Division of Pharmacokinetics and Drug TherapyDepartment of Pharmaceutical Biosciences

Uppsala UniversitySweden

2007-06-15

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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• The theory behind optimal design uses the Cramer-Rao inequality:

• 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.

Optimal Design and theFisher Information Matrix

1CovFIM

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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

*Y. Hashimoto & L.B. Sheiner. Designs for population pharmacodynamics: value of pharmacokinetic data and population analysis. J. Pharmacokinetic. Biopharm: 1991.

0 0.2 0.4 0.6 0.8 10

5

10

15

dose = 2.75 mg

0 5 10 151.5

1.6

1.7

1.8

1.9

2

time (h) conc. (mg/L)

conc

. (m

g/L)

effec

t

dose = 2.75 mg

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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

0 0.2 0.4 0.6 0.8 15 5

5 5

5 5Simultaneous

Time first

Dose first

PK Sampling schedule

time (h)

Remember: 2 PK samples/group, 5 groups => A total of 10 PK samples

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Results, Different strategies, PD

0 0.2 0.4 0.6 0.8 14 2 2 7

6 9

4 1 10Simultaneous

Time first

Dose first

PD Sampling schedule

time (h)

Remember: 3 PD samples/group, 5 groups => A total of 15 PD samples

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1 2 3 4 53 2

2 2 1

2 2 1

Results, Different strategies, Dose

Simultaneous

Time first

Dose first

Optimal doses

dose (mg)

Remember: 1 dose/group, 5 groups => A total of 5 different doses

FIM

3.764e+32

4.967e+32

4.204e+32

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dose (mg)PD

sam

ple

time

(h)

Results, Dose vs. PD Sample(1 group)

FIMFIM

PD sample time (h) 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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1 group 2 groups 3 groups 4 groups 5 groups50

60

70

80

90

100

Dose firstTime first

Results, Strategies, Difference

Change in |FIM| in % compared to simultaneous optimization (Difference)

(design)(simultaneous)FIM

DIFFFIM

Diffe

renc

e (%

)

14

1 group 2 groups 3 groups 4 groups 5 groups94

95

96

97

98

99

100

Dose firstTime first

Results, Strategies, Efficiency

where p = number of parameters

Efficiency in % of different strategies

1/

1/

(design)

(simultanoeus)

p

p

FIMEFF

FIM

Efficie

ncy

(%)

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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