ASYMPTOTICS IN RESPONSE-ADAPTIVE DESIGNS GENERATED BY A TWO-COLOR, RANDOMLY REINFORCED URN

• 成果类型: Article
• 署名作者: May, Caterina; Flournoy, Nancy
• 署名单位: University of Milan; University of Eastern Piedmont Amedeo Avogadro; University of Missouri System; University of Missouri Columbia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS596
• 发表日期: 2009
• 页码: 1058-1078
• 关键词: biased-coin designs; clinical-trials; THEOREMS; randomization; PROPORTION

摘要

This paper illustrates asymptotic properties for a response-adaptive design generated by a two-color, randomly reinforced urn model. The design considered is optimal in the sense that it assigns patients to the best treatment, with probability converging to one. An approach to show the joint asymptotic normality of the estimators of the mean responses to the treatments is provided in spite of the fact that allocation proportions converge to zero and one. Results on the rate of convergence of the number of patients assigned to each treatment are also obtained. Finally, we study the asymptotic behavior of a suitable test statistic.