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

Abstract

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.

to Appear in The Annals of Statistics http://www.imstat.org/aos/future_papers.html, 27 pages + 18 Supplementary materials

References in corpus (12)

• Handling Covariates in the Design of Clinical Trials
• Asymptotic Properties of Covariate-Adjusted Adaptive Designs
• Asymptotic properties of covariate-adaptive randomization
• Asymptotics in randomized urn models
• Asymptotic theorems of sequential estimation-adjusted urn models
• Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn
• Generalized Urn Models of Evolutionary Processes
• Interacting generalized Friedman's urn systems
• Central Limit Theorems of a Recursive Stochastic Algorithm with Applications to Adaptive Designs
• Synchronization of Reinforced Stochastic Processes with a Network-based Interaction
• Multi-objective optimal designs in comparative clinical trials with covariates: The reinforced doubly adaptive biased coin design
• Nonparametric covariate-adjusted response-adaptive design based on a functional urn model

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