimization design

(UPLC/MS-MS)

Quantitative DS

determination

(UPLC/MS-MS)

Type of DoE conducted Fractional Factorial

Design

Central Composite

Design

Custom Central

Composite

Design

ACN percentage (%)

(binary mixture with buffer) 65 – 90 80 – 90 83.5 – 88.5

Buffer concentration (mM) 10 – 50 150 150

pH of mobile phase 3 – 7.5 5 – 10 5.25 – 6.75

Column temperature (°C) 25 25 – 75 50

GluN concentration (ng mL-1) 1000 50 – 500 25 – 500

GalN concentration (ng mL-1) 2000 200 – 1000 200 – 1000

GluN-13C6 concentration (ng mL-1) NA 250 500

Flow rate (μL min-1) 250 300 300

Injection volume (μL) 10 10 10

MS or MS-MS mode GluN and GalN (m/z) 180 180.2 162.2 180.2 162.2

MS or MS-MS mode GluN-13C6 (m/z) NA 186.2 168.2 186.2 168.2

MS source and mode ESI+ ESI+ ESI+

Cone temperature (°C) 100 150 150

Capillary temperature (°C) 400 500 500

Nebulizer gas (L h-1) 100 150 150

Desolvation gas (L h-1) 500 1000 1000

Cone voltage (V) 18 25 25

Capillary voltage (kV) 3.00 3.50 3.50

Source offset (V) NA 60.0 60.0

Collision gas flow rate (mL min-1) NA 0.25 0.25

Nebulizer gas flow (bar) NA 7.00 7.00

MS-MS mode collision energy (eV) NA 7.00 7.00

Dwell time for GluN and GalN (ms) 125 250 250

Dwell time for GluN-13C6 (ms) NA 30 30

NA: Not Applicable; GluN: glucosamine; GalN: galactosamine; GluN-13C6: internal standard

2.5. Optimization study for the selective determination of glucosamine and

galactosamine in human plasma

The determination of the qualitative performance required for the selective

determination of glucosamine and galactosamine (i.e. epimeric compounds) in human plasma

was performed following the QbD approach. This approach, which has been well described in

the scientific literature [23-25], was implemented, taking into account the separation of

glucosamine and galactosamine, as well as some resulting extracted compounds from the

human plasma matrix. The selected responses were the retention times of these compounds

recorded in the Multiple Reaction Monitoring mode at a mass transition (m/z ratio) of


139

180/162. The mass transition (m/z) used for the internal standard was 186/168. In the

present analytical quality-by-design study, the separation criterion (S) was considered as the

most relevant critical quality attribute (CQA). It should be noted that, from ICHQ8 reference

document point of view, this definition of the CQA is slightly different. However, from an

analytical point of view, all the characteristics involved in the optimization of the method can

be considered as a CQA. This is the case of the separation criterion S in the present paper that

must be within an appropriate limit to ensure the desired method quality. Indeed, without an

appropriate separation any quantitative analysis could be performed for that quality purpose.

A first screening DoE was performed for the selection of the column and the influent critical

method parameters (CMPs), allowing the determination of both amino sugars while avoiding

the on-column mutarotation phenomenon. Following this, a central composite design, with

the ACN percentage in the mobile phase (X.ACN) and pH (pH) as factors, was conducted. Based

on the current scientific knowledge of the influence of the temperature factor (T), this

parameter was manually added to the optimization DoE, and was extended as far as possible

within the capabilities of the equipment being used, leading to a custom central composite

design with a total of 13 experimental conditions (n = 15).

The responses measured on each chromatogram were the retention times at the

beginning, apex and end. The methodology, applied in order to calculate the DS based on the

predictive responses and their associated prediction errors, was the same as that explained in

previous papers [14,25,26]. In the present case, the following model was applied:

Y=XB+E, (1)

with εn, the nth line of E , assumed to follow a multivariate Normal distribution, ,

n = 1,…, N , with N representing the number of experiments. X is then the (N x F) centered

and reduced design matrix and B is the (F x M) matrix containing the F effects for each of

the M = 3 x P responses. Σ is the covariance matrix of the residuals.

2.6. A quality-by-design approach for a quantitative design space determination

The responses obtained from implementing the DoE for glucosamine and

galactosamine were modeled in relation to the experimental factors pH and acetonitrile, as

well as the concentrations of glucosamine and galactosamine, resulting in a multivariate

calibration function:

Y = β0 + β1 × pH + β2 × ACN + β3 × concentration + β4 × pH × ACN

+ β5 × concentration × pH + β6 × concentration × ACN + ε


140

From this model, on a fine grid covering the experimental domain, responses for

glucosamine and galactosamine were then simulated a large number of times (i.e. 10,000) for

both the simulated calibration standards and the simulated validation standards. Simulated

results were then computed over the grid of the experimental domain and the predictive

probability of obtaining results within ±15% of the nominal concentration was computed.

2.7. Software

Coding was carried out with the R 2.15.1 software. The e.noval software v3.0 (Arlenda,

Liège, Belgium) was used to compute the validation results of the analytical method and to

obtain the accuracy profiles for the conventional approach to the validation step in order to

quantify glucosamine and galactosamine in human plasma.


141


Scientists traditionally consider all the steps of the method lifecycle as a series of

stand-alone steps. Although the QbD approach is increasingly being applied nowadays, the

pre-validation and validation studies are usually performed separately from this strategy. In

this way, knowledge obtained during these particular steps of the lifecycle is only informative

for one single set of work conditions. The QbD approach, on the other hand, allows a much

broader outlook: working within an operational space while managing the risk.

3.1. Part I: Pre-validation study during the QbD optimization step

The optimization step of a method development considered by a QbD strategy allows

the qualitative performance of the step to be determined within an operational space through

the use of a DoE (i.e. the qualitative DS). If the optimization is successful, this step occurs

immediately before the pre-validation study. Therefore, it seems conceivable that the DoE,

performed during this particular step, could be elaborated further in order to simultaneously

conduct both the optimization step and the pre-validation study phase. In this way, it would

be possible to carry out an evaluation of the design of experiment to be implemented during

the formal validation step. A recently developed stability-indicating method was selected to

illustrate the use of this new approach as part of the pre-validation study. This method allows

the selective determination of two major degradation products (i.e. P4NX99 and P4FX98,

under confidential agreement) of the active principal ingredient of a commonly used medicine

[14].

In order to simultaneously perform the optimization step of the method as well as the

pre-validation study, the DoE used here needed to be adapted. In particular, each condition of

the DoE was reproduced in triplicate, while at the same time, two different concentrations of

P4NX99 and P4FX98 were alternatively tested. These concentrations were selected to

estimate the limit of quantification of the method (i.e. upper and lower). The DoE

implemented during the optimization phase was then conducted once again taking into

account these modifications. The DS obtained during the method development is illustrated in

Fig. 1. This figure also presents the tested conditions of the DoE (red circles). The odd points

were tested with a high concentration of P4NX99 (i.e. 100 ng mL-1) and a low concentration of

P4FX98 (i.e. 50 ng mL-1) and inversely for the even points (25 and 200 ng mL-1, respectively).

