Optimal Adaptive Randomized Designs for Clinical Trials

• Activity Number: 204
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Yi Cheng*+ and Donald A. Berry
• Companies: Indiana University South Bend and University of Texas
• Keywords: backward induction ; decision theory ; randomized sequential allocation ; optimal strategy ; balanced design ; multiple arms

Abstract

We introduce an optimal adaptive design for a fully sequential randomized clinical trial with k arms.The design is under the constraint that for each allocation, each arm has at least probability of r to be chosen, 0< = r < = 1/k. The corresponding optimal allocation strategy is called r-optimal. A design without such a constraint is the special case r=0, and a balanced design is the special case r=1/k. The optimization criterion is to maximize the expected overall utility in a Bayesian theoretical approach, where this is the sum over individual patient utilities. We prove analytically that there exists an optimal design such that at each allocation time, it assigns the subject to one of the arms with probability 1-(k-1)r, and the rest with probability r. We also show that the balanced design is asymptotically r-optimal for any given r, 0< = r < =1/k, which implies that r-optimal design is asymptotically 0-optimal. Numerical computation is formulated by backward induction. Our numerical studies show that, in general, this asymptotic optimality feature for r-optimal design can be accomplished with moderate trial size n if patient horizon N is large enough relative to n.