Optimal Designs for Estimating the Interesting Part of a Dose-Effect Curve

Abstract

We consider a dose-finding trial in phase IIB of drug development. For choosing an appropriate design for this trial the specification of two points is critical: an appropriate model for describing the dose-effect relationship, and the specification of the aims of the trial (objectives), which will be the focus in the present paper.

For many situations it is essential to have a robust trial objective that has little risk of changing during the complete trial due to external information. An important and realistic objective of a dose-finding trial is to obtain precise information about key parts of the dose-effect curve. We reflect this goal in a statistical optimality criterion and derive efficient designs using optimal design theory. In particular, we determine nonadaptive Bayesian optimal designs, i.e., designs which are not changed by information obtained from an interim analysis. Compared with a traditional balanced design for this trial, it is shown that the optimal design is substantially more efficient. This implies either a gain in information, or essential savings in sample size. Further, we investigate an adaptive Bayesian optimal design that uses different optimal designs before and after an interim analysis, and we compare the adaptive with the nonadaptive Bayesian optimal design. The basic concept is illustrated using a modification of a recent AstraZeneca trial.

Key Words:

• Adaptive design
• Bayesian design
• Clinical trial
• Dose-finding
• Optimal design

ACKNOWLEDGMENTS

We would like to thank Ulrika Wählby Hamrén and Matts Kågedal from the Clinical Pharmacology Department of AstraZeneca for their work in deriving the a priori knowledge, Wolfgang Bischoff (University of Eichstätt Ingolstadt) and Rolf Karlsten (Medical Science, AstraZeneca) for discussions and their important points of views and Tord Rikte (Statisticon, Uppsala) for his help with the simulation program. We thank also two unknown referees for their valuable comments. The work of H. Dette was supported in part by a NIH grant award IR01GM072876:01A1 and the Deutsche Forschungsgemeinschaft (SFB 475, “Komplexitätsreduktion in multivariaten Datenstrukturen,” Teilprojekt A2)