Optimal Designs for a Probit Model With a Quadratic Term

Abstract

This article studies optimal designs to analyze dose-response functions with a downturn. Two interesting challenges are estimating the entire dose-response curve and estimating the ED50. Here, I obtain and compare optimal designs for these objectives, separately and together in a two-stage design. I adopt a probit model with a quadratic term to describe the dose-response. Under the probit model, Yang's method is used to obtain the minimal number of support points that maximize any concave function of the Fisher information matrix. Optimal designs are obtained based on the minimal number of support points, and their efficiencies are compared.