Optimal designs for dose response curves with common parameters

TL;DR

This paper develops optimal design strategies for comparing dose response curves in clinical trials when models share common parameters, providing explicit solutions and conditions for optimality.

Contribution

It introduces new optimal design methods for models with shared parameters, including explicit formulas and bounds for support points.

Findings

Derived upper bounds on support points for admissible designs.

Explicit $D$-optimal designs for common-parameter dose response models.

Identified minimally supported designs under shared location and scale parameters.

Abstract

A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in the administration frequency (but not in the sort of drug) a reasonable assumption is that the regression models for the different treatments share common parameters. This paper develops optimal design theory for the comparison of different regression models with common parameters. We derive upper bounds on the number of support points of admissible designs, and explicit expressions for $D$-optimal designs are derived for frequently used dose response models with a common location parameter. If the location and scale parameter in the different models coincide, minimally supported designs are determined and sufficient conditions for their optimality in the class of all designs derived. The results are illustrated in a dose-finding study comparing monthly and weekly administration.