Dose finding designs for continuous responses and binary utility

Often in clinical trials the observed responses are continuous but a regulatory agency will approve the drug only if the probability is sufficiently large that the efficacy measure exceeds a predefined threshold and the toxicity does not exceed another given threshold. Thus the measure of interest (utility) is based on dichotomized responses. We consider normally distributed correlated responses and build a utility function using the probit transform. Locally optimal designs are used as benchmarks for more practical designs such as composite and adaptive designs. We focus on D-criterion (i.e., all parameters of the dose-response model are of interest) and consider only two-stage designs. It is shown that the practice of reporting dichotomized responses leads to a substantial loss in the precision of estimated parameters (or in the power loss).