Sequential versus Simultaneous Optimal Experimental Design on Dose and Sample times

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Sequential versus Simultaneous Optimal
Experimental Design on Dose and Sample times
Joakim Nyberg
Mats O. Karlsson and Andrew Hooker
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Background

• Traditionally Optimal Design (OD) has been about
  optimizing the sampling schedule in experiments.
• But OD is dependent on ALL design parameters.
• Dose
• Covariates
• Number of samples/group
• Number of individuals/group
• Infusion duration
• Start/stop times of studies
• Start/stop times of infusion
• Wash out period length
• All other design parameters that you could think
  of
• Optimal design is a powerful tool, but it has not
  been used widely for optimizing the problems
  above. Optimal sampling times could be easy to
  find by hand compared to many of these other
  design parameters.
• If optimizing on several design parameters,
  should we do it simultaneously or sequentially?

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Optimal Experimental Design

• Optimal Design is a way to find a design that
  will produce as low uncertainty of the parameters
  in a model as possible when re-estimating the
  model with new data
• Optimal Design only depends on the design
  parameters and a prior model

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Optimal Design and theFisher Information Matrix

• The theory behind optimal design uses the
  Cramer-Rao inequality
• Optimal Design only depends on the design
  parameters and a prior model gt FIM only depends
  on the design parameter and the prior model
• Maximizing the determinant of the FIM is called
  D-optimal design. Most common.

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Experiment

• Optimize on a continuous dose and optimize on
  continuous sample times
• Design strategies
• Optimize sample time first, then dose
• Optimize dose first, then sample times
• Optimize dose and time simultaneously
• 1-5 groups (dose arms) with PK-PD measurements
• Used PopED in all experiments

Foracchia, M., Hooker, A., Vicini, P. and
Ruggeri, A., POPED, a software for optimal
experiment design in population kinetics. Comput
Methods Programs Biomed, 2004.
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One-comp IV, direct effect E-max
Concentration
Effect
dose 2.75 mg
dose 2.75 mg
effect
conc. (mg/L)
time (h)
conc. (mg/L)
Y. Hashimoto L.B. Sheiner. Designs for
population pharmacodynamics value of
pharmacokinetic data and population analysis. J.
Pharmacokinetic. Biopharm 1991.
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Experiment

• 1-5 groups
• 2 PK 3 PD samples in each group
• Different doses evenly spread (between groups)
  0, 0.5-5 mg
• Initial sample times evenly spread (within
  groups) 0-1 h

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Results, Different strategies, PK
Remember 2 PK samples/group, 5 groups gt A total
of 10 PK samples
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Results, Different strategies, PD
Remember 3 PD samples/group, 5 groups gt A total
of 15 PD samples
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Results, Different strategies, Dose
Optimal doses
4.967e32
Simultaneous
Time first
4.204e32
Dose first
3.764e32
dose (mg)
Remember 1 dose/group, 5 groups gt A total of 5
different doses
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Results, Dose vs. PD Sample(1 group)

• Dose and sample times are correlated

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Results, Dose vs. Dose(2 groups)
dose group 1 (mg)
dose group 2 (mg)
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Results, Strategies, Difference
Change in FIM in compared to simultaneous
optimization (Difference)
Difference ()
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Results, Strategies, Efficiency
Efficiency in of different strategies
Efficiency ()
where p number of parameters
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Conclusions

• Its important to also optimize on dose in
  optimal design
• Its always more efficient to optimize
  simultaneously compared to sequential optimization

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Future perspectives

• Other areas where optimizing different design
  parameters can be useful are
• Drug-drug interaction studies e.g. wash out
  periods
• PET studies (plenty of samples)
• Provocation experiments (Glucose-Insulin)
• Multiple drug response studies
• Progression studies
• Functionality for this type of optimization has
  already been done in PopED

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Thank you