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Pharmaceutical Chemistry Journal Vol. 38, No. 4, 2004 STRUCTURE OF CHEMICAL COMPOUNDS, METHODS OF ANALYSIS AND PROCESS CONTROL VALIDATION OF HPLC TECHNIQUES FOR PHARMACEUTICAL ANALYSIS N. A. Épshtein1 Translated from Khimiko-Farmatsevticheskii Zhurnal, Vol. 38, No. 4, pp. 40 – 56, April, 2004. Original article submitted June 18, 2002. Validation (evaluation of suitability) of an analytical technique is a procedure aimed at obtaining experimentally justified evidence of the ability of this technique to give results characterized by the required accuracy and precision [1 – 7].2 All analytical techniques used for the development of pharmaceuticals and for the determination of their quality characteristics have to be validated. In the case of using methods stipulated and described in the State Pharmacopoeia, it is not necessary to evaluate their suitability, provided that the analyses are conducted with strict observation of the text of each particular article. In most other cases, especially in cases of modification of the drug composition, the scheme of synthesis, or the analytical procedure, it is necessary to re-evaluate the suitability of the analytical techniques. This paper is aimed at (i) considering the peculiarities of validation of HPLC techniques for pharmaceutical analysis, (ii) critically assessing the main approaches to evaluation of the validation characteristics, and (iii) providing practical recommendations and criteria for finding correct solutions. The USSR State Pharmacopoeia (valid in the Russian Federation) introduced the section “Statistical Analysis of Biological Test Results” in 1968 (Xth Ed.) and the section “ Statistical Processing of Chemical Experimental Data” in 1988 (XIth Ed.). These sections are devoted to problems involved in the metrological attestation of analytical techniques. In 1987, the United States Food and Drug Administration (FDA) issued practical guides on the main principles of vali1 2 “Akrikhin” Chemico-Pharmaceutical Joint-Stock Company, Staraya Kupavna, Moscow Region, Russia. Here and below the terms “accuracy” and “precision” (repeatability, reproducibility) are treated in accordance with the State Standard GOST R ISO 5725–1–2002. Previously, accuracy had the meaning of correctness, but now correctness is described in terms of “trueness.” In justifying the suitability of techniques related to the qualitative determination of substances, statistical processing of the experimental results is obligatory [8]. dation [5] and on the presentation of samples and analytical data pertaining to the validation of methods [6]. In 1993, the International Conference on Harmonization (ICH) developed generalized recommendations on the validation of analytical procedures; these documents were published in 1994 and treated in more detail in 1995 [1 – 3]. In 1994, the US FDA Center for Drug Evaluation and Research (CDER) issued a guide on the validation of chromatographic methods [4]. These documents and some review papers and monographs [9 – 13] provided a basis for extensive implementation of the procedure of validation of analytical methods. The Internet offers the Laboratory Guide to Method Validation and Related Topics at http://www.eurachem.ul.pt /. In recent years, new guides have become available from CDER [15], Waters Company [16], and Labcompliance [17 – 19]. Special sections are devoted to these problems in national and international pharmacopoeias and guides on the validation of analytical procedures [7, 20 – 22]. Also available are computer program packages, such as ELISA Method Validation Templates (Waters) and LaChrom 2000 Validation Manager (Merck) representing electronic tables with incorporated functions of statistical processing of the results of measurements and issuing validation certificates, and monographs on the related subjects [23 – 34]. Tables 1 and 2 summarize the most recent recommendations concerning selection of the validation characteristics depending on the type of analytical procedures. A comparative analysis of these data shows that, according to the United States Pharmacopoeia (USP-26), methods of dissolution testing have to be validated only with respect to precision (repeatability, reproducibility), while the other characteristics “may require validation, depending on the specific test nature.” In contrast, according to the FDA CDER guidelines [15], procedures used for quantitative analysis and dissolution testing need the same validation characteristics. 212 0091-150X/04/3804-0212 © 2004 Plenum Publishing Corporation Validation of HPLC Techniques for Pharmaceutical Analysis 213 Moreover, according to CDER [15], all methods of quantitative analysis have to be characterized with respect to robustness (see below). Robustness is not included in USP-26 [7] because this characteristic has to be studied at the stage of development of an analytical procedure, rather than in the course of validation. Since any analytical situation poses a multifactor problem, validation has to include at least testing of the analytical system as a whole under the conditions stipulated by the description.3 The second task is evaluation of the stability (robustness) of the analytical system with respect to small variations of the main factors (for example, the ratio of the mobile phase components, pH, temperature, etc.). This problem is less important than the first one because it is usually solved at the stage of development of a given analytical procedure. For this reason, problems pertaining to robustness are only briefly mentioned in this review. Let us consider the main stages of validation of the HPLC techniques used in pharmacy. 1. TESTING THE ANALYTICAL PROCEDURE AS A UNIFIED SYSTEM UNDER THE CONDITIONS STIPULATED IN THE DESCRIPTION Figure 1 shows the general scheme of evaluation of the suitability of an analytical procedure, which takes into account specific features of HPLC. As can be seen, testing an analytical procedure as a whole in the general case allows the following validation characteristics to be determined [1 – 7]: (i) specificity; (ii) precision; (iii) linearity; (iv) accuracy; (v) suitability range; (vi) limit of detection; (vii) limit of quantitation; and (viii) stability of solutions.4 Depending on a particular type of the analytical procedure (HPLC technique) only a part rather than all of the above characteristics may be required (see Tables 1 and 2). 1.1. Confirming the Specificity of a Given Analytical Procedure (Separating Power of a Chromatographic System) By the specificity of a system is meant its ability to detect a given substance unambiguously (reliably) in the presence of other components (including impurities) that may be present in the samples [1 – 4]. The proof of specificity depends on the task of a given procedure and on the availability of reference samples of the main impurities. 1.1.1. The specificity of procedures aimed at determination of the content of a parent substance, the parameters of solubility, and the homogeneity of dosage. In order to confirm the specificity of these procedures, it is usually required that peaks of the substances to be determined are sufficiently well resolved between themselves and from peaks of the main impurities, the system components (e.g., of the sample solvent), and the placebo. For this purpose, the sepa3 Specificity (Section 1.1) Recommended requirements to the repeatability of sample injections (Section 3.3) 2.3 Reproducibility. Checked in special cases (Section 1.2.3) 2. Precision (Section 1.2) 2.1 Repeatability (Section 1.2.1) 2.2 Intermediate precision (Section 1.2.2) 3. Linearity (Section 1.3) 4. Accuracy (Section 1.4) 5. Suitability range (Section 1.5) It is expedient to determine these validation characteristics in the course of proof of the analytical system accuracy (using statistical parameters determined for the calibration graph) (Sections 1.3; 1.4; 1.6.2; and 1.7.2) 6. Limit of detection (Section 1.6) 7. Limit of quantitation (Section 1.7) 8. Stability of solutions (Section 1.8.) 9. Robustness (stability) of HPLC procedures with respect to small variations in the main system factors (ratio of the mobile phase components, pH, temperature, etc.). Robustness is usually studied in the stage of development of the given HPLC tecnique (Section 2) Criteria of suitability of a given chromatographic system (Section 3) Fig. 1. The general scheme of validation of HPLC-based analytical procedures. 4 According to this concept, instrumentation, electronics, analytical procedures, and analyzed samples constitute a unified analytical system, which can be considered as a whole [7]. Sometimes, the stability of phases and solutions is considered within the framework of the problem of robustness. ration of peaks is confirmed by a set of chromatograms, at least of (a) the test solution, (b) the reference parent substance solution, (c) the solvent (blank), (d) the placebo (for filled drugs), and (e) the solution used for the evaluation of suitability of the chromatographic system. The degree of peak separation is usually described in terms of the separation coefficient Rs. Recommended values of this coefficient are given below in the Section 3.3. It is recommended to confirm the specificity by investigation of the “purity” of peaks of the parent substance to be determined [4, 27]. This test is usually performed using a diode matrix detector and a special program evaluating spectral homogeneity of the measured peak (e.g., Peak Purity Millennium, Waters). The principle of evaluation of the peak purity is as follows. The sample chromatograms are measured at various detector wavelengths l (numbered n ). Each point of the peak is characterized by a spectrum, which is mathematically described by a vector in the n-dimensional space of the values of absorption (in absorption units, AU) at the preset n wavelengths (the length of this vector is proportional to the substance concentration in the solution studied). The difference between the spectra is evaluated by the angle between the corresponding vectors (called the spectral con- 214 N. A. Épshtein TABLE 1. Validation Characteristics according to th United States Pharmacopoeia (2003) Category Characteristic I II Quantita- Limiting tive tests tests III IV TABLE 2. Validation Characteristics Recommended for Various Tests by the United States FDA (CDER and CBER) [15] Type of analytical procedure Tests for impurities Chatacteristic Identification quantitative limiting Qualitative determination and dissolution tests Accuracy Precision Specificity Limit of detection Limit of quantitation Linearity Suitability range Yes Yes Yes No No Yes Yes Yes Yes Yes No Yes Yes Yes MB No Yes Yes No No MB MB Yes MB MB MB MB MB No No Yes No No No No Notes: Yes = usually studied; No = usually not studied; MB = may be required (depending on a specific test nature). Category I includes analytical methods intended for determination of the content of the main component in parent substances or ready-to-use medicinal forms; category II includes methods of determination of impurities and decomposition products; category III includes methods of determination of the parameters of dissolution, drug release, etc.; category IV includes identification tests; the terms “accuracy” and “precision” (repeatability, reproducibility) are treated in accordance with the State Standard GOST R ISO 5725–1-2002. Accuracy Repeatability Intermediate precision Specificity Limit of detection Limit of quantitation Linearity Suitability range Robustness No No No Yes2 No No No No No Yes Yes Yes1 Yes No3 Yes Yes Yes Yes No No No Yes Yes No No No No3 Yes Yes Yes1 Yes4 No No Yes Yes Yes Notes: Yes = usually studied; No = usually not studied; 1 in cases where the reproducibility is studied, there is no need to specially determine the intermediate precision; 2 insufficient specificity of a given analytical procedure can be compensated by introducing additional tests; 3 may be required in some cases (e.g., when the limit of detection is close to the rated limiting content of an impurity); 4 insufficient specificity of a given analytical procedure can be compensated by determining the content of impurities. trast angle q). If q = 0, the spectra are considered similar (homogeneous). This implies that the value of absorption in one spectrum measured at a given wavelength l can be obtained from the value in another spectrum measured at the same wavelength by multiplying by a certain constant factor. In order to evaluate the spectral homogeneity of a chromatographic peak, the spectral contrast angles q are calculated for all points of this peak relative to the angle at the peak maximum and then the maximum value qp (purity angle) is determined. Two spectra determined for the same substance can differ, for example, because of the influence of the baseline noise. In order to take this into account, a threshold spectral angle qth is determined (i) by determining the maximum spectral angle between pints of the baseline with maximum noise levels or (ii) by taking six chromatograms of a standard sample solution, determining the maximum purity angle qp for each chromatogram, and considering the maximum of these values as the threshold spectral angle qth. This threshold angle characterizes the level below which the difference between two spectra can be considered insignificant. The obtained qp values are compared to qth. For qp < qth, the peak is considered spectrally homogeneous; otherwise the peak is influenced by the presence (i.e., additional absorption) of another substance. In practice, it is possible to use a simplified procedure, whereby the chromatograms of the same peak are measured at two or three wavelengths and the chromatograms are checked for the proportionality (see above) at all points. The latter method is less reliable, be- cause the spectrum can be influenced by variations in the mobile phase composition (e.g., under gradient HPLC conditions), or by deviations from the Lambert – Beer law at high levels of absorption. Therefore, negative results of evaluation of the spectral homogeneity of peaks in the gradient HPLC should be critically assessed and checked for optical densities not exceeding 1 AU. It should be noted that specificity is rarely checked using chromatomass spectroscopy (HPLC – MS) — because of the high cost of this procedure — and the chemical and other analyses of the eluate fractions corresponding to the parent substance, because of tedious procedures. 1.1.2. The specificity of procedures aimed at determination of impurities. In evaluating the specificity of such procedures, it is necessary to differentiate between two cases. Case 1. The main impurities are known and available. In order to confirm the specificity of a procedure used for determining the impurities in a parent substance, it is necessary to show that (i) this procedure allows the peaks of the main products of decomposition of the parent substance to be detected and that (ii) the peaks of impurities are sufficiently well separated between themselves and from peaks of the parent substance and the system components (solvents). Developers of the technology of a parent substance have to prove additionally that (iii) the proposed procedure allows determining the main impurities related to the technological process and that (iv) all such impurities present at an amount of ³ 0.1% are identified [7]. Validation of HPLC Techniques for Pharmaceutical Analysis 215 In order to confirm the specificity of a procedure used for determining impurities in parent substances, it is necessary to demonstrate that (i) this procedure allows the peaks of the main rated impurities to be detected and that (ii) the peaks of these impurities are sufficiently well separated between themselves and from peaks of the parent substance and the system components (solvents). The specificity is confirmed by a set of chromatograms, including at least those of (a) a model solution of the parent substance and the main impurities (prepared by adding these known impurities or their solutions to the parent compound or its mixture with the placebo), (b) the solvent, (c) the placebo (for filled drugs), (d) the test solution, and (e) the solution used for the evaluation of suitability of the chromatographic system. In addition, it is recommended to confirm the specificity of the given analytical procedure by data on the “purity” of the main peaks in the chromatograms of test solutions. Case 2. The main impurities are unknown (unidentified) or absent. In this case, it is expedient to use special experiments involving modification of the parent compound (sometimes called “stress testing” [2, 15, 27]), whereby a solution of the given drug (or of the parent compound) is subjected to factors leading to its partial destruction with the formation of related identifiable compounds. The degree of decomposition can be readily determined from the decrease in the area of the main peak in the chromatogram of the final solution relative to that in the initial solution. The specificity of the given analytical procedure is judged by separation of the peaks of impurities between themselves and from the peak of the main component and by the peak purity of the parent compound. In particular, the specificity of HPLC procedures can be proved using the following methods of chemical modification. (i) Hydrolysis with 0.1 N solutions of HCl or NaOH at room temperature or at elevated temperatures. Example: a granulate was treated with 0.1 N HCl solution for 5 h at 60°C, after which the sample was extracted according to the proposed procedure and analyzed by HPLC. (ii) Oxidation with a 3% hydrogen peroxide solution, 0.05 M iodine solution, etc. Example: captopril was partly oxidized with 0.05 M iodine solution (in order to obtain captopril disulfide — the main technological impurity [22]), extracted according to the proposed procedure, and analyzed by HPLC. (iii) Thermal decomposition by heating to 60 – 100°C. Example: a granulate was kept for 7 days at 80°C. The resulting solid products of decomposition can be stored and used as control substances in the tests for suitability of a chromatographic system. (iv) Photochemical decomposition under illumination (e.g., UV irradiation). (v) Chemical addition reactions, for example, drug bromination at multiple bonds. A mixture of the initial substance and the products of its chemical modification can be used for preparing solutions used for the evaluation of suitability of the chromatographic system. The duration of action used for the chemical modification of drugs is selected taking into account the following factors. (i) The peaks of the products of drug modification are to be clearly distinguishable in the chromatogram. Therefore, the treatment duration must be sufficient to provide for a not less than 10% decrease in the main peak height (area), which is proportional to the drug content. (ii) The peaks of the products of drug modification have to be sufficiently well separated from the main peak, but the main peak height (area) must be comparable with that in the initial test solution. According to [27], it is recommended that the main peak intensity would decrease by no more than 30%. However, this requirement is not as critical, since the stronger decomposition of the parent compound can be compensated by adding it in the necessary amount. (iii) It is desired that the percentage “content” of the products of drug modification determined by the method of internal normalization would be close to the level of maximum permissible content of a single impurity. Further steps in the proof of specificity of the analytical procedure in the case under consideration are the same as in case 1. The validation characteristics additionally include chromatograms obtained in the course of experiments on the chemical modification of the parent compound. Data presentation. The proof of the specificity of an analytical procedure is presented in the form of a set of chromatograms (see above) with discussion of the obtained results. These data are supplemented by the results of calculation of (i) the separation coefficient Rs for two peaks of the most closely spaced components, (ii) the column efficiency N, and (iii) the asymmetry parameters (tailing factors) of the main analytical peaks. It is necessary to make the following remark. Solving the problem of detection and separation of impurities by HPLC is still an art, with the results depending on the skill of developers. It is very important to select the optimum chromatographic columns and mobile phases. Moreover, it is known that, depending on the column loading, it is possible (a) to observe no additional peaks of impurities, (b) to find a certain number of such peaks, a part of which cannot be quantitatively characterized, or (c) to reveal a very large number of additional measurable peaks upon overloading the column with respect to the main drug component. Therefore, in developing and validating the methods of impurity determination (especially in the case of parent compounds), it is expedient to check for the possible presence of additional peaks (i.e., impurities) by chromatography of drug solutions with elevated concentrations providing overloading of the column with respect to the main component. However, this approach is usually inapplicable in the case of ready-to-use drugs containing large amounts of auxiliary substances. 216 N. A. Épshtein 1.2. Confirming the Precision of a Given Analytical Procedure The precision (repeatability, reproducibility) of an analytical procedure characterizes the random scatter (variation) of the results relative to the mean value. It should be emphasized that, in order to obtain reliable results, the sample must have a homogeneous composition. The results have to be statistically treated. Variants leading to rough errors (e.g., using variation range R or the “three sigma” rule [8]) should be rejected. In evaluating the suitability of HPLC procedures (actually, in determining the metrological characteristics), it is necessary to use measuring vessels of class A or special calibrated measuring vessels and take all other possible measures to increase the reproducibility and accuracy of HPLC measurements [27]. The precision (repeatability, reproducibility) of an analytical procedure is evaluated in terms of the standard deviation (SD) of the relative standard deviation (percentage RSD) determined in a series of measurements and calculated by the formulas SD = å( X i - X )2 i =1 m ( m - 1) , RSD(%) = 100SD . X (1) According to the ICH recommendations [4] on the validation of chromatographic procedures, the characteristics of precision are considered at three levels: repeatability, intermediate precision, and reproducibility (Table 3). In [4, 27] and in many other papers, the set of validation characteristics of HPLC procedures includes the injection repeatability. However, the author believes that this is incorrect: this parameter characterizes the quality of injector (e.g., syringe) rather than the suitability of a proposed procedure. TABLE 3. Main Precision Characteristics for the Validation of HPLC Procedures According to ICH [4] Precision characteristic Conditions of determination Repeatability (Rt ) Injection repeatability Determined for the same sample preparation by the same analyst using the same instrument (chromatograph) during a short period of time Intermediate precision (Ip ) Intra-assay precision – Reproducibility (Rp ) – Determined for the same sample preparation by different analysts using various instruments (chromatographs) during a prolonged period of time (not less than two days) The same, in various laboratories This characteristic is not included in the list of CDER [15] and USP-26 [7]. In HPLC validation, data on the injection repeatability should be provided as additional material required in cases of search for the “bottleneck” of a proposed method (dispersion analysis). 