Deux exemples en pharmacocintique de population

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Deux exemples en pharmacocinétique de population

• France MENTRE, Sylvie RETOUT et Xavière PANHARD
• INSERM E03 57
• Dpt dEpidémiologie, Biostatistique et Recherche
  Clinique
• CHU Bichat-Claude Bernard
• (Université Paris 7)

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PLAN

• Introduction à la cinétique de population
• PK de population de lenoxaparine
• données dun essai de phase III (Aventis)
• NONMEM
• Covariables
• SE, CI et bootstrap
• empirical Bayes estimates (PD)
• design
• PK de population du nelfinavir et de M8
• données post AMM (ANRS)
• deux variables
• nlme
• construction du modèle
• covariables
• validation

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2. POPULATION PHARMACOKINETICS OF ENOXAPARINE

Br J Clin Pharmacol, 2003 56, 407-414
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PK enoxaparin

• Enoxaparin (Adventis)
• low-molecular weight heparin
• new development for patients suffering of
  myocardial infarction
• Enoxaparin administration
• 30 mg by IV bolus at t 0
• 1 mg/kg/12h by subcutaneous injection
• Empirical design for phase III population PK
  study

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Empirical design
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Empirical design

• 200 patients 2 samples at D1 replicated at D3
  (5 designs)
• 20 patients 4 samples at D3

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Design execution

• Sampling time distribution (D1 D3)

Theoritical (empirical design)
Observed
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Data from D1 and D3

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Data file in NONMEM
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Pharmacokinetic Model
ka
Volume V
k

• one cp model, first order absorption and
  elimination
• PK parameters ka, CL k.V, V

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Basic mixed-effects model

• Individual model
• yi f(?i, ?i) ei
• ?i individual parameters (size p)
• e gaussian zero mean random error
• var (e) ( sinter sslopef(q, x) )2
• constant CV sinter 0
• Random-effects model
• ?i µ exp bi
• bi N (0, ?)
• ? diagonal wk Var(bik)
• Population parameters y  (size P)
• µ (fixed effects)
• unknowns in ? (variance of random effects)
• sinter and/or sslope (error variance)

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Basic Model
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MINIMUM VALUE OF OBJECTIVE FUNCTION





   
10962.077







FINAL PARAMETER ESTIMATE





  THETA - VECTOR OF FIXED
EFFECTS PARAMETERS     TH
1 TH 2 TH 3 7.52E-01
3.55E00 1.44E-01   OMEGA - COV MATRIX FOR
RANDOM EFFECTS - ETAS  
ETA1 ETA2 ETA1 1.34E-01
ETA2 0.00E00 5.69E-02     SIGMA - COV
MATRIX FOR RANDOM EFFECTS - EPSILONS  
EPS1 EPS1 7.96E-02
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STANDARD ERROR OF ESTIMATE





   
THETA - VECTOR OF FIXED EFFECTS PARAMETERS
    TH 1 TH 2 TH
3 2.13E-02 2.05E-01 1.41E-02    
OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS
    ETA1 ETA2 ETA1
2.23E-02 ETA2 .........
2.68E-02     SIGMA - COV MATRIX FOR RANDOM
EFFECTS - EPSILONS     EPS1
EPS1 8.23E-03 1
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Standard goodness of fit plots
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Covariates
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Covariates model building
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Results of Covariates model building
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Final Model

• Inter-occasion variability
• patients sampled more than once
• K occasions (k1,K)
• additional random effects k
• ex CLik bCL exp(bi kik)
• Fixed effects for covariates
• two additional fixed effects for covariates
• bCLCR creatinine clearance
• bWT weight
• Clik (CL bWT (WTi-82) bCLCR (CLCRi- 87.91))
  exp (bikik)

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Estimated parameters
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 Bootstrap  procedure
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Effect of PK on haemorrhage (1)

• Two PD variables (yes/no)
• Major haemorrhage
• All haemorrhage
• Predictive factors of haemorrhage risk
• Logistic regression (stepwise selection in SAS)
• Individual covariates
• sex, weight, age, CRCL, platelet count,
  haematocrit, haemoglobin, dose
• AUC measure of exposure
• Estimation of individual AUC
• Empirical Bayes estimates of CL
• Final population model
• Individual covaiates and concentrations
• AUC Dose/ CL

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Effect of PK on haemorrhage (2)
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Optimal design for the basic model (1)

• Constraints for design optimisation using PFIM
• 4 samples per patient
• two at D1 (first dose) two at D3 (fifth dose)
• 10 available sampling times
• 0.5, 1, 1.5, 2, 2.5, 4, 6, 8, 10, 12
• Simulation (with NONMEM) of 30 sets for two
  designs
• empirical design
• optimal design
• Analysis
• estimation with NONMEM
• comparison of errors between designs
• comparison of standard errors provided by NONMEM
  and by PFIM1.1

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Optimal design for the basic model (2)
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Efficiency 1.35
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Optimal design for the basic model (3)
Relative errors from the 30 simulated data sets
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RMSE ()
10
5
0
CL
V
KA
OMCL
OMV
SIGMA2
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Optimal design for the basic model (4)
Evaluation of predicted estimation CV on 30
simulations
empirical CV CV predicted by PFIM
histogram NONMEM CV