MonteCarlo-Orlando 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 ECOLE NATIONALE VETERINAIRE T O U L O U S E Third International conference on AAVM Orlando, FL, USA May16-20, 2006

MonteCarlo-Orlando 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-Orlando Monte-Carlo (Monaco) Toulouse What is the origin of the word Monte Carlo?

MonteCarlo-Orlando 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

MonteCarlo-Orlando What is Monte Carlo simulations –Deterministic model –Stochastic model Examines generally only mean values (or other single point values) Gives a single possible value Takes into account variance of parameters & covariance between parameters Gives range of probable values MCs is the term applied to stochastic simulations that incorporate random variability into a model

MonteCarlo-Orlando 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)

MonteCarlo-Orlando Adapted from Dudley, Ambrose. Curr Opin Microbiol 2000;3:515−521 Monte Carlo simulation: applied to PK/PD models Generate random AUC and MIC values across the AUC & MIC distributions that conforms to their probabilities Plot results in a probability chart Calculate a large number of AUC/MIC ratios % target attainment (AUC:MIC, T>MIC) PDF of AUC PDF of AUC/MIC PDF of MIC Model: AUC/MIC

MonteCarlo-Orlando What to do with Monte Carlo simulations (MCs) To assist decisions –Dose selection for pivotal clinical trials –Breakpoints for MIC To explore (understand) complex system To solve problems for which no analytical solution exists To present results easy to understand to the layman

MonteCarlo-Orlando 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 : –Lees et al 2006, in: Antimicrobial resistance in bacteria of animal origin, F Aarestrup (ed) chapter 5

MonteCarlo-Orlando Type of questions solved by Monte Carlo investigations for the prudent use of antibiotics What is the dose of an antibiotic to be administrated to a group of pigs to guarantee that at least 90% of these pigs will achieve an AUC/MIC ratio (the selected PK/PD index) value of 125 in the framework of an empirical antibiotherapy? The so-called target attainment rate (TAR)

MonteCarlo-Orlando Type of questions solved by Monte Carlo investigations for the prudent use of antibiotics What is the clinical MIC breakpoint to select to guarantee that,with the conventional dosage regimen, it is possible to achieve (e.g. in 90% of animals) a clinical (or bacteriological ) cure Monte Carlo simulations will be useful to assist organisations (FDA, CLSI, EUCAST…) to propose such a clinical MIC breakpoint (rather than an epidemiological BP) to promote clinically relevant antimicrobial susceptibility testing

MonteCarlo-Orlando A working example to illustrate what is Monte Carlo simulation

MonteCarlo-Orlando 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-Orlando 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”

MonteCarlo-Orlando Step 1: Define a priori some criteria (constraints) for what is an optimal dosage regimen

MonteCarlo-Orlando 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

MonteCarlo-Orlando 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

MonteCarlo-Orlando 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 MSW yes No Yes

MonteCarlo-Orlando 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 SW yes No Yes MSW< 12h in 90% of pigs

MonteCarlo-Orlando What is an optimal dosage regimen ? 2.Emergence of resistance (2) –MPC should be determined experimentally (like MIC) Typical MPC= 4-8 X MIC –From an operational point of view, to avoid the selective window it is required to be above the MPC or under the MIC for at least 50% of the dosing interval (actually, we ignore what is an appropriate breakpoint for that criteria ) –T>MPC + T<MIC should be higher than 12h (50% of the dosing interval) in 90% of pigs for the selected dosage regimen Actually a time dependent criteria

MonteCarlo-Orlando The 2 assumptions for an optimal dosing regimen 1.Probability of “cure” = POC = Time out of the MSW should be higher than 12h (50% of the dosing interval) in 90% of pigs

MonteCarlo-Orlando Step 2: Determination of the AUC/MIC clinical breakpoint value for the new quinolone in pigs

