ECOLE NATIONALE VETERINAIRE TOULOUSE Bioanalytical methods validation for

ECOLE NATIONALE VETERINAIRE TOULOUSE Bioanalytical methods validation for pharmacokinetic studies P. L. Toutain Toulouse Feb. 2008 Update: 24/020/08 1

Validation methods • Selective and sensitive analytical methods for the quantitative determination of drugs and their metabolites (analytes) are critical for successful performance of PK and bioequivalence studies Update: 24/020/08 2

Validation methods • Validation of analytical methods includes all the procedures recommended to demonstrate that a particular method, for a given matrix, is reliable and reproducible Update: 24/020/08 3

Validation methods 1. A priori validation: – Pre-study validation for analytical method development and method establishment 2. In-life validation (Routine validation) Update: 24/020/08 4

Regulatory requirements • G. L. P. – (e. g. ; bioequivalence, Toxicokinetics) • S. O. P. (standard operating procedure) – (from sample collection to reporting) – Record keeping – Chain of sample custody (chaîne des garanties) – Sample preparation – Analytical tools – Procedures for quality control and verification of results Update: 24/020/08 5

A priori validation makes sure the method is suitable for its intended use Update: 24/020/08 6

A priori validation: criteria to be validated 1. 2. 3. 4. 5. 6. 7. 8. 9. Update: 24/020/08 Calibration curve Accuracy Precision (repeatability, reproducibility) Limit of quantification (LOQ) Limit of detection (LOD) Sensitivity Specificity/selectivity Stability of the analyte in the matrix under study Others (ruggedness, agreement, …) 7

1. Calibration curve Update: 24/020/08 8

Calibration curve Definition It is the relationship between known concentrations and experimental response values Goal Determine the unknown concentration of a sample Update: 24/020/08 9

Calibration curve Y Response: dependent variable Y (observed) (peak, area. . ) Yn y = ax y 1 x 1 Update: 24/020/08 xn X + b Independent variable: exactly known concentrations 10

Calibration curve Y (observed) Y Response: dependent variable Yn y = ax + b y 1 x 1 Update: 24/020/08 xn ^ X estimated concentration X Independent variable: 11

Calibration curve Response x^ GOOD Update: 24/020/08 x^ BAD 12

Calibration curve • Construction – 5 to 8 points over the analytical domain – replicates are required to test linearity • 3 to 5 replicates per levels Update: 24/020/08 13

Standard calibration curve Update: 24/020/08 14

Calibration curve • The calibration curve should be prepared in the same biological matrix (e. g. plasma ) as the sample in the intended study by spiking with known concentration of the analyte (or by serial dilution). Update: 24/020/08 15

Reference Standard • Calibration standards and quality control samples (QC) • Authenticated analytical reference standard should be used to prepare (separately) solution of known concentration – certified reference standards • Never from a marketed drug formulation – commercially supplied reference standards – other material of documented purity Update: 24/020/08 16

Building the calibration curve: a regression problem Update: 24/020/08 17

Building the calibration curve: a regression problem • In statistics, regression analysis is a statistical technique which examines the relation of a dependent variable (response variable or dependent variable i. e. Y) that is for us the response of the analytical apparatus (peak, area. . ) to specified independent variables (explanatory variables or independent variable i. e. X) that is for us the concentration of calibrators. Update: 24/020/08 18

Linear regression : see Wikipedia • Linear regression - Wikipedia, the free encyclopedia Update: 24/020/08 19

Linear regression : Wikipedia • In statistics, linear regression is a regression method that models the relationship between a dependent variable Y, independent variables Xi, i = 1, . . . , p, and a random term ε. The model can be written as: • where β 0 is the intercept ("constant" term), the βis are the respective parameters of independent variables, and p is the number of parameters to be estimated in the linear regression. Update: 24/020/08 20

Linear regression : Wikipedia • This method is called "linear" because the relation of the response (the dependent variable Y) to the independent variables is assumed to be a linear function of the parameters. Update: 24/020/08 21

Linear regression : Wikipedia • It is often erroneously thought that the reason the technique is called "linear regression" is that the graph of Y = β 0 + βx is a straight line or that Y is a linear function of the X variables. But if the model is (for example) • the problem is still one of linear regression, that is, linear in x and x 2 respectively, even though the graph on x by itself is not a straight line. In other words, Y can be considered a linear function of the parameters (α, β, and γ), even though it is not a linear function of x. Update: 24/020/08 22

