A.C. Hooker, M. Dodds, and P. Vicini
Resource Facility for Population Kinetics, Department of Bioengineering, University of Washington, Seattle, Washington, USA
Objectives: Experimental pharmacokinetic-pharmacodynamic (PK-PD) data in the literature are commonly fit to population PK-PD models via simultaneous model fitting, where PK-PD parameters are all adjusted at the same time, based on both PK and PD measurements [4]. On the other hand, optimal design strategies are never computed using simultaneous population PK-PD models. Simplifications of the simultaneous population design approach are used, including: (a) sequential individual-based [2], (b) simultaneous individual-based [1], and (c) sequential population-based PK-PD design optimization [3]. One could argue that these designs are all, in some sense, sub-optimal, if the data is to be fit using a more complicated simultaneous population PK-PD model. The objective of this work was to compare standard optimal design practices with experimental designs that are computed in a manner consistent with the expected model fitting procedure. Specifically, we calculate simultaneous population D-optimal designs of PK-PD experiments and compare these designs via simulation to the simplified experimental designs based on approaches (a)-(c).
Methods: Taking published population PK-PD experiments, we compute simultaneous population D-optimal designs and D-optimal designs based on the simplified techniques (a)-(c). D-optimal designs are computed by minimizing the determinant of the inverse of the Fisher information matrix of model parameters with respect to the design variables (the sampling times). We then simulate numerous replicate experiments (using the assumed true parameter values) based on each D-optimal design. From this simulated data pool, we then simultaneously estimate population PK-PD model parameters. Then, we compare the parameter values, estimated conditionally on the above four designs, to the true parameter values via metrics such as percent bias and percent root mean square error.
Conclusions: Our preliminary results indicate that, even with many fewer samples per subject, population-based optimal designs will achieve similar or better parameter estimation accuracy compared to individually-based optimal designs. One main advantage of population-based optimal designs appears to be that the number of sampling times in the designs can be less than the number of fixed effects in the model (the theoretical limit in individually-based designs). However, in the limit of one sample per individual, the population D-optimal designs seem to be inadequate.
References:
[1] C. Cobelli, A. Ruggeri, J. J. Distefano III and E. M. Landaw. Optimal design of multioutput sampling schedules –- software and applications to endocrine-metabolic and pharmacokinetic models. IEEE Trans Biomed Eng., 32:249-56, 1985.
[2] Y. Hashimoto and L. B. Sheiner. Designs for population pharmacodynamics: value of pharmacokinetic data and population analysis. J. Pharmacokinet. Biopharm., 19:333–353, 1991.
[3] Y. Merl´e and M. Tod. Impact of pharmacokinetic-pharmacodynamic model linearization on the accuracy of population information matrix and optimal design. J. Pharmacokinet. Pharmacodyn., 28:363, 2001.
[4] C. Peck, R. Gieschke, and J. L. Steimer. Current status and future directions of PK/PD in drug discovery and development. In Measurement and kinetics of in vivo drug effects. Advances in simultaneous pharmacokinetic/pharmacodynamic modeling. Part 1., pages 1–7, 2002. M. Danhof, M. Karlsson and R. J. Powel editors.
Reference: PAGE 12 (2003) Abstr 455 [www.page-meeting.org/?abstract=455]
Poster: poster