Isotonic designs for phase I trials

The purpose of a phase I trial in cancer is to determine the level (dose) of the treatment under study that has an acceptable level of adverse effects. Although substantial progress has recently been made in this area using parametric approaches, the method that is widely used is based on treating small cohorts of patients at escalating doses until the frequency of toxicities seen at a dose exceeds a predefined tolerable toxicity rate. This method is popular because of its simplicity and freedom from parametric assumptions. In this payer, we consider cases in which it is undesirable to assume a parametric dose-toxicity relationship. We propose a simple model-free approach by modifying the method that is in common use. The approach assumes toxicity is nondecreasing with dose and fits an isotonic regression to accumulated data. At any point in a trial, the dose given is that with estimated toxicity deemed closest to the maximum tolerable toxicity. Simulations indicate that this approach performs substantially better than the commonly used method and it compares favorably with other phase I designs.