Nonparametric covariate-adjusted response-adaptive design based on a functional urn model
提出一类基于新函数瓮模型的协变量调整响应自适应设计，证明了瓮比例和治疗组分配比例的强相合性，并建立了联合中心极限定理，可用于推断条件响应分布。
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.