ABSTRACT
One-parameter functions are predominantly used in the CRM literature to model the dose-toxicity relationship. An introduction on the use of one-parameter functions is in order-for two reasons. First, these functions are underparameterized and cannot be expected to produce a realistic fit on the entire dose range. Rather, they should be flexible enough to provide a reasonable approximation locally around the target dose. Second, the use of one-parameter models is not common in the other statistical areas, and modeling in the context of CRM is quite different from the conventional approach. This chapter presents a unified framework for CRM models. Section 4.2 introduces a class of dose-toxicity functions that includes the most commonly used CRM models. The required assumptions on a one-parameter CRM model are given in Section 4.3. Proof of the main result in this chapter is given in Section 4.4.