This figure also shows a representative chromatogram for each condition of the DoE as well

as a reminder both of the compounds investigated in each selected ion monitoring

chromatogram and of the critical quality attributes selected.


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Fig. 1. Qualitative DS obtained during the method development. The red circles represent the tested conditions

with their representative chromatogram and estimated probability. Peaks obtained in each chromatogram for

both channels are labeled from “a” to “f”. A summary of the CQAs selected with their acceptance limit (λ) for

obtaining the qualitative DS are also specified. The blue spot represents the set of working conditions selected

for the formal validation of the method (see [14]).

The joint predicted probabilities of meeting all of these CQAs with their acceptance limit (λ)

for each specific point of the DoE as well as for the selected working point (i.e. the set of

conditions selected for the formal validation [14], the blue spot) were also indicated. It should

be noted that, in comparison with the usual optimization DoE, the adaptations did not

increase the working time independently of the repetitions of the DoE points.

From the 9 tested conditions, only 8 and 6 chromatograms were exploitable for

P4FX98 and P4NX99, respectively. Indeed, chromatograms obtained at “P1” could not be used

for either of the two compounds due to the fact that selectivity was made impossible by the

presence of interfering compounds. For the same reason, data from conditions “P2” and “P3”

were also rejected but only in the case of P4NX99. Moreover, a deconvolution process was

required for some conditions, introducing additional uncertainty for these quantitative data.

Based on the exploitable quantitative data, calibration and validation sets were simulated, as

explained in the Experimental section above. In this way, the probability of each point of the

DoE being within the acceptance limits, a priori fixed at ±15%, was calculated and the results

are presented in Table 2. These experiments have also allowed simulating the probability

throughout the area defined by the DoE for each concentration. Unfortunately, with only 5

usable conditions for P4NX99, this simulation was unsuccessful. Figure 2 shows the

distribution of the probability being within the acceptance limits calculated with all the

available quantitative data by concentration level for P4FX98. Fig. 2A shows the results

obtained for a concentration level of 50 ng mL-1, while Fig. 2B presents the concentration level

at 200 ng mL-1.


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Table 2 Probability of obtaining results within the acceptance limits of ±15% for each experimental

point of the DoE.

Experimental

point of the DoE MeOH ACN Buffer

P4FX98

concentration Probability

P2 0.171 0.069 0.76 200.6 0.6927

P3 0.0752 0.0752 0.8496 50.15 0.2001

P4 0.162925 0.033075 0.804 200.6 0.5512

P5 0.1995 0.0405 0.76 50.15 0.9458

P6 0.24 0 0.76 200.6 0.4996

P7 0.10716 0.04324 0.8496 50.15 0.2486

P8 0.1504 0 0.8496 200.6 0.4707

P9 0.1864 0 0.8136 50.15 0.1651

Fig. 2. Simulation of the distribution of the probability of being within the acceptance limits of ±15% for

P4FX98. (A) Concentration level at 50 ng mL-1. (B) Concentration level at 200 ng mL-1.

Following this analysis, several designs of experiments, to be conducted during the validation

step, were tested. The different designs evaluated were a combination of validation series and

repetitions of validation standards during each series. A minimum of three validation series

and a minimum of two repetitions for each series were considered since their combination led

to the smallest Design of Experiments that would need to be implemented during a formal

validation in order to attain sufficient statistical power. Ten thousand simulations were then

computed for each combination in order to assess their probability of producing a successful

validation. A validation was considered successful if the calculated tolerance interval at 95%

was included within the acceptance limits fixed at ±15% for each concentration level. Table 3

shows the probability of a successful validation according to the designs tested for each

experimental condition of the optimization DoE. These results show a high probability of

attaining a successful validation even in the case of a validation DoE considering three series

and three repetitions per series throughout the optimization DoE. This probability

approached 100% when a 4 by 4 DoE was considered. The line highlighted in bold in Table 3

presents the experimental condition of the optimization DoE that comes nearest to the


144

validated working condition (i.e. the blue dot in Fig. 1). As demonstrated by the formal

validation performed during the previous study [14], the tolerance interval at 95% was

included within the acceptance limits fixed at ±15% for the concentration range between

50 ng mL-1 and 200 ng mL-1. In other words, the present study, performed a posteriori,

predicts the success of the validation step as was actually demonstrated during the formal

validation. Quantified guarantees of achieving good levels of total error definitely represent a

movement towards the next steps of the analytical method lifecycle, i.e. robust assessments

and routines that can be used in the laboratory [27].

Table 3 Probability (%) of attaining a successful validation according to the tested designs

(day x repetition) for the acceptance limits of +/- 15% and a probability of 95% of attaining

future results within these limits.

Experimental

point of the

DoE

Probability of validation success (%)

MeOH ACN Buffer 3x3 4x2 4x3 4x4

P2 0.171 0.069 0.76 98.9 98.9 99.6 100.0

P3 0.0752 0.0752 0.8496 99.5 98.9 99.8 99.9

P4 0.162925 0.033075 0.804 99.5 99.1 100.0 100.0

P5 0.1995 0.0405 0.76 99.3 98.2 99.9 100.0

P6 0.24 0 0.76 99.5 98.5 99.8 99.9

P7 0.10716 0.04324 0.8496 99.5 99.3 99.7 99.9

P8 0.1504 0 0.8496 99.4 99.2 99.7 99.9

P9 0.1864 0 0.8136 99.1 98.8 99.7 99.9

3.2. Part II: Validation of an operational space

As a key concept of the method lifecycle, the analytical target profile must firstly, be

selected at an early stage of the QbD methodology and secondly, be exclusively directed by the

final requirements of the user. In this context, the principal objective of a quantitative method

is to quantify with confidence while assessing the risk. A qualitative DS obtained by applying a

QbD strategy represents only a preliminary step in the implementation of an efficient

quantitative method. Indeed, nowadays, the application of this methodology stops at this

point. The quantitative performance of the method is then assessed for a single set of

conditions within this operational space. The second part of the present study focuses on a

similar application of the QbD strategy during the validation step. In order to illustrate this

innovative methodology, a previously developed method, using the quality-by-testing

approach, was selected [22]. This method needed to be optimized in order to allow the

selective determination of glucosamine from galactosamine while avoiding the on-column

mutarotation phenomenon observed with the initial method. The biological matrix

considered was human plasma, while, simultaneously, the equipment being employed was a

triple quadrupole mass detector. In a scenario such as this, where polar drug substances are

analyzed at very low concentration levels in bioanalytical applications, hydrophilic interaction


145

chromatography (HILIC) plays an important role due to its larger retention possibilities for

this kind of compound, which occurs very widely in bioanalysis [26]. The use of large

proportions of highly volatile organic components (e.g., acetonitrile, methanol, etc.) in the

mobile phase provides excellent ionization efficiency with the commonly used MS sources

such as electrospray ionization, and this leads to enhanced sensitivity [28,29].

