The Annals of Statistics

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

Giacomo Aletti, Andrea Ghiglietti, and William F. Rosenberger

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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.

Article information

Ann. Statist., Volume 46, Number 6B (2018), 3838-3866.

Received: June 2017
Revised: November 2017
First available in Project Euclid: 11 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62L20: Stochastic approximation 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory 62L05: Sequential design
Secondary: 62F12: Asymptotic properties of estimators 62P10: Applications to biology and medical sciences

Clinical trials covariate-adjusted analysis inference large sample theory personalized medicine randomization


Aletti, Giacomo; Ghiglietti, Andrea; Rosenberger, William F. Nonparametric covariate-adjusted response-adaptive design based on a functional urn model. Ann. Statist. 46 (2018), no. 6B, 3838--3866. doi:10.1214/17-AOS1677.

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Supplemental materials

  • Online supplementary materials: Nonparametric covariate-adjusted response-adaptive design based on a functional urn model. This supplement gives the analytic expressions used in the paper and the proofs of the theorems.