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Thesis presented to obtain the degree of Doctor in Pharmaceutical Sciences (PhD)

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ACADEMIC YEAR

2007-2008

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ANALYTICAL METHODS LIFE CYCLE

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Thesis presented to obtain the degree of Doctor in Pharmaceutical Sciences (PhD)

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ACADEMIC YEAR

2007-2008

à Cécilia & Xavier

tiens à remercier en particulier.

Mes remerciements vont tout d’abord au Professeur Ph. Hubert, promoteur de cette thèse, qui tout au long de ces années a été d’une très grande disponibilité. Ses conseils, son soutien et sa confiance m’ont permis de mener ce travail à bien. Je souhaite également exprimer ma reconnaissance au Dr. B. Boulanger, co-promoteur de cette thèse, qui m’a transmis sa passion et sa vision de la statistique appliquée à la chimie analytique.

Je souhaite également adresser mes plus vifs remerciements au Dr. P. Chiap sans qui la technique de commutation de colonne me serait probablement encore inconnue aujourd’hui. Qu'il soit remercié aussi pour l’ensemble des collaborations que nous avons eues. Mes sincères remerciements vont aussi à Mr. W. Dewé qui m’a initié à la problématique des transferts de méthodes et m’a introduit dans la commission SFSTP relative à ce sujet. Qu’il soit remercié aussi pour son amitié et pour les bons moments passés, notamment dans le Thalys !

Je tiens également à remercier chaleureusement tous les membres du laboratoire de chimie analytique, pour leur amitié, soutien et les passionnantes discussions. Une atmosphère de travail très agréable existe grâce à vous ! Merci aussi à Mr. F.

Moonen et D. Vandermaesen pour leur amitié, les possibilités d’accès à plusieurs logiciels ainsi que pour les interactions qu’ils m’ont permis d’avoir avec les industries pharmaceutiques.

Pour leur soutien financier, je remercie aussi la Région Wallonne, le Fond Social Européen, Les Fonds Léon Frédéricq et l’Université de Liège, sans qui je n’aurais pu réaliser ces travaux.

Mes remerciements s’adressent également aux membres du Jury qui me font l’honneur de juger cette thèse.

Enfin, je ne pourrais clôturer ces remerciements sans me tourner vers mon épouse, Cécilia, dont la patience, la compréhension, le soutien et l'aide logistique m'ont été indispensables, vers mes parents qui m'ont apporté aide et encouragement, ainsi que

