MONTE CARLO SIMULATION & PK-PD TARGET ATTAINMENT ANALYSIS:

Transcription

1 MONTE CARLO SIMULATION & PK-PD TARGET ATTAINMENT ANALYSIS: Application to Estimation of MIC Breakpoints Paul G. Ambrose, Pharm.D. Director, Division of Infectious Diseases, Cognigen Corporation; Adjunct Professor, University of the Pacific, School of Health Sciences

2 OBJECTIVES! To provide a brief history of Monte Carlo Simulation! To review the types of information gained from nonclinical and clinical PK-PD models of infection! To review the role of Monte Carlo Simulation in PK-PD target attainment analysis in establishing in vitro susceptibility breakpoints.

3 MONTE CARLO SIMULATION Early History! Named after city in Monaco where roulette remains a common game of chance " The roulette wheel may be viewed as a simple random number generator!! Early history may predate the 17 th century Buffon's original form was to drop a needle of length L at random of grid of parallel lines of spacing D. Georges Buffon For For L L less less than than or or equal equal D we we obtain obtain P(needle P(needle intersects intersects the the grid) grid) = 2 L L // PI PI D If If we we drop drop the the needle needle N times times and and count count R intersections intersections we we obtain obtain P P = R // N, N, PI PI = 2 L L N // R D. D.

4 MONTE CARLO SIMULATION Development as a Research Tool! The name Monte Carlo Simulation and modern development dates from World War II! Work involved the direct simulation of the probabilistic problems associated with random neutron diffusion in fissile material John von Neumann

5 MONTE CARLO SIMULATION Application to Antiinfective Drug Development! Introduced to our community of practice by Drusano (presented to CDER, FDA in 1998) 2 George Drusano! Currently being utilized for: " Identification of dose and interval during drug development " In evaluations of the adequacy of drug regimens " Estimating susceptibility breakpoints " Pharmacoeconomic studies

6 THINGS YA REALLY WANT TO KNOW Requirements for Rational Drug Evaluation #Identify pharmacodynamic goal of therapy Can come from non-clinical models of infection or clinical data $Protein binding data don t ignore! %Organism MIC probability mass function(s) can come from local, regional, national or international data &Pharmacokinetic variability can come from Phase-I or Phase-II III population analyses and may focus on special patient populations of interest GL Drusano

7 PK-PD GOAL OF THERAPY In Vitro Models of Infection Hollow-Fiber Cartridge Cross-Section Lumen of hollow fiber Hollow-Fiber PK-PD Model HFC Drug Wall of hollow fiber Bacteria Peripheral compartment Diluent Reservoir Central Reservoir Elimination Reservoir

8 IN VITRO MODEL DATA AUC 24 :MIC & Response: S. pneumoniae Logarithmic phase cultures (5x10 7 CFU/mL) of S. pneumoniae introduced into peripheral compartment Peak:MIC 2.5; elimination half-life altered to provide AUC:MIC ratios of Samples removed from peripheral compartment at 0,2,4,8,12,24,30 hrs Viable bacterial counts measured by plating serial 10-fold dilutions of each sample into Todd-Hewitt agar & incubating overnight at 37 C in 5%CO 2 Lowest dilution plated was 0.1mL. Lister PD. Pharmacodynamics of Gatifloxacin Against Streptococcus pneumoniae in an in vitro Pharmacokinetic Model: Impact of AUC:MIC Ratios on Eradication. Antimicob Agents and Chemother 2002:46:69-74.

9 PK-PD GOAL OF THERAPY Animal Models of Infection -2 Hr 0 Hr Infect Begin Therapy 24 Hr 96 Hr Sacrifice, Harvest, Homogenize Muscle

10 ANIMAL DATA AUC:MIC & Response: S. pneumoniae Survival (Percent) R 2 =82% AUC 24 /MIC (Free Drug) Log 10 CFU/Thigh over 24 Hrs R 2 =76% AUC 24 /MIC (Free Drug) ciprofloxacin, gatifloxacin, gemifloxacin, levofloxacin, moxifloxacin, and sitafloxacin Craig WA, Andes DR. Correlation of the Magnitude of the AUC 24 /MIC for 6 Fluoroquinolones against Streptococcus pneumoniae with Survival and Bactericidal Activity in an Animal Model. In Abstracts of the 40th ICAAC, Toronto, Canada, Sept , Abs-289;

