Download Monte Carlo - Physiologie et Thérapeutique Ecole Véto Toulouse

ECOLE
NATIONALE
VETERINAIRE
TOULOUSE
Use of Monte Carlo simulations to
select PK/PD breakpoints and
therapeutic doses for antimicrobials
in veterinary medicine
PL Toutain
UMR 181 Physiopathologie et Toxicologie Experimentales
INRA/ENVT
Third International conference on AAVM
Orlando, FL, USA May16-20, 2006
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Objectives of the presentation
• To review the role of Monte Carlo
simulation in PK/PD target attainment
in establishing a dosage regimen
– (susceptibility breakpoints)
MonteCarlo-Orlando06 - 2
What is the origin of the word
Monte Carlo?
Toulouse
Monte-Carlo
(Monaco)
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Monte Carlo simulation
• The term Monte Carlo was
coined by Ulman & van
Neumann during their work on
development of the atomic
bomb after city Monte Carlo
(Monaco) on the French Riviera
where the primary attraction are
casinos containing games of
chance
• Roulette wheels, dice.. exhibit
random behavior and may be
viewed as a simple random
number generator
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What is Monte Carlo simulations
MCs is the term applied to stochastic simulations that
incorporate random variability into a model
– Deterministic model
Dose  Clearance  5xMIC
Examines generally only mean
values (or other single point
values)
Gives a single
possible value
– Stochastic model
Takes into account variance of
parameters & covariance
between parameters
Gives range of
probable values
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3 Steps in Monte Carlo
simulations
1. A model is defined (a PK/PD model)
2. Sampling distribution of the model
parameters (inputs) must be known a
priori (e.g. normal distribution with mean,
variance, covariance)
3. MCs repeatedly simulate the model each
time drawing a different set of values
(inputs) from the sampling distribution of the
model parameters, the result of which is a
set of possible outcomes (outputs)
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Monte Carlo simulation: applied to PK/PD models
Model: AUC/MIC
Generate random AUC and
MIC values
across the AUC & MIC
distributions that conforms
to their probabilities
PDF of AUC
PDF of MIC
Calculate a large number
of AUC/MIC ratios
PDF of AUC/MIC
Plot results in
a probability chart
% target attainment
(AUC:MIC, T>MIC)
Adapted from Dudley, Ambrose. Curr Opin Microbiol 2000;3:515−521
MonteCarlo-Orlando06 - 7
Monte Carlo simulation
for antibiotics
• Introduced to anti-infective drug
development by Drusano (1998)
– to explore the consequences of PK and PD
variabilities on the probability of achievement of a
given therapeutic target
• In veterinary medicine not used yet
– Regnier et al AJVR 2003 64:889-893
– Lees et al 2006, in: Antimicrobial resistance in bacteria of animal
origin, F Aarestrup (ed) chapter 5
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A working example to illustrate
what is Monte Carlo simulation
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Your development project
• You are developing a new antibiotic in
pigs (e.g. a quinolone) to treat
respiratory conditions and you wish to
use this drug in 2 different clinical
settings:
– Metaphylaxis (control)
• collective treatment & oral route
– Curative (therapeutic)
• individual treatment & IM route
MonteCarlo-Orlando06 - 13
Questions for the developers
• What are the optimal dosage regimen
for this new quinolone in the 2 clinical
settings
• To answer this question, you have, first,
to define what is an “optimal dosage
regimen”
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Step 1: Define a priori some
criteria (constraints) for what is
an optimal dosage regimen
MonteCarlo-Orlando06 - 15
What is an optimal dosage regimen ?
• Possible criteria to be considered
– Efficacy
– Likelihood of emergence of resistance
(target pathogen & commensal flora)
–
–
–
–
–
Side effects
Residue and withdrawal time
Cost
……….
Monte Carlo simulations can take into account at
once all these criteria to propose a single optimal
dosage
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What is an optimal dosage regimen ?
1. Efficacy :
– it is expected to cure at least 90% of pigs
– “Probability of cure” = POC = 0.90
•
We know that the appropriate PK/PD index
for that drug (quinolone) is AUC/MIC
•
We have only to determine (or to assume) its
optimal breakpoint value for this new
quinolone
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What is an optimal dosage regimen ?
2. Emergence of resistance (1)
–
The dosage regimen should avoid the mutant
selection window (MSW) in at least 90% of pigs
MPC (Mutant prevention concentration)
MIC
yes
No
Yes
MSW
MonteCarlo-Orlando06 - 18
What is an optimal dosage regimen ?