Statistical requirements to build a calibration curve Update: 24/020/08 23

Statistical requirements to build a calibration curve 1. Standard concentration (X) are known without error 2. Variance of response (Y) should be constant over the analytical domain (homoscedasticity hypothesis); this equivalent to say that the random errors εi are homoscedastic i. e. , they all have the same variance. 3. The random errors εi have expected value 0. 4. The random errors εi should be independent from Y and are uncorrelated. These assumptions imply that least-squares estimates of the parameters are optimal in a certain sense Update: 24/020/08 24

Regression can be used for prediction Update: 24/020/08 25

Regression can be used for prediction • These uses of regression (calibration curve) rely heavily on the model assumptions being satisfied. • Calibration curve is misused for these purposes where the appropriate assumptions cannot be verified to hold • The misuse of regression is due to the fact that it take considerably more knowledge and experience to critique a model than to fit a model with a software. Update: 24/020/08 26

Assessing the calibration curve (here a statistical model ) should be checked for two different things: 1. Whether the assumptions of leastsquares are fulfilled • Analysis (inspection) of residuals 2. Whether the model is valid and useful • • Update: 24/020/08 Test of linearity Back calculations 27

Validation of the calibration curve • Homogeneity of variance • Linearity • Back calculations Update: 24/020/08 28

Checking model assumptions • The model assumptions are checked by calculating the residuals and plotting them. • The residuals are calculated as follows : Update: 24/020/08 29

Inspection of residuals The following plots can be constructed to test the validity of the assumptions: 1. A normal probability plot of the residuals to test normality. The points should lie along a straight line. 2. Residuals against the explanatory variables, X. 3. Residuals against the fitted values, Y. 4. Residuals against the preceding residual. • There should not be any noticeable pattern to the data in all but the first plot Update: 24/020/08 30

Validation of the calibration curve Homogeneity of variance Update: 24/020/08 31

Calibration curve: homogeneity of variance Problem of the homogeneity of variance Cochran's test Homogeneous Update: 24/020/08 Non homogeneous "cone shaped" 32

Calibration curve: linearity & homogeneity of variance Inspection of a residuals plot If the linear model and the assumption of homoscedasticity are valid, the residual should be normally distributed and no trends should be apparent Update: 24/020/08 33

Calibration curve: linearity & homogeneity of variance Inspection of a residuals plot The fact that the weighted residuals show a fan-like pattern, getting larger as X increase suggest heteroscedasticity and the use of a weighting procedure to reduce variance heterogeneity Update: 24/020/08 34

Calibration curve: homogeneity of variance • Heterogeneity of variance – Commonly observed – Y has often a constant coefficient of variation • Weighted regression – weighing factor proportional to the inverse of variance (1/X, 1/X²…) • After weighing, the coefficient of correlation (r) can be lower but accuracy and precision of prediction are better Update: 24/020/08 35

Calibration curve: homogeneity of variance Weighing factor=1/x 2 Update: 24/020/08 36

Inspection of the residual plot Weighted residues Unweighted residues Misfit evidenced by visual inspection of residuals despite the use of weighted regression: does the simple linear model holds? ? ? Update: 24/020/08 37

Calibration curve : Linearity - Specific tests of linearity should be used - The coefficient of correlation (r) cannot assess linearity except for r = 1 e. g. : r = 0. 999 can be associated with a calibration curve which is not a straight line Update: 24/020/08 38

Calibration curve: linearity Test of linearity : Coefficient of correlation Response Y r = 0. 99 does not prove linearity Concentration Update: 24/020/08 X 39

Calibration curve: linearity • Test of lack of fit • Requires replicates • Should be carried out after weighing • ANOVA Update: 24/020/08 40

Calibration curve: linearity Test of lack-of-fit It is a comparison of 2 variances Y Response X Concentration Variance 1 Mean estimated from each set of data ? = Variance 2 Mean estimated from the curve The case of very precise technique Update: 24/020/08 41

Calibration curve: linearity • If no replicate • Y = ax + b vs Y= ax + cx² + b Y Test the significance of C Y X X Update: 24/020/08 42

Calibration curve: linearity • If non linearity – use the 2 nd degree polynom – reduce the domain of the calibration curve Update: 24/020/08 43

Calibration curve: Weight=1/X 2 & quadratic component Update: 24/020/08 44

Linear & Unweighted residues Calibration curve: Weight=1/X 2 & quadratic component Quadratic & Weighted residues Linear & Weighted residues Update: 24/020/08 45

Update: 24/020/08 46

Coefficient of correlation Update: 24/020/08 47

Coefficient of correlation Update: 24/020/08 48

Coefficient of correlation Update: 24/020/08 49

Validation of the calibration curve: Back calculations • back calculation of the concentrations of calibration samples using the fitted curve coefficients • The ULOQ calibrator must back-calculate to within ± 15% of the nominal concentration. • At least four out of six non-zero standards should meet the back-calculation criteria, including the LLOQ and ULOQ standards. Update: 24/020/08 50

