Power, Variability, and Optimality in Adaptive Designs

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Proposal ID: DMS-0204232PI: Feifang HuTitle: Power, variability, and optimality in adaptive designsAbstract:Adaptive designs use sequentially accruing data in allocation decisions to reach some objective. In this proposal, the objective is based on an optimization criterion, such as minimizing the cost of an experiment. The investigators use the power of a hypothesis test as a benchmark for comparisons of adaptive designs. They explicitly derive the relationship between power and the design in terms of bias of the target allocation from the actual allocation and variation induced by the design. For four classes of adaptive designs: urn models, sequential maximum likelihood procedures, doubly adaptive biased coin designs, and treatment effect mappings, the investigators will uniquely unify the theory for easy comparison based on power, optimality, and variability.Adaptive designs are useful in many scientific disciplines and have application in clinical research, industrial experiments, bioassay, to name a few areas. The idea is to dynamically use sequentially accruing data in decisions for collecting future data in order to satisfy some objective, which could be minimizing the cost of an experiment, maximizing expected treatment successes in a clinical trial, etc. The use of adaptive designs can improve efficiency of an experiment by incorporating current knowledge into design decisions. Heretofore what has been unknown is the relationship of variability of the adaptive designs to efficiency of the experiment. The investigators will develop guidelines that will allow direct comparison of efficiency of designs by exploring their variability. The grant will involve both undergraduate and graduate students across two campuses and will lead to increased understanding of how to efficiently design costly or ethically demanding experiments.