ECOLE
NATIONALE
VETERINAIRE
TOULOUSE
Bioanalytical methods validation for
pharmacokinetic studies
P.L. Toutain
Toulouse Feb. 2008
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Validation methods 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
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Validation methods 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
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Validation methods 3
Validation 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 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
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Validation methods 5
A priori validation
makes sure the method
is suitable for its
intended use
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Validation methods 6
A priori validation:
criteria to be validated
1.
2.
3.
4.
5.
6.
7.
8.
9.
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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,…)
Validation methods 7
1. Calibration curve
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Validation methods 8
Calibration curve
Definition
It is the relationship between known
concentrations and experimental response
values
Goal
Determine the unknown concentration of
a sample
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Validation methods 9
Calibration curve
Y Response: dependent variable
Y (observed)
(peak,area ..)
Yn
y = ax
y1
x1
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xn
X
+ b
Independent variable:
exactly known
concentrations
Validation methods 10
Calibration curve
Y (observed)
Y Response: dependent variable
Yn
y = ax
+ b
y1
x1
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xn
^
X
estimated concentration
X
Independent variable:
Validation methods 11
Calibration curve
Response
Response
x^
GOOD
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x^
BAD
Validation methods 12
Calibration 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 13
Standard calibration curve
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Validation methods 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).
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Validation methods 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
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Validation methods 16
Building the calibration curve:
a regression problem
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Validation methods 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 .
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Validation methods 18
Linear regression : see Wikipedia
• Linear regression - Wikipedia, the free
encyclopedia
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Validation methods 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 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 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.
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Validation methods 21
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.
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Validation methods 22
Statistical requirements to
build a calibration curve
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Validation methods 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
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Validation methods 24
Regression can be used
for prediction
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Validation methods 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.
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Validation methods 26
Assessing the calibration curve
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
•
•
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Test of linearity
Back calculations
Validation methods 27
Validation of the calibration curve
• Homogeneity of variance
• Linearity
• Back calculations
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Validation methods 28
Checking model assumptions
• The model assumptions are
checked by calculating the
residuals and plotting them.
Re siduals  Yobserved  Yfitted
• The residuals are calculated as
follows :
Re siduals  Yobserved  Yfittted
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Validation methods 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
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Validation methods 30
Validation of the calibration curve
Homogeneity of variance
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Validation methods 31
Calibration curve: homogeneity of variance
Problem of the homogeneity of variance
Cochran's test
Homogeneous
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Non homogeneous
"cone shaped" Validation methods 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
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Validation methods 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
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Validation methods 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
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Validation methods 35
Calibration curve:
homogeneity of variance
Weighing factor=1/x2
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Validation methods 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???
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Validation methods 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
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Validation methods 38
Calibration curve: linearity
Test of linearity : Coefficient of correlation
Response
Y
r = 0.99
does not prove linearity
Concentration
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X
Validation methods 39
Calibration curve: linearity
• Test of lack of fit
• Requires replicates
• Should be carried out after weighing
• ANOVA
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Validation methods 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
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Validation methods 41
Calibration curve: linearity
• If no replicate
• Y = ax + b
vs
Y= ax + cx² + b
Y
Test the significance of C
Y
X
X
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Validation methods 42
Calibration curve: linearity
• If non linearity
– use the 2nd degree polynom
– reduce the domain of the calibration curve
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Validation methods 43
Calibration curve:
Weight=1/X2 & quadratic component
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Validation methods 44
Linear &
Unweighted residues
Calibration curve:
Weight=1/X2 & quadratic
component
Quadratic &
Weighted residues
Linear &
Weighted residues
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Validation methods 46
Coefficient of correlation
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Validation methods 47
Coefficient of correlation
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Validation methods 48
Coefficient of correlation
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Validation methods 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.
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Validation methods 50
Calibration curve: Parallelism
• If samples should be diluted with
blank plasma, parallelism should be
investigated with QC samples
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Validation methods 51
Freeze/thaw stability
• Avoid freeze and thaw cycles
• Enough aliquot samples should be
to be prepared
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Validation methods 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
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Validation methods 53
Long 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 54
Calibration curve: sensitivity
Performance : The slope factor
1
2
Y
X
A1 x^ A2
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A1
^
x
A2
Validation methods 55
Accuracy and precision
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Validation methods 56
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 57
Bias and precision
Gold
Standard
Good Precision
Good Accuracy
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Silver
Standard
Off-Base
Model
Hit or
Miss Model
Poor Precision
Good Accuracy
Good Precision
Poor Accuracy
Poor Precision
Poor Accuracy
Validation methods 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.
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Validation methods 59
Accuracy
The accuracy is calculated using the following
equation :
Accuracy (%) = 100 x
Found value - Theoretical value
Theoretical value
The accuracy at each concentration level must
be lower than 15% except a LOQ (20%)
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Validation methods 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%
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Validation methods 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.
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Validation methods 62
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
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Validation methods 63
Precision… Considered at 3 Levels
• Repeatability
• Intermediate Precision
• Reproducibility
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Validation methods 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)
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Validation methods 65
Intermediate Precision
• Express within-laboratory variations.
• Between days variability
• Known as part of Ruggedness in USP
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Validation methods 66
Reproducibility
• Definition: Ability reproduce data
within the predefined precision
• Repeatability test at two different labs
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Validation methods 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%)
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Validation methods 68
Precision: measurement
• for a single measurement : CV(%)
• for intra-day and inter-day precision
 ANOVA
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Validation methods 69
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
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Validation methods 70
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
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Validation methods 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
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Validation methods 72
ANOVA
• Allows an estimation of the 2 variance terms
– inter-day mean square (BMS)
– intra-day mean square (WMS)
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Validation methods 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
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Validation methods 74
Precision: ANOVA
• CV intra :
5%
• CV inter :
8%
CV inter  CV intra
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Validation methods 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%
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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 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
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Baseline
noise
Np
Most important
deviation (N p )
Validation methods 78
Three analytical areas
LOD
1
LOQ
2
3
Xb
not detected
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Area of
detection
Area of
quantification
or CV<20%
Validation methods 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
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Validation methods 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.
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Recovery: Internal standard
•Recommended to be a close
analog of the analyte of interest
•Advantages and limits
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Validation methods 82
Recovery
Peak _ area _(of _ x _ ng / mL, plasma_ extract)
Re cov ery  100 
Peak _ area _(of _ x _ ng / mL, s tan dard _ solution)
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Validation methods 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
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Validation methods 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
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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 86
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
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In life validation
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In life validation
– should be generated for each run
– no replicate
– should be validated
• back calculation
• quality control (QC)
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In 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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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
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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
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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
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Calibration curve
Intercept : Test hypothesis that the line goes
through the origin
Y
Significant : Origin ?
NS : Keep the intercept
as an empirical
parameter
X
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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)
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In 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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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
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To see this guidance
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To see this guidance
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