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297 activity is most likely. A design is presented that randomizes patients to either a phase II (P-II) component (consisting of several P-If trials of new agents) or a phase III (P-Ill) component (comparing a promising regimen with a standard). Upon disease progression, crossover from PII to P-III components, and from P-Ill to the most promising P-If agent, is allowed. There are a number of advantages to this design: the ability to test new drugs as first-line treatment, while addressing ethical concerns; internal control of the P-If trials; efficient use of patient resources; and efficient logistics of study conduct. Statistical considerations, such as sample size, power, and stratification, as well as clinical/ethical issues, are discussed.

Cost Minimization in Clinical Trials S t e v e n P i a n t a d o s i a n d Larry G. Kessler

Biometw, Branch, National Cancer Institute, National Institutes of Health, Bethesda, Ma~land (54) We consider some problems in minimizing the cost of a clinical trial while simultaneously satisfying the required statistical design features. Investigators can often control some aspects of a trial that affect cost such as accrual and follow-up duration, accrual rate, treatment of allocation ratios, or extent of medical evaluation prior to entry. Other aspects of a trial may be fixed by scientific issues and are essentially constraints. For example, investigators might not wish to modify size and power requirements merely to lower cost. Cost-minimizing values for controllable parameters may be found, after mathematically modeling expenses over time, by minimizing the cost function with respect to one or more parameters, incorporating the statistical design equations as a constraint. Additional design constraints such as minimum patient-years of followup or maximum trial duration may be incorporated into the system of equations. This investigation focuses on the formulation of this problem using a previously defined cost model, simple methods for accomplishing the constrained minimization, and examples, including a breast cancer prevention trial currently budgeted at $100 million.

Enumeration of the Optimal Designs for a Grouped Sequential Trial with Binomial Outcome T. T h e r n e a u , S. W i e a n d , a n d M. C h a n g

Mayo Clinic, Rochester, Minnesota University of Florida, Gainesville, Florida (55) Consider a single-armed study that is to be conducted in a grouped sequential fashion, where each observation yields a 0-1 outcome. The number of stages and the accrual for each stage have been specified in advance, as have the two probabilities p~ and p2 that define cx and 13: c~ = prob (reject/p2). Such trials are common in cancer chemotherapy to obtain an estimate of the response probability of a new agent. Logistical considerations limit the number of stages to two or three and total accrual is limited to 30-40 patients. A given design is optimal if for particular a and [3 it minimizes the expected sample size. We show by a geometric argument that the set of optimal designs (as cx and ~ vary) corresponds to tiling of the triangle (x ~ 0, y ~ 0, x + y <~ 1] with convex polygons, one region for each design. Enumeration is accomplished by an orderly traversal of this polygon "map."

Optimal Restricted Two-Stage Designs L. D o u g l a s Case, T i m o t h y M. M o r g a n , a n d C.E. Davis

Center [or Prevention Research and Biometry Bowman Gray School of Medicine, Winston-Salem, North Carolina (56) A feature of most group sequential designs is that the critical value at the final stage does not equal the critical value corresponding to a fixed sample design. This can lead to confusion when a seemingly significant sample statistic at the final stage fails to reject the null hypothesis. Twostage designs are presented that allow acceptance, rejection, or continuation at the first stage while retaining the fixed sample critical value at the second stage. The designs are optimized under this restriction to minimize either the expected sample size under the null hypothesis, the expected sample size under the alternative hypothesis, or the maximum expected sample size. These restricted designs are almost fully efficient when compared to optimal unrestricted twostage designs. Additionally, one can interpret the hypothesis test at the final stage as though a fixed sample design had been used. Examples are given that illustrate the use of these restricted plans in the design and analysis of clinical trials.