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I. OBJECTIVES ... 1

1. OBJECTIVES... 2

2. THESIS STRUCTURE... 4

II. INTRODUCTION... 7

1. GENESIS OF QUANTITATIVE RESULTS: THE ANALYTICAL METHOD LIFE CYCLE... 8

1.1. Selection... 12

1.2. Development and Optimization ... 15

1.3. Validation ... 19

1.3.1. Validation criteria... 21

1.3.2. Objectives of an analytical procedure... 23

1.3.3. Objective of method validation ... 29

1.3.4. Decision rules... 30

1.4. Methods comparison... 36

1.4.1. Regression analysis ... 38

1.4.2. Correlation Coefficient... 41

1.4.3. Paired t-Test ... 41

1.4.4. The difference plot ... 42

1.5. Robustness ... 44

1.5.1. Selection of the factors and their levels... 47

1.5.2. Selection of the responses ... 48

1.5.3. Selection of an experimental design... 49

1.5.4. Execution of the experimental design, Statistical treatment and interpretation of the results... 50

1.6. Transfer ... 51

1.6.1. Analytical Method Transfer Steps... 52

1.6.2. Evaluation of the Method Transfer... 55

1.7. Inter-laboratory studies ... 58

1.8. Measurement uncertainty ... 61

1.8.1. The ISO “bottom-up” (GUM) approach... 62

1.8.2. The “top-down” approaches ... 65

1.8.2.1. Inter-laboratory studies approach... 65

1.8.2.2. Validation approach ... 65

1.8.2.3. Robustness approach... 66

1.8.3. Uncertainty “expression”... 66

1.9. Routine use ... 67

1.9.1. Shewhart charts ... 70

1.9.2. CUSUM charts ... 73

1.9.3. EWMA charts... 75

1.9.4. Comparison of the different control charts ... 76

2. CONCEPT OF TOTAL ERROR... 79

3. ROLE OF TOLERANCE INTERVALS... 84

3.1. Confidence Interval of the mean of a sample... 84

3.2. Tolerance Intervals... 86

3.2.1. β-Expectation Tolerance Interval or Prediction Interval... 86

3.2.2. β-Content, γ-confidence Tolerance Interval... 88

3.3. Link between tolerance intervals and total error, and applications ... 90

BIBLIOGRAPHY... 92

III. ANALYTICAL METHOD VALIDATION... 118

1. INTRODUCTION... 119

2. REVIEW OF PHARMACEUTICAL REGULATORY DOCUMENTS ON METHOD VALIDATION... 125

3. MINIMUM EXPERIMENTAL PROTOCOLS FOR METHOD VALIDATION... 126

4. STATISTICS TO PERFORM FOR METHOD VALIDATION... 127

5. EXAMPLES OF APPLICATION... 128

5.1. Validation of an on-line SPE-LC-ECD method ... 128

5.2. Validation of an nonaqueous capillary electrophoresis method... 129

5.3. Validation of a LC method for the determination of R-timolol in S-timolol maleate.... 130

5.4. Validation of a NIR spectrophotometry (NIRS) method ... 131

6. IMPROVEMENT OF THE DECISION EFFICIENCY OF THE ACCURACY PROFILE... 132

7. EVALUATION OF THE PREDICTION ABILITY OF THE ACCURACY PROFILE... 133

8. CONCLUSION... 134

IV. ANALYTICAL METHOD TRANSFER ... 138

1. INTRODUCTION... 139

2. TOTAL ERROR FOR METHOD TRANSFER... 144

3. EXAMPLES OF APPLICATION... 145

3.1. Transfer of a LC-UV method ... 145

3.2. Transfer of two fully automated on-line SPE-LC methods ... 146

4. CONCLUSION... 147

V. GENERAL CONCLUSION & PERSPECTIVES... 149

1. GENERAL CONCLUSION... 150

2. PERSPECTIVES... 155

APPENDIX I - LIST OF PUBLICATIONS... 160

I. Objectives

1. OBJECTIVES ... 2 2. THESIS STRUCTURE... 4

1. OBJECTIVES

There are innumerable areas where chemical analyses are important due to the subsequent decisions taken from the results provided, e.g. determination of the quality of manufactured products, food, measurements in support of health and safety, environmental legislation and forensic science. The cost of “wrong results” can be enormous in all areas, e.g. repetition of analyses, court trials, wrong assessment of environmental quality or food products, and leads to loss of confidence in the reliability of analytical results. Reliability of analytical results is a must: it has to be demonstrated to meet the needs of the customers (and all other stakeholders) and thus attract their confidence. For the pharmaceutical industry, it is on the results obtained from analytical laboratories that all the critical decisions are taken, 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, and so on.

The reliability of the decisions taken on this basis depends solely on the reliability and consistency of the results obtained with the analytical methods.

To ensure this reliability, validation of analytical methods are therefore of paramount importance. Validation of analytical methods is only one though essential step in the integral process of demonstrating reliability of analytical results. On the other hand, analytical methods are not always routinely used in the laboratory where they have been developed and validated. This is especially true in the pharmaceutical industry;

here analytical methods are either developed in research and development (R&D) laboratories and transferred to the quality control laboratory of the production site or send to or received by contract research organizations (CROs). These receiving laboratories are the ones that will daily use the method. The transfer should thus

demonstrate that these laboratories will provide reliable analytical results. Moreover, the interpretation and evaluation of the analytical results during these two key steps should be based on sound statistical bases. If not, the significance and the utility of the analytical results generated for decision making will remain unclear.

The main objective of this thesis is to enhance the reliability of decisions made using results obtained from quantitative analytical methods during different steps of their life cycle, namely analytical method validation and transfer.

In order to achieve this, the purpose of quantitative analytical methods and of their validation should be reminded. Furthermore, an attempt to reconcile both will be made. Indeed some shortcomings of existing validation schemes provided by regulatory documents are identified which introduce a gap between validation criteria and the intended use of the method. The next aim will be to propose a minimum experimental design for analytical method validation while clarifying the statistical evaluation of the results of analytical method validation in order to predict the future reliability of the routine results. This will be performed through the use of a specific statistical methodology: β-expectation tolerance interval. Then an illustration of the potential universality of the proposed methodology will be made through the application to several analytical methods as well as a proposition to increase the objectivity of the decision process. Finally the adequacy of the predictions made during method validation for the routine application of the method will be evaluated in order to demonstrate their efficiency.

Concerning the analytical method transfer step, the main objective is to propose a new and original statistical and experimental approach which will ensure the laboratories as well as the regulatory bodies that the receiver will provide reliable results during the future routine exploitation of the transferred method. The possible use of β- expectation tolerance interval to achieve this aim will be investigated. The demonstration of the applicability of this new methodology will be made to different types of analytical methods in order to evaluate its usefulness and suitability.

2. THESIS STRUCTURE

Chapter II is an introduction to the various steps analytical methods will face during their life cycle in order to demonstrate the reliability of the results generated. These steps are method selection, optimization, validation, methods comparison, robustness studies, method transfer, inter-laboratory studies, evaluation of the measurement uncertainty and finally routine use of the method. Focus on the regulatory requirements is made when relevant. Finally, a key concept to assess the reliability of analytical methods is reviewed: “Total Error” as well as the role of a specific statistical methodology to evaluate this Total Error concept: “Tolerance Intervals”.

Chapter III is related to the quantitative analytical method validation issue. It begins with a review of the regulatory guidelines related to the validation of pharmaceutical and bio-pharmaceutical methods, stressing the discrepancies between the various documents as well as the practical implications of theses differences and of the methodologies proposed by these documents. Next, a minimum protocol in terms of

experimental design is proposed, followed by the statistics to perform in order to decide the most adequately whether an analytical method can be declared valid or not using β-expectation tolerance intervals as principal statistical methodology. The interpretation of these tolerance intervals will be made straightforward through the use of a decision graph, the accuracy profile. Some examples of application will subsequently illustrate the proposed methodology using accuracy profiles. Then, a proposition to increase the objectivity of the decision process using innovative quality indexes is made and applied to an example of method validation. Finally, the demonstration that the predictions obtained during the validation step are trustful for decision making is completed showing that it is possible to reconcile the objectives of routine analysis with those of the method validation.

Analytical method transfer from one laboratory to another is discussed in Chapter IV. The first point that is evoked is the development of a new statistical approach to assess the acceptability of method transfer. In the continuity of the works performed for the method validation phase, evaluation of a total error approach to assess method transfer is performed. Consequently, the use of β-expectation tolerance intervals to assess the acceptability of such transfers is envisaged in order to try to keep the aim of method transfer consistent with the objective of quantitative analytical methods. Then this new decision methodology is applied to two distinct case studies: the first one being the transfer of analytical methods dedicated to the quality control of pharmaceutical formulations and the second being the transfer of bio-analytical methods.

Finally, the general conclusions of this thesis along with perspectives for future researches not only in the domain of the prediction of analytical results reliability but particularly in the management of the risks linked to the use of these results are given in Chapter V.

