Optimal dose-finding designs with correlated continuous and discrete responses

In dose-finding clinical studies, it is common that multiple endpoints are of interest. For instance, in phase I/II studies, efficacy and toxicity are often the primary endpoints, which are observed simultaneously and which need to be evaluated together. Motivated by this, we confine ourselves to bivariate responses and focus on the most analytically difficult case: a mixture of continuous and categorical responses. We adopt the bivariate probit dose-response model and quantify our goal by a utility function. We study locally optimal designs, two-stage optimal designs, and fully adaptive designs under different ethical and cost constraints in the experiments. We assess the performance of two-stage designs and fully adaptive designs via simulations. Our simulations suggest that the two-stage designs are as efficient as and may be more efficient than the fully adaptive designs if there is a moderate sample size in the initial stage. In addition, two-stage designs are easier to construct and implement and thus can be a useful approach in practice.