11 PK-PD GOAL OF THERAPY Clinical Data! Clinical validation of PK-PD targets has been slow " Too few target patient population trials collect pharmacokinetic data " Too narrow range of exposures studied (usually one fixed dosing regimen) " Phase-III trials designed to maximize response- few failuresthus, difficult to model exposure-response relationships! However, there are examples " Ciprofloxacin " Levofloxacin X 2 " Grepafloxacin " Gatifloxacin " Everninomicin " Linezolid

12 PK-PD GOAL OF THERAPY Clinical Data: Quinolones & S. pneumoniae! Data from 2 Phase-III, double-blind, randomized, multicenter trials.! Patients received either levofloxacin 500-mg Q24h or gatifloxacin 400-mg Q24h " 778 adult patients with either community-acquired pneumonia or acute exacerbation of chronic bronchitis. " 635 patients were clinically evaluable. " 376 patients were both clinically and microbiologically evaluable. " 58 patients had CAP or ABECB associated with Streptococcus pneumoniae. Ambrose PG, Grasela DM, Grasela TH, et al. Pharmacodynamics of Fluoroquinolones against Streptococcus pneumoniae in Patients with Community-Acquired Respiratory Tract Infection. Antimicrob Agents Chemother 2001;45:

13 CART DETERMINED BREAKPOINT Microbiological Response: Quinolones & S. pneumoniae Patients Patients fu AUC:MIC <33.7 fu AUC:MIC fu AUC:MIC < Patients; Patients; 5 Success, Success, 1 Failure Failure fu AUC:MIC Patients; Patients; 2 Success, Success, 3 Failure Failure Patients; Patients; Success, Success, 0 Failure Failure Implemented in S-Plus 2000 professional series release Ambrose PG, Grasela DM, Grasela TH, et al. Pharmacodynamics of Fluoroquinolones against Streptococcus pneumoniae in Patients with Community-Acquired Respiratory Tract Infection. Antimicrob Agents Chemother 2001;45:

14 CLINICAL DATA AUC 24 :MIC & Response: Quinolones & S. pneumoniae Model fit to assess probability of bacterial eradication:log likelihood chi square 6.379; p= Ambrose PG, Grasela DM, Grasela TH, et al. Pharmacodynamics of Fluoroquinolones against Streptococcus pneumoniae in Patients with Community-Acquired Respiratory Tract Infection. Antimicrob Agents Chemother 2001;45:

15 THINGS YA REALLY WANT TO KNOW Requirements for Rational Drug Evaluation #Identify pharmacodynamic goal of therapy can come from non-clinical models of infection or clinical data $Protein binding data don t ignore! %Organism MIC probability mass function(s) can come from local, regional, national or international data &Pharmacokinetic variability can come from Phase-I or Phase-II III population analyses and may focus on special patient populations of interest GL Drusano

16 PROTEIN BINDING Critical Component to Describing Anti-Infective PK-PD Drug bound to proteins can neither distribute to the site of effect, nor is available to bind to bacterial receptor sites In the simplest cases: total drug ' fu In more complex cases: effect of protein binding depends upon the extent of plasma protein binding and the relative affinity to plasma protein and bacterial receptor sites Simple corrections made for protein binding more likely will closely describe the true PK-PD relationship than not considering it at all PK-PD Working Group. Towards a Consensus and Working Guidelines in Antimicrobial Pharmacodynamics. In Abstracts of the 42nd ICAAC, San Diego, CA, Sept , Abs-164

17 PROTEIN BINDING Free- vs. Total-Drug & Animal Survival Free-Drug Total-Drug AUC 24 :MIC Gati Gemi Levo Moxi Gare Craig WA, Andes DR. In Abstracts of the 40th ICAAC, Toronto, Canada, Sept , Abs-289; Nicolau DP, et al. In Abstracts of the 40th ICAAC, Toronto, Canada, Sept , Abs-290.

18 THINGS YA REALLY WANT TO KNOW Requirements for Rational Drug Evaluation #Identify pharmacodynamic goal of therapy can come from non-clinical models of infection or clinical data $Protein binding data don t ignore! %Organism MIC probability mass function(s) can come from local, regional, national or international data &Pharmacokinetic variability can come from Phase-I or Phase-II III population analyses and may focus on special patient populations of interest GL Drusano

19 QUINOLONES & S. pneumoniae Single-Point PK-PD Analysis 150 Gati better Levo better yet 136 Trova great AUC 24 :MIC Cipro bad Levo good Cipro 750mg BID Levo 500mg QD Gati 400mg QD Levo 750mg QD Trova 200mg QD STANDARD DAILY DOSE