II. Introduction

1. GENESIS OF QUANTITATIVE RESULTS: THE ANALYTICAL METHOD LIFE

CYCLE ... 8

1.1. SELECTION... 12

1.2. DEVELOPMENT AND OPTIMIZATION... 15

1.3. VALIDATION... 19

1.4. METHODS COMPARISON... 36

1.5. ROBUSTNESS... 44

1.6. TRANSFER... 51

1.7. INTER-LABORATORY STUDIES... 58

1.8. MEASUREMENT UNCERTAINTY... 61

1.9. ROUTINE USE... 67

2. CONCEPT OF TOTAL ERROR ... 79

3. ROLE OF TOLERANCE INTERVALS ... 84

3.1. CONFIDENCE INTERVAL OF THE MEAN OF A SAMPLE... 84

3.2. TOLERANCE INTERVALS... 86

3.3. LINK BETWEEN TOLERANCE INTERVALS AND TOTAL ERROR, AND APPLICATIONS... 90

BIBLIOGRAPHY... 92

1. GENESIS OF QUANTITATIVE RESULTS: THE ANALYTICAL METHOD LIFE CYCLE

Fields of applications of analytical methods are extremely diversified for instance for pharmaceutical, bio-pharmaceutical, clinical, forensic, toxicological, environmental, agricultural or food analysis. Whatever the analytical method used and regardless of the industrial sector it is applied to, each laboratory has to be able to produce reliable results when executing analysis for a client or for regulatory purposes in order to answer the analytical problem and thus the socio-economic one as shown in Figure 1.

The overall quality of the results obtained using analytical methods is essential.

Results quality can be broken down in three main criterions: traceability, utility and reliability as shown in Figure 1 [Taverniers et al, 2004; Valcarcel et al., 1999]. All these points are common to the requirements of developing laboratory Quality Assurance systems and are required for accreditations like the ISO 17025 (2000) norm. Traceability refers not only to the establishment of the relationship to well- stated references (standards) but also to the documented “history” of a product (e.g.

result, sample, measuring standard, and instrument) or a system (e.g. analytical method, laboratory) [Valcarcel et al., 1999]. Utility is linked to the definition of the analytical problem [Valcarcel et al., 1997] in order to reach the objective of the end- user (client, consumer or regulatory body). Reliability of the results is linked to the confidence about the produced analytical results. IUPAC [Inczédy J., et al. 1998] and EURACHEM (1998) have combined both of these last two points into the notion of

“fitness of purpose” of analytical methods which expresses the “degree to which data produced by a measurement process enables a user to make technically and administratively correct decisions for a stated purpose.” Indeed the end-users of the

results should be able to make adequate decisions based on these results such decisions being critical: batch release of pharmaceutical products, patient’s health status, bioequivalence of two pharmaceutical formulations, … Inadequate decisions will lead to higher costs, health risks or illegal practices.

Social / Economic Problem:

• Therapeutic role of a pharmaceutical product;

• Presence of toxic species in food.

Analytical Process:

•Sampling strategy;

• Sample treatment;

• Method selection;

• Detection;

• Quantification.

Analytical Properties:

• Selectivity;

• Accuracy;

• Uncertainty;

• Speed;

• Automation;

• Cost;

• …

External Quality

Pharmaceutical product, Food, Regulatory body, …

Requirements to be satisfied:

• Release limits;

• Regulatory concentration limits;

Analytical Problem Analytical Problem

Analytical Quality Traceability Fit for purpose

Utility Reliability

Analytical Quality Traceability Fit for purpose

Utility Reliability

Figure 1: The analytical problem (adapted from Valcarcel et al., 1997).

Results of analytical methods are not obtained in a straightforward manner. The analytical method, which will be used to provide its end-user results in order to reach these highly critical decisions, has to pass different steps that should demonstrate their fitness for purpose. Indeed there is rarely an already available method to answer the problem an analytical chemist is facing. These several related steps the analytical method will have to successfully go through can be described by the “the analytical

answer the goal of the end-user, i.e. that the method is fit for its purpose. Indeed, the analytical method is not a static item; it is rather a dynamic, iterative process: the method of analysis is created; it will mature, and finally die [Feinberg et al., 2004;

Feinberg, 2007]. This continuous evolution of the analytical method can be conveniently described by a simple representation such as the one of Figure 2. This figure illustrates the dynamic flow in which any analytical method is included.

6. Transfer

• Accuracy

• Trueness

• Precision

7. Inter-laboratory studies

• Collaborative studies

• Proficiency tests

• Standardization 2. Development & Optimization

• Design of Experiments

3. Validation

• Response function

• Accuracy

• Trueness

• Precision

• Limit of quantification

9. Routine Use

• Control Charts 1. Selection

4. Robustness

• Design of Experiments

5. Methods comparison

• Regression

• Correlation

• Paired t-test

• Difference plot 8. Uncertainty

6. Transfer

• Accuracy

• Trueness

• Precision

7. Inter-laboratory studies

• Collaborative studies

• Proficiency tests

• Standardization 2. Development & Optimization

• Design of Experiments

3. Validation

• Response function

• Accuracy

• Trueness

• Precision

• Limit of quantification

9. Routine Use

• Control Charts 1. Selection

4. Robustness

• Design of Experiments

5. Methods comparison

• Regression

• Correlation

• Paired t-test

• Difference plot 8. Uncertainty 2. Development & Optimization

• Design of Experiments

3. Validation

• Response function

• Accuracy

• Trueness

• Precision

• Limit of quantification

9. Routine Use

• Control Charts 1. Selection

4. Robustness

• Design of Experiments

5. Methods comparison

• Regression

• Correlation

• Paired t-test

• Difference plot 8. Uncertainty

Figure 2: Analytical method life cycle

As shown in Figure 2, this life cycle can be decomposed in several steps: the method selection, its optimization, the validation of the analytical method, a robustness study, a comparison study, the transfer of the method to another laboratory, inter-laboratory studies and finally its routine use. A central element intimately linked to each of these steps is the estimation of the measurement uncertainty linked to the data generated by the analytical method [Marini, 2006]. After a certain amount of time, the method may be discarded because it is obsolete or because there are new requirements, and another

