Transcript Drusano-45th-ICAAC-I..

Monte Carlo Simulation
G.L. Drusano, M.D.
Co-Director
Ordway Research Institute &
Research Physician
New York State Department of Health
Professor of Medicine & Pharmacology
Albany Medical College
Monte Carlo Simulation
• Monte Carlo simulation was invented by
Metropolis and von Neumann
• This technique and its first cousin
Markov Chain Monte Carlo have been
used since for construction of
distributions (Markov Chain Monte Carlo
was actually described as a solution to
the “simulated annealing problem” in the
Manhattan Project –Metropolis et al)
Monte Carlo Simulation
• The first use of Monte Carlo simulation
for drug dose choice and breakpoint
determination was presented on
October 15, 1998 at an FDA AntiInfective Drug Products Advisory
Committee
• At this time, the drug was presented as
“DrugX” but was evernimicin
• The ultimate outcome was predicted by
the method (but the drug died)
Role of Monte Carlo Simulation for Dose
Choice for Clinical Trials of Anti-Infectives
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
1.
2.
3.
4.
Required Factors for Rational
Dose/Drug Comparison
Pharmacodynamic Goals of
Therapy
Population Pharmacokinetic
Modeling
Target Organism(s) MIC
Distribution
Protein Binding Data in Animal
and Man
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Role of Monte Carlo Simulation for Dose Choice
for Clinical Trials of Anti-Infectives
Drusano GL, SL Preston, C Hardalo, et al. Antimicrob Agents Chemother. 2001;45:13-22.
Monte Carlo Simulation
• What is Monte Carlo simulation, as
applied to Infectious Diseases issues?
• What are the technical issues?
• For what is Monte Carlo simulation
useful?
Monte Carlo Simulation
What is Monte Carlo simulation?
MC simulation allows us to make
use of prior knowledge of how a target
population handles a specific drug to
predict how well that drug will perform
clinically at the dose chosen for clinical
trials and to rationally set breakpoint
values for susceptibility
Monte Carlo Simulation
How is this done?
Through use of the mean
parameter vector and covariance
matrix, derived from a population PK
study, a sampling distribution is set up.
This allows the peak concentrations,
AUC and Time > threshold to be
calculated for all the subjects
Monte Carlo Simulation
How do we use this to predict the clinical
utility of a specific drug dose?
1) Identify the goal of therapy (cell kill,
resistance suppression, etc)
2) Identify the sources of variability that
affect achieving the goal of therapy
a) PK variability (accounted for by MCS)
b) Variability in MIC’s (or EC95, etc)
c) Protein binding (only free drug is
active)
Monte Carlo Simulation
What do we do?
As an example, for a drug that is AUC/MIC
driven in terms of goal of therapy (e.g.
AUC/MIC of 100 for a good microbiological
outcome), we can now take the 2000 (or
10000 or whatever) simulated subjects and
divide the AUC by the lowest MIC in the
distribution, then determine how many achieve
the target of 100. This is then repeated with
higher MIC values until the target attainment is
zero or some low number
Monte Carlo Simulation
How does this help evaluate the utility of a
specific drug dose?
We have target attainment rates
at each MIC value in the organism population
distribution. A specific fraction of the organisms
have a specific MIC. A weighted average for
the target attainment rate (taking an
expectation) can be calculated. This value will
be the overall “expected” target attainment rate
for the outcome of interest for that specific
dose.
Monte Carlo Simulation
Technical Issues
Monte Carlo Simulation
• What are the factors that may affect the
simulation?
