D optimal designs for three Poisson dose-response models

The objective of this paper was to find and investigate the performance of the D optimal designs for three Poisson dose-response models. Phase II dose ranging studies are pivotal in the drug development program, being used to select dose(s) for phase III. Count data is encountered in a number of clinical areas. The Poisson distribution provides an intuitive platform for modelling such data, especially when combined with random effects which allow subjects to differ in their response rates. This work investigated three Poisson dose-response models of increasing complexity. A simple E(max) model was used to describe the drug effect, and D optimal designs under a range of different parameter values (scenarios) were found. The relative performances between scenarios were assessed using: the precision of all parameters, the precision of the drug effect parameters, and the percent coefficient of variation (%CV) of the ED(50) parameter. The results showed that the D optimal designs were similar across models and scenarios, with the D optimal designs consisting of placebo, the maximum dose, and a dose just below the ED(50). However the relative performance of the optimal designs was very different. For example, with 1,000 subjects, the %CV of the ED(50) parameter ranged from 1.4 to 91 %. Performance typically improved with higher baseline counts, smaller random effects, and larger E(max). This work introduces a framework for determining and evaluating the performance of D optimal designs for phase II dose ranging studies with count data as the primary endpoint.