3.2.1. Qualitative DS: an operational space for the validation

The screening part of this study has allowed selecting influential critical method

parameters (CMPs) as well as the column showing the greatest separation efficiency for

glucosamine and galactosamine. This enabled to consider the following CMPs: ACN

percentage (X.ACN varied between 80% and 90%), pH (pH varied between 5 and 10) and

temperature (T varied between 25 and 75 °C). UPLC rather than HPLC was used during the

optimization DoE in order to enhance the selective capabilities and reduce the total run time

of the method. Consequently, a geometric transfer was implemented for the selected column

in order to move it towards the corresponding UPLC geometry. The selected column was a

Waters Acquity UPLC BEH Amide 2.1x100 mm (1.7 μm). Enhanced separative capabilities are

essential when considering the biological matrix during the optimization step. Indeed, a major

concern regarding HILIC-MS(/MS) bioassays and even reversed-phase LC-MS(/MS) bioassays

is the impact of the matrix effect (ME) [30-32]. As recommended by the FDA [33], the ME

should be assessed during the development of the method. The specific methodology

implemented during this study is detailed in the “Supplementary Data” document.

Once the CMPs had been identified (i.e. X.ACN, pH and T) during the screening study, a

custom central composite design (T was added manually) with a total of 13 experimental

conditions (n = 15, central point tested in triplicate) was conducted. Human plasma spiked

with glucosamine, galactosamine and the internal standard as well as non-spiked plasma (for

the ME assessment, as explained in the “Supplementary Data” document) were tested. This

experimental domain was carefully selected on the basis of the preliminary results obtained

with pure chemicals in order to allow the separation of both the epimeric compounds at a

transition of m/z: 180/162. The concentration of the internal standard was fixed at 250 ng

mL-1 for all the solutions. Finally, as is now widely discussed in the scientific literature [23-

25], a qualitative DS was computed using Monte-Carlo simulations from the prediction errors

of a set of CQAs for which the acceptance limits (λ) were fixed, as described below:

- Separation between glucosamine, galactosamine and endogenous plasma compounds

eluted just before epimeric compounds > 0.2 min.

- Total run time < 30 min.


146

A three-dimensional (X.ACN, pH, T) probability surface was then obtained. Three

representative slices of this multi-dimensional surface are presented in Fig. 3. The

two-dimensional representations were obtained by fixing one parameter at its optimal value

in the case of Fig. 3A and 3B, while T was fixed at 50 °C in the case of Fig. 3C, since this was the

selected working temperature for the validation of the operational space. Fig. 3A, where the

fixed parameter was X.ACN at 88.5%, shows that the interaction pH – T was barely significant.

However, a DS with a quality level (π) of more than 0.81 was defined for a pH ranging from

5.2 to 6.4 and a T ranging from 35 °C to 75 °C. The slice where the pH parameter was fixed at

5.75 is presented in Fig. 3B. At 50 °C and above, the level of quality obtained when considering

all the constraints (i.e. the CQAs) was found to be acceptable and relatively constant for the

parameter X.ACN ranging from 83% to 89%. This finding is confirmed by Fig. 3C, which

presents the computed probability surface at a fixed temperature of 50 °C, in particular for

the range of pH between 5 and 6.8. Within this area, dark lines highlight two DS, with a π of

0.825. These DS represent the sets of conditions where the chromatographic performance,

with regard to the separation of glucosamine, galactosamine and endogenous plasma

compounds within a maximum run time of 30 minutes, presented a very acceptable level of

quality.

Fig. 3. Two-dimensional qualitative probability surfaces (i.e. P(CQAs > λ)) with their DS defined by a dark line.

(A) X.ACN was fixed at 88.5%, pH varied between 5 and 10 and T varied between 25 and 75 °C. (B) pH was fixed

at 5.75, X.ACN varied between 80% and 90% and T varied between 25 and 75 °C. (C) T was fixed at 50 °C, pH

varied between 5 and 10 and X.ACN varied between 80% and 90%. The area surrounded by blue dots and blue

lines represents the qualitative DS selected as the operational space. The red dot corresponds to the reference

point selected for the formal validation.

3.2.2. Strategy for the validation of an operational space

Once the qualitative DS has been obtained, the next step of the method lifecycle is the

validation of the method. As with the conventional approach to the validation, a unique set of

conditions within the qualitative DS is chosen. A validation DoE is then applied to the selected

working conditions, considering an approach using accuracy profiles based on statistical

tolerance intervals. Nowadays, this approach is fully approved by the authorities [18], as well

as being widely discussed and applied by scientists [34-35]. Within the qualitative DS


147

centered around the parameter X.ACN at 86% in Fig. 3C, the working conditions defined by

the red dot (i.e. X.ACN = 86%, pH = 6, T = 50 °C) could have been appropriate and therefore

suitable to be subjected to a formal validation. However, this conventional approach only

allows the assessment of the quantitative performance of the method for the selected working

conditions, which represents a break from the QbD process. Indeed, the qualitative

performance of the method is evaluated throughout a defined domain, but the quantitative

performance is only assessed for one single set of conditions. The qualitative DS guarantees

an area of robustness for the studied CMPs in terms of the selected CQAs. Consequently, the

analyst is able to find alternative working conditions, where the qualitative performance is

already demonstrated. This allows him/her to be able to respond to an unexpected or a

scheduled change in the method that originates from a separation issue. Nevertheless, this

learning process is only applicable for the qualitative part of the method, not for its

quantitative performance. How can the quantitative performance of the newly selected

working conditions be assessed? Without any further information, the analyst could be placed

in in the position of selecting, within the operational space, a working condition with a poor

probability of validation success. In order to provide a remedy for this scenario, an innovative

validation approach, based on the QbD concept, was applied to the case study addressed in

this section.

Within the probability surface presented in Fig. 3C, a qualitative DS was selected that

was as large as possible, and with a minimum quality level (π) of 0.5. This is outlined in the

figure by the blue lines. Both the blue dots and the red dot represent the experimental

conditions tested during the validation DoE for this operational space. The red dot represents

the central condition of this custom DoE but also the condition selected as a reference to

compare with a conventional approach to the validation step (i.e. a validation of a unique set

of conditions within the operational space). The parameter T was fixed at 50 °C since the

separative performance compared to the optimal temperature (i.e. 62.5 °C) was similar and

the lower temperature exerted less of a strain on the equipment. The design of experiments

for the validation was developed for a period of 3 series throughout the operational space, as

can be seen in Fig. 4. For each series, a minimum of 2 repetitions of the calibration standard

for each concentration level was tested. In the meantime, a minimum of 5 repetitions of the

validation standard for each concentration level was also tested. Three repetitions were

always performed in the case of the validation standards for the reference points, as flagged

with the red color in Fig. 4. Three concentration levels were tested for glucosamine and

galactosamine, covering a range from 25 to 500 ng mL-1 and from 200 to 1000 ng mL-1

(injected concentrations) in all the standards, respectively. Each sample was spiked with the

internal standard in order to obtain a concentration of 500 ng mL-1 (injected concentration).


148

Fig. 4. Design of Experiments for the validation of the operational space. The flags over the experimental

conditions represent the number of repetitions using the color coding indicated on the top right-hand side

of the figure.

