Power, Variability, and Optimality in Adaptive Designs

提案ID：DMS-0204232 PI：Feifang HuTitle：Power，Variability，and optimality in adaptive designsAbstract：自适应设计在分配决策中使用顺序累积数据以达到某些目标。 在这个提议中，目标是基于优化标准，例如最小化实验成本。 研究人员使用假设检验的力量作为自适应设计比较的基准。 他们明确地推导出功率和设计之间的关系，从实际分配和设计引起的变化的目标分配的偏差。 对于四类自适应设计：瓮模型，序贯最大似然程序，双自适应有偏硬币设计，和治疗效果映射，研究人员将唯一统一的理论，易于比较的基础上的权力，最优性，和variability.Adaptive设计是有用的，在许多科学学科和临床研究，工业实验，生物测定，仅举几个领域的应用。 我们的想法是动态地使用顺序累积数据的决策收集未来的数据，以满足一些目标，这可能是最小化的实验成本，最大限度地提高预期的治疗成功的临床试验等的自适应设计的使用，可以提高效率的实验，将当前的知识到设计决策。 因此，我们还不知道自适应设计的可变性与实验效率之间的关系。 研究人员将制定指导方针，通过探索其可变性来直接比较设计的效率。 该补助金将涉及两个校区的本科生和研究生，并将导致对如何有效设计昂贵或道德要求高的实验的理解增加。

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.