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Exercise 5Monte 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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the 90 % CI of f the ratio

BE accepted

1 2

Decision procedures in bioequivalence trials

- 20%+20%

µt

Mean of ref formulation

BE not accepted

BE not accepted

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The a priori BE interval: why 80-125%

120Θand80Θ21

100Ln

382.4%95.1037848.4)120(

382.4%15.95382.4)80(

60517.4)100(

oforLn

oforLn

Ln

• The reference value is 100 thus

After a logarithmic transformation:

This interval is no longer symmetric around the reference value

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The a priori BE interval: why 80-125%

605.4%95.1037848.4)120(

605.4%15.95382.4)80(

60517.4)100(

oforLn

oforLn

Ln

After a logarithmic transformation:

This interval is no longer symmetric around the reference value

605.4.4%84.1048283.4)125(

605.4%15.95382.4)80(

60517.4)100(

oforLn

oforLn

Ln

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 bioequivalencePopulation dosage regimen

Yes No

Pigs that eat more

Pigs that eat less:Possible

underexposure

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Bioequivalence and withdrawal time

Formulation A Formulation B

Time

Co

nc

entr

ati

on

AUCA = AUCB

A and B are BE

Mean curve

Mean curve

Individualsindividuals

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Bioequivalence and withdrawal time

Formulation A Formulation BWTA < WTB

MRL

Time

Co

nc

entr

ati

on

WTA WTB

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Bioequivalence and theproblem of drug residues

• Bioequivalence studies in food-producing 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 one- sided 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

LOQ

WT

BE

Pionner

Generic WT for the generic

WT for the pionner

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Use of Monte Carlo simulations

37Monte-Carlo(Monaco)

Toulouse

What is the origin of the word Monte Carlo?

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Selecting a model to simulate our data set

Fraction 1 (%)

Fraction 2 (%)

PlasmaVc

Ka1

Ka2

K10

F1 x Dose

F2 x Dose

Fraction 1 (%)

Fraction 2 (%)

PlasmaVc

Ka1

Ka2

K10

F1 x Dose

F2 x Dose

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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 statisticsThe 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.