Power, Variability, and Optimality in Adaptive Designs

摘要：自适应设计在分配决策中使用顺序累积的数据来达到某个目标。在这个建议中，目标是基于一个优化准则，如最小化一个实验的成本。研究人员使用假设检验的力量作为比较适应性设计的基准。他们从实际分配和设计引起的变化中明确推导出功率与设计之间的关系，即目标分配的偏差。对于四类自适应设计：瓮模型、顺序最大似然程序、双重自适应偏置硬币设计和治疗效果映射，研究人员将独特地统一理论，以便基于功率、最优性和可变性进行比较。适应性设计在许多科学学科中都很有用，在临床研究、工业实验、生物测定等领域都有应用。这个想法是动态地在决策中使用顺序累积的数据来收集未来的数据，以满足某些目标，这可能是最小化实验成本，最大化临床试验中的预期治疗成功等。使用自适应设计可以通过将当前知识纳入设计决策来提高实验效率。迄今为止，尚不清楚的是自适应设计的可变性与实验效率的关系。研究人员将制定指导方针，允许通过探索其可变性来直接比较设计的效率。这项资助将涉及两个校区的本科生和研究生，并将加深对如何有效地设计昂贵或道德要求高的实验的理解。

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.