Adaptive Designs to Maximize Power in Clinical Trials with Multiple Treatments

Abstract

We consider a clinical trial with three competing treatments and study designs that allocate subjects sequentially in order to maximize the power of relevant tests. Two different criteria are considered: the first is to find the best treatment and the second is to order all three. The power converges to one in an exponential rate and we find the optimal allocation that maximizes this rate by large deviation theory. For the first criterion the optimal allocation has the plausible property that it assigns a small fraction of subjects to the inferior treatment. The optimal allocation depends heavily on the unknown parameters and, therefore, in order to implement it, a sequential adaptive scheme is considered. At each stage of the trial the parameters are estimated and the next subject is allocated according to the estimated optimal allocation. We study the asymptotic properties of this design by large deviations theory and the small sample behavior by simulations. Our results demonstrate that, unlike the two-treatments case, adaptive design can provide significant improvement in power.

Keywords:

• Adaptive designs
• Clinical trials
• Large deviations
• Optimal allocation
• Power maximization

Subject Classifications:

• 62K05
• 62L05
• 60F10

ACKNOWLEDGMENT

We thank the Editor, an Associate Editor, and two referees for reading the article and suggesting improvements.

Notes

Recommended by William F. Rosenberger