locally Optimal Design for Dose Finding Based on Bhattacharyya Matrix for Logistic Model

Abstract

Fisher information matrix which is used commonly for obtaining optimal designs in GLMs may cause
an inefficient optimal design due to poor estimation of the variance especially for small and moderate
sample size. In many cases, we are interested a function of parameters of model and the fisher information matrix cannot estimated the variance of these function as well as the parameters because the
curvature of the function and second derivatives of the likelihood is not considered here. In this point of
view, local optimal designs are also support minimally. Abdolbasit and Plocket (1983) discussed about
the robustness of minimally supported designs and showed that these designs are not robust against
the some initial values of parameters and don’t provide data for model assumption checking. In this
paper we proposed a new d-optimal criterion based on the Bhattacharyya matrix which considers the rth
derivate of the likelihood. A simple logistic model is considered as an example here. The local optimal
designs with three support points are obtained based on the proposed optimality criterion which lets the
researcher to check the model assumption in the GLM,s