8 Validation Methods 2008-2
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Validation methods 1Update:24/020/08
Bioanalytical methods validation for pharmacokinetic studies
Bioanalytical methods validation for pharmacokinetic studies
P.L. Toutain
Toulouse Feb. 2008
ECOLENATIONALEVETERINAIRE
T O U L O U S E
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Validation methods 2Update:24/020/08
Validation methodsValidation 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
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Validation methods 3Update:24/020/08
Validation methodsValidation methods
• Validation of analytical methods includes all the procedures recommended to demonstrate that a particular method, for a given matrix, is reliable and reproducible
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Validation methods 4Update:24/020/08
Validation methodsValidation methods
1. A priori validation:– Pre-study validation for analytical
method development and method establishment
2. In-life validation
(Routine validation)
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Validation methods 5Update:24/020/08
Regulatory requirementsRegulatory 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
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Validation methods 6Update:24/020/08
A priori validation makes sure the method
is suitable for its intended use
A priori validation makes sure the method
is suitable for its intended use
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Validation methods 7Update:24/020/08
A priori validation: criteria to be validated
A priori validation: criteria to be validated
1. Calibration curve2. Accuracy3. Precision (repeatability, reproducibility)4. Limit of quantification (LOQ) 5. Limit of detection (LOD)6. Sensitivity7. Specificity/selectivity8. Stability of the analyte in the matrix under study9. Others (ruggedness, agreement,…)
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Validation methods 8Update:24/020/08
1. Calibration curve1. Calibration curve
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Validation methods 9Update:24/020/08
Definition It is the relationship between known concentrations and experimental response values
Goal Determine the unknown concentration of a sample
Calibration curveCalibration curve
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Validation methods 10Update:24/020/08
Response: dependent variable(peak,area ..)
Y (
ob
serv
ed)
Y
X
y = ax + b
Independent variable:exactly knownconcentrations
Calibration curveCalibration curve
x1
y1
xn
Yn
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Validation methods 11Update:24/020/08
Response: dependent variable
Y (
ob
serv
ed)
Y
X
y = ax + b
Independent variable:X
estimated concentration^
Calibration curveCalibration curve
x1
y1
xn
Yn
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Validation methods 12Update:24/020/08
x
Response
x
Response
GOOD BAD
^ ^
Calibration curveCalibration curve
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Validation methods 13Update:24/020/08
Calibration curveCalibration curve
• Construction
– 5 to 8 points over the analytical domain
– replicates are required to test linearity
• 3 to 5 replicates per levels
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Validation methods 14Update:24/020/08
Standard calibration curveStandard calibration curve
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Validation methods 15Update:24/020/08
Calibration curveCalibration 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).
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Validation methods 16Update:24/020/08
Reference StandardReference 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
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Validation methods 17Update:24/020/08
Building the calibration curve: a regression problem
Building the calibration curve: a regression problem
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Validation methods 18Update:24/020/08
Building the calibration curve: a regression problem
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 .
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Validation methods 19Update:24/020/08
Linear regression : see WikipediaLinear regression : see Wikipedia
• Linear regression - Wikipedia, the free encyclopedia
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Validation methods 20Update:24/020/08
Linear regression : WikipediaLinear 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 β0 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.
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Validation methods 21Update:24/020/08
Linear regression : WikipediaLinear 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.
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Validation methods 22Update:24/020/08
Linear regression : WikipediaLinear regression : Wikipedia
• It is often erroneously thought that the reason the technique is called "linear regression" is that the graph of Y = β0 + 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 x2 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.
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Validation methods 23Update:24/020/08
Statistical requirements to build a calibration curve
Statistical requirements to build a calibration curve
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Validation methods 24Update:24/020/08
Statistical requirements to build a calibration curve
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
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Validation methods 25Update:24/020/08
Regression can be used for prediction
Regression can be used for prediction
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Validation methods 26Update:24/020/08
Regression can be used for predictionRegression 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.