3.2.3. Validation results

Computation of data gathered via this validation DoE throughout the operational space

was performed as explained in the Experimental section above. A probability surface was

calculated for each concentration level of glucosamine and galactosamine, and this is

presented in Fig. 5A and 5B, respectively. Each probability surface represents the probability

that each future result, for the concentration level tested and throughout the operational

space, will be between ±15% of the true value. This predictive methodology is similar to the

one used during the conventional approach to the validation for the “β-expectation tolerance

interval” and allows the assessment of a key feature of the validation study within an

operational space: the uncertainty regarding the performance of the method. As can be seen

in Fig. 5A, probability surfaces obtained for the validation of the determination of

glucosamine in human plasma were extremely homogenous throughout the operational space

and for the entire considered dosing range. The probability of being within ±15% of the true

value was always higher than 97%, whatever the concentration level. Based on this

evaluation, taking into account all the validation results with their associated uncertainty, the

quantitative performance of the method was guaranteed across the operational space for

glucosamine. The validation data gathered for galactosamine on the other hand led to a

distinctive situation. In this case, the computed probability surfaces, also taking into account

all the validation results with their associated uncertainty, showed a probability of being

within ±15% of the true value ranging between 68% and 72% for concentration levels of

500 ng mL-1 and 1000 ng mL-1. This probability fell between 45% and 72% for the lower


149

concentration level (i.e. 200 ng mL-1). From the perspective of a formal validation, these

results could not be considered as acceptable. However, these probability surfaces led to the

discovery of some very useful information. As can be seen in Fig. 5B, a high percentage of ACN

and pH resulted in a greater chance of achieving a successful validation. With this information,

it would be possible to influence positively the selection of different working conditions,

sometimes necessary during the life cycle of the method (i.e. continuous improvement

process). In addition to computing these probability surfaces, a probability profile could be

computed from those first results for a specific set of working conditions within the

operational space. These probability profiles could then be compared to the risk (α) profiles

obtained during a formal validation (i.e. the risk α = 1 – the probability of being within ±15% of

the true value). Furthermore, accuracy profiles could also be computed from these probability

surfaces for a specific set of working conditions within the operational space.

Fig. 5. Probability of the surface being within ±15% of the true value by concentration level for (A) glucosamine

and (B) galactosamine.


150

3.2.4. Comparison with a conventional approach to the validation step

The DoE of this innovative strategy was wisely elaborated. Indeed, experiments on the

central working conditions were repeated as for a formal validation, testing 3 repetitions of

the validation standards over 3 working days (see Fig. 4). In this context, these experiments

could be independently computed in order to obtain results in the same way as from a formal

validation of the method. As suggested in the section above, an accuracy profile could be

calculated for each working condition within the operational space and for each analyte.

These profiles could thus be compared to those obtained from the formal validation of the

central point, as can be seen in Fig. 6A and Fig. 6B for glucosamine and galactosamine,

respectively. As can be seen on the right hand side of Fig. 6A, the formal validation of the

selected working conditions (i.e. the central point of the validation design of experiments)

was successful for glucosamine. The quantitative performance for this molecule throughout

the operational space was very good and homogenous, as highlighted in Fig. 5A.

Consequently, very accurate predictions for each set of working conditions within the

operational space were obtained when considering all the validation results with their

associated uncertainty. Unlike the glucosamine results, those obtained for galactosamine were

less favorable. Indeed, the quantitative performance throughout the operational space was

found to be less homogeneous. However, as can be seen in Fig. 6B, analysis of the validation

results for the central condition of the validation DoE led to a successful validation when

considering a formal validation process.


151

Fig. 6. Accuracy profile of the validation of the working conditions of the reference point obtained for (A)

glucosamine and (B) galactosamine. On the left-hand side of the figure, accuracy profiles are obtained from the

validation DoE. The accuracy profiles presented on the right-hand side of the figure, were obtained by

performing a formal validation of the selected set of conditions. The plain red lines represent the relative bias,

the dashed lines represent the 95% β-expectation tolerance limits and the dotted curves represent the

acceptance limits (30% at LLOQ and 15% elsewhere).

As the strategy developed for the validation of the operational space considered the

uncertainty throughout that entire operational space, the predictive validation results were

less optimistic than when only a single set of working conditions was considered. These

poorer predictive results may thus have been the result of a lack of statistical power. As with a

formal validation process, an additional validation series (i.e. an additional working day)

could be considered here. The validation DoE presented in Fig. 4 would thus need to be

adapted in order that these additional experiments cover the operational space. Computation

of the results of the validation DoE has also allowed to calculate the probability profiles for

any working conditions within the operational space, as explained in the previous section. In

the case of glucosamine, the risk (α) throughout the dosing range for the central experimental

condition of the validation DoE was calculated and was shown to vary between 0.1% and


152

0.4%. The result regarding the same parameter obtained via the formal validation varied

between 0.1% and 0.5%. This comparison demonstrates the high quality of prediction across

the entire operational space in the case of glucosamine. Moreover, the linearity of the method

throughout the operational space was calculated from all the results of the validation DoE and

compared to the results obtained via the formal validation. In the case of glucosamine, the

slope, the intercept and the coefficient of determination (R2) were equal to 1.00, 0.26 and

0.99, respectively. In the case of the formal validation, the calculations of these results were

equal to 1.00, -0.05 and 0.99, respectively. These results demonstrate once more the high

quality of the prediction obtained by this validation design of experiment. This validation of

the operational space was performed over three working days as for a formal validation,

confirming the quantitative performance of the method across an area rather than for a single

set of conditions during the same time period as used in a conventional validation process.


153

4. Conclusion

Defining the objectives of the method using an analytical target profile (ATP) should be

the first step of the QbD methodology. In the case of the development of a quantitative

method, this ATP should also be focused on the quantitative performance of the method. By

integrating the pre-validation study alongside the QbD optimization phase, some parameters

of the validation can be evaluated. As described in the first part of this study, the design of

experiments for use during a formal validation can be developed simultaneously with the

selection of the qualitative design space, without increasing the working time usually

dedicated to this step of the method lifecycle. Following a similar approach, an estimation of

the calibration model, the accuracy, and the limits of detection/quantification may also be

considered during this step. Consequently, the methodology to be implemented would require

further improvement. In particular, repetitions considered at each experimental point would

need to be made with more than one concentration level in order to improve the quality of the

prediction.

As specified in the latest USP [18] and FDA [36] documents, the validation step of the

method lifecycle must not be an isolated activity but should be part of the continuous

improvement of the method. The routine use of the method allows the continuous acquisition

of information via quality control samples, for instance. However, without a deep

understanding of the method (i.e. qualitative and quantitative knowledge), it is rather difficult

to take advantage of the information gained. For example, with the case study presented here

for glucosamine determination, and even for galactosamine, the quantitative and qualitative

information obtained, would allow the analyst to consider selecting other working conditions

within the operational space with great confidence. Indeed, using this strategy, it would thus

be possible to evaluate the quantitative performance of the method before the selection of

different working conditions. This would allow a corrective action to be implemented or a

preventive action to be initiated following, for instance, a problem encountered during the

routine use of the method. This methodology is not restricted to overcoming routine issues. It

could also be employed when a change of the applicability of the method needs to be

considered, for instance, a change in the biological matrix (gender, species, etc.). It is for this

reason that this innovative strategy combines both a learning process and a thorough

assessment of the risk. However, even though this did not happen with the presented case

study, this innovative approach could lead to the use of a validation protocol that is more

expensive in terms of analytical time. This concern would need to be addressed with further

development of the strategy. Nonetheless, from our point of view, this potential additional

analytical cost should be set against the benefits provided by this approach during the whole

analytical lifecycle.


