# Use of Monte Carlo simulations to select PK/PD breakpoints and therapeutic doses for antimicrobials in veterinary medici

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Use of Monte Carlo simulations to select PK/PD breakpoints and therapeutic doses for antimicrobials in veterinary medicine. ECOLE NATIONALE VETERINAIRE T O U L O U S E. PL Toutain UMR 181 Physiopathologie et Toxicologie Experimentales INRA/ENVT. Third International conference on AAVM
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Use of Monte Carlo simulations to select PK/PD breakpoints and therapeutic doses for antimicrobials in veterinary medicineECOLENATIONALEVETERINAIRET O U L O U S EPL ToutainUMR 181 Physiopathologie et Toxicologie ExperimentalesINRA/ENVTThird International conference on AAVM Orlando, FL, USA May16-20, 2006Objectives of the presentation
• To review the role of Monte Carlo simulation in PK/PD target attainment in establishing a dosage regimen
• (susceptibility breakpoints)
• What is the origin of the word Monte Carlo?ToulouseMonte-Carlo(Monaco)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
• What is Monte Carlo simulationsMCs is the term applied to stochastic simulations that incorporate random variability into a model
• 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 parametersGives range of probable values3 Steps in Monte Carlo simulations
• A model is defined (a PK/PD model)
• Sampling distributionof the model parameters (inputs) must be knowna priori (e.g. normal distribution with mean, variance, covariance)
• MCs repeatedly simulatethe 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)
• Monte Carlo simulation: applied to PK/PD modelsModel: AUC/MICPDF of AUCGenerate random AUC and MIC values across the AUC & MIC distributions that conforms to their probabilitiesPDF of MICCalculate a large number of AUC/MIC ratiosPDF of AUC/MICPlot results in a probability chart% target attainment(AUC:MIC, T>MIC)Adapted from Dudley, Ambrose. Curr Opin Microbiol2000;3:515−521 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
• A working example to illustrate what is Monte Carlo simulation 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
• 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”
• Step 1: Define a priori some criteria (constraints) for what is an optimal dosage regimenWhat 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
• What is an optimal dosage regimen ?
• 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
• What is an optimal dosage regimen ?
• Emergence of resistance (1)
• The dosage regimen should avoid the mutantselection window (MSW) in at least 90% of pigs
• MPC (Mutant prevention concentration)MICyesNoYesMSWWhat is an optimal dosage regimen ?
• Emergence of resistance (3)
• The dosage regimen should avoid the mutant selection window (MSW) in at least 90% of pigs
• MPC (Mutant prevention concentration)MICyesNoYesSWMSW< 12h in 90% of pigsThe 2 assumptions for an optimal dosing regimen
• Probability of “cure” = POC = 0.90
• Time out of the MSW should be higher than 12h (50% of the dosing interval) in 90% of pigs
• Step 2: Determination of the AUC/MIC clinical breakpoint value for the new quinolone in pigs 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 assumedDetermination 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
• Dose to selectedDetermination of the PK/PD clinical breakpoint value from the dose titration trialResponseNS*
• Blood samples were obtained
• MIC of the pathogen is known
• Possible to establish the relationship between AUC/MIC and the clinical success
• *Placebo124Dose (mg/kg)
• Parallel design
• 4 groups of 10 animals
• AUC/MIC vs. POC: MetaphylaxisData points were derived by forming ranges with 6 groups of 5 individual AUC/MICs and calculating mean probability of curePOC10 Control pigs (no drug)AUC/MICAUC/MIC vs POC: MetaphylaxisModelling using logistic regressionProbability of cure (POC)
• Logistic regression was used to link measures of drug exposure to the probability of a clinical success
• sensitivityIndependent variablePlacebo effectDependent variable2 parameters: a (placebo effect) & b (slope of the exposure-effect curve)Conclusion ofstep 2 Metaphylaxis curativePlacebo effect 40% 10%Breakpoint value 80 125 of AUC/MIC to achieve a POC=0.9Step 3What 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)The structural modelBP: 80 or 125PDBioavailabilityOral  IMPKFree fractionAssumption : fu=1Experimental data from preliminary investigations
• 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)Experimental data from preliminary investigations
• 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
• MIC distribution
• (pathogens of interest, wild population)
• MIC90=2µg/mlFrequencyMIC (µg/mL)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
• Computation of the dose with point estimates (mean clearance and F%, MIC90)BP: 80 or 125MIC90=2µg/mL9mL/Kg/hBioavailabilityOral :50% IM:80%Metaphylaxis: 2.88mg/kgcurative: 2.81 mg/kgComputation of the dose with point estimates(worst case scenario for clearance and F%,MIC90)BP: 80 or 125MIC90=2µg/mL15mL/Kg/hBioavailabilityOral :30% IM:70%Metaphylaxis: 8.0 (vs. 2.88) mg/kgcurative: 5.35 (vs. 2.81) mg/kgComputation of the dose using Monte Carlo simulation(Point estimates are replaced by distributions)Log normal distribution: 9±2.07 mL/Kg/hObserved distributionBPmetaphylaxisDose to POC=0.9Uniform distribution: 0.3-0.70An 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
• Metaphylaxis: dose to achieve a POC of 90% i.e. an AUC/MIC of 80(empirical antibiotherapy)Dose distributionComputation of the dose: metaphylaxis(dose=2mg/kg from the dose titration)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
• Sensitivity analysisMetaphylaxis, empirical antibiotherapyContribution of the MIC distributionComputation of the dose using Monte Carlo simulationMetaphylaxis,Targeted antibiotherapyMIC=1µg/mLLog normal distribution: 9±2.07 mL/Kg/hBPmetaphylaxisDose to POC=0.9Uniform distribution: 0.3-0.70Computation of the dose using Monte Carlo simulationTargeted antibiotherapyComputation of the dose: metaphylaxis(dose=2mg/kg from the dose titration)Sensitivity analysis(metaphylaxis, targeted antibiotherapy)F%Computation of the dose (mg/kg):metaphylaxis vs. curative & empirical vs. targetedThe variance–covariance matrixThe second criteria to determine the optimal dose: the MSW & MPCKinetic 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/hF%Uniform distribution: 0.3-0.70Slope=Cl/Vc=0.09 per h (T1/2=7.7h)MPCMICconcentrationsMSWTime>MPC for the POC 90% for metaphylaxis (dose 3.8 mg/kg, empirical antibiotherapy)Time>MPC for the POC 90% for metaphylaxis (dose of 7.1mg/kg, empirical antibiotherapy)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/MICTime>MPC for the POC 90% for curative treatment(dose of 3.8mg/kg,curative treatmentSensitivity analysis (dose of 3.8mg/kg, curative treatment empirical antibiotherapy)ClearanceClearance (slope) is the only influential factor of variability for T>MPC not bioavailability as for metaphylaxisComputation of the dose (mg/kg):metaphylaxis vs. curative treatmentConclusionconclusions
• 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
• 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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