Optimal dose & sample-size selection for dose-response studies
P. Johnson (1), H. Dai (2), S. Neelakantan (2), T. Tensfeldt (2)
(1) Pfizer, Sandwich, U.K.; (2) Pfizer, Groton, U.S.
Objectives: In addition to demonstrating safety, one of the main aims of Phase 2 is to characterise dose-response. When designing such studies, important design factors are dose-selection and sample size. Prior information (pre-clinical and/or clinical) may permit the development of a model describing the dose-response expectation and uncertainty. Theory and software for computing D-optimal design are available and, along with the model, aid in choice of dose and sample size selection. In practice, some optimal solutions are unrealistic given the normal constraint of a limited number of dosing options. Using a modified version of PFIM 1.2 [1], the aim of this presentation is to discuss an iterative approach to discriminate between possible dosing and sample size options and derive a final solution that is robust to model uncertainty.
Methods: Motivated by an internal drug development project at Pfizer, an EMAX dose-response model with random effect on EMAX and normal additive error was assumed. A grid of dosing options was created, derived from all permutations of 12 dosing strengths. The efficiency (criterion of the Fisher information matrix) for each dosing option was estimated using a modified version of PFIM 1.2 [1]. The higher the criterion the more efficient the dosing option. The influence of sample-size was investigated using the same approach with the parameters standard error as the measure for discrimination. The influence of model uncertainty was considered using the same approach iteratively on sampled parameter estimates from the model (non-parametric bootstrap). Details of which will be discussed during the presentation.
Results: Dosing option 1, 2, 50 and 70 mg was recommended. This was selected as it offered near optimal efficiency based on the model expectation and most robust to model uncertainty. As expected, parameter standard errors decreased with increasing sample size. This decrease tended to plateau at 50-55 subjects per group indicating little benefit of increased sample size. This was confirmed by simulation and a sample size of 55 subjects per group was recommended.
Conclusion: We have developed a practical tool to select the optimal dosing option from a range of possible dosing strengths and quickly investigate the influence of sample size. The speed of this tool enables the influence of model uncertainty to be considered and ensure that the final solution is truly robust.
References:
[1] Retout & Mentré. Optimisation of individual and population designs using Splus. Journal of Pharmacokinetics and Pharmacodynamics, 2003, 30(6): 417-443.