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) = x Weight (Kg)
For both genders
FDA Guidance for Industry: Population Pharmacokinetics. February 1999

5. Tobramycin Population analysis based on TDM data
970 sets of Peak & Trough data
470 neonates
Gestational age: wks ( wks)
Birth weight: 1530 g
( 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:

6. Distributions of PK Parameters in Patients Tobramcyin 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: ± (h-1) Vs: ± (L/Kg)
De Hoog et al Ther Drug Monit 24:

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

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 parameters and hence exposure 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
Prior
Probability
New Info
Objective
Function
Posterior Probability
Goals
Control
Population Model
Drug
Levels
Consider
Prior + New
Individual Model
Look at Patient
Think
Calculate Dose

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

13. PPK Model Based Prediction15
PopPK Model - General Medicine:
Ke = • CLcr (CV 64.8%)
Vd = (CV 29.4%)
SD = •C • C2 10
Gentamicin (mg/L) 5 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 6 12 18 24
Time into regimen (h)

15. Bayesian Adaptive Control6 12 18 24 5 10 15
PopPK model
Bayesian estimate
Observed
Time into regimen (h)
Gentamicin (mg/L)

16. PopPK Assisted Individualization12 24 36 48 60 72 84 5 10 15
Follow-up level
Initial level
Time into regimen (h)
Gentamicin (mg/L)
TDM study patient:
75-yr-old, 80 kg. Gram-neg infection. Gentamicin: 240mg load, 180mg q12h maintenance

17. Active Therapeutic Management benefits patient outcomes10 20 30 40 50 25 75
100
n = 62
vs. 48
18.0 ± 1.4 vs 12.6 ± 0.8 days
p < 0.001
controls
intervention
deceased patients
Time in hospital (days)
% of patients
PopPK-PD cost-effectiveness study; van Lent-Evers et al. Ther Drug Monit 1999;21:63-73

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

19. Ceftazidime Model-Based Predictions in 31 CF patientsK
e, CrCl
Kcp
Kpc V1 V2
input iv
Vc = L/Kg (± CV22%)
R2=0.63
Kel= * CLcr
(± CV32%)
Vinks et al. Antimicrob Agents Chemother 1996;40:

20. Simulation of ceftazidime diffusion into sputum and P
Simulation of ceftazidime diffusion into sputum and P. aeruginosa strains
Time (hours)
Concentration (mg/L) 5 10 15 20 25 50
100
150 A
bolus injections
Time (hours) 5 10 15 20 25 50
100
150 B
continuous infusion
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. in vitro PD - in vivo PK Link Models
Stationary Concentration 6 12 18 24 30 36 1 10
100
number of bacteria 4 8
model fit
ceftazidime concentration
Growth=Kill
regrowth
Time (h)
concentration (mg/L)
log CFU/ml
Mouton, Vinks and Punt. Antimicrob Agents Chemother 1997;41(4):733-8.
Mouton & Vinks, Clin Pharmacokinet 2005;44(2):

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. Ceftazidime Model Generated PK Profiles1 2 3 50
100
150
200
Mean conc CF patients
95% CI
Mean conc volunteers
Time (days)
Ceftazidime (mg/L)
Mouton, Punt and Vinks. Clin Ther 2005;27(6):

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

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

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