1.2.1. Injection repeatability and intra-assay precision. In the general case, repeatability (Rp) characterizes the reproducibility of a given analytical procedure for the same sample preparation, as performed by the same analyst using the same instrument (chromatograph) during a relatively short period of time. For evaluating the repeatability in a given laboratory, the same analyst prepares samples of a model mixture or the same batch of a parent compound or a drug: (a) not less that nine samples of solutions covering the rated range of concentrations. For example: a homogenized powder of triturated tablets from the same batch is used to prepare drug solutions with concentrations equal to 50, 100, and 150% of the reference sample solution concentration according to the proposed procedure, or (b) not less than six samples of solutions in the region of concentrations close to the nominal value. For example: a homogenized powder of a parent compound or triturated tablets from the same batch is used to prepare six solutions with nominal concentration according to the proposed procedure. Note that each sample solution is (i) prepared independently of the other solutions and (ii) chromatographed at least three times. Each solution is characterized by the drug content X i (i = 1, …, N ), the average value X = S X i N , the standard deviation SD, the relative standard deviation RSD of particular measurements, and the confidence interval (for P = 95%) of the average value. It is required to show that the average results are statistically equivalent (e.g., in terms of the Student t-criterion) or, which is more convenient for the practical analysis, that RSD £ 1.0% for determination of parent compounds, RSD £ 2.0% for drugs, or RSD £ 10.0% for impurities [13, 27].5 1.2.2. Intermediate precision. This value characterizes the reproducibility of results obtained in the same laboratory by different analysts using various instruments (chromatographs) during a prolonged period of time (not less than two days) for the same homogeneous sample or a model drug mixture according to the proposed analytical procedure. Typically, not less than six solutions are prepared with concentrations close to the nominal value (see the preceding section). Each sample solution is (i) prepared independently of the other solutions and (ii) chromatographed at least three times. 5 For small values of the standard deviation (SD << 1), the t-criterion may give statistically significant differences even for close (almost identical) values of the compared average concentrations. This is related to the fact that this criterion is proportional to the ratio of systematic and random errors. Validation of HPLC Techniques for Pharmaceutical Analysis 217 These solutions are characterized by the average drug content according to the results obtained by each of the analysts, X i and X j (i, j = 1, …, N ). These data are statistically processed and characterized by generalized average values X 1 = S X i N and X 2 = S X j N and the corresponding standard deviations (SDi, SDj ) and relative standard deviations (RSDi, RSDj ) of particular measurements. First, it is required to show that the proposed procedure of determination of the drug content and the impurity coincentraiton provides for the statistically equivalent standard deviations SDi and SDj of the results obtained by different analysts (in terms of the Fisher F-criterion). Then, it is necessary to demonstrate that the average results of these (for certainty, two) analysts are statistically reliably (P = 95%) identical in terms of the t-criterion calculated as t= | X 1 - X 2| 2 SD1 m1 + SD 2 2 m2 = | X 1 - X 2| 2 SD1 + SD 2 2 m , where X 1 , X 2 are the average results of analyses performed by analysts 1 and 2 and SD1, SD2 are the standard deviations in the particular series of m1 and m2 parallel determinations (usually m1 = m2 = m ). This t value is compared to tabulated values of the Student criterion t (P = 95%, f = m1 + m2 – 2), where P = 95% is the confidence probability and f = m1 + m2 – 2 is the number of degrees of freedom. If the calculated parameter t is lower than the tabulated value, the difference of average values can be considered as statistically insignificant with a 95% confidence probability. Otherwise, the average results differ to a greater extent than that admitted by random errors in both series [35]. In pactice, validation of the procedures of determination of the content of impurities is sometimes performed using a less strict method [13], by showing that the scatter (RSD) of the results of one analyst (characterized by a greater standard deviation (SDi or SDj ) relative to the average result of another analyst (with a lower SDi or SDj) does not exceed a certain preset level, for example, so that RSD £ 10% for impurities with a rated content up to 1%, RSD £ 25% for an impurity content within 0.1 – 1%, and RSD £ 50% for an impurity level below 0.1%. It should be noted that, according to USP-26 [7], it is in most cases sufficient to determine only the repeatability for proper validation of an analytical procedure, while the intermediate precision and reproducibility characteristics should be determined for procedures included in the pharmacopoeial articles. 1.2.3. Reproducibility. This characteristic is determined by comparing the results obtained upon analysis of the same samples in different laboratories using a proposed analytical procedure. The necessary statistical methods are described in monograph [35, Chapter 8.4] and in the State Standard GOST R ISO 5725-2002. It should be noted that for reliable evaluation of the statistical significance of the difference be- tween the results obtained in such investigation, it is necessary that the round robin tests involve not less than five laborqtories [35]. In practice, however, the reproducibility is usually evaluated using two or three laboratories and characterized by less strict estimates. For example, validation of a procedure proposed for the quantitative determination of a parent compound is performed by demonstrating the statistical equivalence of the standard deviations SDi and SDj of the results obtained in different laboratories (in terms of the Fisher F-criterion). Then, it is demonstrated that the scatter (RSD) of the results of analyses in one laboratory (characterized by the maximum standard deviation (SDi or SDj) relative to the average results of analyses in other laboratories (with lower SDi or SDj values) does not exceed a certain preset level [13]. The full-scale reproducibility of analytical procedures is rarely validated because (i) it is necessary to involve certified laboratories capable of reproducing the proposed procedure with high precision and (ii) this requires high organizational facilities and expenditures. 1.3. Confirming Linearity of the Response to Drug Concentration Linearity characterizes the ability of a proposed analytical procedure to give (within the suitability range) a response signal with the magnitude Y (e.g., peak height or area) directly proportional to the amount C (concentration) of a drug to be determined: Y = a + bC. According to ICH recommendations [3], the linearity in practice is first visually estimated from the linear appearance of the plot of Y versus C. If the plot appears linear, this relation is studied by methods of regression analysis in terms of the linear equation Y = a + bC. For the analytical procedures for determining the content of a parent compound, CDER recommends establishing the criterion of linearity at a level of the correlation coefficient r not lower than 0.999 [4]. However, even such a high level of correlation may be accompanied by significant deviations from linearity in the regions of high and low drug concentrations [13]. For this reason, ICH [3] recommends that the linearity be validated by a plot of the difference Y–C showing deviations (residuals) of the calculated values yi = a + bC from the measured Yi values as the function of the concentration Ci. The “outbursts” of the points (xi, yi ) relative to the regression model can be determined by calculating the parameter t using the formula [36] t= SD 0 | y i -Y i | (Y i - y ) 2 1 1+ + N ( N - 1) × SD 2 y , Here, yi and Yi are the calculated and experimentally measured values of the response, respectively; y = Syi /N; N is the total number of experimental points (xi , yi ), and 218 N. A. Épshtein SD 0 = S( y i - Y i ) 2 S( y i - y ) 2 , SD y = . N -2 N -1 The calculated t value is compared to tabulated values of the Student criterion t (P = 95%, f = N - 2). If the calculated parameter is greater than the tabulated value, the given point can be considered as deviating from the adopted regression model with a 95% confidence probability. In practice, validation of the procedures of determination of the content of impurities with respect to linearity is sometimes performed proceeding from a correlation coefficient of r ³ 0.98 [13]. According to our estimates, use of the calibration graphs with such correlation coefficients may lead to RSD values on the order of 20% and above. Therefore, it would be more correct to establish the criterion of linearity at least at the level of r ³ 0.990. The linearity should be validated based on the analysis of at least five solutions with various concentrations covering the entire suitability range of a proposed analytical procedure [35]. According to ICH recommendations [3], the linearity can be demonstrated directly by using the reference parent substance (dilutions of a standard solution) and/or model artificial mixtures including components of the drug studied. The most adequate approach consists in taking thoroughly weighed aliquots of the drug components and preparing solutions according to the proposed procedure, since all operations of the analyst should correspond strictly to those stipulated in the description. In practice, however, an “intermediate” approach recommended by ICH [3] is frequently employed. According to this, solutions are partly prepared using weighed aliquots of the drug components and the other are obtained by diluting these stock solutions. It should be emphasized that the linearity of a proposed analytical procedure should be confirmed in the course of validation of the accuracy, which reduces expenditures and saves time. The usual procedures are as follows. (a) For the analysis of parent compounds, it is common practice to prepare a reference solution of the compound with a concentration at or above the upper limit of the expected concentration interval (suitability range of the proposed procedure). Then, a series of dilutions is prepared so as to cover the entire range. Each solution is studied in a series of two or three injections. (b) For the analysis of ready-to-use drugs, the linearity is frequently checked in the same way as for the parent compound (i.e., using solutions of the parent compound as described in (a)). However, it is incorrect to ignore the possibility that auxiliary components (placebo) may influence the results. Therefore, it is more correct to validate the linearity