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. 

Optimal experimental design for dose-finding studies often focuses on one drug only. Paper III calculates D-optimal designs for the efficacy Emax model of two drugs that might interact. Three conditions can occur in drug combination trials. When there is a positive interaction, we deal with synergy; when it is negative, we have antagonism; and when the interaction is zero, it is called additivity.

Finally, in Paper IV, we present a low dimensional regression model with a distortion term. The distortion term, which in our case is a stochastic process, contributes to the regression. Thus, we estimate the combined model, which is a mixed effect model. Optimal designs for this model are derived by applying the Fedorov Algorithm.