lifecycle begins. It can thus be understood that each step of the analytical method life cycle should allow to ensure that the analytical method is “fit for its purpose”. For instance in the subclause 5.4.5.3 of the ISO 17025 standard, performance criteria to demonstrate that analytical methods are fit for purpose can be made through several of these steps: “The techniques used for the determination of the characteristics of a method should be one of, or a combination of, the following: calibration using reference standards or reference materials, comparison of results with other methods, interlaboratory comparisons, systematic assessment of the factors influencing the result, assessment of the uncertainty of the results based on scientific understanding of the theoretical principle of the method and practical experience.”

In particular, as shown in Figure 2, method validation together with method transfer, since they are the last steps before routine applications of the analytical methods should demonstrate this fitness for purpose of the analytical methods. Indeed it is from the results obtained during the routine analysis that “technical and administrative” decisions are taken. In the following sections, each of these steps will be succinctly described.

1.1. Selection

The first step in the method lifecycle (Figure 2) is the selection of the method. This can be a difficult process. It involves translating a given problem into chemical measurements, such as, for example, controlling the amount of a given active substance and its degradation products in a pharmaceutical formulation or monitoring the availability of active substances in biological fluids. In such situations, one or several analytes may need one or many specific methods of analysis, together with their previous sample clean up or extraction procedures. The expertise of the analytical chemist is of central importance to select the most adequate method.

In order to select the adequate method trivial questions such has the following should be answered:

What is the analyte (s)?

What is the nature of the sample such as the physical and chemical properties of the sample?

What information is needed (qualitative, quantitative)?

What level(s) of analyte(s) is (are) expected?

What level of accuracy is required?

What are the acceptance limits of the method performances?

Which others constituents of the sample are generally present?

How many samples will have to be analyzed?

Indeed it is of prime importance to know as much information as possible about the sample that will be analyzed. Simple and obvious points to resolve can be the

expected components in the sample (excipients, contaminants, side products, degradation products, metabolites, …), which components are of interest, characteristics such as volatility of the sample, possible solvents, presence of acids and/or bases, history of the sample like details about the synthesis. Answer to these questions will help to choose the appropriate method. The chemical properties of the compound being analyzed are also extremely important for method selection. These may include, but are not limited to, the presence of functional groups (chromophores), ionizability, and polarity.

The most commonly used detection method is UV/VIS for drug compounds with one or more chromophoric functional groups. The detection techniques with higher selectivity and sensitivity such as electrochemical, fluorescence and mass spectrometric detection may also be considered when direct or separation-based UV detection is deemed unsuitable. Occasionally, chemical modification or derivatization may be used for analysis of a drug compound lacking any chromophores.

If quantitative analysis is desired, the quantification threshold, precision, trueness and accuracy required can help to select the method. Some relatively important general criteria such as the specificity/selectivity of the method with regard to possible interferences, the limit of detection, the analyte range, sampling methods (gas, liquid, solid), sample preparation (solid phase extraction, digestion, etc.), accuracy, speed, automation, ease of use, efficiency, cost, temporal and spatial resolution, regulations (FDA, EPA, GLP, ISO) may be useful to orient the method selection.

Separation-based detection methods such as HPLC methods can be helpful to eliminate the interference from samples. The use of appropriate sample treatment can also eliminate matrix interferences. The use of selective detection methods such as fluorescence, electrochemical and mass detection can be considered too for analyzing

drug compounds in highly complex samples that would pose significant analytical interference with direct UV/VIS detection and even with separation-based methods.

Even if method selection rely on knowledge, experience and skill, looking at the literature may provide useful information and clues to select the adequate method

1.2. Development and Optimization

Once the method is selected, it is often necessary to perform several experiments in order to either adapt to the laboratory conditions or fully optimize the method. This optimization of the method can be quite complex with an original procedure. Indeed due to the large number of parameters involved in analytical methods development, it is difficult to find the best set of such parameters which optimize the analytical method development by trial and error or by one factor at a time variations.

Experimental designs and response surface methodology can be used to achieve this task [Duarte et al., 2006]. Whatever the statistical design, the minimum and maximum values of each factor will have to be defined in order to determine the experimental domain that will be investigated during the optimization. The most common designs used to build response surfaces are the full and fractional factorial designs, the central composite one, Box-Behnken, Doehlert and mixture designs [Siouffi et al., 2000;

Ferreira et al., 2007]. However the factorial designs are mostly used to determine the factors that do affect significantly the results. The usual steps involved for analytical method optimization using Designs of Experiments (DOE) are:

(i) Defining the optimization criteria: either a single or multicriteria will be selected (resolution, analysis time, precision, …).

(ii) Defining the factors to be considered: for chromatographic methods for instance there is a great number of possibilities: pH, proportion of organic solvent in mobile phase, temperature, …

(iii) Choosing the levels of the factors in order to define the experimental domain.

(iv) Screening these factors in order to find the most significant ones using Plackett-Burman or fractional factorial designs [Siouffi et al., 2000;

Montgomery, 2005].

(v) Choosing a statistical design to investigate the experimental domain of interest for the significant factors in order to define a response surface, (vi) Performing the experiments usually in random order and by blocking

when necessary,

(vii) Perform analysis of variance to evaluate the most appropriate model without any evidence of lack-of-fit,

(viii) Perform validation of the model in order to know if the method is effectively optimized. This last point is however rather sparsely executed in the domain of optimization of analytical methods [Ferreira et al., 2007].