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Validation methods 27Update:24/020/08
Assessing the calibration curve Assessing the calibration curve
the calibration curve (here a statistical model ) should be checked for two different things:
1. Whether the assumptions of least-squares are fulfilled
• Analysis (inspection) of residuals
2. Whether the model is valid and useful• Test of linearity• Back calculations
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Validation methods 28Update:24/020/08
Validation of the calibration curveValidation of the calibration curve
• Homogeneity of variance
• Linearity
• Back calculations
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Validation methods 29Update:24/020/08
Checking model assumptions Checking model assumptions
• The model assumptions are checked by calculating the residuals and plotting them.
• The residuals are calculated as follows :
fittedobserved YYsiduals Re
fitttedobserved YYsiduals Re
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Validation methods 30Update:24/020/08
Inspection of residualsInspection 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
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Validation methods 31Update:24/020/08
Validation of the calibration curveValidation of the calibration curve
Homogeneity of variance
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Validation methods 32Update:24/020/08
Problem of the homogeneity of variance Cochran's test
Homogeneous Non homogeneous"cone shaped"
Calibration curve: homogeneity of varianceCalibration curve: homogeneity of variance
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Validation methods 33Update:24/020/08
Calibration curve: linearity & homogeneity of varianceInspection of a residuals plot
Calibration curve: linearity & homogeneity of varianceInspection 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
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Validation methods 34Update:24/020/08
Calibration curve: linearity & homogeneity of varianceInspection of a residuals plot
Calibration curve: linearity & homogeneity of varianceInspection 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
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Validation methods 35Update:24/020/08
• 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
Calibration curve: homogeneity of varianceCalibration curve: homogeneity of variance
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Validation methods 36Update:24/020/08
Calibration curve: homogeneity of variance
Calibration curve: homogeneity of variance
Weighing factor=1/x2
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Validation methods 37Update:24/020/08
Inspection of the residual plotInspection 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???
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Validation methods 38Update:24/020/08
Calibration curve : LinearityCalibration 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
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Validation methods 39Update:24/020/08
Res
po
nse
Y
X
Calibration curve: linearityCalibration curve: linearity
Concentration
Test of linearity : Coefficient of correlation
r = 0.99does not prove linearity
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Validation methods 40Update:24/020/08
Calibration curve: linearityCalibration curve: linearity
• Test of lack of fit
• Requires replicates
• Should be carried out after weighing
• ANOVA
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Validation methods 41Update:24/020/08
YResponse
Test of lack-of-fit It is a comparison of 2 variances
Variance 1Mean estimated from
each set of data
Variance 2Mean estimated from the curve
?=
XConcentration
The case of very precise technique
Calibration curve: linearityCalibration curve: linearity
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Validation methods 42Update:24/020/08
Calibration curve: linearityCalibration curve: linearity
• If no replicate
• Y = ax + b vs Y= ax + cx² + b
Y
X
Y
X
Test the significance of C
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Validation methods 43Update:24/020/08
Calibration curve: linearityCalibration curve: linearity
• If non linearity
– use the 2nd degree polynom
– reduce the domain of the calibration curve
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Validation methods 44Update:24/020/08
Calibration curve:Weight=1/X2 & quadratic component
Calibration curve:Weight=1/X2 & quadratic component
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Validation methods 45Update:24/020/08
Calibration curve:Weight=1/X2 & quadratic
component
Calibration curve:Weight=1/X2 & quadratic
component
Linear &Weighted residues
Linear &Unweighted residues
Quadratic &Weighted residues
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Validation methods 46Update:24/020/08
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Validation methods 47Update:24/020/08
Coefficient of correlationCoefficient of correlation
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Validation methods 48Update:24/020/08
Coefficient of correlationCoefficient of correlation
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Validation methods 49Update:24/020/08
Coefficient of correlationCoefficient of correlation
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Validation methods 50Update:24/020/08
Validation of the calibration curve:Back calculations
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.
