Post on 05-Jan-2016
Population PK-PD Modeling of Population PK-PD Modeling of Anti-Infective AgentsAnti-Infective Agents
Alexander A. Vinks, PharmD, PhD, FCPAlexander A. Vinks, PharmD, PhD, FCP
Professor and DirectorProfessor and Director
Pediatric Pharmacology Research UnitPediatric Pharmacology Research Unit
Cincinnati Children’s Hospital and Medical CenterCincinnati Children’s Hospital and Medical Center
Why Population Modeling and Why Population Modeling and SimulationSimulation??
To describe and understand To describe and understand Drug PK/PD BehaviorDrug PK/PD Behavior
Collect informative data to Collect informative data to use as Bayesian priors for use as Bayesian priors for designing model-based, designing model-based, individualized dosing individualized dosing regimensregimens
To Predict and therefore To Predict and therefore ControlControl the system (i.e. the the system (i.e. the serum & other serum & other compartments) compartments)
Change passive “Monitoring” Change passive “Monitoring” to active “Management”to active “Management”
Clinical Applications of PPK Clinical Applications of PPK ModelsModels
Designing dosing regimensDesigning dosing regimens– Identifying central tendency of PK parameter Identifying central tendency of PK parameter
estimates and variability in the targeted patient estimates and variability in the targeted patient populationpopulation
– Identifying clinically useful covariatesIdentifying clinically useful covariates Bayesian Adaptive Control StrategiesBayesian Adaptive Control Strategies Clinical Trial DesignClinical Trial Design
– Determining PK characteristics in other tissues and Determining PK characteristics in other tissues and compartments with sparse samplingcompartments with sparse sampling
– D-Optimal design and Trial SimulationD-Optimal design and Trial Simulation Optimizing Target Attainment ratesOptimizing Target Attainment rates
– Monte Carlo SimulationMonte Carlo Simulation
Identification of Pharmacokinetic Identification of Pharmacokinetic VariabilityVariability
CL (ml/min) = 19.3 x (Weight CL (ml/min) = 19.3 x (Weight (Kg)/75)(Kg)/75)2.552.55
– For malesFor males CL (ml/min) = 12.1 x (Weight (Kg)/65)CL (ml/min) = 12.1 x (Weight (Kg)/65)2.752.75
– For femalesFor females
Vd (L) = 12 + 0.5 x Weight (Kg) Vd (L) = 12 + 0.5 x Weight (Kg) – For both gendersFor both genders
FDA Guidance for Industry: Population Pharmacokinetics. February 1999
Tobramycin Population analysisTobramycin Population analysisbased on TDM databased on TDM data
470 neonates470 neonates Gestational age: 31.6 Gestational age: 31.6
wks (23.7-42.9 wks)wks (23.7-42.9 wks) Birth weight: 1530 g Birth weight: 1530 g
(485-5245 g)(485-5245 g) Dose: Dose:
– <28 wks 3.5 mg/kg q24<28 wks 3.5 mg/kg q24– 28-36 wks 2.5 mg/kg 28-36 wks 2.5 mg/kg
q18hq18h– >36 wks 2.5 mg/kg q12h>36 wks 2.5 mg/kg q12h
970 sets of Peak & Trough data970 sets of Peak & Trough data
0 12 24 36 48 60 720
5
10
15
Time into regime (h)
To
bra
myc
in (
mg
/L)
De Hoog et al. Clin Pharmacol Ther 1997;62:392-9And Ther Drug Monit 2002;24: 359-65
Distributions of PK Parameters in Distributions of PK Parameters in PatientsPatients
Tobramcyin in 470 neonatesTobramcyin in 470 neonates
Mean Subpopulation
Inter-patient Variability
Volume of Distribution (L/Kg)Volume of Distribution (L/Kg)Elimination rate Elimination rate (h-1)(h-1)
Distribution of Parameter Distribution of Parameter Estimates Estimates Tobramycin PK in 470 neonatesTobramycin PK in 470 neonates
De Hoog et al. 2002. Ther Drug Monit 24: 359-65
Elimination rate (hElimination rate (h-1-1)) Distribution volume (L/Kg)Distribution volume (L/Kg)
Ke: 0.072 ± 0.033 (h-1) Vs: 0.575 ± 0.332 (L/Kg)
Population PK of Tobramycin in Neonates
NPEM Model predictions
De Hoog et al. 2002. Ther Drug Monit 24: 359-65
Model-based predictionModel-based prediction Prediction using post hocPrediction using post hocBayesian estimates Bayesian estimates
R2 = 0.98R2 = 0.43
KEL: 0.072 ± 0.033 (h-1)VS : 0.575 ± 0.332 (L/Kg)
Storing Past Experience Storing Past Experience in Population Modelsin Population Models
Volume of distribution - Relation to weight:Volume of distribution - Relation to weight: Vs (in L/kg)Vs (in L/kg)
Elimination rate - Renal function:Elimination rate - Renal function:Kslope model as Ke = Knr + Ks · CLcr Kslope model as Ke = Knr + Ks · CLcr
with:with: Knr = non-renal elimination rate (Ki or Kelm)Knr = non-renal elimination rate (Ki or Kelm) Ks = linear relationship creatinine clearance (CrCL) and Ks = linear relationship creatinine clearance (CrCL) and
elimination rate constant elimination rate constant Inter-patient variability (%CV)Inter-patient variability (%CV) Assay error pattern: SD = x + y•C + z•CAssay error pattern: SD = x + y•C + z•C22
Principle of Bayesian estimationPrinciple of Bayesian estimation
Statistical approach taking in account Statistical approach taking in account previous experience with similar patients previous experience with similar patients (conditional probability)(conditional probability)
Gives estimates of Gives estimates of PK parametersPK parameters and henceand hence exposure indicesexposure indices (AUC, Cmax, Tmax …)(AUC, Cmax, Tmax …)
Allows estimation of whole Allows estimation of whole [C][C]bloodblood = f(time) = f(time) curve, using 2 or 3 blood concentrations:curve, using 2 or 3 blood concentrations:
Used routinely for aminosides, vancomycin, Used routinely for aminosides, vancomycin, etc.etc.