►Model mis-specification
►Choice of distribution
►Covariance matrix (full vs diagonal)
►Simulating the world from 6 subjects
Monte Carlo Simulation
Model Mis-specification
Monte Carlo Simulation
• Model mis-specification
Sometimes, data are only available
from older studies where full parameter
sets and their distributions were not
reported
• Some investigators have used truncated
models for simulation (1 cmpt vs 2 cmpt)
• This may have more effect for some drugs
relative to others (β lactams vs
quinolones)
Monte Carlo Simulation
Choice of Distribution
Monte Carlo Simulation
• There are many underlying distributions
possible for parameter values
• Frequently, there are insufficient numbers of
patients to make a true judgement
• One way to at least make the choice rational
is to examine how one distribution vs
another recapitulates the mean parameter
values and measure of dispersion
• A quinolone example follows (N vs Log-N)
Monte Carlo Simulation
Param Pop
Mean
Vol
23.32
Sim
Mean
22.80
Pop
SD
33.51
Sim
SD
30.15
Distr
Kcp
2.662
2.985
9.591
11.84
LN
Kpc
0.9327 0.7515 12.03
4.388
LN
SCL
6.242
4.303
LN
6.252
4.360
LN
Monte Carlo Simulation
Param Pop
Mean
Vol
23.32
Sim
Mean
36.82
Pop
SD
33.51
Sim
SD
24.23
Distr
Kcp
2.662
8.926
9.591
6.311
N
Kpc
0.9327 9.914
12.03
7.370
N
SCL
6.242
4.360
3.817
N
6.936
N
Monte Carlo Simulation
• Here, it is clear that the Log-normal
distribution better recaptures the mean
parameter values and, in general, the
starting dispersion (except Kpc)
• And for AUC distribution generation, it is
clear that Log-normal is preferred because it
performs better for the parameter of interest
(SCL) for both mean value and dispersion
• We have seen examples where there is no
substantive difference (N vs Log-N)
Monte Carlo Simulation
Full vs Major Diagonal
Covariance Matrix
Monte Carlo Simulation
• Sometimes, only the population standard
deviations are available and only a major
diagonal covariance matrix can be formed
• Loss of the off-diagonal terms will generally
cause the distribution to become broader (see
example)
• One can obtain an idea of the degree of impact
if the correlation among parameters is known
(of course if this is known, one could calculate
the full covariance matrix!)
Monte Carlo Simulation
0.10
1000
900
0.08
800
Count
0.06
600
500
0.04
400
300
Proportion per Bar
700
0.02
200
100
0
0.00
0
200
400
600
800 1000
Levofloxacin 750 mg AUC-Full Covariance Matrix
Mean
= 139.6
Mean
= 140.4
Median = 120.2
Median = 121.4
SD
SD
= 82.4
95% CI = 41.2-348.8
= 83.5
95% CI = 40.7-351.4
Monte Carlo Simulation
Simulating the World
From 6 Subjects
Monte Carlo Simulation
n=6
n = 50
n = 25
Monte Carlo Simulation
• Obviously, the robustness of the conclusions
are affected by the information from which
the population PK analysis was performed
• If the “n” is small, there may be considerable
risk attendant to simulating the world
• One of the underlying assumptions is that
the PK is reflective of that in the population
of interest – care needs to be taken and
appropriate consideration given to the
applicability of the available data to the
target population
Monte Carlo Simulation
• But, in the end, something is probably
better than nothing, so simulate away, but
interpret the outcomes conservatively
• It is also important to examine the SD’s, as
drawing inferences on drug dose from
volunteer studies, where CV%’s are
sometimes circa 10% may be risky
• How many simulations should be done?
- Answer: as always, it depends
• To stabilize variance in the far tails of the
distribution (> 3 SD), it is likely that one
would require > 10000 simulations
Monte Carlo Simulation
• Utility of Monte Carlo simulation, a nonexhaustive list:
► Determination of drug dose to attain a
specific endpoint
► Determination of a breakpoint
► Examine variability in drug penetration
Monte Carlo Simulation
Some New Stuff:
1) Effect simulations for combinations
2) Use of estimated GFR in simulations
3) Identification of a resistancecounterselective dose
Monte Carlo Simulation
Hope W et al. J Infect Dis 2005;192:673-680.
Monte Carlo Simulation
Greco Model for Combination Chemotherapy
Hope W et al. J Infect Dis 2005;192:673-680.
Monte Carlo Simulation
Greco Model for Combination Chemotherapy
Hope W et al. J Infect Dis 2005;192:673-680.
Monte Carlo Simulation
Hope W et al. J Infect Dis 2005;192:673-680.