MonteCarlo-Orlando 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

MonteCarlo-Orlando 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-Orlando Determination of the PK/PD clinical breakpoint value from the dose titration trial Placebo Dose (mg/kg) Response 1 24 * * NS Dose to selected Blood samples were obtained MIC of the pathogen is known Possible to establish the relationship between AUC/MIC and the clinical success – Parallel design – 4 groups of 10 animals

MonteCarlo-Orlando AUC/MIC vs. POC: Metaphylaxis Data points were derived by forming ranges with 6 groups of 5 individual AUC/MICs and calculating mean probability of cure 10 Control pigs (no drug ) AUC/MIC POC

MonteCarlo-Orlando AUC/MIC vs POC: Metaphylaxis Modelling using logistic regression

MonteCarlo-Orlando Probability of cure (POC) Logistic regression was used to link measures of drug exposure to the probability of a clinical success Dependent variable Placebo effect sensitivity Independent variable 2 parameters: a (placebo effect) & b (slope of the exposure-effect curve)

MonteCarlo-Orlando Metaphylaxis (collective treatment) Curative (individual treatment)

MonteCarlo-Orlando Conclusion of step 2 Metaphylaxiscurative Placebo effect40%10% Breakpoint value of AUC/MIC to achieve a POC=0.9

MonteCarlo-Orlando 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-Orlando The structural model BP: 80 or 125 PD PK Free fraction Assumption : fu=1 Bioavailability Oral  IM

MonteCarlo-Orlando 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)

MonteCarlo-Orlando 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% Experimental data from preliminary investigations

MonteCarlo-Orlando Experimental data from preliminary investigations Frequency MIC (µg/mL) 3.MIC distribution (pathogens of interest, wild population) MIC 90 =2µg/ml

MonteCarlo-Orlando 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. MIC 90 ) –Can show the range of outcomes By Monte Carlo Simulations –Based on probability distribution –Give the probability of outcomes

MonteCarlo-Orlando Selection of a model to compute the dose of the new quinolone Deterministic –All the input are fixed (mean, MIC 90,…) Stochastic –Some or all the model parameters have some degree of random variability associated with them Deterministic=stochastic simulation where variability is set equal to 0

MonteCarlo-Orlando Computation of the dose with point estimates (mean clearance and F%, MIC 90 ) BP: 80 or 125 MIC 90 =2µg/mL Bioavailability Oral :50% IM:80% 9mL/Kg/h Metaphylaxis: 2.88mg/kg curative: 2.81 mg/kg

MonteCarlo-Orlando Computation of the dose with point estimates (worst case scenario for clearance and F%, MIC 90 ) BP: 80 or 125 MIC 90 =2µg/mL Bioavailability Oral :30% IM:70% 15mL/Kg/h Metaphylaxis: 8.0 (vs. 2.88) mg/kg curative: 5.35 (vs. 2.81) mg/kg

MonteCarlo-Orlando Computation of the dose using Monte Carlo simulation (Point estimates are replaced by distributions) Dose to POC=0.9 BP metaphylaxis Log normal distribution: 9±2.07 mL/Kg/h Uniform distribution: Observed distribution

MonteCarlo-Orlando 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

MonteCarlo-Orlando Metaphylaxis: dose to achieve a POC of 90% i.e. an AUC/MIC of 80 (empirical antibiotherapy) Dose distribution

MonteCarlo-Orlando Empirical antibiotherapy The MIC of the subject under treatment is unknown but the population MIC distribution is established It is necessary to examine the full distribution of MICs MIC 90 (worst case scenario is not ideal for that because there may be a “maldistribution” i.e. MIC mainly located at one end or at the other range of MIC)

MonteCarlo-Orlando Computation of the dose: metaphylaxis (dose=2mg/kg from the dose titration) PK/PD ModelDose (mg/kg) Mean2.88 Worst case scenario8.00 Monte Carlo (empirical antibiotherapy) Monte Carlo (targeted antibiotherapy) ???

