Affiliations: [a] School of Medicine, University of Missouri-Columbia, Columbia, MO, USA | [b] Johnson and Johnson Medical Devices, Irvine, CA, USA
Corresponding author: Anqing Zhang, School of Medicine, University of Missouri-Columbia, 182B Galena Hall, Columbia, MO 65212, USA. Tel.: +1 573 882 9627; E-mail: [email protected].
Abstract: Under nonlinear models, optimal design truly depends on the pre-specified values of model parameter. If the nominal values of the parameter are not close to the true values, optimal designs become far from optimum. In this study, we focus on constructing an optimal design that works well for estimating multiple EDps taking into account the parameter uncertainty. To address the parameter dependency, an adaptive design technique is applied by incorporating Bayesian paradigm. One challenging task for the Bayesian approach is that it requires heavy computation when search for the Bayesian optimal design. To overcome this problem, a clustering method can be employed. We propose an adaptive Bayesian c-optimal design that works fairly well for estimating multiple values of EDp simultaneously, whilst accounting for the parameter uncertainty. We use the flexible 4-paramter logistic model to illustrate the methodology but our approach can be extended to other types of nonlinear models. We also examine the performance of our proposed design by comparing with other traditional designs through different scenarios of simulations given a wide range of mis-specified model parameters.