2. Emergence of resistance (3)
–
The dosage regimen should avoid the mutant
selection window (MSW) in at least 90% of pigs
MPC (Mutant prevention concentration)
MIC
yes
No
Yes
SW
MSW< 12h in 90% of pigs
MonteCarlo-Orlando06 - 19
The 2 assumptions for an optimal dosing
regimen
1. Probability of “cure” = POC = 0.90
2. Time out of the MSW should be
higher than 12h (50% of the dosing
interval) in 90% of pigs
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Step 2: Determination of
the AUC/MIC clinical
breakpoint value for the
new quinolone in pigs
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The PK/PD index is known
(AUC/MIC) for quinolones but its
breakpoint values for metaphylaxis
(control) or curative treatments have
to be either determined
experimentally or assumed
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Determination of the PK/PD
clinical breakpoint value
• Dose titration in field trials :
– 4 groups of 10 animals
– Blood samples were obtained
– MIC of the pathogen is known
 Possible to establish the relationship
between AUC/MIC and the clinical
success
MonteCarlo-Orlando06 - 24
Determination of the PK/PD clinical breakpoint
value from the dose titration trial
Response NS
*
Blood samples were obtained
MIC of the pathogen is known
*
Dose to selected
Placebo
1
2
4
Possible to establish the
relationship between AUC/MIC
and the clinical success
Dose (mg/kg)
– Parallel design
– 4 groups of 10 animals
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AUC/MIC vs. POC: Metaphylaxis
1
0.9
0.8
POC
POC
0.7
Data points were derived by forming
ranges with 6 groups of 5 individual
AUC/MICs and calculating mean
probability of cure
0.6
0.5
0.4
0.3
0.2
10 Control pigs (no drug)
0.1
0
0
50
100
150
200
AUC/MIC
AUC/MIC
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AUC/MIC vs POC: Metaphylaxis
1
0.9
0.8
0.7
POC
0.6
0.5
0.4
0.3
Modelling using logistic regression
0.2
0.1
0
0
50
100
150
200
AUC/MIC
MonteCarlo-Orlando06 - 27
Probability of cure (POC)
• Logistic regression was used to link measures of drug
exposure to the probability of a clinical success
POC 
Dependent
variable
1
1  e a bf  AUC MIC 
Placebo
effect
sensitivity
Independent
variable
2 parameters: a (placebo effect) & b (slope of the exposure-effect curve)
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Conclusion of step 2
Placebo effect
Metaphylaxis
curative
40%
10%
Breakpoint value
80
of AUC/MIC
to achieve a POC=0.9
125
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Step 3
What is the dose to be administrated
to guarantee that 90% of the pig
population will actually achieve an
AUC/MIC of 80 (metaphylaxis) or 125
(curative treatment) for an empirical
(MIC unknown) or a targeted
antibiotherapy ( MIC determined)
MonteCarlo-Orlando06 - 31
The structural model
BP: 80 or 125
PD
 AUC 
Clearance (per hours)  
  MIC
 MIC BP
Dose 
fu  F %
PK
Free fraction
Assumption : fu=1
Bioavailability
Oral  IM
MonteCarlo-Orlando06 - 32
Experimental data from preliminary
investigations
1. Clearance : control AUC (exposure)
– Typical value : 0.15 mL/kg/min (or
9mL/kg/h)
– Log normal distribution
– Variance : 20%
(same value for metaphylaxis and curative
treatments)
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Experimental data from preliminary
investigations
2. Bioavailability :
– Oral route (metaphylaxis):
•
•
•
Typical value : 50 %
Uniform distribution
From 30 to 70%
– Intramuscular route (curative):
•
•
•
Typical value : 80%
Uniform distribution
From 70 to 90%
MonteCarlo-Orlando06 - 34
Experimental data from preliminary
investigations
3. MIC distribution
(pathogens of interest, wild population)
60
MIC90=2µg/ml
Frequency
50
40
30
20
10
0
0.5
1
2
4
MIC (µg/mL)
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Solving the structural model to compute
the dose for my new quinolone
• With point estimates
– (mean, median, best-guess value…)
• With range estimates
– Typically calculate 2 scenarios: the best case &
the worst case (e.g. MIC90)
– Can show the range of outcomes
• By Monte Carlo Simulations
– Based on probability distribution
– Give the probability of outcomes
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Computation of the dose with point
estimates (mean clearance and F%, MIC90)
BP: 80 or 125
MIC90=2µg/mL
9mL/Kg/h
 AUC 
Clearance (per hours)  
  MIC
 MIC  BP
Dose 
F%
Metaphylaxis: 2.88mg/kg
curative: 2.81 mg/kg
Bioavailability
Oral :50%
IM:80%
MonteCarlo-Orlando06 - 38
Computation of the dose with point estimates
(worst case scenario for clearance and F%, MIC90)
BP: 80 or 125
MIC90=2µg/mL
15mL/Kg/h
 AUC 
Clearance (per hours)  
  MIC
 MIC  BP
Dose 
F%
Metaphylaxis: 8.0 (vs. 2.88) mg/kg
curative: 5.35 (vs. 2.81) mg/kg
Bioavailability
Oral :30%
IM:70%
MonteCarlo-Orlando06 - 39
Computation of the dose using Monte Carlo simulation
(Point estimates are replaced by distributions)
Log normal distribution: 9±2.07 mL/Kg/h
Observed distribution
BP
metaphylaxis
Clearance  80  MIC
Dose 
F%
Dose to POC=0.9
Uniform distribution: 0.3-0.70
MonteCarlo-Orlando06 - 40
• An add-in design to help
Excel spreadsheet
modelers perform Monte
Carlo simulations
• Others features
– Search optimal solution (e.g.
