Pharmacometrics, biostatistics and computational biology postgraduate training:-

How can we integrate courses?

Julie SimpsonHead of Biostatistics Unit

Centre for Epidemiology and BiostatisticsMelbourne School of Population and Global Health

WCoP, 23 August 2016

Population pharmacokinetic modelling2

Kloprogge F et al. Br J Clin Pharm 2015

Population pharmacokinetic modelling:-Let’s unpack the skill set required….

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Pharmacokinetics – absorption, volume of distribution, clearance

Applied mathematics – ordinary differential equations

Population pharmacokinetic modellingLet’s unpack the skill set required….

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• Estimating model parameters • Evaluating how well the model fits the data.

Population pharmacokinetic modelling:-Let’s unpack the skill set required….

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1) Begin with statistical computing (e.g. R), linear regression, statistical inference (confidence intervals – asymptotic or bootstrap),regression diagnostics

Yi= β0 + β1𝑋𝑖 + ε𝑖

120

130

140

150

160

Sys

tolic

Blo

od P

ress

ure,

mm

Hg

30 40 50 60 70Age in years

-20

-10

010

20

Res

idua

ls

-10 0 10Inverse Normal

-20

-10

010

20

Res

idua

ls

130 135 140 145 150Fitted values

Population pharmacokinetic modelling:-Let’s unpack the skill set required….

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2) Progress to linear mixed-effects modelling

Yij= (β0 + 𝑏0𝑖) + (β1 + 𝑏1𝑖)𝑡𝑖𝑚𝑒𝑖𝑗 + ε𝑖𝑗

Population pharmacokinetic modelling:-Let’s unpack the skill set required….

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3) And then on to nonlinear regression

𝐶𝑗 𝑡 =𝑑𝑜𝑠𝑒. 𝛽𝑘𝑎

𝛽𝑉/𝐹𝛽𝑘𝑎 − 𝛽𝐶𝑙/𝐹𝑒−

𝛽𝐶𝑙/𝐹𝛽𝑉/𝐹

𝑡𝑗− 𝑒−𝛽𝑘𝑎𝑡𝑗 + 𝜀𝑗

010

2030

Con

cent

ratio

n (m

g/L)

0 7 14 21 28Time

Population pharmacokinetic modelling:-Let’s unpack the skill set required….

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3) Followed by nonlinear mixed-effects modelling

- NONMEM®, Monolix

𝐶𝑖𝑗 𝑡 =𝑑𝑜𝑠𝑒𝑖𝛽𝑘𝑎𝑖

𝛽𝑉/𝐹𝑖𝛽𝑘𝑎𝑖 − 𝛽𝐶𝑙/𝐹𝑖𝑒−(

𝛽𝐶𝑙/𝐹𝑖𝛽𝑉/𝐹𝑖

)𝑡𝑖𝑗− 𝑒−𝛽𝑘𝑎𝑖𝑡𝑖𝑗 + 𝜀𝑖𝑗

Population pharmacokinetic-pharmacodynamicmodelling:- Further skills required…

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• Identifiability of mathematical systems

• Monte Carlo Markov Chain (MCMC) methods

Systems pharmacology model of the coagulation networkGulati A et. al. CPT PSP 2014

Why is proper training in all these areas important?10

Times Higher Education(THE) Top 16 universities for Clinical, Pre-clinical and Health 2015-16

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Rank Institution Country Master of Biostatistics Master of Pharmacometrics Master of Computational Biology

1 University of Oxford UK √ (MSc Applied Stats) X X

2 Harvard University USA √ X √

3 University of Cambridge UK X X √

4 University College London UK √ X X

=5 University of California, Berkeley USA √ X √ (1st year PhD)

=5 Imperial College London UK X X X

7 Stanford University USA √ (1st year PhD) X √ (1st year PhD)

8 King’s College London UK X X X

9 Johns Hopkins University USA √ X X

10 Columbia University USA √ X X

11 University of Toronto Canada √ X X (undergraduate training)

12 University of Edinburgh UK X X X

13 Karolinksa Institute Sweden X X X

14 Duke University USA √ X √ (1st year PhD)

=15 University of California, Los Angeles USA √ X √ (MSc Biomathematics)

=15 University of Melbourne Australia √ X X

Master of Biostatistics (11 Universities):–Skill set for PK-PD modelling

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2

4

6

8

10

12

StatisticalComputing

StatisticalInference

Linear Regression Generalised LinearModels

Linear mixed-effects modelling

Nonlinearregression &

nonlinear mixed-effects modelling

Bayesian methods

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MSc – Pharmacometrics, University of MarylandCurriculum• Basic Pharmacometric Tools

Statistical Computing:- Phoenix, NONMEM and R

• Basic PKPD ModellingFundamentals of PK and PD modelling and hands on training of PK-PD analysis and simulation software

• Statistics for Pharmacometricians I Basic statistical principles required for a pharmacometrician

• Dose-Response Trials Basics of designs such as parallel, cross-over, flexible-dose, titration, withdrawal, adaptive and enrichment trials. Learn how to perform clinical trial simulation.

• Strategic Communication & NegotiationsCommunication & negotiation skills

• Intermediate PKPD Modelling IIntroduction of population analysis concepts.

• Intermediate PKPD Modelling II Nonlinear mixed-effects modelling

• Statistics for Pharmacometricians IILogistic regression, Poisson regression and survival analysis – analysis of real data examples and simulation. 14

Pharmacometrics postgraduate training:-What is the way forward?

Master of Pharmacometrics

• Develop curriculum that includes key subjects from Master of Biostatistics and Master of Computational Biology.

• Online course taught by multiple institutions – Biostatistics Collaboration of Australia (www.bca.edu.au )

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Pharmacometrics postgraduate training:-What is the way forward?

Master of Biostatistics/ Computational Biology –Pharmacometrics stream

Develop subjects – e.g. pharmacokinetics, nonlinear mixed-effects modelling, etc., which are offered as electives.

Pharmacometrics

Computational Biology

Biostatistics