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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 presentationTo 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 simulationThe 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 modelDeterministic 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 simulationsA 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 antibioticsIntroduced 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 projectYou 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 developersWhat 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 regimenProbability 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 valueDose 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 investigationsClearance : 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 investigationsBioavailability : 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 investigationsMIC distribution (pathogens of interest, wild population) MIC90=2µg/mlFrequencyMIC (µg/mL)Solving the structural model to compute the dose for my new quinoloneWith 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 simulationsOthers 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 analysisAnalyze 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 treatmentConclusionconclusionsMCs 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 Thanks for your attention

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