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Population PK-PD Modeling of Anti-Infective Agents

Population PK-PD Modeling of Anti-Infective Agents. Alexander A. Vinks, PharmD, PhD, FCP Professor and Director Pediatric Pharmacology Research Unit Cincinnati Children’s Hospital and Medical Center. Why Population Modeling and Simulation ?. To describe and understand Drug PK/PD Behavior

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Population PK-PD Modeling of Anti-Infective Agents

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  1. Population PK-PD Modeling of Anti-Infective Agents Alexander A. Vinks, PharmD, PhD, FCP Professor and Director Pediatric Pharmacology Research Unit Cincinnati Children’s Hospital and Medical Center

  2. Why Population Modeling and Simulation? • To describe and understand Drug PK/PD Behavior • Collect informative data to use as Bayesian priors for designing model-based, individualized dosing regimens • To Predict and therefore Control the system (i.e. the serum & other compartments) • Change passive “Monitoring” to active “Management”

  3. Clinical Applications of PPK Models • Designing dosing regimens • Identifying central tendency of PK parameter estimates and variability in the targeted patient population • Identifying clinically useful covariates • Bayesian Adaptive Control Strategies • Clinical Trial Design • Determining PK characteristics in other tissues and compartments with sparse sampling • D-Optimal design and Trial Simulation • Optimizing Target Attainment rates • Monte Carlo Simulation

  4. Identification of Pharmacokinetic Variability • CL (ml/min) = 19.3 x (Weight (Kg)/75)2.55 • For males • CL (ml/min) = 12.1 x (Weight (Kg)/65)2.75 • For females • Vd (L) = 12 + 0.5 x Weight (Kg) • For both genders FDA Guidance for Industry: Population Pharmacokinetics. February 1999

  5. Tobramycin Population analysisbased on TDM data 970 sets of Peak & Trough data • 470 neonates • Gestational age: 31.6 wks (23.7-42.9 wks) • Birth weight: 1530 g (485-5245 g) • Dose: • <28 wks 3.5 mg/kg q24 • 28-36 wks 2.5 mg/kg q18h • >36 wks 2.5 mg/kg q12h De Hoog et al. Clin Pharmacol Ther 1997;62:392-9 And Ther Drug Monit 2002;24: 359-65

  6. Distributions of PK Parameters in PatientsTobramcyin in 470 neonates Mean Subpopulation Inter-patient Variability Elimination rate (h-1) Volume of Distribution (L/Kg)

  7. Distribution of Parameter Estimates Tobramycin PK in 470 neonates Elimination rate (h-1) Distribution volume (L/Kg) Ke: 0.072 ± 0.033 (h-1) Vs: 0.575 ± 0.332 (L/Kg) De Hoog et al. 2002. Ther Drug Monit 24: 359-65

  8. Population PK of Tobramycin in NeonatesNPEM Model predictions Model-based prediction Prediction using post hoc Bayesian estimates R2 = 0.43 R2 = 0.98 KEL: 0.072 ± 0.033 (h-1) VS : 0.575 ± 0.332 (L/Kg) De Hoog et al. 2002. Ther Drug Monit 24: 359-65

  9. Storing Past Experience in Population Models • Volume of distribution - Relation to weight: Vs (in L/kg) • Elimination rate - Renal function: Kslope model as Ke = Knr + Ks · CLcr with: • Knr = non-renal elimination rate (Ki or Kelm) • Ks = linear relationship creatinine clearance (CrCL) and elimination rate constant • Inter-patient variability (%CV) • Assay error pattern: SD = x + y•C + z•C2

  10. Principle of Bayesian estimation • Statistical approach taking in account previous experience with similar patients (conditional probability) • Gives estimates of PK parametersand henceexposure indices(AUC, Cmax, Tmax …) • Allows estimation of whole [C]blood = f(time)curve, using 2 or 3 blood concentrations: • Used routinely for aminosides, vancomycin, etc. • Pre-requisite: a population PK model

  11. Principles of Bayesian Estimation

  12. intervention Target Patient concentration PK PK Patient dosing model data intervention Target Concentration Approach • Implementation ofgoal-oriented model-based dosing • Maximize Peak/MIC ratio (~10) and optimize total exposure (interval) • Outcomes - clinical and economical benefits Van Lent et al. Cost-effectiveness of model based TDM. Ther Drug Monit 1999;21:63-73

  13. PPK Model Based Prediction 15 PopPK Model - General Medicine: Ke = 0.00244 • CLcr (CV 64.8%) Vd = 0.2793 (CV 29.4%) SD = 0.0382+0.0197•C+ .0008 • C2 10 Gentamicin (mg/L) 5 0 0 6 12 18 24 Time into regimen (h) TDM study patient: 75-yr-old, 80 kg. Gram-negative infection. Gentamicin load: 240mg.