154

Acknowledgments

The authors are very grateful to the anonymous reviewers for providing valuable

comments that led to significant improvements in this article. Special thanks are due to

Charlotte De Bleye for her help during the reviewing process of this paper.


155

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Supplementary data

A. Matrix effect assessment

Enhanced separative capabilities were essential when considering the biological

matrix during the optimization step. Indeed, A major concern about HILIC/MS(-MS) bioassays

or even reversed-phase LC/MS(-MS) bioassays is the impact of the matrix effect (ME). The ME

refers to the ionization suppression or enhancement caused by unobserved substances

co-eluted from biological matrix. This kind of co-elution competition takes place between

compounds during the ionization process, and especially when considering ESI mode [25-27].

Therefore, minimizing this phenomenon is crucial. In the case of this study, a generic protocol

combining acidified organic protein precipitation (i.e. ACN with 1% formic acid) and specific

extraction of phospholipids was conducted using Phree Phospholipid Removal Plates from

Phenomenex by the mean of a vacuum manifold. However, as recommended by FDA [28], the

lack of ME has to be assessing during the development of the method. This can be done by the

monitoring of the variability of the MS response for the analyte using a post-column infusion

scheme during the analysis of an extracted blank matrix sample. This methodology allows

identifying the chromatographic region where compounds responsible of the ME are eluted

for the tested experimental condition. As the ME could be due to many endogenous

compounds, it is difficult to manage this response such as a unique compound. Consequently,

this methodology only leads to a categorical response: the lack or not of a matrix effect at the

retention time of target analyte. This king of response is difficult to model throughout the

entire experimental space. Therefore, a more specific methodology was envisaged in order to

assess this problematic. In the case of HILIC method, ME is largely encountered due to a

co-elution between early-eluted analytes and endogenous phospholipids or formulation

vehicles [27]. Other endogenous compounds typically responsible of the ME in

reversed-phase mode are potentially present but are directly eluted in HILIC mode. In this

framework, precursor ion scans with the product ion of m/z: 184 (i.e. the specific daughter

ion from the hydrophilic head of the phospholipids) were performed with the scan range from

490 to 890 m/z for each experimental condition with none spiked plasma. A combination of

all recorded spectra during the run time for each experimental condition were performed in

order to identify potential phospholipids remaining after plasma preparation. Specific

transition of identified phospholipids (i.e. m/z: 496-184, 760-184 and 786-184, principally)

were then extracted from each chromatogram in order to compare the retention time of this

particular phospholipids with the retention time of glucosamine and galactosamine obtained

from the analysis of spiked plasmas. This methodology allowed modeling the

chromatographic behavior of remaining phospholipids in order to introduce a separation

criteria of remaining phospholipids, glucosamine and galactosamine as a CQA if necessary (i.e.

if remaining phospholipids were eluted within the retention windows of glucosamine or


159

galactosamine). Thanks this methodology, the separative DS could manage the ME throughout

the envisaged experimental domain as requested by FDA recommendations. In the case of the

present study, no remaining phospholipids were found to elute within the retention time

windows of glucosamine or galactosamine for any experimental condition.

Chapitre IV

Conclusions et perspectives

Chapitre IV : Conclusions et perspectives

163

Le contexte réglementaire auquel est indubitablement liée l’industrie pharmaceutique

a, au cours du temps, imposé à cette dernière d’étendre le concept d’assurance de qualité à

tout le cycle de vie du produit. Plus particulièrement dans le cadre qui nous occupe, ce

concept s’étend à l’intégralité du cycle de vie des méthodes analytiques. Dans le contexte du

médicament au sens large, les référentiels tels que ceux proposés par l’ICH [1] mettent

l’accent sur la maîtrise scientifique du produit et donc, de facto, sur la maîtrise du processus

analytique. En effet, l’évaluation et la gestion du risque associé au cycle de vie permettent

d’envisager l’amélioration du processus analytique en fonction de l’évolution de la

connaissance acquise non seulement au cours de chaque étape de la mise au point de celui-ci,

mais également au cours de son utilisation en routine. Cela permet donc d’identifier et de

prioriser les zones d’amélioration inhérentes aux méthodes analytiques. A travers les

différents cas étudiés tout au long de ce travail, nous avons pu aborder plusieurs étapes clés

du cycle de vie des méthodes analytiques et également pu confirmer ou proposer des

stratégies novatrices. Pour ce faire, nous avons abordé des notions telles que l’« Analytical

Target Profil (ATP) » décrivant les performances attendues de la méthode analytique. Cette

notion est le point de départ d’une stratégie de type « Analytical Quality-by-Design (AQbD) »

contrairement à l’approche de type « essai/erreur » ou stratégie « Quality-by-Testing ». Ce

concept AQbD s’appuie sur l’utilisation combinée de plans d’expériences associés à la

définition d’un espace de conception, le « Design Space ». La validation a également fait partie

des travaux présentés dans cette thèse. L’aspect prédictif du profil d’exactitude à travers

l’utilisation des intervalles de tolérance a non seulement été abordé, mais une stratégie

novatrice combinant l’étape d’optimisation et de validation a également été proposée. C’est

d’ailleurs par cette dernière étape de validation que nos travaux ont débuté.

En effet, nous nous sommes donc tout d’abord intéressés, dans la section III.1, à la

validation en tant qu’étape critique avant l’implémentation du processus analytique en

routine. Son rôle est de démontrer la fiabilité de ce dernier. En effet, sur base des expériences

menées lors de cette étape, l’analyste doit prendre une décision sur la capacité de la méthode

par rapport à son utilisation future. Le profil d’exactitude, utilisant un intervalle de tolérance,

permet de prédire une région où une proportion définie de futures mesures sera observée.

Prendre la décision d’accepter ou de rejeter une méthode sur base des prédictions obtenues

par l’intermédiaire d’un intervalle de tolérance est donc parfaitement en accord avec l’« ATP »

tel que défini. Dans les quatre exemples présentés au cours de la section III.1, il apparaît

clairement qu’une décision basée sur la prédiction obtenue à l’aide de l’intervalle de tolérance

est parfaitement acceptable pour prendre une décision avec un risque maîtrisé. En effet, la

proportion attendue d’échantillons de contrôle de qualité (« QC ») était dans tous les cas

[1] ICH Harmonized Tripartite Guideline, Q8(R2), Pharmaceutical Development (2009), Q9,

Quality Risk Management (2005), Q10, Pharmaceutical Quality System (2008) et Q11,

Development and manufacture of drug substances (2012).


164

étudiés, inclue dans l’intervalle de tolérance défini en phase de validation. A titre d’exemple,

96% des « QC » obtenus lors de l’utilisation en routine d’une méthode permettant la

détermination du lévonorgestrel contenu dans une matrice polymérique se trouvaient dans

les limites de l’intervalle de tolérance (« β-expectation tolerance intervals » à 95%) défini lors

de la phase de validation. Ces données ont été obtenues à partir de plus de 250 « QC » répartis

sur 21 séries.