The central composite designs is the most used for optimization of chromatographic methods as reported by Ferreira et al. (2007), it has been used to optimize extraction steps, derivatization reactions, separations steps for methods dedicated to the analysis of chemical substances in drugs or in biological matrixes. The Box-Behnken and Doehlert designs have also been used for the optimization of the same steps in other situations but with a less extent. However, reasons for choosing an experimental design are not usually explained in reported papers [see for e.g.: Dewé et al., 2004 where justifications of the selected design is made]. These can be [Govaerts et al., 1998]:

Practical aspects: number of experiments to perform, positions and numbers of the levels of the factors, possibility to perform the design in

sequential experiments (with respect to the factors, model or experimental domain),

Statistical properties of the DOE: such as rotatability, orthogonality or D-optimality,

Nature of the factors: if the factors are components of a mixture, then special designs such as mixture designs should be used.

Application of experimental designs to method optimization will not only allow to find the levels of factors which will answer the more adequately the faced analytical problem. It will also provide a tool to obtain robust optimization of the analytical method. This fits adequately the ICH Q2R1 demand [ICH, 2005]: “The evaluation of robustness should be considered during the development phase and depends on the type of procedure under study. It should show the reliability of an analysis with respect to deliberate variations in method parameters”. Indeed the response surface will allow to find a region in the experimental domain where slights deliberate modifications of the parameters will not affect the responses studied. This type of method optimization allows to circumvent the robustness study (see section 1.5 Robustness) which is sometimes required by drugs registration authorities after the validation process in the framework of New Drug Application (NDA) or Marketing Authorization files.

The optimization of analytical methods using response functions is only one family of optimization scheme available. Another approach is based on models for the retention of the solutes [Siouffi et al., 2000]. The advantage of response surface methodology is that it does not require an explicit equation for the criteria (e.g.: retention); however it requires usually a large number of experiments, boundaries of the experimental

domain are not easy to define, and thus the response surface is only valid in the defined domain. Approaches to method optimization using retention models are also available [Siouffi et al., 2000]. Finally attempts to realize methods optimization by relating molecular structure to retention are made in order to predict the retention behavior of structurally related compounds; these are Quantitative Structure Retention Relationship (QSRR) studies [Siouffi et al., 2000; Héberger, 2007].

1.3. Validation

When the development and optimization phase is ended, the draft of the standard operating procedure (SOP) can be written. Method validation is ‘‘... the confirmation by examination and the provision of objective evidence that the particular requirements for a specific intended use are fulfilled’’ [ISO 17025, 2000]. A distinction between intra-laboratory (or in-house) and inter-laboratory (or collaborative) validation can be made. The first is universal and compulsory, the second is mainly applicable to methods that will be used by several laboratories (refer to section 1.7 Inter-laboratory studies). For example, in the pharmaceutical industry, it is useless or impossible to perform a collaborative study for a new molecule under development. On the other hand, all methods used for food safety control must be inter-laboratory validated [Feinberg et al., 2004]. The specific objective of the analytical method must be defined before starting any validation. Indeed as stated earlier a method must be fit for a given purpose.

The validation process must always satisfy three requirements, also commonly called

“golden rules” [EURACHEM, 1998]:

1. The whole method must be validated. The focus should not only be made on the detection technique or the instrumental measurement but also on the previous steps of sample pre-treatment, extraction or pre-concentration. Indeed they also belong to the analytical method and are of utmost importance.

2. The whole range of concentrations must be validated. This can be a difficult task to comply with as a method may work in one particular concentration range but not in others.

3. The whole range of matrices must be validated. Indeed the matrix can have a decisive effect on the analysis.

Furthermore, the validation study should include the sources of variability that may be commonly encountered during routine application of the method such as, at least, the various types of equipment and the different analysts that will run the method every day. If the analysis is always performed with the same equipment and by the same operator, then other equipments or operators need not be taken into account. Finally, before the equipment is used for the validation step as well as for routine analysis, its performance must be checked.

The framework of method validation is defined by several regulatory or reference texts such as ICH [ICH, 2005], FDA [FDA, 2001], EURACHEM [EURACHEM, 1998], IUPAC [Thompson et al., 2002], AOAC [AOAC, 1990]. They define the criteria of validation to test but they do not propose experimental approaches and mostly limit themselves to general concepts. For these reasons several practical guidelines have been proposed [Caporal-Gautier et al., 1992; Hartmann et al., 1998;

Hubert et al., 1999; Hubert et al., 2004] to help the analysts to validate their analytical procedures.

These guides have significantly contributed to making progress in the validation of dosage procedures. Nevertheless, the first guide of the Société Française des Sciences et Techniques Pharmaceutiques (SFSTP) [Caporal-Gautier et al., 1992] was said to be too exclusively dedicated to pharmaceutical specialties. It showed weaknesses with regard to the objective of analytical method validation. For example, the analyst can be penalized if he develops a procedure that is too precise. In addition, the analyst is

confronted to a lot of statistical tests that sometimes complicates his decision rather than helping him. This confusion between the diagnosis and decision rules can also be found in the second SFSTP guide [Hubert et al., 1999] which is dedicated to bioanalytical procedures. Nevertheless, the concept of accuracy profile proposed in this SFSTP guide could be extended to other activity sectors such as environment or food processing. For this reason, the recent SFSTP guide [Hubert et al., 2004] aimed at aligning the objectives of the validation according to the objectives of the analytical procedure. It also aimed to validate the analytical procedure in the same way in which it will be used in routine. Finally it aimed to provide a simple decision rule by using the tolerance intervals (refer to section 3 Role of Tolerance Intervals). This new guide also aimed to propose a consensus on the norms usually recognized, while widely incorporating the ISO terminology [ISO 5725-1, 1994]. It also presented an experimental strategy for the validation of dosage procedures, regardless of the industrial sector, to optimally use experiments performed, to extract a maximum of information from the results and to minimize in routine the risks to re-analyze samples [Hubert et al., 2007a et 2007b]. This approach should therefore considerably reduce the risk either to accept a procedure that would not provide sufficiently accurate results or, on the contrary, to reject a procedure that would be appropriate.

