Optimal Designs for Contingent Response Models

We study D and c optimal designs for the contingent response models of Li, Durham and Flournoy [LDF95]. In the contingent response model there are two types of failure. We call one failure type toxicity and the other disease failure. No toxicity and no disease failure is a success or cure. We assume disease failures are contingent on toxicity in that they can only be observed in the absence of toxicity. We also assume the probability of toxicity increases with the dose, and the probability of disease failure given no toxicity decreases with dose. Interest is in finding c-optimal designs for estimating the dose that maximizes the cure probability.