Transcript Exercise 4 Computation of a withdrawal time and bioequivalence

Exercise 5
Monte Carlo simulations,
Bioequivalence and
Withdrawal time
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Objectives of the exercise
• To understand regulatory definitions of Bioequivalence
and Withdrawal time
• To understand the principles and goals of Monte Carlo
simulation (MCS)
• To simulate a data set using MCS with Crystal Ball (CB)
to show that two formulations of a drug (pioneer and
generic) can be bioequivalent while having different
withdrawal times.
• To compute a Withdrawal time using the EMEA
software (WT 1.4 by P Heckman)
• To compute a Bioequivalence using WNL (crossover
design)
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Origin of the question
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A regulatory decision
• The new EMEA guideline on
bioequivalence (draft 2010) states that it
is possible to get a marketing
authorization for a new generic without
having to consolidate the withdrawal time
associated with the pioneer formulation
except if there are tissular residues at the
site of injection.
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The EMA guideline
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Comments on guideline by EMA
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The question
• As an expert, you have to express your
opinion on this regulatory decision.
• As a kineticist you know that the statistical
definitions of Withdrawal time (WT) and
bioequivalence (BE) are fundamentally
different
•
So, you decide to demonstrate, with a
counterexample, it is not true and for that you
have to build a data set corresponding to a
virtual trial for which BE exist while WT are
different
• For that you will use MCS
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EMA definition of BE (2010)
• For two products, pharmacokinetic equivalence
(i.e. bioequivalence) is established if the rate
and extent of absorption of the active substance
investigated under identical and appropriate
experimental conditions only differ within
acceptable predefined limits.
• Rate and extent of absorption are estimated by
Cmax (peak concentration) and AUC (total
exposure over time), respectively, in plasma.
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EMA definition of BE
• The EMA consider the ratio of the population
geometric means (test/reference) for the parameters
(Cmax or AUC) under consideration.
•
For AUC, the 90% confidence intervals for
the ratio should be entirely contained within the a
priori regulatory limits 80% to 125%.
• For Cmax, the a priori regulatory limits 70% to 143%
could in rare cases be acceptable
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Decision procedures in bioequivalence trials
BE not
accepted
1
- 20%
the 90 % CI of f the ratio
BE accepted
2
BE not
accepted
+20%
µt
Mean of ref
formulation
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The a priori BE interval:
why 80-125%
• The reference value is 100 thus
Θ1  80 and Θ2  120
Ln100 
After a logarithmic transformation:
Ln(100)  4.60517
Ln(80)  4.382 or 95.15% of 4.382
Ln(120)  4.7848 or103.95% of 4.382
This interval is no longer symmetric around the
reference value
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The a priori BE interval:
why 80-125%
After a logarithmic transformation:
Ln(100)  4.60517
Ln(80)  4.382 or 95.15% of 4.605
Ln(120)  4.7848 or 103.95% of 4.605
This interval is no longer symmetric around the reference value
Ln(100)  4.60517
Ln(80)  4.382 or 95.15% of 4.605
Ln(125)  4.8283 or 104.84% of 4.4.605
This interval is now symmetric around the reference value in the Ln domain
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Different types of bioequivalence
• Average (ABE) : mean
• Population (PBE) : prescriptability
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Average bioequivalence
reference
test1
test2
AUC: Same mean but different distributions
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Population bioequivalence
Population dosage regimen
No
Yes
Pigs that eat less:
Possible
underexposure
Pigs that eat
more
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Bioequivalence and withdrawal time
Formulation A
Formulation B
AUCA = AUCB
A and B are BE
Concentration
Mean curve
Mean curve
Individuals
individuals
Time
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Bioequivalence and withdrawal time
Formulation A
WTA < WTB
Formulation B
Concentration
MRL
WTA
Time
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WTB
Bioequivalence and the
problem of drug residues
• Bioequivalence studies in foodproducing animals are not
acceptable in lieu of residues
data: why?
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Definitions ans statistics
associated to (average)
bioequivalence and withdrawal
time are fundamentally
different
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EMA guidance for WT
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Definition of WT by EMA
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The EU statistical definition
of the Withdrawal Time
"WT is the time when the upper onesided 95% tolerance limit for residue is
below the MRL with 95% confidence"
Tolerance limits: Limits for a percentage of a population
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WT definition is related to a
tolerance interval (limits)
• Tolerance interval is a statistical interval within
which a specified proportion of a population falls
(here 95%) with some confidence (here 95%)
• To compute a WT you have to specify two
different percentages.
– The first expresses what fraction (percentage) of the
values (animals) the interval will contain.
– The second expresses how sure you want to be
– If you set the second value (how sure) to 50%, then a
tolerance interval is the same as a prediction
interval (see our first exercise).