Pre-requisite: a population PK modelPre-requisite: a population PK model
2
1
2
12
m
k k
kkn
i i
ii
S
EC
Principles of Principles of Bayesian Bayesian
PriorPrior
ProbabiliProbabilityty
New InfoNew InfoObjectiveObjective
FunctionFunction
Posterior Posterior ProbabilitProbabilit
yyGoalsGoals ControlControl
PopulatiPopulation Modelon Model
Drug Drug
LevelsLevels
ConsiderConsider
Prior + Prior + NewNew
IndividuaIndividual Modell Model
Look at Look at PatientPatient
ThinkThink
CalculatCalculate Dosee Dose
EstimationEstimation
Target Concentration ApproachTarget Concentration Approach
Implementation ofImplementation of goal-oriented goal-oriented model-based model-based dosingdosing
Maximize Peak/MIC Maximize Peak/MIC ratio (ratio (~10) ~10) and and optimize total optimize total exposure (interval)exposure (interval)
OutcomesOutcomes - - clinical clinical and economical and economical benefits benefits
Van Lent et al. Cost-effectiveness of model based TDM. Ther Drug Monit 1999;21:63-73
Patient data
PK model
PK dosing
PatientTargetconcentration
intervention
intervention
PPK Model Based PredictionPPK Model Based Prediction
PopPK Model - General Medicine:PopPK Model - General Medicine:Ke = 0.00244 • CLcr (CV 64.8%)Ke = 0.00244 • CLcr (CV 64.8%)Vd = 0.2793 (CV 29.4%) Vd = 0.2793 (CV 29.4%) SD = 0.0382+0.0197•C+ .0008 • SD = 0.0382+0.0197•C+ .0008 • CC22
TDM study patient: 75-yr-old, 80 kg. Gram-negative infection. Gentamicin load: 240mg.
0 6 12 18 240
5
10
15
Time into regimen (h)
Ge
nta
mic
in (
mg
/L)
Model Prediction with Feed-BackModel Prediction with Feed-Back
0 6 12 18 240
5
10
15PK Model Prediction
Observed Concentration
Time into regimen (h)
Gen
tam
icin
(m
g/L)
Bayesian Adaptive ControlBayesian Adaptive Control
0 6 12 18 240
5
10
15
PopPK modelBayesian estimateObserved
Time into regimen (h)
Gen
tam
icin
(m
g/L
)
PopPK Assisted IndividualizationPopPK Assisted Individualization
TDM study patient:75-yr-old, 80 kg. Gram-neg infection. Gentamicin: 240mg load, 180mg q12h maintenance
0 12 24 36 48 60 72 840
5
10
15Follow-up level
Initial level
Time into regimen (h)
Ge
nta
mic
in (
mg
/L)
Active Therapeutic Management Active Therapeutic Management benefits patient outcomesbenefits patient outcomes
PopPK-PD cost-effectiveness study; van Lent-Evers et al. Ther Drug Monit 1999;21:63-73
0 10 20 30 40 500
25
50
75
100n = 62 vs. 4818.0 ± 1.4 vs 12.6 ± 0.8 daysp < 0.001
controls
intervention
deceased patients
Time in hospital (days)
% o
f p
ati
ents
PK-PD Modeling of Ceftazidime in CFPK-PD Modeling of Ceftazidime in CFIntermittent Intermittent vs.vs. continuous infusion continuous infusion
Vinks et al. Antimicrob Agents Ther 1996;40:1091-97l
0 4 81
10
100
1000
24 36 50 300 550
Time into regimen (h)
Cef
tazi
dim
e (m
g/L
) BolusBolus Continuous infusionContinuous infusion
Ceftazidime Model-Based PredictionsCeftazidime Model-Based Predictionsin 31 CF patientsin 31 CF patients
Predicted concentration (mg/L)
Ob
serv
ed c
on
cen
trat
ion
(m
g/L
)
0 10 20 30 40 50 600
10
20
30
40
50
60
Vinks et al. Vinks et al. Antimicrob Agents Chemother Antimicrob Agents Chemother 1996;40: 1091-971996;40: 1091-97
R2=0.63Vc = 0.183 L/Kg (± CV22%)Vc = 0.183 L/Kg (± CV22%)
Kel=0.065 + 0.0060 * CLcrKel=0.065 + 0.0060 * CLcr(± CV32%)(± CV32%)
Ke, CrCl
Kcp
KpcV1 V2
input iv