1.3.1. Validation criteria

The main validation criteria are those widely recognised and commonly used in analytical laboratories [EURACHEM, 1998; FDA, 2001; ICH, 2005]. These criteria are the following:

• specificity-selectivity,

• response function (calibration curve),

• linearity (of the results),

• precision (Repeatability and Intermediate Precision),

• trueness,

• accuracy

• limit of detection (LOD),

• limit of quantitation (LOQ),

• assay range,

In addition, according to the domains concerned, other specific criteria can be required, for example the following [FDA, 2001]:

• analyte stability,

• extraction recovery,

• effect of the dilution,

• etc.

It is also important to specify that there is not yet a global consensus between the various regulatory documents on the definition of the criteria to be tested during the validation step. For example, the linearity criterion can appear or not and its interpretation can be different from one document to another. This is also the case for the trueness that can be confounded with the accuracy depending on the referential used. In the last SFSTP guide [Hubert et al., 2004] to avoid this, the ISO norm has been selected as main referential for the definition of the validation criteria.

It must be underlined that the validation criteria mentioned above must be evaluated, as much as possible, in the same matrix as that of the samples intended to be analysed [FDA, 2001]. Every new analytical procedure will have to be validated for each type of matrix (e.g. for each type of biological fluid and for each animal species).

Nevertheless, the definition of a matrix depends on analyst responsibility and some matrix regrouping, generally admitted by the profession for a given application domain, can be made. Moreover, each modification of a previously validated method automatically involves a revalidation, the extent of which depends on the modifications done and their potential influence on the results and thus on specific validation criteria.

1.3.2. Objectives of an analytical procedure

Should a good analytical procedure aimed at showing that on average the response evolves linearly with the introduced concentration, at demonstrating that the average bias of the procedure is inferior to x%, at defining that the observed precision on a given number of measures is inferior to x%? This is evidently not the case. The objective of any quantitative analytical procedure is to be able to quantify as accurately as possible each of the unknown quantities that the laboratory will have to determine. In other terms, what all analysts expect from an analytical procedure is that the difference between the returned result (xi) and the unknown "true value" of the sample (µT) be smaller than an acceptance limit (±λ), i.e.:

λ µ λ

µ

λ< − <+ ⇔ − <

− x_{i T} x_{i T} Eq. 1

The acceptance limit λ can be different depending on the requirements of the analyst or the objective of the analytical procedure. The objective is linked to the requirements usually admitted by the practice (e.g. 1% or 2% on drug substances, 5%

on active substances in pharmaceutical specialties, 15% for biological samples, environment, etc.). Two principles are emerging: on one hand, a notion of limit of acceptance for the quality of the results generated by an analytical procedure, on the other hand, implicitly, the responsibility of the analyst in the decision to accept or not a procedure according to its performances and future use.

All quantitative analytical procedures can be characterized by a “true bias” δ_M (systematic error), and a “true precision” σ_M² (random error measured by a standard deviation or a variance). These two parameters are properties of all analytical procedures and are as unknown as the "true value" µ_T of the sample to determine.

Indeed, the experiments performed in phase of validation allow the user to obtain estimates of bias and of variance (precision). The reliability of these estimates depends on the adequacy of the experiments made on known samples -the validation standard (VS)- the adequacy depending on the experimental design and the number of experiments made. These estimates of bias and variance are not objectives per se; they are an intermediary but obligatory step for the evaluation of the ability of the analytical procedure to quantify with sufficient accuracy each of the unknown quantities, i.e. to fulfill its objective.

Figure 3 graphically illustrates these concepts as well as equation 1. This figure represents the distribution of 95% of the results given by four different (hypothetical)

analytical procedures having each a true bias δ_M and a true precision σ_M² as well a common acceptance limit ±λ. In this illustration, theses limits are ± 15%, a classical requirement for bioanalytical procedures [FDA, 2001].

-30 -15 0 15 30

-30 -15 0 15 30

Procedure 4 Bias %

-30 -15 0 15 30

-30 -15 0 15 30

-30 -15 0 15 30

-30 -15 0 15 30

-30 -15 0 15 30

-30 -15 0 15 30

Procedure 3

Procedure 2

Procedure 1

Figure 3: Examples of procedures having the same acceptance limits ±λ=±15%. The bias is expressed in % of difference to the true value and the precision as a

relative standard deviation (RSD).

As illustrates Figure 3, procedure 3 (0% of bias, 20% precision relative standard deviation (RSD)) does not fulfill its objective since too many results are obtained beyond +15% or -15% of the true value of the samples. Notice that this procedure can be characterized by a negligible bias, but shows an unsatisfactory precision. Procedure

4 does not fulfill its objective either. The proportion of measures obtained outside the acceptance limits is far too important. Note nevertheless that procedure 4 characterizes itself by a bias (+7%) and a precision (12% RSD) that are both inferior to 15%, as required by the FDA (2001). In contrast, procedures 1 and 2 fulfill the objective. They can be declared as valid procedures. With these two procedures, the analyst has the guarantee that at least 95% of the results will be obtained inside the acceptance limits. Nevertheless, if Figure 3 is more carefully examined, one will note that procedure 1 presents a bias (+7%), but is very precise (3% RSD). Whereas Procedure 2 is characterized by a negligible bias (+1%), but is less precise (8% RSD).

The differences between these two procedures do not matter since in both cases the results obtained are never too far from the true value of the sample to quantify. The quality of the results is by far more important than the intrinsic characteristic properties of the procedure in terms of bias or precision.

