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

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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

)

- 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

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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

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