Directed walk designs for dose-response problems with competing failure modes

We examine adaptive allocation designs for the problem of determining the optimal therapeutic dose for subjects in early-phase clinical trials. A subject can fail due to lack of efficacy or due to a toxic reaction. Successful subjects will have both a positive response and no toxic side effects. Thus, we seek to maximize the product of the nontoxicity and efficacy dose-response curves. We are interested in sampling rules that perform well along several criteria, including the ethical criterion that, as often as possible, experimental subjects be treated at or close to the maximum in question. Statistically, we wish to identify the optimum dose with high probability at the close of the experiment. Here, we propose designs that combine new allocation policies, directed walks, with new smoothed shape-constrained curve-fitting techniques. These are compared with a variety of other curve-fitting techniques and with up-and-down and equal allocation rules.