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Bioanalytical methods validation for pharmacokinetic studies

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### Bioanalytical methods validation for pharmacokinetic studies

NATIONALE

VETERINAIRE

T O U L O U S E

P.L. Toutain

Toulouse Feb. 2008

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

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

Validation methods

- A priori validation:
- Pre-study validation for analytical method development and method establishment
- In-life validation

(Routine validation)

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

A priori validation makes sure the method is suitable for its intended use

A priori validation: criteria to be validated

- 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,…)

Calibration curve

Definition

It is the relationship between known

concentrations and experimental response

values

Goal

Determine the unknown concentration of

a sample

y1

xn

x1

Calibration curveY

Response: dependent variable

(peak,area ..)

y = ax + b

Y (observed)

Independent variable:

exactly known

concentrations

X

y1

xn

x1

Calibration curveY

Response: dependent variable

y = ax + b

Y (observed)

Independent variable:

^

X

X

estimated concentration

Calibration curve

- Construction
- 5 to 8 points over the analytical domain
- replicates are required to test linearity
- 3 to 5 replicates per levels

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 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 Wikipedia

- Linear regression - Wikipedia, the free encyclopedia

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 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.

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.

Linear 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.

Statistical requirements to build a calibration curve

- Standard concentration (X) are known without error
- 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.
- The random errors εi have expected value 0.
- 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

- 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

the calibration curve (here a statistical model ) should be checked for two different things:

- Whether the assumptions of least-squares are fulfilled
- Analysis (inspection) of residuals
- Whether the model is valid and useful
- Test of linearity
- Back calculations

Validation of the calibration curve

- Homogeneity of variance
- Linearity
- Back calculations

Checking model assumptions

- The model assumptions are checked by calculating the residuals and plotting them.
- The residuals are calculated as follows :

Inspection of residuals

The following plots can be constructed to test the validity of the assumptions:

- A normal probability plot of the residuals to test normality. The points should lie along a straight line.
- Residuals against the explanatory variables, X.
- Residuals against the fitted values, Y .
- 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 curve

Homogeneity of variance

Calibration curve: homogeneity of variance

Problem of the homogeneity of variance

Cochran's test

Homogeneous

Non homogeneous

"cone shaped"

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

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

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

Calibration curve: homogeneity of variance

Weighing factor=1/x2

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???

- 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

Test of linearity : Coefficient of correlation

Y

Response

r = 0.99

does not prove linearity

X

Concentration

Calibration curve: linearity

- Test of lack of fit
- Requires replicates
- Should be carried out after weighing
- ANOVA

Calibration curve: linearity

Test of lack-of-fit

It is a comparison of 2 variances

Y

Response

X

Concentration

Variance 2

Mean estimated from the curve

Variance 1

Mean estimated from each set of data

?

=

The case of very precise technique

Calibration curve: linearity

- If no replicate
- Y = ax + b vs Y= ax + cx² + b

Test the significance of C

Y

Y

X

X

Calibration curve: linearity

- If non linearity
- use the 2nd degree polynom
- reduce the domain of the calibration curve

Calibration curve:Weight=1/X2 & quadratic component

Linear &

Unweighted residues

Quadratic &

Weighted residues

Linear &

Weighted residues

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: Parallelism

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

Freeze/thaw stability

- Avoid freeze and thaw cycles
- Enough aliquot samples should be to be prepared

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

High sensitivity

2

1

Concentration (X)

added quantity

Long term freezer stability

- Required for some analytes and for retrospective investigations
- Re-assay QC after the study is completed

Origin of the error :Accuracy and precision

- Systematic (not random)
- bias
- impossible to be corrected
- accuracy
- Random
- can be evaluated by statistics
- precision

Bias and precision

Off-Base

Model

Silver

Standard

Hit or

Miss Model

Gold

Standard

Poor Precision

Good Accuracy

Good Precision

Poor Accuracy

Good Precision

Good Accuracy

Poor Precision

Poor Accuracy

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.

The accuracy is calculated using the following

equation :

Found value - Theoretical value

Accuracy (%) = 100 x

Theoretical value

The accuracy at each concentration level must

be lower than 15% except a LOQ (20%)

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%

Precision

The closeness of replicate determinations of a sample by an assay. The acceptance criteria is 15% CV. At LOQ, 20% deviation is acceptable.

Precision

Repeatability (r)

Agreement between successive measurements on the same sample under the same conditions

Reproducibility (R)

The closeness of agreement between results

obtained with the same method under different

conditions

Precision… Considered at 3 Levels

- Repeatability
- Intermediate Precision
- Reproducibility

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 Precision

- Express within-laboratory variations.
- Between days variability
- Known as part of Ruggedness in USP

Reproducibility

- Definition: Ability reproduce data within the predefined precision
- Repeatability test at two different labs

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%)

Precision: measurement

- for a single measurement : CV(%)
- for intra-day and inter-day precision
- ANOVA

Precision: data analysis

- Single level of concentration with repetition

e.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 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 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

ANOVA

- Allows an estimation of the 2 variance terms
- inter-day mean square (BMS)
- intra-day mean square (WMS)

Repeatability 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

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)

- 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 noise

(a)

W : Peak width

1

Sample chromatogram

Blanc chromatogram

(b)

Largest variation

of the baseline

noise

(N )

Baseline

noise

N

p

p-p

N

p-p

Most important

deviation (N )

p

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

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.

Recovery: Internal standard

- Recommended to be a close analog of the analyte of interest
- Advantages and limits

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

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

Specificity / Selectivity (3)

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

Stability

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

In life validation

- should be generated for each run
- no replicate
- should be validated
- back calculation
- quality control (QC)

In life validation

- 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

- 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 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 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

Calibration curve

Intercept : Test hypothesis that the line goes

through the origin

Y

Significant : Origin ?

NS : Keep the intercept

as an empirical

parameter

X

Robustness/Stability assay of a drug

Calculated concentration

(mg/ml)

1.80

+ 2 SD

1.60

1.40

Mean

1.20

- 2 SD

1.00

0.80

0.60

0

4

8

12

16

20

Time (days)

In life validation: the QC

- to evaluate accuracy
- to evaluate precision
- to confirm LOQ
- to evaluate robustness of the method
- to confirm sample stability

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: 1551-1557

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