using model mixtures of the parent compound and placebo. (c) For the determination of impurities using the method of internal normalization of the peak areas or heights, it is possible to evaluate the linearity by preparing dilutions of the reference sample solution (with a concentration equivalent to the rated value) in the model impurity solution so as to obtain drug concentrations in the range from 0.05% (dilution by a factor of 2000!) to 2.5%. Instead of making some dilutions, it is possible to use a proportional decrease in the volume of applied sample (which saves the mobile phase). Data presentation. The validation characteristics include (i) a regression equation of the Si = a + bC type (for example, S = 15536 + 15833969C [mg/ml]), (ii) the correlation coefficient (e.g., r = 0.9998), and (iii) a plot visually confirming the linearity of relationship between S and C. 1.4. Confirming the Accuracy of a Given Analytical Procedure The accuracy characterizes the proximity of the experimental results, obtained using a proposed analytical procedure, to the “true” value in the entire suitability range of this procedure. The accuracy represents a combination of the random and systematic error.6 In order to provide for accurate HPLC determinations, it is recommended to use standard solutions with concentrations close to within 10% of the test solution concentration. The accuracy of analytical procedures should be determined using homogeneous samples with exactly known concentrations of the compounds to be determined. For validation purposes a series of such solutions is prepared using the reference parent compound. According to ICH recommendations and USP-26 [1, 7, 15], the accuracy can be expressed both in the classical form, as the difference X – m between the average experimental value (X ) and the true value (m) with the corresponding confidence interval DX ,7 (2) ( X - m ) ± DX , and in an alternative (and more illustrative) form, in terms of the percentage recovery of the known amount of the compound to be determined, ( found content ) (3) R= ´ 100%. ( introduced content ) The author believes that the content recovery testing should be preferred for evaluating the accuracy. This approach provides a more illustrative characteristic of the reliability of results obtained using a proposed analytical procedure and reveals the need for additional checks in the case of a significant systematic error (see below). On the other hand, the recovery defined by formula (3) incompletely characterizes the accuracy, since this quantity is also random and requires knowledge of the corresponding confidence interval. Thus, it is recommended to determine both the recovery R (%) and the confidence interval at a preset probability (P = 95%), representing the accuracy in a form analogous to expression (2): (4) R ± DR . Obviously, the proposed methods should not involve significant systematic errors. In the absence of systematic er6 7 Accordiong to the State Standard GOST R ISO 5725-1–2002 the systematic error usually characterizes “trueness.” The value of DX characterizes random errors. Validation of HPLC Techniques for Pharmaceutical Analysis 219 rors, the error is determined by the precision. Based on the permissible RSD values (see above), experimental experience, and analysis of the published data [13, 27], it is possible to draw the conclusion that there is no need to verify a proposed analytical procedure in the absence of a significant systematic error, provided that it is established that the recovery with allowance of the confidence interval does not fall outside the following limits: 99.0–101.0%, for the quantitative analysis of parent substances with a high rated content of the active component (98% and above); 98.0–102%, for the quantitative analysis of parent substances with a lower rated content of the active component (98% and below) and ready-to-use drugs; 90.0–110%, for the quantitative determination of impurities with a rated maximum content of up to 1%; 75–125%, for the quantitative determination of impurities with a rated maximum content from -0.1 to 1%; 50.0–150%, for the quantitative determination of impurities with a rated maximum content below 0.1%. 1.4.1. The procedure of accuracy evaluation. ICH recommends making three determinations (i.e., analyze three model mixtures) for three different concentrations. However, this approach does not allow the accuracy to be determined together with linearity and other validation characteristics. The author believes that the accuracy should be evaluated using not less than nine determinations at various concentrations covering the entire range of suitability of the proposed procedure. This provides for the possibility of determining this characteristic simultaneously with the calibration graph parameters and their statistical characteristics (for evaluating the linearity according to Section 1.3), the limit of quantitation (Section 1.7.2), and the limit of detection (Section 1.6.2). It should be emphasized that these determinations should include all stages of the proposed analytical procedure. For parent substances, the accuracy of analysis is usually determined by comparison to a reference sample. According to this, the reference sample (or a high-purity substance) is analyzed using the standard procedure and the results are compared to data in the certificate of the reference sample or to the results of analysis of the high-purity parent substance performed by an alternative method (e.g., titration) with known accuracy and precision. It is recommended that, for parent substances with a high rated content of the active component, the average recovery should be not less than 99 – 101% at each level [13]. For ready-to-use drugs, the accuracy is evaluated through the analysis of mixtures containing known amounts of the parent compounds and placebo; for the quantitative determination of impurities, this characteristic is determined by the analysis of such mixtures containing known amounts of these impurities. These analyses are performed using two principal methods. The method of recovery of a parent compound introduced into the placebo (matrix). This method, used for the analysis of drugs comprising mixtures of parent and auxiliary compounds, is based on determining the recovery of a known amount of the parent substance introduced into the placebo. The placebo is prepared separately and then introduced in a nominal (or proportional) amount into measuring flasks. Then, thoroughly weighed amounts of the parent compound or its concentrated solutions are added so that (upon filling the flasks to the marks) the sample concentrations would cover the entire expected suitability range of the proposed analytical procedure. For example, a parent compound can be introduced into a placebo solution at a level of 80, 100, and 120% of the nominal concentration indicated on the label (or the reference solution concentration). The method of standard additives. This method is generally analogous to that described above but is applied only when it is impossible to prepare a solution of placebo free from the parent compound or when this compound is present in the placebo in an unknown amount (e.g., in biological samples). In these cases, the reference sample of the parent compound is added at an amount of 50, 80, 100, 120, and 150% of its expected content in the analyzed solution. Using the proposed procedure, the amount of the parent compound is determined (found content) and compared to the known additive (introduced content). Alternatively, it is possible to compare the results of analyses performed using the proposed method and the data obtained for the same samples by validated alternative methods. For the validation of analytical procedures intended for the analysis of ready-to-use drugs, it is expedient to use the same reference substance for preparing both model mixtures and standard solutions. This eliminates errors related to the possible uncertainty of the composition indicated on the label of the reference sample and allows using commercial samples instead of special reference compounds. At a low concentration of the parent compound in the mixture (when it is impossible to add a thoroughly weighed amount of this compound), one may add a known amount of concentrated solution and then fill the measuring flask with a solvent stipulated by the proposed analytical procedure. For the quantitative determination of impurities, the accuracy of evaluation has certain peculiarities. In this case, the method of recovery of a parent compound introduced into the placebo and the method of standard additives have limited applicability because these validation procedures require large amounts of identified impurities. In this case, the accuracy is most frequently checked using the method described below. The method of internal normalization with or without response factors. According to this method, identified impurities are characterized by the response factors with respect to the parent compounds determined by the analytical procedure under consideration. These coefficients depend on the mobile phase composition and the analytical wavelength. For reproduction (or modification) of the analytical procedure, the detector wavelength is not changed, while the mobile phase composition can be corrected for the difference in the 220 N N. A. Épshtein parameters of chromatographic columns. In the case of a considerable change in this composition (see Section 4), it is necessary to re-determine at least the values of the response factors. For determining unidentified and accidental impurities, these factors are conventionally taken equal to unity (assuming that the sensitivity for these impurities is the same as that for the parent compound). If the reference samples of impurities and decomposition products are unavailable, the validation has to be performed using alternative methods. 1.4.2. Testing for systematic error. The analytical procedure can be checked for the absence of systematic errors by one of the three methods considered below. Method based on the Student t-criterion without regression analysis [8]. Each sample (whose total number is N ³ 5) with known values m (introduced content) of the component to be determined is analyzed in m = 3 – 6 parallel determinations. The total data array is characterized by the dispersion (SD0) and the Student criterion8 t= | m - x| m SD 0 SD 2 = 0 k =1 2 å SD k N . Finally, the Student t-criterion is calculated as t = (| m - x |× m ) SD 0 (6) This t value is compared to tabulated values of the Student criterion t (P, f = m – 1). If the calculated parameter is greater than the tabulated value for P = 95% and f = m – 1. t > t (P, f ), the results obtained using the proposed method can be considered as involving a systematic error d. This error is calculated by the formula d= | x - m| 100%. m (5) The standard deviation SD0 in a particular analysis is calculated using the set of all m parallel determinations performed for N (or g in the notation of [8]) samples. This allows the SD0 value to be reduced and the sensitivity of determination of the systematic error to be increased with a simultaneous decrease in the confidence interval for the results of analysis, DX = t SD0/ m, where t is the Student criterion for f = m – 1 degrees of freedom. The algorithm of these calculations is as follows. Each kth sample is characterized by the deviation of the experimental value from average, d i = X i - X , and the dispersion æm ö SD 2 = ç å d i2 ÷ ( m - 1). Then, the difference between the k è i =1 ø maximum and minimum values of the dispersion SD 2 is k checked to be insignificant in terms of the Fisher