8 Validation Methods 2008-2

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


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



• Validation of analytical methods includes all the procedures recommended to demonstrate that a particular method, for a given matrix, is reliable and reproducible



1. A priori validation:– Pre-study validation for analytical

method development and method establishment

2. In-life validation

(Routine validation)


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


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


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,…)


1. Calibration curve1. Calibration curve


Definition It is the relationship between known concentrations and experimental response values

Goal Determine the unknown concentration of a sample

Calibration curveCalibration curve


Response: dependent variable(peak,area ..)

Y (

ob

serv

ed)

Y

X

y = ax + b

Independent variable:exactly knownconcentrations


x1

y1

xn

Yn


Response: dependent variable

Y (

ob

serv

ed)

Y

X

y = ax + b

Independent variable:X

estimated concentration^


x1

y1

xn

Yn


x

Response

x

Response

GOOD BAD

^ ^




• Construction

– 5 to 8 points over the analytical domain

– replicates are required to test linearity

• 3 to 5 replicates per levels


Standard calibration curveStandard 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).


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


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 .


Linear regression : see WikipediaLinear regression : see Wikipedia

• Linear regression - Wikipedia, the free encyclopedia


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.



• 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.



• 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.


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


Regression can be used for prediction

Regression can be used for prediction


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.


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


Validation of the calibration curveValidation of the calibration curve

• Homogeneity of variance

• Linearity

• Back calculations


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


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


Validation of the calibration curveValidation of the calibration curve

Homogeneity of variance


Problem of the homogeneity of variance Cochran's test

Homogeneous Non homogeneous"cone shaped"

Calibration curve: homogeneity of varianceCalibration curve: homogeneity of variance


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




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


• 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


Calibration curve: homogeneity of variance

Calibration curve: homogeneity of variance

Weighing factor=1/x2


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???


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


Res

po

nse

Y

X

Calibration curve: linearityCalibration curve: linearity

Concentration

Test of linearity : Coefficient of correlation

r = 0.99does not prove linearity



• Test of lack of fit

• Requires replicates

• Should be carried out after weighing

• ANOVA


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




• If no replicate

• Y = ax + b vs Y= ax + cx² + b

Y

X

Y

X

Test the significance of C



• If non linearity

– use the 2nd degree polynom

– reduce the domain of the calibration curve


Calibration curve:Weight=1/X2 & quadratic component

Calibration curve:Weight=1/X2 & quadratic component


Calibration curve:Weight=1/X2 & quadratic

component

Calibration curve:Weight=1/X2 & quadratic

component

Linear &Weighted residues

Linear &Unweighted residues

Quadratic &Weighted residues


Coefficient of correlationCoefficient of correlation


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.


Calibration curve: ParallelismCalibration curve: Parallelism

• If samples should be diluted with blank plasma, parallelism should be investigated with QC samples


Freeze/thaw stabilityFreeze/thaw stability

• Avoid freeze and thaw cycles

• Enough aliquot samples should be to be prepared


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


Long term freezer stabilityLong term freezer stability

• Required for some analytes and for retrospective investigations

• Re-assay QC after the study is completed


1

2

A1 A2 A2A1x x

Performance : The slope factor

Y

X^ ^

Calibration curve: sensitivityCalibration curve: sensitivity


Accuracy and precisionAccuracy and precision


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


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


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.


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%)


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%


PrecisionPrecision

The closeness of replicate determinations of a sample by an assay.

The acceptance criteria is 15% CV. At LOQ, 20% deviation is acceptable.


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


Precision… Considered at 3 Levels

Precision… Considered at 3 Levels

• Repeatability

• Intermediate Precision

• Reproducibility


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)


Intermediate PrecisionIntermediate Precision

• Express within-laboratory variations.

• Between days variability

• Known as part of Ruggedness in USP


ReproducibilityReproducibility

• Definition: Ability reproduce data

within the predefined precision

• Repeatability test at two different labs


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%)


Precision: measurementPrecision: measurement

• for a single measurement : CV(%)

• for intra-day and inter-day precision ANOVA


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


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


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


ANOVAANOVA

• Allows an estimation of the 2 variance terms

– inter-day mean square (BMS)

– intra-day mean square (WMS)


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


Precision: ANOVAPrecision: ANOVA

• CV intra : 5%

• CV inter : 8%

CV inter CV intra


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%


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%


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)


Three analytical areasThree analytical areas

1 2 3

Xb

not detected Area of detection

Area of quantification

or CV<20%

LOD LOQ


•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


•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


•Recommended to be a close analog of the analyte of interest

•Advantages and limits

Recovery: Internal standardRecovery: Internal standard


RecoveryRecovery

)_tan,/___(_

)_,/___(_covRe

solutiondardsmLngxofareaPeak

extractplasmamLngxofareaPeakery 100


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



• 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



• If more than 10% of the blank samples exhibit significant interference, the method should be changed to eliminate interference


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


In life validationIn life validation



– should be generated for each run

– no replicate

– should be validated

• back calculation

• quality control (QC)



• Validation performed in each batch (day) of study samples to be analyzed

• Validation of the routine calibration curve

QC samples


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


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


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


Y

X

Significant : Origin ?NS : Keep the intercept as an empirical parameter

Intercept : Test hypothesis that the line goes through the origin



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)


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


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


To see this guidance


To see this guidanceTo see this guidance

8 Validation Methods 2008-2

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