Abstract
A semi-parametric stochastic ordering model (SPSO) is introduced to characterize functional relationships between dose level and the probabilities of binary Efficacy and Toxicity events. This model is used to implement a Bayesian adaptive phase I-II clinical trial using one of two different optimality criteria, either dose desirability defined as a function of the marginal Efficacy and Toxicity probabilities, or mean utility based on numerical scores of the four possible (Efficacy, Toxicity) events. A simulation study is conducted to compare designs using the SPSO model to the parametric EffTox model described in Thall and Cook, with each (model, optimality criterion) combination. Each of these four designs adaptively assigns patient cohorts to estimated optimal dose levels after restricting assignments to dose levels that are acceptably efficacious and safe. The simulation study shows that different design configurations may have superior performance depending on the assumed true dose-outcome scenario.