F-criterion. If this difference is actually insignificant, the SD 2 value is 0 calculated as the sum of square deviations for all samples divided by the number of samples, 8 This t value is essentially the ratio of the systematic error | x - m | and the random error SD0/ m. and compared to tabulated values of the Student criterion t (P, f ) for f = N(m – 1) degrees of freedom. It should be emphasized that, for small (practically insignificant) systematic error and small random error, the calculated t-criterion can be greater than the tabulated value. However, a small systematic error can be ignored in practice when the analytical problem does not require high accuracy of determination. This approach is also valid for other methods of evaluation of the accuracy of a proposed analytical procedure. Method of regression analysis with the Student t-criterion [35, 38]. This method seems to be the most effective, since it provides for the possibility of using the calibration graph for the accuracy evaluation and determination of some other validation characteristics (see the generalized scheme in Fig. 1). For simultaneous determination of the constant and variable systematic errors, not less than N = 5 samples with known values of the parent compound are studied and the relationship between the “introduced content” (mt ) and the “found content” (mf ) is processed by least squares in terms of the equation mf = a + bmi. Using these data, the parameters ta = |a|/SD0 and tb = |1 – b|/SD0 are calculated and compared to the critical (tabulated) values of the Student criterion t (P, f ) for the confidence probability P = 95% and f = N – 2 degrees of freedom. Using the results of regression analysis, it is possible to judge with 95% probability about the absence of a constant systematic error, provided that ta £ t (P, f = N – 2), and the absence of a linear variable systematic error, provided that tb £ t (P, f = N – 2). It is expedient to perform validation of the accuracy of an analytical procedure together with checking for the linearity of the system response (area or height of the peak) as a function of the concentration of the parent compound to be determined (in fact, linearity of the calibration graph in terms of the criteria described in Section 1.3) and with finding the limit of detection (Section 1.6.2) and the limit of quantitation (Section 1.7.2). Method of regression analysis with the Fisher F-criterion. This method is based on the assumption that a linear variable systematic error can be ignored. This assumption is justified because HPLC in pharmacy is used in a relatively narrow range of sample solution concentrations. The measurements are performed for not less than N ³ 5 samples (model mixtures) with known values of the parent compound, after which the relationship between the “introduced content” (mt ) and “found content” (mf ) is processed Validation of HPLC Techniques for Pharmaceutical Analysis 221 be < 3, then DX is expressed by a value with two significant digits. 1.5. Validation of the Suitability Range of a Given Analytical Procedure The range of suitability of a given analytical procedure is the interval between minimum and maximum concentrations (amounts) of a compound to be determined in which (i) the linearity is observed, (ii) the characteristics of repeatability fall within permissible (preset) limits, and (iii) the accuracy is maintained at a sufficiently high level [1 – 3]. This interval must contain all values of the concentrations (amounts), which can be encountered in the course of routine analyses. The range of suitability of a given analytical procedure is expressed in the same units as the results of analyses. It should be noted that, in practice, it is not necessary to determine the maximum possible range of suitability for an HPLC procedure. If it were necessary, this range could be determined using threshold RSD values obtained in the course of validation of the linearity and precision. For example, RSD must not exceed 3% for HPLC procedures aimed at determination of the parent compounds and 10% for procedures of impurity determination [13]. In practice, it is sufficient to show that a given range of suitability covers “with margin” the rated limiting concentrations of the substances to be determined, as indicated in the corresponding pharmacopoeial articles. For this reason, it is recommended that the range of suitability of a given analytical procedure be not less than the following intervals [3, 7]. (i) For the quantitative determination of the main component concentration in parent compounds and ready-to-use drugs: from 80 to 120% of the nominal content (i.e., the concentrations of test solutions should range within 80 – 120% relative to the concentration of a reference sample solution used accordsing to the proposed procedure). (ii) For evaluation of the homogeneity of dosage: from 70 to 130% of the nominal content, provided that a wider interval is not required (in special cases such as aerosols). (iii) For dissolution tests: ± 20% (absolute percentage) of the rated value of drug release. For example, for monitoring the behavior of a drug with delayed release of a parent compound, for which the release is rated as 20% within the first hour and up to 90% within a 24-h period of time, the suitability range must extend from 0 to 110% of the nominal drug content. (iv) For the quantitative determination of impurities by the method of external standard: from 50 to 120% of the nominal content. It should be noted that, in view of the possibility of RSD values amounting up to 50% (Section 1.2.2), it would be more correct to establish the upper limit at 150% of the nominal content. For impurities exhibiting a very high biological activity, toxicity, or unpredictable behavior, the limits of detection and quantitation must correspond to the level at which these impurities have to be controlled.10 (v) In cases where the quantitative determination of a parent compound and the detection of impurities are per- by least squares in terms of the relation mf = a + bmt. The absence of a constant systematic error is confirmed by the insignificance of the coefficient a [35] at a commonly accepted confidence probability level of P = 95%. For this purpose, the Fisher criterion calculated is as F ( P, f 1 = N – 1, f 2 = N – 2 ) = SD 2 ( N – 1) – SD 2 ( N – 2 ) 01 02 SD 2 ( N 02 – 2) (7), , where SD01 and SD02 are the standard deviations obtained for the above relations without the free term (mf = bmt ) and with the free term (mf = a + bmt ). If the calculated F value is smaller than the tabulated (critical) values F (P = 95%, f1, f2), the free term a is in fact insignificant and the error is absent to within a 95% confidence probability. 1.4.3. Data presentation and evaluation of the systematic error. The final judgment about the accuracy of a proposed analytical procedure can be made upon validation of its specificity, precision (repeatability, reproducibility), and linearity.9 It is necessary to indicate a particular method of normalization of the content of impurities (weight fractions, percentage of the area under the peak of the main component, etc.). The validation results are presented by data on the recovery of the amount of introduced parent compound with a confidence interval, R ± DR , or the difference between the average experimental value X and the true value m with the corresponding confidence interval: ( X - m ) ± DX . The proposed procedure involves no significant systematic error, provided that the recovery with allowance of the confidence interval does not fall outside the following limits: 99.0–101.0%, for the quantitative analysis of parent substances with a high rated content of the active component (98% and above); 98.0–102%, for the quantitative analysis of parent substances with a lower rated content of the active component (98% and below) and ready-to-use drugs; 90.0–110%, for the quantitative determination of impurities with a rated maximum content of up to 1%; 75–125%, for the quantitative determination of impurities with a rated maximum content from – 0.1 to 1%; 50.0–150%, for the quantitative determination of impurities with a rated maximum content below 0.1%. The numerical result of a particular analysis, X (or R), must contain the last significant digit in the same position as that in the numerical value of the error of determination, DX (or DR) [37]. The number of significant digits in the latter value is determined as follows. If the first significant digit in the error is ³ 3, then DX is expressed by a value with one significant digit; should the first significant digit in the error 9 It is expedient to confirm the linearity together with determining the accuracy. 222 N. A. Épshtein formed jointly and only the reference sample solution of the main component at a nominal concentration is used, the suitability range must extend from the rated LPI value (more precisely, from half of this value, see the preceding point) up to 120% of the nominal concentration of the parent compound. If the LPI value is unknown (e.g., during the development of an analytical procedure) the initial lower limit of the suitability range according to the ICH recommendations should be established at 0.1% of the nominal concentration of the parent compound for a daily drug dose below 1 g; should this dose exceed 1 g, the lower limit of the suitability range should be reduced to 0.05% of the nominal drug concentration. 1.6. Determining the Limit of Detection of a Given Analytical Procedure The limit of detection (LOD) is determined as the minimum concentration of analyzed substance in the sample, which (i.e., the corresponding response) can be detected under preset conditions [3, 4, 7]. For HPLC procedures used for the determination of parent compounds and ready-to-use drugs, the LOD is required for the detection of limiting impurity concentrations. Obviously, the LOD may depend on the HPLC detectors and pumps. For this reason, this characteristic has to be rated for various instruments, including those available for potential users. Irrespective of the method used for evaluation, it is necessary to have a chromatogram showing that a response peak exceeding the baseline noise is actually observed at a concentration corresponding to the LOD of the substance to be detected. According to USP-26 [7], it is usually not necessary to determine the actual LOD of the analyzed substances (except for analytical procedures intended for monitoring the cleanness of technological equipment). In most other cases, it is sufficient to show that the impurity of interest is reliably detected at a preset level (see Section 1.6.5). 1.6.1. Determining the LOD from the Standard Deviation of the Response and the Slope of the Calibration Curve. According to this method [3], the LOD value is calculated by the formula LOD = 3.3(SDa/b ), (8) (a) Using the calibration curve S = a + bC constructed using the results of analyses for a series of the reference sample solutions with decreasing concentrations in the region of the LOD. Using these data, a regression equation S = a + bC of the area under peak S versus concentration C is calculated and the standard deviation SDa of the free term is determined. Alternatively, the standard deviation is determined for the intersections of several regression lines of the calibration curve with the ordinate axis, constructed using several series of reference sample solutions with concentrations in the region of the LOD. (b) Using the standard deviation of the area under the peak in the chromatograms of an impurity with concentrations within 0.01 – 0.05% of the nominal drug concentration determined using the given analytical procedure, typically for ten sequential injections. 