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Tolerance limits vs Confidence limits
How sure we are (risk fixed to 95%)
95% for EMA and 99% for FDA
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Bioequivalence and withdrawal time
• Bioequivalence is related to a confidence interval for a
parameter (e.g. mean AUC-ratio for 2 formulations)
• Withdrawal time is related to a tolerance limit (quantile
95% EU or 99% in US) and it is define as the time
when the upper one- sided 95% tolerance limit for
residue is below the MRL with 95% confidence“
• The fact to guarantee that the 90% confidence
interval for the AUC-ratio of the two formulations lie
within an acceptance interval of 0.80-1.25 do not
guarantee that the upper one- sided 95% tolerance
limit for residue is below the MRL with 95%
confidence for both formulations“
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Who is affected by an inadequate
statistical risk associated to a WT
• It is not a consumer safety issue
• It is the farmer that is protected by the
statistical risk associated to a WT
–It is the risk, for a farmer, to be controlled
positive while he actually observe the WT.
–When the WT is actually observed, at least
95% of the farmers in an average of 95% of
cases should be negative
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How to build a counterexample to
show that it is possible to have
two formulations complying with
BE requirements while their WTs
largely differ.
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Counterexample
• In mathematics, counterexamples are
often used to show that certain
conjectures are false,
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How to build a counter example
• Considering that BE is demonstrated using
plasma concentration over a rather short
period of time (e.g. 24 or 48h) but that WT
is generally much longer (e.g. 12 days),
you can expect that two bioequivalent
formulations exhibiting a so-called very
late terminal phase could have different
WT.
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Bioequivalence and withdrawal time
• Withdrawal time are generally much more longer
than the time for which plasma concentration
were measured for BE demonstration
Pionner
Generic
BE
WT for the generic
WT for the pionner
LOQ
WT
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Use of Monte Carlo simulations
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What is the origin of the word
Monte Carlo?
Toulouse
Monte-Carlo
(Monaco)
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Selecting a model to simulate our
data set
F1 x Dose
Fraction 1 (%)
Ka1
Plasma
Vc
F2 x Dose
Fraction 2 (%)
Ka2
K10
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Equation describing our model
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Step1: Implementation of the selected
model in an Excel sheet
• We have to write this equation in Excel
and to solve it for:
– times ranging from 0 to 144h for plasma
concentrations for BE
– from 144 to 1440 h for tissular concentrations
for WT.
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Implementation of the selected
model in an Excel sheet
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Step2: Monte Carlo simulation to
establish a data set using CB
• For the BE trial, we need 12 animals to carry out a 2x2
crossover design i.e. 24 vectors of plasma
concentrations from time 0 to 144h (12 vectors for
formulation1 and 12 vectors for formulation 2).
• For the WT we are planning a trial with 4 different
slaughter times (14, 21, 28 and 45 days) and for each
slaughter time, we need 6 samples i.e. 24 animals per
formulation; thus the total number of animals to simulate
for the WT is 48.
• The total number of vectors to simulate is of n=72 i.e. 36
for formulation1 and 36 for formulation2.
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Step2: Monte Carlo simulation to establish a
data set using CB
• Only variability is introduced in F1;
– for the first formulation F1 is normally
distributed with a mean F1=0.7 associated
with a relatively low inter-animal variability of
10%.
– For the second formulation we also fixed
F1=0.7 but with an associated CV of 30%
meaning more variability between animals for
this second formulation but the same average
PK parameters.
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Step2: Monte Carlo simulation to establish a
data set using CB
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Simulated concentrations at 120h post dosing
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Plasma concentration profiles for
formulation A and B
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NCA of the data set
• Computation of AUC using the NCA by WNL
• Computation of some statistics using the
statistical tool of WNL.
– It appeared that the ratio of the AUC (geometric
means) was 0.83 (659.2/788.8).
– This point estimate is to close to the a priori lower
bound of the a priori confidence interval for a BE trial
(lower bound is 0.8) thus I know a priori that it will be
impossible to conclude to a BE with this data set
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New simulation
• So, I decided to re-run my simulations but
with a lower variances for the second
formulation
• Second simulation CV=10 and 20% for
formulations A and B respectively; same
mean F=0.70.
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Results of the second simulation
Descriptive statistics
The point estimate of the AUCs ratio is now of 0.89 and I can expect
to demonstrate a BE.
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Assessment of bioequivalence of the
two formulations
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Bioequivalence in WNL
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Bioequivalence output
• Cmax:
– the regulatory 90% CI was from 73.9-:98.3
• AUC
– the regulatory CI 90% was : 80.2- 98.9
I permuted the 2 CI in the document?)
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Computation of withdrawal time
for the two formulations
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How to obtain raw data
• Simulate the model between 144 and 1440 h
(i.e. from 6 to 60 days)
• You need 6 tissular samples for each of the four
sampling times
• Sampling times: 14, 21 ,28 and 45 days
• Tissular concentrations are 100 times plasma
concentrations
• Thus for the 6 first animals, you select forecasts
at day 14, then forecasts at day 21 for animals 7
to 12 and so on.
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MRL=30
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Computation of a WT
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Conclusion
• This example shows that we are in
position to demonstrate that an average
bioequivalence between two formulations
is not a proof to guarantee that the
formulations have identical withdrawal
times.
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