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Validation methods 51Update:24/020/08
Calibration curve: ParallelismCalibration curve: Parallelism
• If samples should be diluted with blank plasma, parallelism should be investigated with QC samples
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Validation methods 52Update:24/020/08
Freeze/thaw stabilityFreeze/thaw stability
• Avoid freeze and thaw cycles
• Enough aliquot samples should be to be prepared
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Validation methods 53Update:24/020/08
Calibration curve: sensitivityCalibration curve: sensitivity
The sensitivity of an analytical method is itsability to give response to small changes inthe absolute amount of analyte present
1
2
3
High sensitivity
Concentration (X)
added quantity
Response (Y)measuredquantity
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Validation methods 54Update:24/020/08
Long term freezer stabilityLong term freezer stability
• Required for some analytes and for retrospective investigations
• Re-assay QC after the study is completed
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Validation methods 55Update:24/020/08
1
2
A1 A2 A2A1x x
Performance : The slope factor
Y
X^ ^
Calibration curve: sensitivityCalibration curve: sensitivity
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Validation methods 56Update:24/020/08
Accuracy and precisionAccuracy and precision
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Validation methods 57Update:24/020/08
Origin of the error :Accuracy and precision
Origin of the error :Accuracy and precision
• Systematic (not random)– bias
– impossible to be corrected accuracy
• Random– can be evaluated by statistics precision
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Validation methods 58Update:24/020/08
Good PrecisionGood Accuracy
Poor PrecisionGood Accuracy
Good PrecisionPoor Accuracy
Poor PrecisionPoor Accuracy
Gold Standard
Silver Standard
Off-Base Model
Hit or Miss Model
Bias and precisionBias and precision
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Validation methods 59Update:24/020/08
AccuracyAccuracy
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.
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Validation methods 60Update:24/020/08
Accuracy Accuracy
The accuracy is calculated using the followingequation :
Accuracy (%) = 100 x Found value - Theoretical value
Theoretical value
The accuracy at each concentration level mustbe lower than 15% except a LOQ (20%)
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Validation methods 61Update:24/020/08
AccuracyAccuracy
• 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%
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Validation methods 62Update:24/020/08
PrecisionPrecision
The closeness of replicate determinations of a sample by an assay.
The acceptance criteria is 15% CV. At LOQ, 20% deviation is acceptable.
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Validation methods 63Update:24/020/08
Repeatability (r)
Agreement between successive measurements on the same sample under the same conditions
Reproducibility (R)
The closeness of agreement between resultsobtained with the same method under different conditions
PrecisionPrecision
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Validation methods 64Update:24/020/08
Precision… Considered at 3 Levels
Precision… Considered at 3 Levels
• Repeatability
• Intermediate Precision
• Reproducibility
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Validation methods 65Update:24/020/08
Repeatability Repeatability
• Express the precision under the same
operating conditions over a short
interval of time.
• Also referred to as Intra-assay precision
– (within day)
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Intermediate PrecisionIntermediate Precision
• Express within-laboratory variations.
• Between days variability
• Known as part of Ruggedness in USP
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Validation methods 67Update:24/020/08
ReproducibilityReproducibility
• Definition: Ability reproduce data
within the predefined precision
• Repeatability test at two different labs
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Validation methods 68Update:24/020/08
Precision: measurementPrecision: 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%)
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Validation methods 69Update:24/020/08
Precision: measurementPrecision: measurement
• for a single measurement : CV(%)
• for intra-day and inter-day precision ANOVA
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Validation methods 70Update:24/020/08
Precision: data analysisPrecision: data analysis
• Single level of concentration with repetitione.g. 12, 13, 12, 14, 13, 14 µg/mL– mean : 13.0 µg/mL– SD: 0.8944 µg/mL– CV% = SD/mean * 100 = 6.88%
• CV% is also known as the relative standard deviation or RSD
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Validation methods 71Update:24/020/08
Precision: data analysisPrecision: data analysis• Several levels of concentration and several days
day 1 levels (µg/mL) 0.5 5 20
Repetitions 0.4 5.2 20.5
0.5 5.1 21.0
0.4 4.9 19.8
0.6 5.2 18.8
day 2 and 3 : same protocol
ANOVA
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Validation methods 72Update:24/020/08
Precision: the statistical modelPrecision: the statistical model
• The statistical model (for each concentration level)
Y = μ+ day + – μ: general mean
– day: an effect (day, technician, or any factor = inter )
– : error-random = intra
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Validation methods 73Update:24/020/08
ANOVAANOVA
• Allows an estimation of the 2 variance terms
– inter-day mean square (BMS)
– intra-day mean square (WMS)
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Validation methods 74Update:24/020/08
Repeatability and reproducibilityRepeatability and reproducibility
• SD for repeatability
r = Var(e)
• SD for reproducibility
R = ²(day) + ²(r)
variance for reproducibility is the sum of the variance for repeatability and the inter-day variance
Inter-day intra-day
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Validation methods 75Update:24/020/08
Precision: ANOVAPrecision: ANOVA
• CV intra : 5%
• CV inter : 8%
CV inter CV intra
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Validation methods 76Update:24/020/08
The limit of quantification (LOQ)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%
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Validation methods 77Update:24/020/08
Limit of quantification (LOQ)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%
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Validation methods 78Update:24/020/08
Estimation of chromatographic baseline noiseEstimation of chromatographic baseline noise
Np-pNp
W : Peak width1
Baseline noise
Largest variationof the baseline noise (N )p-p
Most important deviation (N )p
Sample chromatogram
Blanc chromatogram
(a)
(b)
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Validation methods 79Update:24/020/08
Three analytical areasThree analytical areas
1 2 3
Xb
not detected Area of detection
Area of quantification
or CV<20%
LOD LOQ
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Validation methods 80Update:24/020/08
•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
Recovery: definitionRecovery: definition
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Validation methods 81Update:24/020/08
•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.
