Selection of number of dose levels and its robustness for binary response data

Muller & Schmitt (1990) have considered the question of how to choose the number of doses for estimating the median effective dose (ED50) when a probit dose-response curve is correctly assumed. However, they restricted their investigation to designs with doses symmetrical about the true ED50. In this paper, we investigate how the conclusions of Muller & Schmitt may change as the dose designs become slightly asymmetric about the true ED50. In addition, we address the question of the robustness of the number of doses chosen for an incorrectly assumed logistic model, when the dose designs are asymmetric about the assumed ED50. The underlying true dose-response curves considered here include the probit, cubic logistic and Aranda- Ordaz asymmetric models. The simulation results show that, for various underlying true dose-response curves and the uniform design density with doses spaced asymmetrically around the assumed ED50, the choice of as many doses as possible is almost optimal. This agrees with the results obtained for a correctly assumed probit or logistic dose-response curve when the dose designs are symmetric or slightly asymmetric about the ED50.