Nonparametric covariate-adjusted response-adaptive design based on a functional urn model

摘要

In this paper we propose a general class of covariate-adjustedresponse-adaptive (CARA) designs based on a new functional urn model. We provestrong consistency concerning the functional urn proportion and the proportionof subjects assigned to the treatment groups, in the whole study and for eachcovariate profile, allowing the distribution of the responses conditioned oncovariates to be estimated nonparametrically. In addition, we establish jointcentral limit theorems for the above quantities and the sufficient statisticsof features of interest, which allow to construct procedures to make inferenceon the conditional response distributions. These results are then applied totypical situations concerning Gaussian and binary responses.