Simulation of ceftazidime diffusion Simulation of ceftazidime diffusion into sputum and into sputum and P. aeruginosaP. aeruginosa
strainsstrains
USCPACK sphere model and data from: Bolister JAC 1991 and Gordon JAC 1988
Time (hours)
Co
nce
ntr
atio
n (
mg
/L)
0 5 10 15 20 250
50
100
150
Abolus injections
Time (hours)
0 5 10 15 20 250
50
100
150
Bcontinuous infusion
N}EC+C
C-)N
N-(1{=
dt
dN
50
max
Growth Kill
Mouton et al. AAC 1997
Growth rate Max kill rate
EC50 the concentration of the antibiotic at which 50% of the maximum effect is obtainedγ, the Hill coefficient;N, number of viable bacteria; Nmax, Maximum number of bacteria or attainable bacterial density
in vitroin vitro PD - PD - in vivoin vivo PK Link Models PK Link Models
Stationary Concentration
0 6 12 18 24 30 361
10
100
number of bacteria
4
6
8
10
model fit ceftazidime concentration
Growth=Kill
regrowth
Time (h)
con
cen
trat
ion
(m
g/L
)10lo
g C
FU
/ml
Mouton, Vinks and Punt. Antimicrob Agents Chemother 1997;41(4):733-8.Mouton & Vinks, Clin Pharmacokinet 2005;44(2):201-10.
Use of PopPK Models to Determine Use of PopPK Models to Determine BreakpointsBreakpoints
MCS powerful tool to determine the MCS powerful tool to determine the probability of attaining PK/PD index values probability of attaining PK/PD index values
Can be expressed as Target Attainment Can be expressed as Target Attainment Rates (TARs)Rates (TARs)
Analysis of interdependency of parameter Analysis of interdependency of parameter estimates - Covariance or Correlation estimates - Covariance or Correlation matrix matrix
Will results in better estimation in CI (less Will results in better estimation in CI (less bias)bias)
Ceftazidime Model Generated PK Ceftazidime Model Generated PK ProfilesProfiles
Mouton, Punt and Vinks. Clin Ther Mouton, Punt and Vinks. Clin Ther 2005;27(6):762-772.2005;27(6):762-772.
0 1 2 30
50
100
150
200Mean conc CF patients
95% CIMean conc volunteers95% CI
Time (days)
Cef
tazi
dim
e (m
g/L
)
%T>MIC as a function of the MIC %T>MIC as a function of the MIC based on mean PK parameter based on mean PK parameter
estimatesestimates
Mouton, Punt and Vinks. Clin Ther Mouton, Punt and Vinks. Clin Ther 2005;27(6):762-772.2005;27(6):762-772.
MCS Breakpoints need to be based MCS Breakpoints need to be based on PK data from Patients, not on PK data from Patients, not
healthy Subjectshealthy Subjects
Healthy volunteers 2000 mg q8h 2000 mg q8h
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
% Time > MIC % Time > MIC
CF patients
Mouton, Punt and Vinks. Clin Ther Mouton, Punt and Vinks. Clin Ther 2005;27(6):762-772.2005;27(6):762-772.
ConclusionsConclusions
Population PK-PD models:Population PK-PD models: Are increasingly important in defining optimum Are increasingly important in defining optimum
dosing strategies in different populationsdosing strategies in different populations Can be important extensions of TDM and help Can be important extensions of TDM and help
with clinical interpretationwith clinical interpretation Can be powerful tools in clinical trial design Can be powerful tools in clinical trial design
and simulation and simulation
Need to develop better tools to link these models Need to develop better tools to link these models with Pharmacogenetic (PG), Adverse Events with Pharmacogenetic (PG), Adverse Events and clinical outcomes dataand clinical outcomes data