Aiming to develop a procedure without bias and without error has a considerable cost.

It is not an acceptable strategy for an analyst that generally has little time upfront. To overcome this dilemma, the analyst will have to take minimal risks (or at least compatible with the analytical objectives). To control this risk, one can invert the reasoning and set up upfront an acceptable maximum proportion of results that can be accepted outside the acceptance limits, e.g. 5% or 20% of the results outside of the acceptance limits. This proportion therefore represents the maximum risk that the analyst is ready to take.

Inside the triangles of Figure 4 are represented the “true” region of acceptable analytical procedures being characterized by a "true bias" and a "true precision".

Acceptable procedures are procedures for which most results, i.e. 95%, 80% or 66%

are likely to fall within the +/-15% acceptance limits (in this example, following recommendations of the FDA, 2001). It is therefore in this space that the "good analytical procedures" are located with respect to the proportion of measures that the analyst would like to have within acceptance limits (i.e. 95%, 80% or 66%). The proportion desired will depend on the objectives of the analytical procedure. In Figure 4, the inner bell shape area represents the area of all the analytical procedures for which it is required that, 99 times out of 100, the result x_i will be included within the acceptance limits settled by the analyst according to the constraints of his activity domain.

Figure 4: True acceptance regions of analytical procedures according to their “true bias” (δ) and their “true precision” (standard deviation, σ) for acceptance limits settled

at +/- 15%. π represents the proportion of results included inside the region delimited by the bell shaped curves [Boulanger et al., 2007].

Figure 4 shows four other bell shape areas corresponding respectively to proportions of 95%, 90%, 80% and 66 % of the results included within the acceptance limits. The proportion of 80% is given for information only and does not correspond to any known regulatory requirement. However, Boulanger et al., (2007) have shown that in order to fulfill the 4-6-15 in-study validation rule (evaluating the performances of the quality control samples during routine analysis) of the FDA (2001) a minimum proportion of 80% should be taken in the pre-study validation (or formal validation phase by opposite to the in-study validation phase). Indeed, they have shown that by taking a proportion of 80% at the validation phase, the probability to pass correctly the 4-6-15 in-routine rule is at least 90%. This contrasts with the (intuitive) proposal frequently encountered in the literature [Desilva et al., 2003; Hoffman et al., 2005]

that 4/6 or 66.7% of the results should lie within the acceptance limits ±15%.

Adopting 66.7% as the minimum proportion of results to be included in the acceptance limits during the validation phase can lead to up to 32% of the acceptable routine runs being rejected with the 4-6-15 rule [Boulanger et al., 2007].

A procedure can be qualified as acceptable if it is very likely (“guarantee”) that the difference between every measurement (xi) of a sample and its "true value" (µT) is inside the acceptance limits that the analyst had predefined. The notion of "good analytical procedure" with a known risk can translate itself by the following equation:

β λ µ < ≥

− )

(x_{i T}

P Eq. 2

where β is the proportion of results inside the acceptance limits, and λ being the acceptance limits fixed a priori by the analyst according to the objectives of the method.

1.3.3. Objective of method validation

Knowing that the characteristics of "true bias" and of "true precision" are parameters that will always remain unknown, but that will be estimated by the measures that will be obtained in the phase of validation, what is then the objective of the validation?

It seems reasonable to claim that the objective of the validation is to give to the laboratories as well to the regulatory bodies guarantees that every single result that the laboratory will produce during routine analysis will be close enough to the unknown

"true value" of the sample. The goal is to minimize consumer risks as well producer risks. Consequently, the objective of the validation is not simply to obtain estimates of bias and precision; it is to evaluate these risks or guarantees. And both estimates of bias and precision are required to evaluate the risks

With respect to this objective, two basic notions should be explained in detail,

- ”close enough”, meaning, for example, that the obtained results during routine analysis will be less than λ% of its unknown “true value” (cf. Eq. 1).

- ”Guarantees”, meaning that it is very likely that whatever the results, it will be

“close enough” to the true unknown value (cf. Eq. 2).

In that perspective, trueness, precision, linearity, … are no longer “statistics”

quantifying these guarantees. In fact, one expects from an analytical procedure to be able to quantify, and not to be precise, even if the precision itself, of course, increases the likelihood to be successful. In this perspective, it is necessary again to differentiate between the statistics that allow taking a decision (the procedure is declared valid or not) and that helps to make a diagnosis (e.g. that standard curve is not linear).

In fact, the adequate decision tool really needed must give guarantees that future results will fall inside the acceptance limits. If the guarantees offered by the decision rule are not satisfactory, then the diagnosis tools will help the analyst to identify the possible causes of the problem; but only if the guarantees are not satisfied.

1.3.4. Decision rules

As regulatory documents related to method validation are general, there is room for interpretation by the analysts in order to choose the decision rule that will allow to declare valid an analytical method.

The classical decision processes encountered for method validation either in the pharmaceutical industry or in the scientific literature can be classified into three groups:

the descriptive approach which uses only point estimates of statistical parameters: bias and intermediate precision [Boulanger et al., 2003],

the difference approach which uses two sided hypothesis statistical tests such as Student t-tests [Hartmann et al., 1995 and 1998; Boulanger et al., 2003], the equivalence approach which compares parameters confidences intervals to

acceptance limits [Schuirmann, 1987; Hartmann et al., 1995 and 1998;

Boulanger et al., 2003].

Beside these classical approaches, an original one based on accuracy profile using tolerance intervals and total measurement error as single statistical decision tool has been recently introduced [Hubert et al., 2004, 2007a and 2007b]. Facing the availability of these different approaches, it is the duty of the analyst to choose the most appropriate approach.

The descriptive approach is not an adequate decision rule as it controls neither the risk to reject a valid method (producer risk) nor the one to accept a method not valid in reality (consumer risk).