Monte Carlo Simulation
A
5-FC 30 mg/Kg/day
Amphotericin B 1 mg/Kg/day
B
5-FC 30 mg/Kg/day
Amphotericin B 0.6 mg/Kg/day
C
5-FC 30 mg/Kg/day
Amphotericin B 0.3 mg/kg/day
Monte Carlo Simulation
• It is straightforward to model combinations of
agents
• Our laboratory has also done so for antiretrovirals
• For Amphotericin B/5-FC, it is clear that the
current dose of 5-FC is far too large (at least for
C. albicans) and only adds toxicity
• Monte Carlo simulation shows that use of 30
mg/Kg 5-FC with Ampho B doses as low as 0.3
mg/Kg gives up little effect, but would have
significantly diminished toxicity
Population Pharmacokinetic Parameter Values for Ceftobiprole
Kh
Vc
K23
K32
CLsl
CLint
Units
h-1
L
h-1
h-1
L/h
L/h
Mean
51.8
7.65
3.05
1.10
0.510 2.35
Median
59.9
7.05
1.20
0.960 0.484 2.46
S.D.
17.5
3.89
5.14
0.951 0.318 1.98
Observed vs. Predicted Plot after the Bayesian Step
Observed = 1.003 x Predicted + 0.627; r2 = 0.947; p << 0.001
Fractional Target Attainment
Ceftibiprole 500mg IV Q12H,30% Dosing Interval, 1hr Inf
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.1
ClCr (ml/min)
1.0
MIC (mg/L)
10.0
20
40
60
80
100
120
Target Attainment Probabilities for a 500 mg dose of ceftobiprole administered as a 1
hour, constant rate intravenous infusion every 12 hours. Target was maintaining free
drug concentrations in excess of the MIC for 30% of the dosing interval. Estimated
creatinine clearances were held constant for each analysis at the indicated values
between 20 ml/min and 120 ml/min.
Gumbo et al. J Infect Dis 2004;190:1642-1651.
dX 1 dt  R(1)  (( SCL / Vc )  X 1
dN S dt  K g max  S  (1  LS )  N S  E  K k max  S  MS  N S
dN R dt  K g max  R  (1  LR )  N R  E  K k max  R  N R  MR
E  (1  ( N R  N S ) / POPMAX )
L  ( X 1 / Vc ) H /(( X 1 / Vc) H  EC50H )
M  ( X 1 / Vc ) /(( X 1 / Vc)  EC
H
H
H
50
The model system delineated above was applied to all the data simultaneously
Gumbo et al. J Infect Dis 2004;190:1642-1651.
Monte Carlo Simulation
Moxifloxacin Concentrations
Total Population
Gumbo et al. J Infect Dis 2004;190:1642-1651.
Resistant Population
Monte-Carlo Simulation and
Moxifloxacin in Mtb Therapy
• Therapeutic target; moxifloxacin AUC/MIC of 53
in patients for resistance suppression
• Moxifloxacin doses of 400 mg a day, 600 mg a
day, and 800 mg a day taken by 10,000
simulated patients
• Prior information: published population
pharmacokinetic parameters
Moxifloxacin 400 mg a day.
Target attainment=59.3%
The target here and in the next two slides is suppression of the resistant population
Moxifloxacin 600 mg a day.
Target attainment=86.4%
Moxifloxacin 800 mg a day.
Target attainment=93.1%
Moxifloxacin and M.tuberculosis Conclusion
• Moxifloxacin resistance in sub-therapeutic exposure
occurs early during 2nd week of therapy.
• Drug doses associated with excellent microbial kill
may amplify resistant population.
• Drug exposure associated with suppression of
resistance is an AUC0-24/MIC of 53.
• Moxifloxacin daily dose of 800 mg may be better for
MDRTB as opposed to current 400 mg a day dose
recommended by CDC/IDSA/ATC because of
resistance issues. Such a dose would need careful
clinical evaluation because of QTc prolongation
Monte Carlo Simulation
Overall Conclusions
• MCS is useful for rational breakpoint determination
• MCS allows insight into the probability that a
specific dose will attain its target
• This has been prospectively validated
• The technique rests upon certain assumptions and
is as reliable as the assumptions
• Care needs to be taken when applying the method,
particularly as regards applicability of the
population studied and population size, among
other issues
Monte Carlo Simulation
Sense and Non-Sense
• WE CAN DO BETTER AND WE SHOULD!
– As an aside, I have trying since the early 1980’s
to interest the infectious diseases community
(and granting agencies) in pharmacodynamic
modeling, notably WITHOUT SUCCESS!
– WELL!
George