SCIENTISTCLINICAL PHARMACOLOGY, MODELING AND SIMULATION

SHARVARI BHAGWAT

R IN PHARMACOMETRICS, MODELING AND SIMULATION

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• Introduction to pharmacometrics and model based drug development

– What is pharmacometrics

– Model based drug development

• Use of R as a simulation tool

• Use of R as a model assessment tool

• Conclusion

PRESENTATION OUTLINE

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INTRODUCTION

• Pharmacokinetics - What the body does to the drug

• Pharmacodynamics - What the drug does to the body

• Pharmacometrics – “the science of developing and applying mathematical and statistical methods to

characterize, understand and predict a drug’s pharmacokinetic, pharmacodynamics and biomarker-

outcomes behavior”

Ette E., Williams P., “Pharmacometrics: The Science of Quantitative Pharmacology”, Wiley Interscience, 2007

What is pharmacometrics

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INTRODUCTION

Model based drug development

Bonate P., “Pharmacokinetic-Pharmacodynamic Modeling and Simulation”, Springer, 2011

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• Pharmacostatistical models of drug efficacy and safety are developed from

preclinical and available clinical data

• MBDD based approaches can be used to facilitate quantitative decision

making

• Models can be used to summarize essential information in an efficient way, so

that knowledge from different studies and external sources can be integrated.

MODEL BASED DRUG DEVELOPMENT (MBDD)

Miller, R., Ewy, W., Corrigan, B. W., Ouellet, D., Hermann, D., Kowalski, K. G., … Lalonde, R. L. (2005). How Modeling and Simulation Have Enhanced Decision

Making in New Drug Development. Journal of Pharmacokinetics and Pharmacodynamics, 32(2), 185–197.

Kimko, H., & Pinheiro, J. (2014). Model-based clinical drug development in the past , present and future : a commentary. British Journal of Clinical Pharmacology.

https://doi.org/10.1111/bcp.12341

USE OF R AS A SIMULATION TOOL

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Kimko, H., & Pinheiro, J. (2014). Model-based clinical drug development in the past , present and future : a commentary. British Journal of Clinical Pharmacology.

Step 1 - Describing the structural PK model

– In this example, a two compartment model with zero order input and

first order elimination was used

– a closed form equation was used to describe the structural model

STRUCTURAL PK MODEL

• 𝐶 𝑡 =𝐷

𝑇𝑖𝑛𝑓

𝐴

α1 − 𝑒−α(𝑡 −𝑡𝐷) +

𝐵

β1 − 𝑒−β(𝑡−𝑡𝐷) if t-tD ≤ Tinf

• 𝐶 𝑡 =𝐷

𝑇𝑖𝑛𝑓

𝐴

α1 − 𝑒_α𝑇𝑖𝑛𝑓)𝑒−α(𝑡 −𝑡𝐷−𝑇𝑖𝑛𝑓)

+𝐵

β1 − 𝑒_β𝑇𝑖𝑛𝑓)𝑒−β(𝑡−𝑡𝐷−𝑇𝑖𝑛𝑓)

if not

tD = time of infusion

Tinf = infusion length

D = total dose

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• The deterministic structural PK model can

be used to get an estimate of exposures

and compare exposures between different

scenarios

• 100 mg of drug given over different

infusion lengths

STRUCTURAL PK MODEL

Hypothetical data for representation

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• How would the maximum exposure

change with doses?

STRUCTURAL PK MODEL

Hypothetical data for representation

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Step 2 - Describing the statistical model

There are generally two sources of variability

– Between subject variability (BSV)

• Most parameters are distributed log-normally since they cannot be negative

– Residual variability

• This is the unexplained variability in the concentrations across subjects

– If the mean and variance is known from previous studies/literature, a distribution of the

variability can be simulated

STATISTICAL MODEL

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Step 3 - Describing the covariate effects

Effects of covariates such as weight, age etc. on pharmacokinetic parameters can be

incorporated in the parameter definitions when writing the model in R

COVARIATE MODEL

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• Structural model + statistical model +

covariate model = population

pharmacokinetics

– Can be used to predict the variability in clinical

trial exposures

– Can be used to support decisions regarding

clinical trial design.

SIMULATING POPULATION PK USING THE COMPLETE MODEL

Hypothetical data for representation

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Functions can be written in C++ and loaded into R

SIMULATING LARGE CLINICAL TRIALS

• There are scenarios where multiple doses need to be simulated using complex models

over a long period of time.

• Number of subjects in the trial could be very large and/or simulation of multiple trials may

be needed

• If simulations are coded with differential equations, they can take several hours to

complete

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TMDD model schematic

– This model is described using the differential equations

shown below in the white box

– Since it would be tedious to integrate these equations and

obtain a close form equations, simulations are done using

the differential equations

SIMULATING POPULATION PHARMACOKINETICS USING THE TARGET MEDIATED DRUG DISPOSITION MODEL

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– Hypothetical drug showing TMDD

– Dosing 100 mg every 8 weeks for 8 cycles

– Simulate a trial with 500 subjects

Simulation conditions

SIMULATING POPULATION PHARMACOKINETICS USING THE TARGET MEDIATED DRUG DISPOSITION MODEL

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COMPILING SIMULATIONS IN R USING C++ (UBIQUITY)

• Ubiquity – A model development and deployment tool (ubiquity.grok.tv)

• Developed by John Harrold and Anson Abraham

• Uses C++ to compile simulations in a fraction of the time as compared to R

• Can be customized to simulate using any PK model

• Can be used to conveniently simulate complex scenarios

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GENERATING AN R-SHINY GUI USING UBIQUITY

Hypothetical data for representation

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GENERATING AN R-SHINY GUI USING UBIQUITY

Simulation time - ~56 seconds with Ubiquity

>30 min if done using only RHypothetical data for representation

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GENERATING AN R-SHINY GUI USING UBIQUITY

Hypothetical data for representation

USE OF R AS A MODEL ASSESSMENT TOOL

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• While simulations are commonly done in R, modeling of clinical

data is mostly done using dedicated modeling software such as

NONMEM

• However, R is used for generating diagnostic plots when

assessing model fits

USE OF R AS A MODEL ASSESSMENT TOOL

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DIAGNOSTIC PLOTS

Hypothetical data for representation

Observed concentrations vs population predicted and individual predicted

concentrations

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DIAGNOSTIC PLOTS

Conditional weighted residuals vs population predicted concentration and

time

Hypothetical data for representation

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DIAGNOSTIC PLOTS

Covariate analysis

Hypothetical data for representation

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VISUAL PREDICTIVE CHECK

Dose n

orm

aliz

ed c

oncentr

atio

n

Time

Data for representation

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• R can be used in the model based drug development process at

various stages

• It can be used as a versatile clinical trial simulation tool

• It is commonly used for model assessment and for generating

diagnostic plots using NONMEM output

• User-friendly Shiny interfaces can be created for ease of use

CONCLUSION