dose) by finding the best
combination of decision
variables for the best possible
results
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Metaphylaxis:
dose to achieve a POC of 90% i.e. an AUC/MIC of 80
(empirical antibiotherapy)
Dose distribution
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Computation of the dose: metaphylaxis
(dose=2mg/kg from the dose titration)
PK/PD Model
Dose (mg/kg)
Mean
2.88
Worst case scenario
8.00
Monte Carlo
3.803
(empirical antibiotherapy)
Monte Carlo
???
(targeted antibiotherapy)
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Sensitivity analysis
• Analyze the contribution of the different
variables to the final result (predicted dose)
• Allow to detect the most important drivers of
the model
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Sensitivity analysis
Metaphylaxis, empirical antibiotherapy
Contribution of
the MIC
distribution
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Computation of the dose using Monte Carlo simulation
Metaphylaxis, Targeted antibiotherapy
MIC=1µg/mL
Log normal distribution: 9±2.07 mL/Kg/h
BP
metaphylaxis
Clearance  80  MIC
Dose 
F%
Dose to POC=0.9
Uniform distribution: 0.3-0.70
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Computation of the dose using Monte Carlo simulation
Targeted antibiotherapy
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Computation of the dose: metaphylaxis
(dose=2mg/kg from the dose titration)
PK/PD model
Dose (mg/kg)
Mean
2.88
Worst case scenario
8.00
Monte Carlo
3.803
(empirical antibiotherapy)
Monte Carlo
2.24
(targeted antibiotherapy
against a bug having a
MIC=1µg/mL)
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Sensitivity analysis
(metaphylaxis, targeted antibiotherapy)
F%
MonteCarlo-Orlando06 - 51
Computation of the dose (mg/kg):
metaphylaxis vs. curative & empirical vs. targeted
PK/PD model
curative
metaphylaxis
Mean
2.81
2.88
Worst case
scenario
5.35
8.00
Monte Carlo
3.379
3.803
1.86
2.24
(empirical antibiotherapy)
Monte Carlo
(targeted antibiotherapy)
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The variance–covariance matrix
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The second criteria to
determine the optimal dose:
the MSW & MPC
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Kinetic disposition of the new quinolone for the
selected metaphylactic dose (3.8 mg/kg)
(monocompartmental model, oral route)
Log normal distribution: 9±2.07 mL/kg/h
F%
Uniform distribution: 0.3-0.70
Slope=Cl/Vc=0.09 per h (T1/2=7.7h)
concentrations (µg/mL)
concentrations
8
MPC
7
6
5
MIC
4
Série1
3
2
MSW
1
0
0
5
10
15
20
25
30
Time (min)
MonteCarlo-Orlando06 - 58
Time>MPC for the POC 90% for metaphylaxis
(dose 3.8 mg/kg, empirical antibiotherapy)
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Time>MPC for the POC 90% for metaphylaxis
(dose of 7.1mg/kg, empirical antibiotherapy)
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Sensitivity analysis
(dose
of 7.1mg/kg, metaphylaxis, empirical antibiotherapy)
Clearance (slope) is the most
influential factor of variability
for T>MPC ,not bioavailability
as for the AUC/MIC
MonteCarlo-Orlando06 - 61
Time>MPC for the POC 90% for curative treatment
(dose of 3.8mg/kg,curative treatment
MonteCarlo-Orlando06 - 62
Sensitivity analysis
(dose
of 3.8mg/kg, curative treatment empirical antibiotherapy)
Clearance
Clearance (slope) is the only
influential factor of variability for
T>MPC not bioavailability as for
metaphylaxis
MonteCarlo-Orlando06 - 63
Computation of the dose (mg/kg):
metaphylaxis vs. curative treatment
Monte Carlo
curative
metaphylaxis
Efficacy
3.379
3.803
To guarantee
T>MPC in 90% of
pigs for 50% the
dosage interval
3.8
7.1
MonteCarlo-Orlando06 - 64
Conclusion
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conclusions
– MCs allow to explore explicitly early
in drug development both PK and
microbiological (MIC) variabilities to
evaluate how often such a target is
likely to be achieved after different
doses of a drug
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The weak link in MCs is Absence of a priori
knowledge on PK & PD distribution
• Population PK are needed to document
influence of different factors on drug
exposure
• Health vs. disease; age; sex; breed…
• PD: MIC distributions
• Truly representative of real world (prospective
rather than retrospective sampling)
• Possibility to use diameters distribution if the
calibration curve is properly defined
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