20 PROBABILITY DISTRIBUTIONS Gatifloxacin & S. pneumoniae.095 Gatifloxacin AUC 24 Distribution 0.8 Gatifloxacin S. pneumoniae MIC Distribution 0.7 N = 6,700 Probability mg Q24 hr, steady state AUC 24 (mcg h/ml) MIC (mcg/ml) Ambrose PG, Grasela DM. The Use of Monte Carlo Simulation to Examine the Pharmacodynamic Variance of Drugs: Fluoroquinolone Pharmacodynamics Against Streptococcus pneumoniae. Diagnostic Microbiology and Infectious Disease 2000;38:

21 LIMITATIONS Single-point PK-PD Analysis Variability in the pharmacokinetic and microbiological data are not taken into consideration. The metrics developed apply to a limited number of clinical instances. Provide information on what is possible, not on what is probable. Ambrose PG, Quintiliani R. Limitations of Single-Point Pharmacodynamic Analysis. Pediatric Infectious Disease Journal 2000;19:769.

22 PK-PD ANALYSIS An Ideal one should... Take into account all possible drug exposures and their probabilities following standard dosing Include all pathogen MIC values treated clinically This will provide more complete information regarding the likelihood an agent will effectively treat a patient infected with a particular organism.

23 MONTE CARLO SIMULATION Applied to PK-PD Generate Random PK PK and and MIC MIC Values From Data Set Set Calculate PK-PD Exposure Measure Plot Plot Results in in a Probability Chart Dudley MN, Ambrose PG. Pharmacodynamics in the study of drug resistance and establishing in vitro susceptibility breakpoints: ready for prime-time. Current Opinion in Microbiology 2000;3:

24 A CASE STUDY Issue before the NCCLS Initial breakpoints of 0.5-, 1.0-, and 2.0-mcg/mL for both ceftiaxone and cefotaxime against S. pneumoniae Manufacturer of ceftriaxone submits robust data supporting breakpoint change to 1.0-, 2.0-, and 4.0- mcg/ml Significantly less data available for cefotaxime Historically both agents have been treated as therapeutic alternatives Different breakpoints for each agent likely to be problematic for clinical laboratories

25 CEFTRIAXONE Model Assumptions CEFTRIAXONE VOLUME OF DISTRIBUTION Mean 9.0 L SD mg LITERS Time > MIC (hours) = (In Dose/(Vd/fu) - In MIC) (0.693/T 1/2 ) CEFTRIAXONE SERUM T1/2 Mean 6.2 hrs SD TIME-HOURS MIC Relative Probability TSN Database-USA 01/01/ /30/1999; Patel IH, et al. Pharmacokinetics of Ceftriaxone in Humans. Antimicrob Agents Chemother 1991;20: ; Yuk J, et al. Clinical Pharmacokinetics of Ceftriaxone. Clin Pharmacokinet 1989;17:

26 RESULTS-CEFTRIAXONE 1-Gm Q24 hrs. PK-PD Target Attainment Rate PK-PD Target (T>MIC) MIC 30% 40% 50% 60% S? I? R? Entire MIC Dist PCN-S PCN-I PCN-R Dudley MN, Ambrose PG. Monte Carlo Simulation of new cefotaxime, ceftriaxone and cefepime susceptibility breakpoints for S. pneumoniae, including strains with reduced susceptibility to penicillin. In Abstracts of the 42nd ICAAC, San Diego, CA, Sept , Abs-635

27 RESULTS-CEFOTAXIME 1-Gm Q8 hrs. PK-PD Target Attainment Rate PK-PD TARGET (T>MIC) MIC 30% 40% 50% 60% S? I? R? Entire MIC Dist PCN-S PCN-I PCN-R Dudley MN, Ambrose PG. Monte Carlo Simulation of new cefotaxime, ceftriaxone and cefepime susceptibility breakpoints for S. pneumoniae, including strains with reduced susceptibility to penicillin. In Abstracts of the 42nd ICAAC, San Diego, CA, Sept , Abs-635

28 RESULTS-CEFOTAXIME 1-Gm Q12 hrs. PK-PD Target Attainment Rate PK-PD TARGET (T>MIC) MIC 30% 40% 50% 60% S? I? R? Entire MIC Dist PCN-S PCN-I PCN-R Dudley MN, Ambrose PG. Monte Carlo Simulation of new cefotaxime, ceftriaxone and cefepime susceptibility breakpoints for S. pneumoniae, including strains with reduced susceptibility to penicillin. In Abstracts of the 42nd ICAAC, San Diego, CA, Sept , Abs-635

