Efficient randomized-adaptive designs

TL;DR

This paper introduces a new family of response-adaptive randomization procedures that are simple, attain optimal variance bounds, and are analyzed using stochastic process stopping times, with validation through examples and simulations.

Contribution

It proposes a novel class of response-adaptive designs with optimal variance properties, addressing nondifferentiability issues in asymptotic analysis.

Findings

Procedures attain Cramer--Rao lower bounds on allocation variances.

Discontinuous allocation probability functions are effectively analyzed.

Demonstrated effectiveness through simulations and comparisons.

Abstract

Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer--Rao lower bounds on the allocation variances for any allocation proportions, including optimal allocation proportions. The allocation probability functions of proposed procedures are discontinuous. The existing large sample theory for adaptive designs relies on Taylor expansions of the allocation probability functions, which do not apply to nondifferentiable cases. In the present paper, we study stopping times of stochastic processes to establish the asymptotic efficiency results. Furthermore, we demonstrate our proposal through examples, simulations and a discussion on the relationship with earlier works, including Efron's biased coin design.