Transcript Slide 1

Sequential versus Simultaneous
Optimal Experimental Design on
Dose and Sample times
Joakim Nyberg
Mats O. Karlsson and Andrew Hooker
Division of Pharmacokinetics and Drug Therapy
Department of Pharmaceutical Biosciences
Uppsala University
Sweden
2007-06-15
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 the
Fisher Information Matrix
• The theory behind optimal design uses the
Cramer-Rao inequality:
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Cov 
FIM
• Optimal Design only depends on the design
parameters and a prior model => 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
2
1.9
effect
conc. (mg/L)
15
10
1.8
1.7
5
1.6
0
0
0.2
0.4
0.6
time (h)
0.8
1
1.5
0
5
10
15
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
PK Sampling schedule
Simultaneous
Time first
Dose first
5
5
5
5
5
5
0
0.2
0.4
0.6
0.8
1
time (h)
Remember: 2 PK samples/group, 5 groups => A total of 10 PK samples
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Results, Different strategies, PD
PD Sampling schedule
Simultaneous
Time first
Dose first
10
1
4
9
6
0
7
2 2
4
0.2
0.4
0.6
0.8
1
time (h)
Remember: 3 PD samples/group, 5 groups => A total of 15 PD samples
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Results, Different strategies, Dose
Optimal doses
Simultaneous
Time first
Dose first
2
2
2
2
1
4.967e+32
1
3
4.204e+32
FIM
2
1
2
3
4
5
3.764e+32
dose (mg)
Remember: 1 dose/group, 5 groups => A total of 5 different doses
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Results, Dose vs. PD Sample
(1 group)
FIM
PD sample time (h)
FIM
PD sample time (h)
dose (mg)
dose (mg)
• Dose
and sample times are correlated
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Results, Dose vs. Dose
(2 groups)
FIM
dose group 1 (mg)
dose group 2 (mg)
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Results, Strategies, Difference
Change in |FIM| in % compared to simultaneous optimization (Difference)
100
Dose first
Time first
Difference (%)
90
80
70
60
50
1 group
DIFF 
2 groups
3 groups
4 groups
5 groups
FIM (design)
FIM (simultaneous)
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Results, Strategies, Efficiency
Efficiency in % of different strategies
100
Dose first
Efficiency (%)
99
Time first
98
97
96
95
94
1 group
EFF 
2 groups
FIM (design)
3 groups
4 groups
5 groups
1/ p
FIM (simultanoeus)
1/ p
where p = number of parameters
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Conclusions
• It’s important to also optimize on dose in
optimal design
• It’s 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
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