Calibration curve: Parallelism • If samples should be diluted with blank plasma, parallelism should be investigated with QC samples Update: 24/020/08 51

Freeze/thaw stability • Avoid freeze and thaw cycles • Enough aliquot samples should be to be prepared Update: 24/020/08 52

Calibration curve: sensitivity The sensitivity of an analytical method is its ability to give response to small changes in the absolute amount of analyte present Response (Y) measured quantity 3 2 1 High sensitivity Concentration (X) added quantity Update: 24/020/08 53

Long term freezer stability • Required for some analytes and for retrospective investigations • Re-assay QC after the study is completed Update: 24/020/08 54

Calibration curve: sensitivity Performance : The slope factor 1 2 Y A 1 x^ A 2 Update: 24/020/08 A 1 ^ x X A 2 55

Accuracy and precision Update: 24/020/08 56

Origin of the error : Accuracy and precision • Systematic (not random) – bias – impossible to be corrected Þ accuracy • Random Update: 24/020/08 – can be evaluated by statistics Þ precision 57

Bias and precision Gold Standard Good Precision Good Accuracy Update: 24/020/08 Silver Standard Off-Base Model Hit or Miss Model Poor Precision Good Accuracy Good Precision Poor Accuracy Poor Precision Poor Accuracy 58

Accuracy Closeness of determined value to the true value. The acceptance criteria is mean value 15% deviation from true value. At LOQ, 20% deviation is acceptable. Update: 24/020/08 59

Accuracy The accuracy is calculated using the following equation : Accuracy (%) = 100 x Found value - Theoretical value The accuracy at each concentration level must be lower than 15% except a LOQ (20%) Update: 24/020/08 60

Accuracy • Determination – by replicate analysis of the sample containing known amount of analyte – 5 samples for at least 3 levels – The mean value should be within 15% of the actual value except at LOQ where it should not deviate by more than 20% Update: 24/020/08 61

Precision The closeness of replicate determinations of a sample by an assay. The acceptance criteria is 15% CV. At LOQ, 20% deviation is acceptable. Update: 24/020/08 62

Precision Repeatability (r) Agreement between successive measurements on the sample under the same conditions Reproducibility (R) The closeness of agreement between results obtained with the same method under different conditions Update: 24/020/08 63

Precision… Considered at 3 Levels • Repeatability • Intermediate Precision • Reproducibility Update: 24/020/08 64

Repeatability • Express the precision under the same operating conditions over a short interval of time. • Also referred to as Intra-assay precision – (within day) Update: 24/020/08 65

Intermediate Precision • Express within-laboratory variations. • Between days variability • Known as part of Ruggedness in USP Update: 24/020/08 66

Reproducibility • Definition: Ability reproduce data within the predefined precision • Repeatability test at two different labs Update: 24/020/08 67

Precision: measurement • Should be measured using a minimum of 5 determinations per concentration – A minimum of 3 concentrations in the range of expected concentrations – The precision at each concentration should not exceed 15% except for the LOQ (20%) Update: 24/020/08 68

Precision: measurement • for a single measurement : CV(%) • for intra-day and inter-day precision ® ANOVA Update: 24/020/08 69

Precision: data analysis • Single level of concentration with repetition e. g. 12, 13, 12, 14, 13, 14 µg/m. L – mean : 13. 0 µg/m. L – SD: 0. 8944 µg/m. L – CV% = SD/mean * 100 = 6. 88% • CV% is also known as the relative standard deviation or RSD Update: 24/020/08 70

Precision: data analysis • Several levels of concentration and several days day 1 levels (µg/m. L) Repetitions 0. 5 5 20 0. 4 5. 2 20. 5 5. 1 21. 0 0. 4 4. 9 19. 8 0. 6 5. 2 18. 8 day 2 and 3 : same protocol ANOVA Update: 24/020/08 71

Precision: the statistical model • The statistical model (for each concentration level) Y = μ+ day + e – μ: general mean – day: an effect (day, technician, or any factor = inter ) – e: error-random = intra Update: 24/020/08 72

ANOVA • Allows an estimation of the 2 variance terms – inter-day mean square (BMS) – intra-day mean square (WMS) Update: 24/020/08 73

Repeatability and reproducibility • SD for repeatability – r = Var(e) • SD for reproducibility – R = ²(day) + ²(r) Inter-day intra-day variance for reproducibility is the sum of the variance for repeatability and the inter-day variance Update: 24/020/08 74

Precision: ANOVA • CV intra : 5% • CV inter : 8% CV inter CV intra Update: 24/020/08 75

The limit of quantification (LOQ) • LOQ is the lowest amount of analytes in a sample which can be determined with defined precision and accuracy • LOQ : 20% Update: 24/020/08 76

