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I. BACKGROUND

Clinical drug trials are categorized within phases I, II, and III. Phase I addresses side effects and such issues as drug metabolism. Phase II addresses the relationships between dose and effectiveness and between dose and side effects. Phase III consists of large, randomized trials comparing one or two doses of the experimental drug with placebo (if possible) and perhaps also with therapies known to be active.

In the standard type of phase II efficacy trial, patients are assigned to a dose from among those being considered (usually 4 to 12 in number). Assignment is random, usually with equal numbers of patients assigned to each dose. Based on the results of the trial, a decision is made to either enter phase III in the drug's development, stop the drug's development, or conduct another phase II trial.

Such a design is inefficient, in terms of both time and resources. If the drug is effective then the dose-response curve has a positive slope for some dose. The sloping part of the curve may be located at doses greater than or less than those considered in the trial. In either case many of the observations at the opposite end from where the greatest slope occurs may be wasted. If the sloping part of the curve is in the middle of the doses considered and if the slope is large (relative to the interval between doses) then observations at both ends of the range are wasted. The case in which the drug is ineffective is similar to that in which a positive slope occurs at doses larger than those considered in the trial, namely, most of the observations at lower doses are wasted. Moreover, even if the doses considered are judged to be appropriate in retrospect, the variability in the responses may be greater or less than originally anticipated. In the former case the sample size chosen was too small and in the latter case it was unnecessarily large. Therefore, a common retrospective view of trials with this type of design is that a different allocation to doses would have been more informative, or a different sample size would have been more appropriate.

II. DESCRIPTION

We have developed an innovative class of designs that we are introducing into practice. In this case study we will describe the designs, address difficulties in implementing them in actual clinical trials, and relay our experience with using them--including experience with the FDA and other regulatory agencies.

For simplicity, the description below considers "dose" to be one-dimensional. In practice it can be multidimensional and, for example, it could include dosing frequency and duration of administration. Our designs can be viewed as having two stages; the first involves dose finding and the second is confirmatory.

A. Dose Finding Stage

The first stage allows for a wide range and a large number of doses, including placebo. The purpose of this stage is to assess dose-response in an informative and efficient way. Assignment to dose is sequential, in the following sense. As patients are treated, they are followed and their responses are communicated to a central database. Doses are assigned to subsequent patients so as to obtain maximal and rapid information about the dose-response curve. As time passes, the "current" posterior distributions of the various parameters are updated (on a daily basis). The dose of the next patient is assigned centrally. The endpoint of interest is response at a fixed number N of days following treatment. In our calculational procedure we impute missing N-day responses using their predictive distributions given current responses and given assigned doses.

The next patient's dose depends on the currently available response information formalized in the posterior distribution of unknown parameters. But it also depends on the existence of the current "information bank." At any particular time, patients will have been assigned to various doses and will have responded only partially in the sense that their N-day outcome is not yet known. Such patients serve as a bank of information about the doses assigned. This information will become known gradually, with patients having maturing outcome data being replaced in the information bank with recently treated patients. Our assignment scheme takes into consideration the existence of and doses assigned to patients in this information bank.

The assignment algorithm used is complicated to describe. Roughly speaking, it starts with a wide range of doses and homes in on a narrower range as it learns about critical features of the dose-response curve. If this narrower range is the set of highest doses and the results are sufficiently poor then the algorithm recommends stopping the trial.

B. Confirmatory Stage

To qualify with regulatory agencies as a "pivotal" phase III trial, a large number of patients must be randomized to drug and placebo. As information accrues about dose-response from the dose-finding stage, if this information is suggestive that the drug is effective then the assignment procedure shifts to a confirmatory stage. Two doses will be identified based on the dose-response information and patients will be randomized to these two doses and placebo in a balanced fashion. The shift will be seamless and not recognizable by physicians and others involved in the trial (except for members of the trial's data and safety monitoring committee).

The timing of the shift from dose-finding to pivotal is critical. Whether to shift will be based on a Bayesian decision analysis using forward simulation and dynamic programming. A decision to shift will depend on the available information about dose-response, the costs of entering additional patients, and the requirements of the FDA and other regulatory agencies concerning information needed for eventual marketing approval of the drug. Although the design and the determination of the sample size of the pivotal stage is Bayesian, but the decision analysis recognizes the need to provide regulatory agencies with a frequentist analysis of the trial results.

III. BENEFITS AND POTENTIAL IMPACT

Our efficient dose assignment scheme more accurately identifies effective drugs and it more accurately identifies ineffective drugs. Moreover, efficient dose assignment can significantly shorten a drug's clinical development. First, the number of patients in a sequential trial will usually be substantially smaller than when using standard designs. This has important economical and ethical implications. Second, a seamless transition between the dose-finding and confirmatory stages eliminates the time required to set up a second trial.

The performance of a sequential design is enhanced by rapid transmittal of information. Our formal use of probability modeling in the dose finding phase allows the use of early, partial information and does not require waiting for a full N days to observe the final response.

We will consider a particular class of drugs. However, the problem we address and our solution applies to all classes of drugs. Therefore, the impact of our design is potentially far reaching. And it suggests that our presentation will attract attendees from throughout the pharmaceutical industry.