1.6.2. Determining the LOD Using the Free Term and the Coordinates of the Midpoint of the Calibration Curve. This is the most convenient way to determine the LOD. According to this method, the calibration curve is described by the regression equation Y = a + bC, where Y is the response (peak area of height) and C is the concentration. For this relation, the LOD is calculated by the formula LOD = 2C × t ( P, f ) × SD 0 Y - a + t ( P, f ) × SD 0 nj nj , (9) assuming that the response – concentration relation is linear in the range from the maximum possible concentration of the analyzed compounds down to zero. It is recommended to determine the slope b of the calibration curve using reference sample solutions with concentrations in the vicinity of the LOD (see Section 1.7). The value of the standard deviation SD can be determined using one of the two methods: 10 For the analysis of impurities, it was recommended [27, p. 695] to perform tests in the range from the limit of quantitation with respect to the main component (typically, below 0.1%) up to a 5% concentration in solution. where C and Y are the coordinates of the midpoint; a is the free term; SD0 is the standard deviation of the experimental values from the calculated ones; nj is the number of parallel determinations for each experimental point (typically, nh = 2 – 3); t (P, f = N – 2) is the Student criterion (F = 99% [35]) for f = N – 2 degrees of freedom; and N is the number of experimental points on the calibration graph. It should be noted that a different formula for the LOD was presented in [35], according to which the background (i.e., the free term) did not influence this value. The error has been eliminated in the new edition of this monograph. 1.6.3. Determining the LOD for the Signal-to-Noise Ratio S/N¢ » 3. The method of evaluation of the LOD using the S/N¢ ratio (for S/N¢ » 3) [3, 4] should not be used for the validation of HPLC procedures because the baseline noise strongly depends on the experimental conditions. On a scale comparable with the noise intensity, the baseline appears as a broken line of complicated shape and admits only a very subjective estimate of the maximum noise N¢. 1.6.4. Evaluating the LOD from the Minimum Concentration for Which the RSD is Below a Preset Value. According to calculations [39], the relative error of the LOD amounts to at least 20%. For this reason, the LOD can be theoretically evaluated as the minimum solution concentration for which the RSD for the peak area (height) of the analyzed compound for five sequential determinations does not exceed 20%. However, this approach is not convenient in practice because it requires numerous analyses. For example, it Validation of HPLC Techniques for Pharmaceutical Analysis 223 was pointed out [40] that evaluation of the LOD by this method in accordance with FDA recommendations (defining the LOD as the minimum concentration for which the RSD does not exceed 15%) would require 288 determinations. In order to take into account the influence of the drug matrix on the LOD, it was suggested [30] to take into account the so-called “specific LOD.” These values are determined using mixtures of a given parent substance with a placebo instead of a solution, which takes into account the effect of asymmetry of the peaks of other components on the LOD. According to ICH [3], the LOD has to be refined using various columns and instruments because this characteristic depends on the noise level (and, hence, on the working life of the column, on the properties of the detector, etc.) and on the peak shape. 1.6.5. Alternative Proof of the Reliable Detection of Impurities in Parent Substances and Ready-to-Use Drugs. For a test solution concentration of about 1 mg/ml, the response signal at a level of not less than 1 V can be readily obtained. For an impurity concentration of 0.01%, this corresponds to a response on the order of 100 mV, which is one order of magnitude higher than the noise level of modern detectors. For validating the reliable detection of impurities, it is sufficient to present the chromatogram of a reference (or test) solution diluted D = 2L times, where L is an integer indicating the ratio of the main component concentration to the minimum rated concentration of the impurity. This chromatogram must visually confirm the possibility of reliably detecting impurities at the level of about half of their rated content. For example, if the content of an individual impurity must not exceed 0.5%, the above ratio is D = 2(100/0.5) = 400. For the normalized total impurity content, D = 2000, which corresponds to an individual impurity content of 100/D = 0.05% (the British Pharmacopoeia does not take into account impurities with concentrations below 0.05%, except for highly toxic substances). In many cases, this approach eliminates the need to establish the LOD during the determination of impurities in parent compounds and ready-to-use drugs. Data presentation. According to ICH [3], it is necessary to validate the LOD value and indicate the method of determination. If the LOD was calculated from experimental data, it is necessary to present the results of analysis of the required number of samples with the content of a detected component close to the LOD. If the LOD was estimated by visual assessment of chromatograms, it is necessary to present chromatograms confirming reliable detection of the peaks of parent compounds or impurities. The number of significant digits in the LOD [39] is determined as follows. If the first significant digit in the LOD value is > 3, then this limit is expressed by a value with one significant digit and rounded to the closest integer; should the first significant digit in the LOD be £ 3, then the LOD can be is expressed by values with two significant digits and the second digit should be rounded to 0 or 5. 1.7. Validation of the Limit of Quantitation of a Given Analytical Procedure The limit of quantitation (LOQ ) is the minimum concentration of analyzed substance that can be determined at an acceptable precision (repeatability, reproducibility) and accuracy under rated conditions of analysis by a given method [1, 15]. The ICH [3] and USP-26 [7] recommend several methods of determining LOQ for the impurity analysis. 1.7.1. Evaluating the LOQ for the signal-to-noise ratio S/N¢ = 10. This is the most widely used method of determining the LOQ. However, since this procedure makes use of the peak heights (rather than areas), it is more suited for the HPLC techniques using this measure of the response. This approach does not take into account the requirements on reproducibility of the HPLC procedure. According to this method, an initial reference solution of the analyzed compound is determined for which the signal-to-noise ratio is at least 30 [27]. Then, this solution is sequentially diluted until this ratio decreases to S/N¢ » 10. The corresponding concentration is considered as the LOQ. For this evaluation of the LOQ, it is recommended to determine the maximum baseline noise near a peak of the analyzed compound, in the interval of retention times within ± 10W0.5, where W0.5 is the full width at half maximum (FWHM) of this peak [22]. For HPLC procedures used in pharmacy, it would be interesting to study the influence of the maximum noise N¢ on the relative standard deviation of results for a nearly Gaussian peak shape. According to [27], RSD[%] = 50 , S N¢ (10) where S is the detector signal intensity. A simple calculation shows that, at S/N¢ = 10, the noise influence alone can make RSD as large as » 5% (!). 1.7.2. Evaluating the LOQ using the calibration curve. The ICH [3] recommends determining the LOQ by the formula LOQ = 10(SD/b ), (11) where b is the slope of the calibration curve and SD is the standard deviation of the response signal. The peculiarities of this approach were considered in Section 1.6.1. A significant disadvantage of this approach (as well as of some others) recommended by ICH is the inability to take into account the requirement of acceptable reproducibility (see above). The author believes that a more correct estimate of the LOQ from the calibration graph, with allowance for the reproducibility requirements, can be obtained in the following way [41]. First, the values of response Y (area under the peak of the analyzed component) within the limits of the calibration curve Y = a + bC are used to calculate (i) the theoretical values of C = (Y – a)/b and (ii) the standard deviations 224 N. A. Épshtein (SDc) and relative standard deviations (RSD = SDc/C ´ 100) of the results of analysis. Then, the plot of RSD versus C is used to determine the concentration Cp corresponding to a permissible RSD value preset for the analytical procedure under consideration. This permissible concentration Cp is taken to be LOQ with allowance for the RSD (i.e., for the reproducibility) requirements. The values of standard deviations of the results of analyses are calculated by the formula [35] SD 0 b 1 1 æ SD b + +ç N m ç b è ö ÷ ÷ ø 2 SD c = æ Y s -Y ç ç SD è 0 ö ÷ ÷ ø 2 (12) for f = N – 2 degrees of freedom, where SD0 is the standard deviation of the linear relation (calibration curve), N is the number of experimental points on the calibration curve, Ys is the response (area under the peak), m is the number of parallel (independent) determinations, b is the slope of the calibration curve, SDb is the corresponding standard deviation, and Y = Yk/N is the average response of all experimental points used for constructing the calibration graph. 1.7.3. Other methods. Other methods of determining the LOQ are not theoretically justified and did not find wide use. In particular, it was suggested to determine the LOQ as the minimum concentration of the analyzed compound for which six sequential injections give RSD £ 3.0% [27, p.695] or RSD £ 2.0% [29]. With this approach, the LOQ is essentially defined as the concentration at which the RSD becomes greater than a certain preset value. 1.7.4. Allowance of the matrix effect on the LOQ. It was suggested to determine the so-called specific LOQ p30]. This characteristic is determined under the same conditions as described above for the LOD, but in a real test solution, and therefore takes into account the influence of asymmetry of the other peaks on the LOQ of the analyzed compound. Data presentation. The LOQ value is presented with indication of the method used for its determination. If this characteristic is evaluated using the signal-to-noise ratio, it is necessary to present chromatograms showing the reliability of detection of the peak due to the analyzed component or impurity. If the LOQ was determined by calculation or extrapolation, it is necessary to present the results of analysis of a sufficiently large number of samples with the content of the analyzed compound close to the LOQ level. 1.8. Stability of Solutions. 1.8.1. Confirming the stability of solutions using the regression relation for the area under the peak versus the time. As a rule, the analytical solutions are used for a relatively short period of time (th ) for which the content of the analyzed substances (proportional to the areas under the corresponding peaks) remains practically unchanged. In order to confirm this statistically, it is sufficient to determine the coefficient b in the regression relation St = S0 + bt (or St – S0 = bt ) between the area St under the peak at the time t (within the interval from 0 to th ) and the area S0 at the initial moment, calculate the parameter tb = |b |/SDb, and compare this value with the critical (tabulated) Student criterion t (P = 99%, f = N – 1) for the confidence probability P = 99% and f = N – 1 degrees of freedom, where N is the number of experimental points on the above interval. If tb is smaller than the tabulated t (P = 99%, f = N – 1) value, the coefficient b is statistically insignificant and, hence, there is no significant difference between the areas under the peak (and, hence, the solution concentration) at the initial time and at any other moment up to the last experimental point. 