Après avoir démontré que l’étape de validation, conduite par l’intermédiaire du profil

d’exactitude, permet de s’assurer de l’adéquation de la méthode quant à son objectif

quantitatif, notre intérêt s’est porté sur l’étape d’optimisation. Les cas étudiés ont été centrés

sur des problématiques actuelles. L’identification et le dosage sélectif de « petites molécules »

(< 200 Da) [2] dans des matrices complexes et à de faibles concentrations restent en effet un

challenge analytique. Cela se complexifie encore quand ces molécules sont polaires. Au cours

de la section III.2, nous avons cependant pu montrer que, même dans ces cas, une approche

conventionnelle de type « Quality-by-Testing » couplée à une stratégie de validation

s’appuyant sur le profil d’exactitude, peut s’avérer adéquate et ainsi permettre d’aboutir à des

performances quantitatives maîtrisées. En effet, une nouvelle méthode chromatographique,

sensible et sélective, faisant appel à la chromatographie liquide d’interactions hydrophiles

(« HILIC ») couplée à la spectrométrie de masse simple quadripôle permettant le dosage de la

glucosamine à partir de plasma canin a pu être développée même si la présence de glucose en

grande quantité dans le plasma a rendu le travail ardu suite à la suppression d’ionisation. Afin

de minimiser cet effet, il s’est donc avéré nécessaire de préparer l’échantillon préalablement à

son analyse par une extraction en phase solide et ce, en utilisant une phase à base

polymérique de type échangeuse de cations forts. Cette méthode a ensuite été validée sur

base du profil d’exactitude pour une gamme de concentration allant de 50,5 ng/mL à

1010,0 ng/mL et a été utilisée pour la détermination de faibles concentrations plasmatiques

de glucosamine lors d’une étude préliminaire de pharmacocinétique sur des chiens.

Bien que cet exemple montre que l’approche « QbT » peut mener à une méthode fiable

et utilisable en routine, le développement de celle-ci par l’intermédiaire de cette stratégie ne

permet cependant pas d’acquérir une connaissance et une maîtrise approfondies de tout le

processus analytique. En effet, lorsqu’un problème survient l’analyste est souvent amené à

modifier les conditions opératoires de la méthode. Suivant cette approche itérative, ce dernier

n’a aucune information lui permettant de maîtriser l’impact de ces changements ainsi que le

risque associé à ceux-ci. Par conséquent, il apparaît donc clairement que la maîtrise du risque

associé à l’étape de développement de la méthode fait également partie du challenge

analytique. Il nous est dès lors apparu nécessaire de proposer des stratégies de

développement adaptées en ce sens reposant sur une stratégie dite de « Quality-by-Design ».

Elle permet une globalisation du processus analytique amenant au premier plan l’objectif final

[2] C.A. Lipinski, Lead- and drug-like compounds: the rule-of-five revolution, Drug Discov. Today 1 (2004) 337.


165

qui, dans le cas d’une méthode analytique, est l’obtention d’un résultat fiable à l’aide d’une

méthode robuste. C’est dans cette optique que nous avons présenté, dans la section III.3, une

étude comparative entre une approche novatrice de type « QbD » et l’approche traditionnelle

« QbT ». Dans l’exemple sélectionné nous avons abordé l’optimisation d’une méthode

permettant le dosage, en très faibles quantités, d’analogues structurels de poids moléculaires

faibles et proches. Par ailleurs, l’abondance isotopique des éléments présents sur ces

molécules rend leur analyse en spectrométrie de masse encore plus difficile. Cette

optimisation s’est avérée nécessaire afin de résoudre un problème de sélectivité entre deux

impuretés, l’une connue provenant de la dégradation du principe actif et l’autre inconnue et

dont l’apparition est survenue en toute fin d’une étude de stabilité à long terme. Dans un

premier temps, des conditions chromatographiques robustes permettant le dosage du

principe actif et de ses impuretés connues ont été trouvées. Dans un second temps, le « Design

Space » établi durant cette étape initiale a été exploré afin de définir un ensemble de

conditions expérimentales pour lesquelles la spécificité chromatographique était vérifiée.

Lors de cette étape, des matrices vieillies ont été utilisées afin de disposer d’échantillons

contenant un maximum d’impuretés potentiellement présentes lors d’analyses de routine en

fin d’étude de stabilité. Cette stratégie « QbD » a donc mené à l’établissement d’un « DS »

réduit rencontrant les critères de qualité fixés. Finalement, à la suite de cette optimisation,

cette méthode de dosage des impuretés a été validée sur base du profil d’exactitude pour une

condition sélectionnée et ensuite utilisée en routine. Nous avons pu démontrer au cours de

cette étude que la stratégie « QbD » permettait d’acquérir une meilleure maîtrise de la

méthode et une gestion du risque associé à des ajustements de conditions opératoires lorsque

cela s’avérait nécessaire. Cette stratégie innovante s’inscrit parfaitement dans la notion

d’amélioration continue actuellement prônée dans le contexte réglementaire pharmaceutique.

L’étape de développement et de validation étant maîtrisée, nous nous sommes alors

posé la question suivante : « Est-il envisageable de combiner celles-ci dans une stratégie

globale et novatrice tirant parti des avantages de la stratégie « QbD » ? Cette nouvelle stratégie

avait pour but de mettre en avant, en une seule étape, tous les objectifs de l’« ATP » définis

comme suit : « Une procédure analytique doit être capable de quantifier un analyte en présence

d’autres composés dans une gamme de concentration définie et centrée sur une valeur nominale

avec une exactitude et une incertitude de telle sorte que le résultat obtenu soit compris dans des

limites fixées a priori autour de la vraie valeur avec une probabilité minimum définie et

déterminée avec un niveau de confiance fixé ». Dès lors nous avons abordé l’étape de validation

suivant une approche combinant les plans d’expériences mis en œuvre dès l’optimisation de

la méthode avec l’établissement d’espaces de conception quantitatif. En d’autres termes, ceci

nous a permis de proposer une approche « DoE-DS quantitatif ». La faisabilité de cette

stratégie a été évaluée, dans la section III.4, à partir de l’optimisation de la méthode de dosage

de la glucosamine dans des matrices plasmatiques initialement abordée suivant l’approche

« QbT ». Suite à l’obtention de la surface de probabilité définie en fonction des critères de


166

qualité fixés, un « DS », à l’intérieur duquel les performances qualitatives attendues étaient

rencontrées, a été sélectionné. Un nouveau plan d’expériences a alors été construit. Les

différentes expériences de celui-ci ont cette fois été fixées de sorte à acquérir des données

quantitatives sur une gamme de concentration déterminée. Par l’intermédiaire de cette

approche novatrice, les données sur les performances quantitatives de la méthode ont été

évaluées sur un domaine expérimental et plus uniquement pour un set de conditions. Nous

avons démontré pour la première fois qu’il était tout à fait envisageable de valider, sur base

du profil d’exactitude, tout un ensemble de conditions opératoires. Cette stratégie permet

donc de donner une nouvelle dimension au « Design Space ». En effet, celui-ci n’est plus

uniquement l’espace opérationnel où des performances qualitatives attendues sont

rencontrées, mais il devient également un espace où l’on évalue et où l’on maîtrise les aspects

quantitatifs de la méthode analytique. Une comparaison entre l’approche de la validation de

manière intégrée au concept « QbD » et l’approche « classique » de validation d’un set de

conditions opératoires a montré des résultats de validation tout à fait concordants. En effet, à

titre d’exemple, le risque α calculé sur l’ensemble de l’intervalle de dosage pour une condition

opératoire varie entre 0,1% et 0,4% lorsqu’il est calculé sur base de l’approche « DoE-DS

quantitatif » et entre 0,1% et 0,5% dans l’approche de validation « classique ». Une

comparaison similaire a également été faite pour le critère de linéarité. La pente, l’ordonnée à

l’origine ainsi que le coefficient de détermination (R2) étaient extrêmement comparables.

