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

1. 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 Orlando, FL, USA May16-20, 2006

2. Objectives of the presentation • To review the role of Monte Carlo simulation in PK/PD target attainment in establishing a dosage regimen • (susceptibility breakpoints)

3. What is the origin of the word Monte Carlo? Toulouse Monte-Carlo (Monaco)

4. 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

5. What is Monte Carlo simulations MCs 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 parameters Gives range of probable values

6. 3 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)

7. Monte Carlo simulation: applied to PK/PD models Model: AUC/MIC PDF of AUC Generate random AUC and MIC values across the AUC & MIC distributions that conforms to their probabilities 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 Microbiol2000;3:515−521

8. 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

9. A working example to illustrate what is Monte Carlo simulation

10. 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

11. 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”

12. Step 1: Define a priori some criteria (constraints) for what is an optimal dosage regimen

13. 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

14. 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

15. 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) MIC yes No Yes MSW

16. What 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) MIC yes No Yes SW MSW< 12h in 90% of pigs

17. The 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

18. Step 2: Determination of the AUC/MIC clinical breakpoint value for the new quinolone in pigs

19. 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

20. 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

21. Dose to selected 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 • Possible to establish the relationship between AUC/MIC and the clinical success * Placebo 1 2 4 Dose (mg/kg) • Parallel design • 4 groups of 10 animals

22. 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 POC 10 Control pigs (no drug) AUC/MIC

23. AUC/MIC vs POC: Metaphylaxis Modelling using logistic regression

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

25. Conclusion ofstep 2 Metaphylaxis curative Placebo effect 40% 10% Breakpoint value 80 125 of AUC/MIC to achieve a POC=0.9

26. 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)

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

28. Experimental 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)

29. 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%

30. Experimental data from preliminary investigations • MIC distribution • (pathogens of interest, wild population) MIC90=2µg/ml Frequency MIC (µg/mL)

31. 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

32. Computation of the dose with point estimates (mean clearance and F%, MIC90) BP: 80 or 125 MIC90=2µg/mL 9mL/Kg/h Bioavailability Oral :50% IM:80% Metaphylaxis: 2.88mg/kg curative: 2.81 mg/kg

33. 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 Bioavailability Oral :30% IM:70% Metaphylaxis: 8.0 (vs. 2.88) mg/kg curative: 5.35 (vs. 2.81) mg/kg

34. 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 Dose to POC=0.9 Uniform distribution: 0.3-0.70

35. 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

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

37. Computation of the dose: metaphylaxis(dose=2mg/kg from the dose titration)

38. 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

39. Sensitivity analysisMetaphylaxis, empirical antibiotherapy Contribution of the MIC distribution

40. Computation of the dose using Monte Carlo simulationMetaphylaxis,Targeted antibiotherapy MIC=1µg/mL Log normal distribution: 9±2.07 mL/Kg/h BP metaphylaxis Dose to POC=0.9 Uniform distribution: 0.3-0.70

41. Computation of the dose using Monte Carlo simulationTargeted antibiotherapy

42. Computation of the dose: metaphylaxis(dose=2mg/kg from the dose titration)

43. Sensitivity analysis (metaphylaxis, targeted antibiotherapy) F%

44. Computation of the dose (mg/kg):metaphylaxis vs. curative & empirical vs. targeted

45. The variance–covariance matrix

46. The second criteria to determine the optimal dose: the MSW & MPC

47. 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) MPC MIC concentrations MSW

48. Time>MPC for the POC 90% for metaphylaxis (dose 3.8 mg/kg, empirical antibiotherapy)

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

50. 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