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