Implementing optimal allocation in sequential binary response experiments

• 成果类型: Article
• 署名作者: Tymofyeyev, Yevgen; Rosenberger, William F.; Hu, Feifang
• 署名单位: Merck & Company; Merck & Company USA; George Mason University; University of Virginia; University of Virginia
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214506000000906
• 发表日期: 2007
• 页码: 224-234
• 关键词: tests; POWER

摘要

For sequential experiments with K treatments, we establish two formal optimization criteria to find optimal allocation strategies. Both criteria involve the sample sizes on each treatment and a concave noncentrality parameter from a multivariate test. We show that these two criteria are equivalent. We apply this result to specific questions: (1) How do we maximize power of a multivariate test of homogeneity with binary response?, and (2) for fixed power, how do we minimize expected treatment failures? Because the solutions depend on unknown parameters, we describe a response-adaptive randomization procedure that targets the optimal allocation and provides increases in power along the lines of 2-4% over complete randomization for equal allocation. The increase in power contradicts the conclusions of other authors who have explored other randomization procedures for K = 2 and have found that the variability induced by randomization negates any benefit of targeting an optimal allocation.