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

TL;DR

This paper introduces a flexible covariate-adjusted response-adaptive design using a novel functional urn model, enabling nonparametric estimation and inference of response distributions conditioned on covariates.

Contribution

It develops a new functional urn model for covariate-adjusted response-adaptive designs with proven consistency and asymptotic normality, allowing nonparametric response distribution estimation.

Findings

Proves strong consistency of the urn proportion and treatment assignment.

Establishes joint central limit theorems for key quantities.

Applies results to Gaussian and binary response scenarios.

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.