Bayesian optimal designs for dose-response curves with common parameters

TL;DR

This paper develops Bayesian optimal design methods for dose-response clinical trials with models sharing parameters, providing robust and efficient designs for determining drug dose and frequency.

Contribution

It introduces approximate Bayesian D-optimal design theory for nonlinear models with common parameters, including analytical characterizations for key dose-response models.

Findings

Derived analytical forms of Bayesian D-optimal designs.

Showed robustness of Bayesian designs to parameter misspecification.

Numerical examples demonstrate design advantages.

Abstract

The issue of determining not only an adequate dose but also a dosing frequency of a drug arises frequently in Phase II clinical trials. This results in the comparison of models which have some parameters in common. Planning such studies based on Bayesian optimal designs offers robustness to our conclusions since these designs, unlike locally optimal designs, are efficient even if the parameters are misspecified. In this paper we develop approximate design theory for Bayesian $D$-optimality for nonlinear regression models with common parameters and investigate the cases of common location or common location and scale parameters separately. Analytical characterisations of saturated Bayesian $D$-optimal designs are derived for frequently used dose-response models and the advantages of our results are illustrated via a numerical investigation.