Optimal designs for estimating the interesting part of a dose-effect curve

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 modi. cation of a recent AstraZeneca trial.