The difference rule of decision used in the phase of validation is based on the use of a two sided Student t-test:

H0 : bias = 0 ↔ H0 : relative bias = 0 % ↔ H0 : recovery = 100 % Eq. 3

with the bias = xi-µT, the relative bias = (xi-µT /µT)100 and the recovery = (xi/µT)100 A procedure is declared not biased and wrongly qualified as accurate and thus valid using such decision method, when the 95% confidence limits of the average relative bias includes the value of 0% as shown in Figure 5(a).

But this test is inadequate in the frame of the validation of analytical procedures:

- The greater the variance, i.e. the worse the precision, then the more likely it is that the confidence interval will contain the 0% relative bias value as illustrated by case 4 and 5 of Figure 5(a).

- The smaller the variance, i.e. the better the precision, then the more likely it is that the confidence interval will not contain the 0% relative bias value, leading to reject the procedure as illustrated by case 2 of Figure 5(a).

This is obviously not the objective desired.

The equivalence approach as decision rule, by opposite to the difference one, uses a decision limit defined according to the objectives of the procedure and allows

overcoming this contradiction as shown in Figure 5(b). The statistical hypothesis of this test is now:

H01: relative bias ≤ −∆ vs H11: relative bias > −∆ Eq. 4a and

H02: relative bias ≥ ∆ vs H12: relative bias < ∆, Eq. 4b

where ∆(%) is the decision limit, i.e. the maximal difference that is tolerated for the relative bias of the method.

The decision rule changes, as illustrated by the two horizontal lines representing the decision limits of ±5%. With this rule, procedures 4 and 5 are now rejected, while procedure 2 is now considered as valid.

(a) (b)

0%

1 2 3 4 5

+5 %

-5 % 0%

1 2 3 4 5

Relative bias(%) Relative bias(%)

(a) (b)

0%

1 2 3 4 5

+5 %

-5 % +5 % +5 %

-5 % -5 % 0%

1 2 3 4 5

Relative bias(%) Relative bias(%)

Figure 5: Method validation decision rules for five different situations (1 to 5) with respect to the method relative bias; (a) The

difference approach for the relative bias, (b) the equivalence approach for the relative bias with decision limits set at +/- 5%.

However the equivalence approach as decision rule is not enough. It does not answer the previously stated objective of method validation. It is not because the relative bias and the intermediate precision RSD are included in predefined limits that the results are acceptable as illustrated by Figure 6. However the opposite is always true:

acceptable results are obtained by analytical methods with acceptable bias and intermediate precision RSD (Figure 6).

BiasPrecision

% Bias< 15%

% RSD< 15%

Results Method

µ_T X

BiasPrecision

% Bias< 15%

% RSD< 15%

Results Method

µ_T X (a)

(b) BiasPrecision

% Bias< 15%

% RSD< 15%

Results Method

µ_T X

BiasPrecision

% Bias< 15%

% RSD< 15%

Results Method

µ_T X

BiasPrecision

% Bias< 15%

% RSD< 15%

Results Method

µ_T X (a)

(b)

Figure 6: Good methods do not necessarily provide good results (a), but good results are obtained only by good methods (b); µ_T is the true value; X is the mean of the

results; the red circle is the acceptance limits of the results ±λ%

In this context, the most adequate decision rule consists in the use of the accuracy profile to be included in the acceptance limits (±λ) [Hubert et al., 2004, 2007a and 2007b]. The accuracy profile, constructed from tolerance intervals (see section 3 Role of Tolerance Intervals), allows therefore, as illustrated by Figure 7, to decide if the analytical procedure is able to give enough results inside acceptance limits or not. The area in gray describes the dosage interval in which the procedure is able to quantify with a known accuracy and a risk fixed by the analyst. If the analyst is ready to take, for example, a risk of 5%, he will be able, at the end of the validation of his procedure, to guarantee that on average 95% of the future results given by his analytical method will be included in the acceptance limits fixed according to the requirements (e.g.: 1% or 2% on bulk, 5% on pharmaceutical specialties, 15% in bioanalysis, …).

C₁ C₂ C₃ C₄

RANGE

LLQ ULQ

Bias (%)

+ λ

Concentration

−λ

Error(%)

C₁ C₂ C₃ C₄

RANGE

LLQ ULQ

Bias (%)

+ λ

Concentration

−λ

Error(%)

Figure 7: Illustration of the accuracy profile as decision tools. LLQ: lower limit of quantification; ULQ: upper limit of quantification.

Since the true bias and the true precision of an analytical method are unknown, the

the tolerance interval that allows evaluating the proportion of expected measures inside the acceptance limits. This is obtained from the available estimates of the bias and precision of the analytical procedure (by concentration level) after the phase of validation at the concentration level of the validation standard. This tolerance interval used is a β-expectation tolerance interval (see section 3 Role of Tolerance Intervals).

The estimates of the bias and variance are essential elements to compute the tolerance intervals but the decision is not made on these estimates of bias and variance.

The accuracy profile, represented in Figure 7, is simply obtained by connecting together the lower limits of the tolerance interval on one hand and the upper limits on the other hand. If, as illustrated in Figure 7, for the concentration levels C1 and C4, a subsection of the accuracy profile falls outside the acceptance limits, then new limits of quantification are to be defined, and by consequence, a new dosage interval.

Figure 7 represents these new limits ULQ (upper limits of quantification) and LLQ (lower limit of quantification) that are in perfect agreement with the definition of this criterion, i.e. the highest and smallest quantity of the substance to analyze that can be measured with a defined accuracy (trueness + precision), respectively.

The use of the accuracy profile as a single decision tool, allows not only reconciling the objective of the validation with the one of the analytical method, but also to visually grasp the capacity of the procedure to fulfill its analytical objective [Hubert et al., 2004, 2007a and 2007b].