STATISTICS IN MEDICINE, VOL. 11, 1377-1389 (1992) BAYESIAN METHODS FOR PHASE I CLINICAL TRIALS zy CONSTANTINE GATSONIS zyxw Department zyxwvutsrqp of Biostatbtics. Harvard School zyxwvuts of Public Health, 677 Huntington Avenue, Boston, M A 0211S, U.S.A. AND JOEL B. GREENHOUSE Department of Statistics, Carnegie Mellon University, Pittsburgh. PA 15213, U.S.A. SUMMARY Phase I clinical trials are conducted to determine the dose-response curve of a new drug with respect to toxic side effects and, in particular, to estimate the maximum tolerated dose (MTD). In this paper we take a Bayesian approach to the problem of making inferences about the MTD. Working with broad classes of priors, we obtain the posterior distribution of the MTD and study its properties. We also address the question of providing updated assessments of the risk of toxicity for new patients entering the study at a specific dose level. These assessments would be useful in deciding issues of study management and ethics. Our analysis pays particular attention to the sensitivity of the inferences and risk assessments to the choice of prior and the choice of model for the dose-response relationship. 1. INTRODUCTION Before conducting a randomized controlled clinical trial to evaluate the efficacy of a new drug, it is necessary to determine the dose levels of the drug that are safe to administer to humans. Such a study is known as a phase I clinical trial. Although information about the drug’s efficacy is often available from a phase I trial, the main purpose of such a study is to estimate the dose-response curve of the new drug with respect to toxic side effects and, in particular, to estimate the maximum tolerated dose (MTD).’ zyxwvu - ’ Until recently, statistical considerations have been mostly absent from the design, analysis and reporting of these studies. In fact, 1981 FDA guidelines state that statistical considerations may not be necessary for phase I trials.2 Nevertheless, phase I trials pose challenging problems for inference about the MTD, for the ethical conduct of these studies, and for the efficient design of these studies, all of which have important statistical content. No unique standard design is used in phase I studies. However, an example of a typical phase I trial of cancer treatment is as follows. Patients are entered into a trial in groups of fixed size (usually 3) and are administered a dose of the drug. If none of the patients in the first group has a toxic response then the next set of patients receives a higher dose, and so on. When a prespeci- fied number of patients (oftenjust one) at a given dose level has a toxic response, another group of patients is entered at the same dose. If at least one patient has a toxic response in this new group the trial is stopped. The MTD is often estimated as the penultimate dose. The starting dose in a phase I trial is usually determined from an estimate of the dose-response curve for mortality obtained from animal s t u d i e ~ . ~ A common plan for dose escalations is to increase the dose by multiples according to a ‘modified Fibonacci sequence’, such as the sequence 1, 2, 3, 5, 7,9, 12, 16.I.j zyxwvuts 02774715/92/101377-13$11.50 Received August 1991 zy 0 1992 by John Wiley & Sons, Ltd. Revised January 1992