In this chapter we tackle “early phase” problems, specifically those associated with phase I trials for safety and appropriate dosing of a new treatment. Representing the first application of a new drug to humans, early phase trials are typically small – say, 20 to 50 patients. The main goal in the early phases is to establish the safety of a proposed drug, and to study what the body does to the drug as it moves through the body (pharmacokinetics), and what the drug in turn does to the body (pharmacodynamics). Determining an appropriate dosing schedule for a drug, or dose-finding, is a major component of phase I studies. For relatively nontoxic agents, phase I trials may start with healthy volunteers. For agents with known toxicity, such as cytotoxic agents in cancer therapy, phase I trials are conducted among cancer patients for whom standard therapies have failed. We will use drug development in cancer therapy as our main example in this and subsequent chapters to demonstrate the application of adaptive Bayesian methods, but stress that the methods are equally applicable in a wide variety of non-cancer drug and device settings. For developing a cytotoxic agent, the highest possible dose is sought,

since the benefit of the new treatment is believed to increase with dose. Unfortunately, the severity of toxicity is also expected to increase with dose, so the challenge is to increase the dose without causing an unacceptable amount of toxicity in the patients. Thus the primary goal of a phase I study is to identify this dose, the maximum tolerated dose (MTD) in a dose-escalation fashion. Key elements of phase I studies include (a) defining the starting dose, (b)

defining the toxicity profile and dose-limiting toxicity (DLT), (c) defining an acceptable level of toxicity, the target toxicity level (TTL), and (d) defining a dose escalation scheme. For the first study in humans, the starting dose is often chosen as one tenth of the LD10 (a lethal dose for 10% of the animals) in mice, or one third of the lowest toxic dose in dogs, as these doses have been shown to be safe in humans for cytotoxic agents (Collins et al., 1986). While starting with a safe and low dose is important, investigators must balance the risk of toxicity with the risk of treating patients with drugs at ineffective doses. For most drugs, we assume that as the dose increases,

the probability of toxicity and the probability of efficacy will both increase. Hence, the goal is to define the MTD or the recommended phase II dose (RP2D) which yields an acceptable TTL – typically between 20% and 33%. The dose escalation scheme contains three components: (i) a dose in-

crement, (ii) a dose assignment, and (iii) a cohort size. Many studies use pre-determined dose increments at fixed doses, such as 10 mg, 20 mg, 30 mg, and so on. Alternatively, we may specify a general scheme for setting the doses, such as doubling the current dose when no toxicities are observed, reducing to a 50% dose increment when non-dose-limiting toxicities are observed, and reducing to a 25% dose increment when a DLT is observed. In the examples of this chapter, we assume that all the dose levels are specified in advance. We also generally assume that new patients are treated in cohorts of a prespecified size (say, 1, 3, or 6). Dose assignment refers to how to new patients enrolled in the trial are

assigned to dose levels. Based on dose assignment, phase I trials can be classified into rule-based methods and model-based methods. The next two sections consider each of these broad areas in turn.