Optimal design for dose-finding studies

Abstract

One of the most complex tasks during the clinical development of a new drug is to find a correct dose. Optimal experimental design has as a goal to find the best ways to perform an experiment considering the available resources and the statistical model. Optimal designs have already been used to determine the design of dose-finding studies.  In this thesis, optimal designs are considered for the simultaneous response of efficacy and safety in a bivariate model, for the drug combination trials, and for general regression problems, including but not limited to dose-finding analysis.

The thesis consists of four papers:  In Paper I, the dose that maximizes the clinical utility index based on an efficacy-safety Emax model gives us the desirable balance between effects and side effects. In order to make use of a symmetry property, we use a log-transformed dose scale. The geometric characterization of the multivariate Elfving method is used to derive c-optimal points and weights for arbitrary c-vectors.  The second paper is an extension of the first one.  We still use the log-transformed dose scale bivariate model and consider now also the placebo effect and side-effect.  Fedorov’s exchange algorithm is applied in order to derive locally D-optimal designs numerically.