Durant notre thèse, nous avons démontré le pouvoir prédictif du profil d’exactitude,

mais aussi l’utilité d’une approche de type « QbD » en termes, non seulement de gestion du

risque, mais également en tant qu’outil d’apprentissage approfondi et continu de la méthode.

L’approche novatrice du concept « QbD », présentée au cours de la dernière section de nos

travaux, permet d’envisager un niveau d’intégration encore supérieur du risque analytique,

tant quantitatif que qualitatif, au travers du cycle de vie des méthodes analytiques.

Au terme de notre travail, nous avons en effet démontré la faisabilité d’une nouvelle

stratégie pour la validation de plusieurs conditions opératoires, l’approche « DoE-DS

quantitatif ». Cependant, des investigations restent à mener car, même si cela n’est pas

survenu dans le cadre du cas étudié, cette approche pourrait entrainer des protocoles de

validation plus couteux en termes de temps d’analyse. Ceci devra donc faire l’objet d’une

étude plus approfondie, mais il nous semble que ce coût potentiel supplémentaire devra,

avant tout, être mis en regard des bénéfices qu’une telle approche intégrée peut apporter.

De plus, comme nous l’avons démontré au cours de cette même étude, une étude de

pré-validation peut également être envisagée en parallèle du plan d’expériences réalisé pour

l’optimisation de la méthode. Il pourrait alors être notamment possible d’estimer le modèle de

calibration, l’intervalle de dosage ainsi que ses limites de quantification et de détection et ce,

préalablement à la validation. Ensuite, il nous semble également important de confirmer

l’applicabilité de cette stratégie novatrice sur un nouveau cas d’étude et ce, dès le début de


167

l’établissement de la problématique, permettant ainsi la réalisation des étapes de

pré-validation et de validation de manière concomitante à la phase d’optimisation.

Il serait également intéressant de démontrer que les données prédictives de validation

de différentes conditions opératoires sont effectivement rencontrées lors de l’utilisation de la

méthode en routine à l’instar de ce qui a été démontré pour le profil d’exactitude lors de la

première partie de nos travaux.

Enfin, il nous paraît important d’envisager l’application de cette approche novatrice à

d’autres techniques analytiques quantitatives.

Chapitre V

Résumé de la thèse

Chapitre V : Résumé de la thèse

171

Le cycle de vie des méthodes analytiques se décompose en une succession d’étapes qui

commencent invariablement par une question posée à l’analyste. Sur cette base, celui-ci doit

tout d’abord définir les performances attendues de la méthode ou « Analytical Target Profil

(ATP) ». S’en suivront les étapes de développement et de validation de la méthode avant son

utilisation en routine. De plus, le contexte réglementaire auquel est lié l’industrie

pharmaceutique lui impose depuis peu d’évaluer et de maîtriser le risque associé à toutes les

étapes du cycle de vie du produit, en ce inclus le processus analytique et, par conséquent,

chaque étape de son propre cycle de vie.

Dans ce contexte, nos travaux se sont tout d’abord centrés sur l’étape de validation

dont le rôle est de démontrer que la méthode est adaptée à l’objectif défini par l’« ATP ». A

cette fin, nous nous sommes attachés à confirmer expérimentalement le caractère prédictif de

l’intervalle de tolérance et, par la même occasion, la puissance du profil d’exactitude. Mais

plus encore, il était pour nous essentiel de s’assurer de l’adéquation de cet outil décisionnel

quant à sa capacité à maîtriser une partie du risque lié au cycle de vie d’une méthode

analytique avant d’aborder l’étape relative à son développement.

Le plus souvent, cette étape liminaire du cycle de vie analytique est abordée de

manière itérative par une stratégie appelée « Quality-by-Testing (QbT) ». Au travers d’un

exemple complexe, nous avons montré que cette approche ponctuée d’une validation

reposant sur le profil d’exactitude permettait déjà d’appréhender le risque lié à l’utilisation de

cette méthode en routine même si son domaine expérimental n’avait pas été exploré.

Afin de pallier ce manquement, nous nous sommes ensuite tournés vers une stratégie

multivariée ou « Quality-by-Design (QbD) », alliant la puissance de plans d’expériences à la

définition d’un « Design Space (DS) ». Cet espace de conception nous a permis d’intégrer les

paramètres critiques du processus en amenant au premier plan l’objectif final qui, dans le cas

d’une méthode analytique, est l’obtention de résultats fiables à l’aide d’une méthode robuste.

Une étude comparative de ces deux approches a clairement mis en évidence les bénéfices de

l’approche « QbD » en regard de sa capacité à évaluer le risque associé aux aspects qualitatifs

de la méthode analytique étudiée.

Enfin, nous avons étudié la possibilité d’intégrer en une seule et même stratégie ces

deux étapes fondamentales du cycle de vie des méthodes analytiques. Tirant parti des

avantages de la stratégie « QbD », nous avons été les premiers à proposer une stratégie

globale de gestion du risque analytique. Nous avons en effet démontré qu’il était tout à fait

possible de valider au moyen du profil d’exactitude tout un ensemble de conditions

opératoires, donnant de la sorte une nouvelle dimension au « Design Space ». Celui-ci n’est

donc plus uniquement un espace opérationnel où des performances qualitatives attendues

sont rencontrées, mais il devient ainsi un domaine où il est à la fois possible d’évaluer et de

maîtriser les risques liés aux aspects quantitatifs d’une méthode analytique.

Chapitre V : Résumé de la thèse

172

En conclusion, durant notre thèse, nous avons confirmé le pouvoir prédictif du profil

d’exactitude, mais aussi l’utilité d’une approche de type « QbD » en termes, non seulement de

gestion du risque, mais également en tant qu’outil d’apprentissage approfondi et continu de la

méthode. L’approche novatrice du concept « QbD », présentée au cours de la dernière partie

de nos travaux, permet d’envisager un niveau d’intégration encore supérieur du risque

analytique, tant quantitatif que qualitatif, au travers du cycle de vie des méthodes analytiques.