1.8.2. Methods of evaluation. The stability of test and reference solutions ST (%) can be evaluated using the following methods. (i) For continuous testing within a relatively short period of time — by the ratio of the area St under the peak of the analyzed compound (or impurity) at the moment t to the initial area S0: ST = 100St /S0. (13) (ii) Irrespective of the duration of experiment — by the ratio of the amount mt (concentration) of the analyzed compound (or impurity) at the moment t to the initial value m0: ST = 100mt /m0. (14) The test and reference solutions are prepared according to the given procedure and analyzed with certain time intervals. The maximum possible duration of measurements depends on the practical requirements on the possible storage time of the given solution (which may not necessarily be equal to the maximum rated storage time). The solutions can be considered stable until the difference |100 – ST | does not exceed the relative error of determination of the main component (or impurity) according to the given analytical procedure.11 Data presentation. The stability of solutions is confirmed by data on the storage times of solutions and mobile phases used in the analyses. 2. EVALUATION OF THE STABILITY OF ANALYTICAL SYSTEMS WITH RESPECT TO SMALL VARIATIONS OF PARAMETERS (ROBUSTNESS) The robustness of an analytical procedure is the characteristic of its stability with respect to small variations of the system parameters possible under real conditions. This stability is usually evaluated in terms of the RSD of the results of analyses compared to the analogous data obtained using strictly observed conditions according to the validated analytical procedure. A more correct procedure based on evaluation of the statistical significance of the difference between these results in terms of the Student t-criterion is rarely applied to the HPLC techniques. 11 The absolute value of |100 – ST | is taken because ST can be greater than 100% due to random errors. Validation of HPLC Techniques for Pharmaceutical Analysis 225 Robustness is usually studied at the stage of development of the analytical procedure. Typical parameters capable of influencing the results of analyses and, hence, studied in the course of validation, are as follows:11 (i) the content of the organic solvent in the eluent ( ± 2%); (ii) the amount of additives (salts, ion-pair reagents, etc.) in the eluent ( ± 10%); (iii) pH of the buffer solution ( ± 0.5); (iv) HPLC column temperature ( ± 5 °C); (v) time of extraction of the analyzed compound from a drug eluent ( ± 20%); (vi) extractant composition ( ± 5%); (vii) eluent concentration gradient ( ± 2%); (viii) mobile phase flow rate; (ix) column type and/or manufactirer. The parameters (called critical) influencing the results of analyses should be indicated in the validation report. The description of the given analytical procedure must provide the corresponding warning remarks. In order to decrease the number of tests necessary for the validation of robustness of a given analytical procedure, it is expedient to use the methods of experiment planning, which are capable of quantitatively following the effect of several parameters (factors) varied simultaneously [32 – 34, 42]. There is no need for special additional investigations of robustness if no critical parameters were revealed in the course of development and/or implementation of the proposed analytical procedure. Data presentation. The validation report should include the chromatograms and tables showing the effects of each critical parameter on the results of analyses (in comparison to the normal values) and the absence of such effects for the other most important parameters (see above). It is desired that the proposed analytical procedure be robust with respect to all the important parameters, which makes this procedure suitable for routine laboratory use. 3. CRITERIA OF SUITABILITY OF A CHROMATOGRAPHIC SYSTEM USP-26 [7] stipulates the System Suitability Test (SST) intended to establish that the separating power and reproducibility of a given chromatographic system provide for the adequate solution of the task of analysis. It is assumed that the equipment, electronics, analytical procedures, and samples comprise a unified system investigated as a whole. Upon chromatography of a special SST solution, the results are checked for obeying the SST requirements (see below). The SST solution must contain the analyzed compound and all other additives necessary for evaluating the suitability of the given system for implementing the required analyses. 12 Values in parentheses indicate recommended limits of variation relative to the values stipulated by the given procedure. The additives may include other analyzed components, identified impurities, possible decomposition products, and substances playing the role of internal standards. Effective means for finding SST solutions is provided by experiments on the chemical modification of a particular drug under consideration (see Section 1.1.2). The solutions and substances obtained in such experiments contain the products of destruction of the main drug components and/or compounds structurally close to the analyzed parent substances. Such solutions are expediently used in the tests for suitability of a given chromatographic system and frequently allow one to reject expensive standard samples of impurities. The author believes that the suitability of a given chromatographic system is adequately described by the following main criteria. (i) Criteria of the separating power of the chromatographic system. (ii) Criteria of reliable determination of the beginning and end of a peak (and/or of the peak height) of the analyzed compound on the chromatogram. (iii) Criteria of reproducibility of the results of measurements (repeatability of injections) (iv); Additional criteria should be introduced only provided that critical parameters (see above) were established in the course of robustness evaluation. The SST criteria should not be overloaded by numerous extra parameters, since this may lead to a situation where only HPLC columns and equipment used for the validation purposes will be formally suitable for all analytical procedures. 3.1. Separating Power of a Chromatographic System The criteria of separating power include the separation coefficient Rs , the peak-to-valley ratio h/v (see below), and the relative retention times of components. 3.1.1. Relative retention times. For analytical procedures intended for the quantitative analysis of drugs, homogeneous dosing tests, and determination of the drug’s dissolution characteristics, it is usually sufficient to characterize the separating power by the relative retention times of several substances, including the main drug component, a structurally close compound, and/or an internal standard. The relative retention time of the main component is usually taken equal to unity. The author believes that the retention times should not be used as characteristics of suitability of a chromatographic system because these values depend on the eluate flow rate, temperature, and dead volume of the system. On the other hand, the retention times do not influence the accuracy and precision of an analytical procedure (provided that other suitability requirements are satisfied). It is more correct to indicate the recommended values (or intervals) of retention times of the main components in the description of the analytical procedure and characterize the other substances by their relative retention times. 226 N. A. Épshtein 3.1.2. Peak separation coefficient. For analytical procedures intended for the determination of impurities, the system suitability requirements should indicate the minimum possible values of the peak separation coefficient Rs at least for the main (rated) impurities. In the case of HPLC procedures intended for the quantitative analysis of drugs, homogeneous dosing tests, and determination of the drug dissolution characteristics, it may be necessary to introduce the peak separation coefficient into the system suitability requirements if (i) a high content of some impurity is admitted, (ii) there is a possibility of partial overlap between the peaks of the main components, or (iii) the peaks of the placebo components occur in the vicinity of the main analytical peaks. The minimum possible values of the separation coefficient Rs are determined proceeding from the following considerations. If the peaks are not significantly different in heights and possess nearly Gaussian shapes, their complete separation at the baseline level requires that Rs ³ 1.5. This condition is recommended by the British Pharmacopoeia and by the EEC Pharmacopoeia. If the peaks have significantly different heights (e.g., used in the determination of impurities) and/or exhibit tailing, CDER recommends that Rs ³ 2.0 [4]. It should be noted that this situation is most frequently encountered in practice during the analysis of drugs. For separating peaks with large tailing factors ( > 2.5, see below), it is recommended to restrict the separation coefficient to Rs ³ 2.5. This situation is quite rare, being only typical of drugs containing several heteroatoms capable of forming strong hydrogen bonds with silanol groups of the sorbent. Higher “critical” Rs values are usually unnecessary, because the condition Rs > 2.5 ensures good separation virtually at the baseline level. On the other hand, it should be noted that, due to the availability of highly effective columns and computer-optimized systems, values of Rs < 1.2 cannot be justified, except for (i) the isomer peaks, (ii) the peaks of some components in complex multicomponent mixtures (such as extracts of biological objects, antibiotics, alkaloids, and multivitamin preparations), and (iii) the peaks of minor components (impurities, aromatic and color additives, etc.). It should be noted that the British Pharmacopoeia (BP 2001, Appendix III, p. A143) indicates that, in tests for the content of related compounds (when the peaks of main components and impurities are incompletely separated), the system suitability requirements may describe the peak separation in terms of the peak-to-valley ratio p/v = hp/hv, where hp is the peak height relative to the extrapolated baseline and hv is the height of the lowest point in the valley separating the peaks (relative to the same extrapolated baseline). This parameter is rarely used during the analysis of impurities in drugs: sometimes it is convenient for the description of impurity peaks occurring immediately in front of the main analytical peak. For suitability of the chromatographic system, it is usually required that hp > hv. For example, in the analysis of fluoxetin hydrochloride, it is required that hp/hv ³ 1.1/0.1 = 9. 