1. Division of Pharmacokinetics and Drug Therapy Department of Pharmaceutical Biosciences Uppsala University Sweden 2007-06-15 Sequential versus Simultaneous Optimal Experimental Design on Dose and Sample times Joakim Nyberg Mats O. Karlsson and Andrew Hooker

2. 2 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?

3. 3 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

4. 4 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 the Fisher Information Matrix

5. 5 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.

6. 6 One-comp IV, direct effect E-max* ConcentrationEffect *Y. Hashimoto & L.B. Sheiner. Designs for population pharmacodynamics: value of pharmacokinetic data and population analysis. J. Pharmacokinetic. Biopharm: 1991. dose = 2.75 mg time (h) conc. (mg/L) effect dose = 2.75 mg

7. 7 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

8. 8 Results, Different strategies, PK Simultaneous Time first Dose first PK Sampling schedule time (h) Remember : 2 PK samples/group, 5 groups => A total of 10 PK samples

9. 9 Results, Different strategies, PD Simultaneous Time first Dose first PD Sampling schedule time (h) Remember : 3 PD samples/group, 5 groups => A total of 15 PD samples

10. 10 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 3.764e+32 4.967e+32 4.204e+32

11. 11 dose (mg) PD sample time (h) Results, Dose vs. PD Sample (1 group) PD sample time (h) dose (mg) Dose and sample times are correlated

12. 12 Results, Dose vs. Dose (2 groups) dose group 1 (mg) dose group 2 (mg)

13. 13 Results, Strategies, Difference Change in |FIM| in % compared to simultaneous optimization (Difference) Difference (%)

14. 14 Results, Strategies, Efficiency where p = number of parameters Efficiency in % of different strategies Efficiency (%)

15. 15 Conclusions It’s important to also optimize on dose in optimal design It’s always more efficient to optimize simultaneously compared to sequential optimization

16. 16 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

17. 17 Thank you