Chapitre V : Thesis summary

173

Analytical method lifecycle is composed of several steps, but always starts with a

question defining the problem. Analytical method performances are consequently specified by

the analyst trough the definition of the “Analytical Target Profile (ATP)”, as proposed by the

regulatory bodies. Subsequent steps (namely the development and validation steps) then take

place, followed by routine use of the analytical procedure. In the specific context of the

pharmaceutical industry, regulatory authorities have recently imposed the assessment and

management of risk throughout the entire product lifecycle. This includes the analytical

procedure and consequently its own lifecycle.

Working in this context, our concerns were initially focused on the validation step of

the method lifecycle. Indeed, the objective of analytical method validation is to demonstrate

that this method is suited for quantifying the target analytes with an established and suitable

level of accuracy, as defined by the “ATP”. This is sometimes called the “fit-for-future-

purpose” concept. In the course of this study we have experimentally confirmed that a

decision regarding the validity of a method based on prediction can be achieved by using the

“β-expectation tolerance interval” (accuracy profile) as a decision tool. Indeed, it seemed

essential to demonstrate the capability of this approach to manage a part of the analytical risk

before addressing the development step.

Typically this step of the analytical procedure lifecycle is addressed using a “Changing

One Separate Factor a Time (COST)” approach (also known as the “Quality-by-Testing (QbT)”

approach). By means of a complex case study, and considering validation of the method

through the accuracy profile, we have shown that this strategy can lead to a suitable method

for assessing the risk of routine use, even where the experimental domain is not examined.

In order to consider an experimental domain rather than a set of specific experimental

conditions during the development phase, we have evaluated a multivariate approach: the

“Quality-by-Design (QbD)” strategy. This strategy allows the definition of a “Design Space

(DS)” by means of design of experiments (DoE). This DS, computed considering critical

method parameters, allows the analyst to focus on the main objective of an analytical method:

obtaining reliable results using a robust method. A comparative study of the QbT versus QbD

approach was performed. In the course of this study, the benefits of the QbD strategy in terms

of managing the qualitative part of the analytical risk were highlighted.

Finally, we have focused our research on the development of a global strategy allowing

the unification of the development and validation phases in a single step. With this innovative

approach, we are the first to propose a strategy allowing the management of global analytical

risk (i.e., both qualitative and quantitative risk). Indeed, we have demonstrated that it is

possible to validate an experimental domain by means of the accuracy profile. With this

innovative strategy, the DS is no longer simply the place where qualitative performances are

obtained, but also the space where quantitative performances of the analytical procedure are

assessed and managed.

Chapitre V : Thesis summary

174

In conclusion, during this thesis, we have confirmed the predictive capabilities of the

accuracy profile. Moreover, we have highlighted the benefits of a QbD strategy in terms of risk

management. We have also demonstrated that this methodology can be used as a learning

tool, facilitating the continuous improvement of the analytical procedure. Furthermore, with

the innovative strategy presented during the latter part of this work, we have demonstrated

that qualitative and quantitative risk can be assessed and managed throughout the entire

analytical method lifecycle.

Chapitre VI

Liste des publications

Chapitre VI : Liste des publications

177

1. C. Henrist, K. Traina, C. Hubert, G. Toussaint, A. Rulmont, R. Cloots, Study of the

morphology of copper hydroxynitrate nanoplatelets obtained by controlled double jet precipitation and urea hydrolysis, Journal of Crystal Growth, 254 (2003) 176.

2. E. Rozet, A. Ceccato, C. Hubert, E. Ziemons, R. Oprean, S. Rudaz, B. Boulanger, Ph. Hubert, Analysis of recent pharmaceutical regulatory documents on analytical method validation, Journal of Chromatography A, 1158 (2007) 111.

3. C. Hubert, E. Rozet, A. Ceccato, W. Dewé, E. Ziemons, F. Moonen, K. Michail, R.

Wintersteiger, B. Streel, B. Boulanger, Ph. Hubert, Using tolerance intervals in pre-study validation of analytical methods to predict in-study results. The fit-for-future-purpose concept, Journal of Chromatography A, 1158 (2007) 126.

4. R. Marini Djang’Eing’A, E. Rozet, C. Hubert, E. Ziemons, Ph. Hubert, Estimation of

uncertainty from the total error strategy: Application to internal and normative methods, Acta Clinica Belgica, 65 (2010) 100.

5. C. Hubert, S. Houari, F. Lecomte, V. Houbart, C. De Bleye, M. Fillet, G. Piel, E. Rozet, Ph.

Hubert, Development and validation of a sensitive solid phase extraction/hydrophilic interaction liquid chromatography/mass spectrometry method for the accurate determination of glucosamine in dog plasma, Journal of Chromatography A, 1217 (2010) 3275.

6. C. Hubert, E. Ziemons, E. Rozet, A. Breuer, A. Lambert, C. Jasselette, C. De Bleye, R. Lejeune,

Ph. Hubert, Development and validation of a quantitative method for the selective determination of tin species in tin octoate by differential pulse polarography, Talanta, 80 (2010) 1413.

7. A. Bouabidi, E. Ziemons, R. Marini Djang’Eing’A, C. Hubert, M. Talbi, H. Bourichi, M. El

Karbane, B. Boulanger, Ph. Hubert, E. Rozet, Usefulness of capability indices in the framework of analytical methods validation, Analytica Chimica Acta, 714 (2012) 47.

8. F. Lecomte, C. Hubert, S. Demarche, C. De Bleye, A. Dispas, M. Jost, F. Frankenne, A.

Ceccato, E. Rozet, Ph. Hubert, Comparison of the quantitative performances and measurement uncertainty estimates obtained during method validation versus routine applications of a novel hydrophilic interaction chromatography method for the determination of cidofovir in human plasma, Journal of Pharmaceutical and Biomedical Analysis, 57 (2012) 153.

Chapitre VI : Liste des publications

178

9. C. Hubert, P. Lebrun, S. Houari, E. Ziemons, E. Rozet, Ph. Hubert, Improvement of a

stability-indicating method by Quality-by-Design versus Quality-by-Testing: A case of a learning process, Journal of Pharmaceutical and Biomedical Analysis, 88 (2014) 401.

10. C. Hubert, S. Houari, E. Rozet, P. Lebrun, Ph. Hubert, Towards a full integration of

optimization and validation phases: An Analytical-Quality-by-Design approach, Journal of Chromatography A, 1395 (2015) 88.

11. C. De Bleye, E. Dumont, C. Hubert, P.Y. Sacré, L. Netchacovitch, P.-F. Chavez, Ph. Hubert, E. Ziemons, A simple approach for ultrasensitive detection of bisphenols by multiplexed surface-enhanced Raman scattering, Submitted for publication (2015).

Une liste complète des communications scientifiques est disponible sur ORBi :

http://orbi.ulg.ac.be/browse?type=authorulg&rpp=20&value=Hubert%2C+Cédric+p004025

http://orbi.ulg.ac.be/browse?type=authorulg&rpp=20&value=Hubert%2C+Cédric+p004025

MEMBRES DU JURY :

Prof. Corinne CHARLIER (Président)

Prof. Serge RUDAZ

Prof. Jean-Michel KAUFFMANN

Prof. Bruno BOULANGER

Dr. Patrice CHIAP

Prof. Jacques CROMMEN

Prof. Marianne FILLET (co-Promoteur)

Prof. Philippe HUBERT (Promoteur)

Documents

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