Recovery: DeterminationRecovery: Determination
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Validation methods 82Update:24/020/08
•Recommended to be a close analog of the analyte of interest
•Advantages and limits
Recovery: Internal standardRecovery: Internal standard
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Validation methods 83Update:24/020/08
RecoveryRecovery
)_tan,/___(_
)_,/___(_covRe
solutiondardsmLngxofareaPeak
extractplasmamLngxofareaPeakery 100
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Validation methods 84Update:24/020/08
Specificity / Selectivity (1)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
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Validation methods 85Update:24/020/08
Specificity / Selectivity (2)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
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Validation methods 86Update:24/020/08
Specificity / Selectivity (3)Specificity / Selectivity (3)
• If more than 10% of the blank samples exhibit significant interference, the method should be changed to eliminate interference
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Validation methods 87Update:24/020/08
Definition The drug must keep all its properties during the investigations
Stability at room temperature An experiment should cover 6 to 24h
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
StabilityStability
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Validation methods 88Update:24/020/08
In life validationIn life validation
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Validation methods 89Update:24/020/08
In life validationIn life validation
– should be generated for each run
– no replicate
– should be validated
• back calculation
• quality control (QC)
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Validation methods 90Update:24/020/08
In life validationIn life validation
• Validation performed in each batch (day) of study samples to be analyzed
• Validation of the routine calibration curve
QC samples
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Validation methods 91Update:24/020/08
In life validation: validation of the calibration curve
In life validation: validation of the calibration curve
• Prepare routine calibration in the matrix of interest– calibration samples, n6 including blank
• Validation of the routine calibration curve– QC samples
– 3 concentration levels
– 3 QC per level
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Validation methods 92Update:24/020/08
In life validation: calibration curveIn life validation: calibration curve
• separately prepared QC samples should be analyzed with test samples
• QC in duplicate at 3 different concentrations (one <=3X LOQ, one in midrange and one close to the high end of range) should be incorporated in each run
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Validation methods 93Update:24/020/08
In life validation: calibration curveIn 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
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Validation methods 94Update:24/020/08
Y
X
Significant : Origin ?NS : Keep the intercept as an empirical parameter
Intercept : Test hypothesis that the line goes through the origin
Calibration curveCalibration curve
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Validation methods 95Update:24/020/08
In life validation:Robustness/Stability assay of a drug
In life validation:Robustness/Stability assay of a drug
1.00
0.80
1.20
1.40
1.60
1.80
0.60
0 4 8 12 16 20
Time (days)
+ 2 SD
- 2 SD
Mean
Calculated concentration(mg/ml)
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Validation methods 96Update:24/020/08
In life validation: the QCIn life validation: the QC
• to evaluate accuracy
• to evaluate precision
• to confirm LOQ
• to evaluate robustness of the method
• to confirm sample stability
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Validation methods 97Update:24/020/08
ReferencesReferences
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: 1551-1557
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Validation methods 98Update:24/020/08
To see this guidance
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Validation methods 99Update:24/020/08
To see this guidanceTo see this guidance