Nonlinear regression models addressing both efficacy and toxicity outcomes
are increasingly used in dose-finding trials, such as in pharmaceutical drug
development. However, research on related experimental design problems for
corresponding active controlled trials is still scarce. In this paper we derive
optimal designs to estimate efficacy and toxicity in an active controlled
clinical dose finding trial when the bivariate continuous outcomes are modeled
either by polynomials up to degree 2, the Michaelis- Menten model, the Emax
model, or a combination thereof. We determine upper bounds on the number of
different doses levels required for the optimal design and provide conditions
under which the boundary points of the design space are included in the optimal
design. We also provide an analytical description of the minimally supported
D-optimal designs and show that they do not depend on the correlation between
the bivariate outcomes. We illustrate the proposed methods with numerical
examples and demonstrate the advantages of the D-optimal design for a trial,
which has recently been considered in the literature.Comment: Keywords and Phrases: Active controlled trials, dose finding, optimal
design, admissible design, Emax model, Equivalence theorem, Particle swarm
optimization, Tchebycheff syste