Optimal designs for active controlled dose finding trials with efficacy-toxicity outcomes
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Date
2016
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Abstract
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.
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Keywords
Active controlled trials, Tchebycheff system, Particle swarm optimization, Equivalence theorem, Emax model, admissible design, optimal design, dose finding