  14. Model Prediction with Feed-Back PK Model Prediction 15 Observed Concentration 10 Gentamicin (mg/L) 5 0 0 6 12 18 24 Time into regimen (h)

  15. PopPK model Bayesian estimate 15 Observed 10 Gentamicin (mg/L) 5 0 0 6 12 18 24 Time into regimen (h) Bayesian Adaptive Control

  16. Initial level Follow-up level 15 10 Gentamicin (mg/L) 5 0 0 12 24 36 48 60 72 84 Time into regimen (h) PopPK Assisted Individualization TDM study patient: 75-yr-old, 80 kg. Gram-neg infection. Gentamicin: 240mg load, 180mg q12h maintenance

  17. n = 62 vs. 48 18.0 ± 1.4 vs 12.6 ± 0.8 days 100 p < 0.001 75 deceased patients % of patients 50 controls 25 intervention 0 0 10 20 30 40 50 Time in hospital (days) Active Therapeutic Management benefits patient outcomes PopPK-PD cost-effectiveness study; van Lent-Evers et al. Ther Drug Monit 1999;21:63-73

  18. PK-PD Modeling of Ceftazidime in CFIntermittent vs. continuous infusion Bolus Continuous infusion Vinks et al. Antimicrob Agents Ther 1996;40:1091-97l

  19. input iv Kcp V1 V2 Kpc K e, CrCl Ceftazidime Model-Based Predictionsin 31 CF patients Vc = 0.183 L/Kg (± CV22%) R2=0.63 Kel=0.065 + 0.0060 * CLcr (± CV32%) Vinks et al. Antimicrob Agents Chemother 1996;40: 1091-97

  20. A B continuous infusion bolus injections 150 150 100 100 Concentration (mg/L) 50 50 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Time (hours) Time (hours) Simulation of ceftazidime diffusion into sputum and P. aeruginosa strains USCPACK sphere model and data from: Bolister JAC 1991 and Gordon JAC 1988

  21. Growth Kill Growth rate Max kill rate EC50 the concentration of the antibiotic at which 50% of the maximum effect is obtained γ, the Hill coefficient; N, number of viable bacteria; Nmax, Maximum number of bacteria or attainable bacterial density Mouton et al. AAC 1997

  22. Stationary Concentration 100 10 10 8 concentration (mg/L) Growth=Kill 10 log CFU/ml 6 regrowth 4 1 0 6 12 18 24 30 36 Time (h) ceftazidime concentration model fit number of bacteria in vitro PD - in vivo PK Link Models Mouton, Vinks and Punt. Antimicrob Agents Chemother 1997;41(4):733-8. Mouton & Vinks, Clin Pharmacokinet 2005;44(2):201-10.

  23. Use of PopPK Models to Determine Breakpoints • MCS powerful tool to determine the probability of attaining PK/PD index values • Can be expressed as Target Attainment Rates (TARs) • Analysis of interdependency of parameter estimates - Covariance or Correlation matrix • Will results in better estimation in CI (less bias)

  24. 200 Mean conc CF patients ± 95% CI 150 Mean conc volunteers ± 95% CI Ceftazidime (mg/L) 100 50 0 0 1 2 3 Time (days) Ceftazidime Model Generated PK Profiles Mouton, Punt and Vinks. Clin Ther 2005;27(6):762-772.

  25. %T>MIC as a function of the MIC based on mean PK parameter estimates Mouton, Punt and Vinks. Clin Ther 2005;27(6):762-772.

  26. Healthy volunteers 2000 mg q8h CF patients 2000 mg q8h % Time > MIC % Time > MIC MIC (mg/L) 30 40 50 60 30 40 50 60 0.5 100 100 100 100 100 100 100 100 1 100 100 100 100 100 100 100 100 2 100 100 100 100 100 100 100 99 4 100 100 100 100 100 100 99 96 8 100 100 100 100 100 99 93 78 16 100 100 94 60 99 84 53 25 32 78 27 3 0 52 14 3 0 TAR 100% 16 16 8 8 8 4 2 1 MCS Breakpoints need to be based on PK data from Patients, not healthy Subjects Mouton, Punt and Vinks. Clin Ther 2005;27(6):762-772.

  27. Conclusions Population PK-PD models: • Are increasingly important in defining optimum dosing strategies in different populations • Can be important extensions of TDM and help with clinical interpretation • Can be powerful tools in clinical trial design and simulation Need to develop better tools to link these models with Pharmacogenetic (PG), Adverse Events and clinical outcomes data

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