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Use of Modelling for PKPD Studies in Infectious Diseases
Joe Standing
Infectious Diseases and Microbiology UnitUCL Institute of Child Health, London
ESPID May 20121
Outline
• Principles of PKPD in microbiology and infectious diseases
• Introduction to nonlinear mixed effects modelling
• Scaling pharmacokinetics between adults and children
2
Mathematical model
mathematical model n. a description or representation of something conceived or presented in mathematical terms. (OED)
Population modelling with nonlinear mixed effects is recommended
3
Principles of antimicrobial PKPD
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Principles of antimicrobial PKPD
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In vitro PKPD
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7
Principles of antimicrobial PKPD
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Clinical data: Cmax/MICRATE OF CLINICAL RESPONSE VS. CMAX/MIC RATIO
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Clinical data: AUC/MIC
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Clinical data: AUC/MIC
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Clinical data T>MIC
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Clinical evidence lacking…
Clinical data T>MIC
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…although some promising findings in critically ill patients with Pseudomonas:
Infusion length: T>MIC
Figure 3 Optimal infusion time plotted against MIC for meropenem. Green shaded area represents Eucast E.coli breakpoints of 2 and 8mg/L
Standing et al 2011 PAGE14
Be careful …
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Antiviral PKPD
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Standing et al 2012 AAC in press
Antiviral PKPD
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HIV viral load/CD4
HIV viral load/CD4
Outline
• Principles of PKPD in microbiology and infectious diseases
• Introduction to nonlinear mixed effects modelling
• Scaling pharmacokinetics between adults and children
20
Variability
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Individual Drug Concentration vs Time
0
1000
2000
3000
4000
5000
6000
0 1 2 3 4 5 6 7 8
Time (hr)
Pla
sm
a C
on
ce
ntr
ati
on
(n
mo
l/L
)
Possible modelling approaches
22
Individual Drug Concentration vs Time
0
1000
2000
3000
4000
5000
6000
0 1 2 3 4 5 6 7 8
Time (hr)
Pla
sm
a C
on
ce
ntr
ati
on
(n
mo
l/L
)
- Naïve Pooled- Two-stage- Non-linear mixed effects
Nonlinear mixed effects modelling
• Mixed effects:
–Fixed effects, population typical values (e.g.: CLpop, VDpop, Kapop)
–Random effects
• Inter and intraindividual variability
• Residual variability
NONMEM• NON linear Mixed Effects Modelling• Structural model e.g.
• Error model – Describes difference between observation and
model prediction
• Mixed effects: Fixed effects (structure) and Random effects (error)
C= Ka∙DVሺKa−Keሻ∙൫𝑒−Ke∙t −𝑒−Ka∙t൯
All models are wrong, some are useful
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Using models
• Simulations
• Minimising utility functions
26
Outline
• Principles of PKPD in microbiology and infectious diseases
• Introduction to nonlinear mixed effects modelling
• Scaling pharmacokinetics between adults and children
27
“Children are not small adults”Kearns 2003
VS.
“Children are small adults”Tod 2008 and adults?
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“Children are small adults”
• CL often better correlated with BSA than wt (Cawford 1950)
• BMR correlated with wt0.75 (Kleiber 1947)
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“Children are small adults”
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“Children are small adults”
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Scaling in PK: Tod et al 2008
• MF = maturation function• OF = organ function
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Scaling in PK: Maturation
• Anderson 2010, Midazolam maturation
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Outline
• Principles of PKPD in microbiology and infectious diseases
• Introduction to nonlinear mixed effects modelling
• Scaling pharmacokinetics between adults and children
34
35
Scaling in PK – Organ Function
• Ceriotti et al 2008
Note: Age in years
36