Limit of quantification (LOQ) • The lowest standard on the calibration curve is the LOQ if: – no interference is present in the blanks at retention time of the analyte for this concentration – the response (analyte peak) has a precision of 20% and accuracy 80 -120% Update: 24/020/08 77

Estimation of chromatographic baseline noise W 1 : Peak width (a) Sample chromatogram Blanc chromatogram (b) Largest variation of the baseline noise (N p-p ) Np-p Update: 24/020/08 Baseline noise Np Most important deviation (N p ) 78

Three analytical areas 1 LOD 2 LOQ 3 Xb not detected Update: 24/020/08 Area of detection Area of quantification or CV<20% 79

Recovery: definition • The recovery of an analyte in an assay is the detector response obtained from an amount of the analyte added to and extracted from the biological matrix, compared to the detector response obtained for the true concentration of the pure authentic standard • The recovery allows to determine the percent of lost drug during sample preparation • Minimal extraction ratio required to ensure a good repeatability Update: 24/020/08 80

Recovery: Determination • Absolute recovery is evaluated using low, medium, and high QC samples and at least three times for each level • The extraction recovery of the analyte (s) and internal standard(s) should be higher than 70%, precise, and reproducible. Update: 24/020/08 81

Recovery: Internal standard • Recommended to be a close analog of the analyte of interest • Advantages and limits Update: 24/020/08 82

Recovery Update: 24/020/08 83

Specificity / Selectivity (1) • Specificity : for an analyte – ability of the method to produce a response for a single analyte • metabolites • enantiomers • Selectivity: for a matrix Update: 24/020/08 84

Specificity / Selectivity (2) • Analyses of blank samples from different subjects (n=6) • Blanks should be tested for interference using the proposed extraction procedure and other chromatographic conditions • Results should be compared with those obtained with aqueous solution of the analyte at a concentration near the LOQ • Blank plasma and pre-dose samples should be without interference Update: 24/020/08 85

Specificity / Selectivity (3) • If more than 10% of the blank samples exhibit significant interference, the method should be changed to eliminate interference Update: 24/020/08 86

Definition Stability The drug must keep all its properties during the investigations Stability at room temperature An experiment should cover 6 to 24 h Stability in frozen biological samples : (-20°C or -80°C) Stability sample should allow assay from day 0 to day 20 Stability during a freeze / thaw cycle Samples should be frozen and submitted to three freeze / thaw cycles Aliquotage is better than repeated freeze / thaw cycles Update: 24/020/08 87

In life validation Update: 24/020/08 88

In life validation – should be generated for each run – no replicate – should be validated • back calculation • quality control (QC) Update: 24/020/08 89

In life validation • Validation performed in each batch (day) of study samples to be analyzed • Validation of the routine calibration curve QC samples Update: 24/020/08 90

In life validation: validation of the calibration curve • Prepare routine calibration in the matrix of interest – calibration samples, n 6 including blank • Validation of the routine calibration curve – QC samples – 3 concentration levels – 3 QC per level Update: 24/020/08 91

In life validation: calibration curve • separately prepared QC samples should be analyzed with test samples • QC in duplicate at 3 different concentrations (one <=3 X LOQ, one in midrange and one close to the high end of range) should be incorporated in each run Update: 24/020/08 92

In life validation: calibration curve • Decision rule – at least 4 of 6 QC should be within 20% of their respective nominal value – 2 out of 6 QC may be outside the 20% of their respective nominal value but not at the same level Update: 24/020/08 93

Calibration curve Intercept : Test hypothesis that the line goes through the origin Y Significant : Origin ? NS : Keep the intercept as an empirical parameter X Update: 24/020/08 94

In life validation: Robustness/Stability assay of a drug Calculated concentration (mg/ml) 1. 80 1. 60 + 2 SD 1. 40 Mean 1. 20 - 2 SD 1. 00 0. 80 0. 60 0 4 8 12 16 20 Time (days) Update: 24/020/08 95

In life validation: the QC • to evaluate accuracy • to evaluate precision • to confirm LOQ • to evaluate robustness of the method • to confirm sample stability Update: 24/020/08 96

References See Guidance for Industry (main guidances in the world) • Bioanalytical Method Validation – FDA May 2001: Bioanalytical Method Validation – ICH 1995 – EMEA: no specific document • Published Workshop Reports • Shah, V. P. et al, Pharmaceutical Research: 1992; 9: 588 -592 • Shah, V. P. et al, Pharmaceutical Research: 2000; 17: 15511557 Update: 24/020/08 97

To see this guidance Update: 24/020/08 98

To see this guidance Update: 24/020/08 99