NONPARAMETRIC COVARIATE-ADJUSTED RESPONSE-ADAPTIVE DESIGN BASED ON A FUNCTIONAL URN MODEL

• 成果类型: Article
• 署名作者: Aletti, Giacomo; Ghiglietti, Andrea; Rosenberger, William F.
• 署名单位: University of Milan; Catholic University of the Sacred Heart; George Mason University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1677
• 发表日期: 2018
• 页码: 3838-3866
• 关键词: randomly reinforced urn; controlled clinical-trial; central limit-theorems; biased-coin designs; play-winner rule; prognostic-factors; asymptotic properties; branching-processes; randomization; allocation

摘要

In this paper, we propose a general class of covariate-adjusted response adaptive (CARA) designs based on a new functional urn model. We prove strong consistency concerning the functional urn proportion and the proportion of subjects assigned to the treatment groups, in the whole study and for each covariate profile, allowing the distribution of the responses conditioned on covariates to be estimated nonparametrically. In addition, we establish joint central limit theorems for the above quantities and the sufficient statistics of features of interest, which allow to construct procedures to make inference on the conditional response distributions. These results are then applied to typical situations concerning Gaussian and binary responses.