3.2. Criteria of Reliable Determination of the Beginning and End (and/or the Height) of a Chromatographic Peak The peak asymmetry is described in terms of the tailing fgactor T0.05 [7]. This parameter, which characterizes the asymmetry at a level of 0.05% of the peak height, is especially important for the procedures of quantitative analyses. According to BP 2001 [22], the recommended values fall within T0.05 = 0.8 – 1.5. Under this condition, the peaks are sufficiently symmetric and exhibit no significant tailing, which favors reliable determination of the beginning and end of the peak (and, hence, of the peak area) and reduces the probability of overlap. An analysis of the corresponding articles of the BP 2001 and USP-26 showed that the permissible T0.05 interval extends from 0.75 to 2.5. Asymmetric peaks with T0.05 outside the 0.75 – 2.5 range should be avoided: for peaks with T0.05 on the order of 3 and above or 0.7 and below, the boundaries of peaks practically cannot be determined. An additional criterion of peak separation is provided by the efficiency of a chromatographic column (N ) with respect to the main analytical peak. This parameter characterizes the peak width at half height (FWHM) and is calculated by the conventional formula [7]. The ICH recommends using columns with efficiencies N ³ 2000 theoretical plates, which can be considered as the lower limit for the procedures of impurity determination in parent compounds. According to practical experience it is usually sufficient to require that N ³ 1000 theoretical plates. In some cases in the HPLC determination of the main drug components, USP-26 admits N ³ 400 theoretical plates. However, even this is not the minimum possible level: rapid analyses are sometimes performed using short chromatographic columns with 3.5-mm (and smaller) sorbent particles, which provide for a relatively low error of determination (< 1.5%) even at N » 250 – 300 theoretical plates. The above criteria of suitability of the chromatographic system with respect to the N value are not absolute: this parameter must only provide for the required accuracy and precision of the proposed analytical procedure. 3.3. Criteria of Reproducibility of the Results of HPLC Measurements The criterion of reproducibility of the results of HPLC measurements with respect to the repeatability of injections is usually formulated in terms of the relative standard deviation RSD of the peak areas or heights. In the quantitative analysis of drugs, the permissible value is usually restricted at RSD £ 2.0% for the main components and RSD £ 5.0% for impurities. Higher RSD values should be avoided or their validity should be additionally justified. The quantitative analysis of parent compounds requires increased accuracy because the rated content of the main active component is typically allowed to differ from 100% only Validation of HPLC Techniques for Pharmaceutical Analysis 227 within 1 – 3%. For this reason, it is usually required that the sequentially measured chromatograms (three to six) have RSD of the peak areas or heights not exceeding 1%. However, even this value does not always provide an acceptable confidence interval. For this reason, PR 2001 [22] suggested a formula for determining the maximum possible RSD values depending on the upper rated limit (B ) of the drug content and the number of repeated injections m. According to this, the possible RSD (Table 4) is calculated for a series of injections of a reference solution as RSD max = Here, K = 0.349 K = ( 0.6 2 ) × ( t 0.90%,5 BK m , t 90% , m - 1 (15) TABLE 4. Maximum Permissible Values of the Relative Standard Deviation RSD Depending on the Upper Limiting Content (B) of the Analyzed Compound and the Number of Sequential Injections (m) m=3 B, % Maximum permissible RSD, % m=4 m=5 m=6 1.0 1.5 2.0 2.5 3.0 4.0* 5.0* * 0.21 0.31 0.41 0.52 0.62 0.83 1.04 0.30 0.44 0.59 0.74 0.89 1.19 1.49 0.37 0.55 0.73 0.92 1.10 1.47 1.83 0.42 0.64 0.85 1.06 1.27 1.70 2.13 Values calculated in this study. is a constant calculated as 6 ), where 0.6/ 2 is the “required” system. Until now, there is no commonly accepted opinion which kinds of modification of the chromatographic system can be considered insignificant and requiring additional revalidation of the entire procedure. Nevertheless, some acceptable limits of variation of the main parameters have been published [22, 31], which can be considered as a basis for assessing the need for revalidation even of an “insignificantly modified” analytical procedure. REFERENCES 1. Int. Conf. on Harmonization (ICH), Text on Validation of Analytical Procedures (1994). 2. Int. Conf. on Harmonization (ICH) of Technical Requirements for the Registration of Pharmaceuticals for Human Use, Validation of Analytical Procedures, ICH-Q2A, Geneva (1995). 3. Int. Conf. on Harmonization (ICH) of Technical Requirements for the Registration of Pharmaceuticals for Human Use, Validation of Analytical Procedures: Methodology, ICH-Q2B, Geneva (1996). 4. Reviewer Guidance: Validation of Chromatographic Methods. Center for Drug Evaluation and Research (CDER), Washington (1994). 5. US FDA, General Principles of Validation, Center for Drug Evaluation and Research (CDER), Rockville, MD (1987). 6. US FDA, Guidelines for Submitting Samples and Analytical Data for Methods Validation, Center for Drugs and Biologies, Department of Health and Human Services, Rockville, MD (1987). 7. U. S. Pharmacopoeia. Validation of Compendial Methods, USP-26-NF21 (2003). 8. USSR State Pharmacopoea (XIth Ed.) [in Russian], Moscow (1998), Vol. 1, pp. 200 – 220. 9. T. O. Wilson, J. Pharm. Biomed. Anal., 8, 389 – 400 (1990). 10. P. A. D. Edwardson, G. Bhaskar, and J. E. Fairbrother, Pharm. Biomed. Anal., 8, 929 – 933 (1990). 11. J. Caporal-Gautier, J. M. Nfivet, P. Algranti, et al., Rapport d’une Commission SFSTP, STP Pharma Pratiques, No. 2, 205 – 239 (1992). 12. H. Wegscheider, “Validation of analytical methods,” in: Accreditation and Quality Assurance in Analytical Chemistry, H. Guenzler (ed.), Springer Verlag, Berlin (1996). RSD for six injections at B = 1.0; m is the number of repeated injections of the reference solution (3 £ m £ 6); t 90%(m – 1) is the Student coefficient for a 90% confidence probability (two-sided) and f = m – 1 degrees of freedom. A disadvantage of this approach is introduction of the constant K involving an empirical “required RSD = 0.6/ 2. For example, if the rated content of the main component is 98.0 – 101.0%, the RSD for a suitable chromatographic system can be determined for B = 1.0% (Table 4). According to this table, the RSD of the peak area (height) must not exceed 0.21% for three parallel determinations and 0.42% for six determinations. 4. REVALIDATION OF HPLC PROCEDURES Repeated validation may be required in the following cases [7]: (i) modification of the ready-to-use drug; (ii) modification of the parent drug synthesis technology; (iii) modification of the analytical procedure. According to the USP, users of the analytical procedures described in this pharmacopoeia and the National Formulary need not perform revalidation and only have to check for the suitability of method under real analytical conditions [7]. This implies that, if a laboratory makes a reference to some method stipulated in the USP, it is obliged to use this procedure exactly as described (nonmodified) in order to avoid the need for complete revalidation of a “modified” method. Obviously, all procedures of sample preparation for the tests have to be thoroughly performed without any deviations from the validated procedure. A special feature of HPLC (and other chromatographic techniques) is the dependence of the parameters of the chromatographic system on the sorbent type (C8, C18, etc) and on the grade and even manufacturer of a particular sorbent. For this reason, it is usual practice in HPLC (and other chromatographic techniques) to perform an objectively unavoidable modification of the chromatographic conditions as compared to those stipulated by the validated procedure, with observation of the criteria of suitability of the chromatographic 228 N. A. Épshtein 13. J. M. Green, A Practical Guide to Analytical Method Validation, Analytical Chemistry News & Features, May 1, 305A – 309A (1996). 14. Chemical Encyclopedia [in Russian], Moscow (1992), Vol. 3, pp. 72 – 74. 15. Guidance for Industry. Analytical Procedures and Methods of Validation (Chemistry, Manufacturing, and Controls Documentation) Draft Guidance, U.S. Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research (CDER), Center for Biologies Evaluation and Research (CBER), Rockville, MD (2000). 16. M. E. Swartz and I. S. Krull, Analytical Methods: Development and Validation, Marcel Dekker Inc., New York (1997). 17. L. Huber, BioPharm, 12, 64 – 66 (1999); L. Huber, Validation of Analytical Methods: Review and Strategy, LC-GC, 1997 – 1, Version February 21 (1999). 18. L. Huber, Validation of Computerized Analytical Systems, Interpharm Press, Buffalo Grove, IL (1995). 19. L. Huber, Validation and Qualification in Analytical Laboratories, Interpharm Press, Buffalo Grove, IL (1998). 20. Validation of Analytical Methods and Tests [in Russian], Farmakom, No. 6, 44 – 58 (1999). 21. Pharmeuropa. Technical Guide for the Elaboration of Monographs (3-rd Ed.), (1999), Ch. III, Analytical Validation. 22. British Pharmacopoeia (2001), Vol. 11, Appendix III, A141 – A144. 23. R. J. Bopp, T. J. Wozniak, S. L. Anliker, and J. Palmer, “Development and validation of liquid chromatographic assays for the regulatory control of pharmaceuticals,” in: Pharmaceutical and Biomedical Applications of Liquid Chromatography, Ch. 10, Riley C. M., Lough W. J., and Wainer I. W. (eds.), Elsevier – Pergamon (1994), pp. 315 – 344. 24. G. C. Hokanson, part I: Pharm. Tech., Sept. (1994), pp. 118 – 130; part II: Pharm. Tech., Oct. (1994), pp. 92 – 100. 25. Renger, H. Jehle, M. Fisher, and W. Funk, J. Planar Chrom., No. 8, 269 – 278 (1995). 26. Development and Validation of Analytical Methods, Progress in Pharmaceutical and Biomedical Analysis, Vol. 3, C. M. Riley and T. W. Rosanske (eds.), Elsevier – Pergamon, Tarryton, NY (1996). 27. L. R. Snyder, J. J. Kirkland, and J. L. Glajch, Practical HPLC Method Development (2nd ed.), J. Wiley, New York (1997). 28. I. Krul and M. Swartz, Quantitation in Method Validation, LC-GC, 16(12), 1084 – 1090 (1998). 29. J. Adamovics, Chromatographic Analysis of Pharmaceuticals, Marcel Dekker, New York (1997). 30. U. D. Neue, HPLC Columns: Theory, Technology, and Practice (1997), pp. 334 – 337. 31. W. B. Furman, J. G. Dorsey, and L. R. Snyder, Pharmaceutical Technology, 22(6), 58 (1998); W. B. Furman, J. G. Dorsey, and L. R. Snyder, System Suitability Tests in Regulatory Liquid and Gas Chromatographic Methods: Adjustments Versus Modifications, Discussion Paper in Internet, LC-GC (1999). 32. Y. Van der Heyden and D. L. Massart, “Review of the use of robustness and ruggedness in analytical chemistry,” in: Robustness of Analytical Methods and Pharmaceutical Technological Products, A. Smilde, J. de Boerm and M. Hendriks (eds.), Elsevier, Amsterdam (1996), pp. 79 – 147. 33. A. Nijhuis, H. C. M. van der Knaap, S. de Jong, and B. G. M. Vandeginste, Anal. Chim. Acta, 391, 187 – 202 (1999). 34. Y. Van der Heyden, M. Jimidar, E. Hund, et al., J. Chromatogr. A, 845, 145 – 154 (1999). 35. K. Doerfel', Statistics in Analytical Chemistry [Russian translation], Mir, Moscow (1969), pp. 190 – 194; (1994), pp. 173 – 175. 36. S. Burke, LC-GC Europe Online Supplement. Statistics and Data Analysis (2002), pp. 13 – 18. 37. R. I. Alekseev and Yu. I. Korovin, A Guide to Calculations and Processing of Results of Quantitative Analyses [in Russian], Atomizdat, Moscow (1972), p. 15. 38. N. A. Épshtein, Khim.-Farm. Zh., 36(12), 37 – 41 (2002). 39. A. K. Charyshev, Mathematical Processing of the Results of Chamical Analyses [in Russian], Khimiya, Leningrad (1984). 40. P. C. Meier and R. E. Zund, Statistical Methods in Analytical Chemistry, John Wiley & Sons, New York (2000). 41. N. A. Épshtein, Khim.-Farm. Zh., 36(11), 52 – 54 (2002). 42. R. Romero, D. Gazquez, and M. Sanchez-Vinas, LC-GC, 20(1), 72 – 80 (2002).

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