MonteCarlo-Orlando MIC 90 or MIC distribution? Distributions with the same MIC 90 % Patients with an AUIC > auic AUIC

MonteCarlo-Orlando 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

MonteCarlo-Orlando Sensitivity analysis Metaphylaxis, empirical antibiotherapy Contribution of the MIC distribution

MonteCarlo-Orlando Computation of the dose using Monte Carlo simulation Metaphylaxis, Targeted antibiotherapy Dose to POC=0.9 BP metaphylaxis Log normal distribution: 9±2.07 mL/Kg/h Uniform distribution: MIC=1µg/mL

MonteCarlo-Orlando Computation of the dose using Monte Carlo simulation Targeted antibiotherapy

MonteCarlo-Orlando Computation of the dose: metaphylaxis (dose=2mg/kg from the dose titration) PK/PD modelDose (mg/kg) Mean2.88 Worst case scenario8.00 Monte Carlo (empirical antibiotherapy) Monte Carlo (targeted antibiotherapy against a bug having a MIC=1µg/mL) 2.24

MonteCarlo-Orlando Sensitivity analysis (metaphylaxis, targeted antibiotherapy) F%

MonteCarlo-Orlando Computation of the dose (mg/kg): metaphylaxis vs. curative & empirical vs. targeted PK/PD modelcurativemetaphylaxis Mean Worst case scenario Monte Carlo (empirical antibiotherapy) Monte Carlo (targeted antibiotherapy)

MonteCarlo-Orlando The variance–covariance matrix

MonteCarlo-Orlando The variance–covariance matrix When models are fitted to PK data, the PK parameters estimates and their measure of dispersion are not independent, in which case population modeling must be performed in order to obtain the covariance matrix for estimated PK parameters MCs failing to take the covariance into account lead to over- or under estimates of the dispersion of the simulated AUC/MIC ratios

MonteCarlo-Orlando Computation of the dose using Monte Carlo simulation using a population model (mean vector parameters & variance-covariance matrix) BP fixed Log normal distribution: 9±2.07 mL/Kg/h Uniform distribution: Observed distribution Normal distribution:0.5±0.05 Variance- Covariance matrix

MonteCarlo-Orlando Computation of the dose using Monte Carlo simulation using a population model (mean vector parameters & variance-covariance matrix) Covariance between F% & clearance (Correlation coefficients) Computed doses (mg/kg)

MonteCarlo-Orlando The second criteria to determine the optimal dose: the MSW & MPC

MonteCarlo-Orlando Kinetic disposition of the new quinolone for the selected metaphylactic dose (3.8 mg/kg) (monocompartmental model, oral route) Slope=Cl/Vc=0.09 per h (T1/2=7.7h) Log normal distribution: 9±2.07 mL/kg/h MPC Uniform distribution: F% concentrations MIC MSW

MonteCarlo-Orlando Time>MPC for the POC 90% for metaphylaxis (dose 3.8 mg/kg, empirical antibiotherapy)

MonteCarlo-Orlando Time>MPC for the POC 90% for metaphylaxis (dose of 7.1mg/kg, empirical antibiotherapy)

MonteCarlo-Orlando 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-Orlando Time>MPC for the POC 90% for curative treatment (dose of 3.8mg/kg,curative treatment

MonteCarlo-Orlando Sensitivity analysis ( dose of 3.8mg/kg, curative treatment empirical antibiotherapy) Clearance (slope) is the only influential factor of variability for T>MPC not bioavailability as for metaphylaxis Clearance

MonteCarlo-Orlando Computation of the dose (mg/kg): metaphylaxis vs. curative treatment Monte Carlocurativemetaphylaxis Efficacy To guarantee T>MPC in 90% of pigs for 50% the dosage interval

MonteCarlo-Orlando Conclusion

MonteCarlo-Orlando conclusions MCs help to maximize the information generated from preclinical studies (dose titration) for use in decision support for preclinical dose selection & preliminary MIC breakpoint

MonteCarlo-Orlando 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

MonteCarlo-Orlando 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

MonteCarlo-Orlando