T. Waterhouse (1), J. Eccleston (1), S. Duffull (2)
(1) School of Physical Sciences, University of Queensland, Australia; (2) School of Pharmacy, University of Queensland, Australia
Introduction: The use of theoretical techniques for developing optimal designs for PKPD experiments has received some treatment in the pharmacology literature. Most of the work has been oriented toward designs that optimise the estimation of parameters for a specified, usually non-linear, model. A generalisation of this work has lead to the development of compound criteria for optimising designs for 2 or more proposed models [1]. In addition, criteria for discrimination between competing models has also been proposed [2] but has received very little treatment in the pharmacology literature.
Objective: To investigate the utility of various criteria for optimising designs for parameter estimation and model discrimination for a number of competing models.
Methods: The D-optimality criterion (det(I), where I is the information matrix) was used for assessing designs with respect to parameter estimation of a single model; a compound criterion (det(IM1)1/p1 x det(IM2)1/p2, where IM1 is the information matrix for model 1 and p1 is the number of parameters for model 1) was used for assessing designs for 2 or more models; and T-optimality for discrimination between models. The current work pertains to two competing PD models, the linear model and the Emax model. Four general methods for combining multiple criteria are assessed.
- Maximise the compound criterion as defined above.
- A sequential method, where the T-optimal design points are computed initially and then the compound D-optimal design points estimated conditional on the T-optimal design.
- A joint criterion was developed that is the combination of the T-optimal and compound D-optimal criteria.
- Simulated annealing is used to determine a class of designs that optimise all three criterion independently and simultaneously [3].
Results: The table below shows the marginal efficiencies of each design in terms of the linear model, the Emax model and model discrimination. A design which is optimal in terms of each of the 3 criteria does not exist. However, there is a small class of designs produced by method 4 which is at least 65% efficient in terms of the linear model, at least 90% efficient in terms of the Emax model, and least 85% efficient for the T-optimal criterion. This class of designs includes those found in the 3 previous methods.
| Method | Efficiency | ||
|---|---|---|---|
| Linear | Emax | T-optimality | |
| 1 | 67% | 100% | 86% |
| 2 | 68% | 92% | 90% |
| 3 | 68% | 98% | 89% |
| 4 | >65% | >90% | >85% |
Conclusion: The methods presented here offer an opportunity for experimenters to design experiments which are efficient with respect to parameter estimation and model discrimination over two and potentially more, competing models. This research is ongoing with investigations of joint criteria and modifications, and the consideration of more than two competing models.
References:
[1] Walter, E. and Pronzato, L. (1997) Identification of Parametric Models. (Transl. John Norton) Chapter 6: Experiments. Springer, Masson, London.
[2] Atkinson, A.C. and Fedorov, V.V. (1975) The design of experiments for discriminating between two rival models. Biometrika 62(1):57-50.
[3] Eccleston, J. A. and Whitaker, D. (1999) Optimal change-over experiments using multi-objective simulated annealing. Statistics and Computing 9:37-42.
Reference: PAGE 12 () Abstr 423 [www.page-meeting.org/?abstract=423]
Poster: poster