Quentin F. Stout
University of Michigan
Abstract: We consider response adaptive designs for problems involving multiple conflicting goals. The often referenced clinical trial dilemma of trying to determine the better of two independent Bernoulli populations while simultaneously increasing successful results during the trial is used. In evaluating the continuum of performance tradeoffs between the two objectives it is shown that only minor decreases in the efficiencies of the objectives are needed to obtain nearly optimal performance on both.
A Bayesian model is used and the analysis is carried out by combining both objectives into a single objective function and using dynamic programming to optimize the result. By varying the relative weights of the objectives one can see the entire range of optimal tradeoffs possible. A number of ad hoc approaches are also evaluated and it is shown that among these approaches a modified 2-armed bandit strategy exhibits the best behavior when it comes to balancing these objectives. Pointwise examinations of the operating characteristics of all designs are also considered.
Keywords: response adaptive sampling design, sequential allocation, controlled clinical trial, optimal tradeoff, Gittins index, multiple objectives, design of experiments, bandit problem, dynamic programming.
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