29 PK-PD and Monte Carlo Simulation Powerful Tool with Drug Development, Regulatory and Clinical Application Pharmacokinetics PK Parameter!Animal!Phase-I!Phase-II!Patient Population Microbiology MIC!Local Surveillance!National Surveillance Mathematical Model Pharmacodynamics Change in Log CFU/Thigh 0 vs. 24h Cp t = A ' e -αt 1 - e -ατ + B ' e-βt + C ' e-δt 1 - e -βτ 1 - e -δτ ' fu !In vitro Free Drug AUC:MIC models!animal models!human data

30 THANK YOU FOR YOUR ATTENTION

31 MONTE CARLO SIMULATION RESULTS Ceftazidime PK-PD Target Attainment Rate CEFTAZIDIME Every 6 Hrs Every 8 Hrs Every 12 Hrs % T>MIC hrs >MIC g MIC: g MIC: Recommend: S I R Rationale/comments: Most frequent clinical use Q 8 h dosing 2 g dose covers intermediate range Paul G. Ambrose/Mike N. Dudley

32 MONTE CARLO SIMULATION RESULTS Cefepime PK-PD Target Attainment Rate CEFEPIME Every 8 Hrs Every 12 Hrs % T>MIC hrs >MIC g MIC: g MIC: Recommend: S I R Rationale/comments: Most frequent clinical use Q 12 h dosing 2 g dose covers intermediate range Paul G. Ambrose/Mike N. Dudley

33 MONTE CARLO SIMULATION RESULTS Ceftriaxone PK-PD Target Attainment Rate CEFTRIAXONE Every 12 Hrs Every 24 Hrs % T>MIC hrs >MIC g MIC: g MIC: Recommend: S I R Rationale/comments: Most frequent clinical use1 g Q 24 h dosing 2 g dose covers intermediate range Paul G. Ambrose/Mike N. Dudley

34 MONTE CARLO SIMULATION RESULTS Cefotaxime PK-PD Target Attainment Rate CEFOTAXIME Every 6 Hrs Every 8 Hrs Every 12 Hrs % T>MIC hrs >MIC g MIC: g MIC: Recommend: S I R Rationale/comments: Most frequent clinical use 1 g Q 8 h dosing 2 g dose covers intermediate range Paul G. Ambrose/Mike N. Dudley

35 MONTE CARLO SIMULATION Structural Model or Population Model? Depends upon the agent s place in development Depends upon the question being asked of the data Time > MIC (hours) = (In Dose/(Vd/fu) - In MIC) (k e ) Mean Vector Parameters Cl Vc Ka Cp t = A ' e -αt 1 - e -ατ + B ' e-βt + C ' e-δt 1 - e -βτ 1 - e -δτ ' fu 9.36E E E+01 Variance-Covariance Matrix Cl Vc Ka Cl 2.23E-02 fu AUC 24 :MIC = fu ' AUC 24 MIC Vc Ka -6.22E E E E E-01

36 PROTEIN BINDING Free- vs. Total-Drug & Animal Survival Drug MIC % Peak T 1/2 (mg/l) bound (mg/l) (hr) 50 (1) CD 50 (mg/kg) (2) (3) (4) (5) (6) (7) % free antibiotic Merrikin DJ, Briant J, Rolinson GN. Effect of Protein Binding in Antibiotic Activity in vivo. J Antimicrob Chemother 1983;11:

37 Animal Models of Infection T>MIC & Response to Therapy: S. pneumoniae Mice rendered neutropenic & infection induced by IM injection of 0.1mL of 10 5 to 10 6 CFU S. pneumoniae Animals received 7 mg/kg alone or in combination with clavulanate (ratio 4:1) every 8 hrs. Each data point represents the mean of two thighs. Andes D, Craig WA. In vitro activities of amoxicillin and amoxicillin-clavulanate against Streptococcus pneumoniae: Application to breakpoint determination. Antimicrob Agents Chemother 1998;42:

38 CEFOTAXIME Model Assumptions One compartment model: is Time > MIC (hours) = (In Dose/(Vd/fu) - In MIC) (0.693/T 1/2 ) where Vd is the volume of distribution, T 1/2 is the serum elimination half-life, and fu the fraction of unbound drug Log-normal distribution for pk parameters: T 1/2 : hours Vd: L/kg Protein-binding 31 to 41% MIC PDF from 1998 SENTRY data (n=5928) 1-Gram intravenous dose of cefotaxime Q8 & Q12 hours