Optimal Designs for Binary Logistic Regression with a Qualitative Classifier with Independent Levels

Abstract

Dose response studies arise in many medical applications. Often, such studies are considered within the framework of binary-response experiments such as success-failure. In such cases, popular choices for modeling the probability of response are logistic or probit models. Design optimality has been well studied for the logistic model with a continuous covariate. A natural extension of the logistic model is to consider the presence of a qualitative classifier. In this work, we explore D-, A-, and E-optimal designs in a two-parameter, binary logistic regression model after introducing a binary, qualitative classifier with independent levels.

Keywords:

• A-optimality
• D-optimality
• E-optimality
• Information matrix
• Qualitative classifier

Mathematics Subject Classification:

• 62K05
• 02-04

Acknowledgment

The authors would like to thank the Associate Editor and two referees for their insightful comments which helped improve the draft immensely. The first author would also like to acknowledge the Department of Mathematics, Statistics and Philosophy at the University of Tampere, Finland for their support, where much of this work was completed during her academic visit.