Efficient randomized-adaptive designs

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.

Randomized Trial of Four Financial-Incentive Programs for Smoking Cessation

“…Randomization was stratified according to two dichotomous variables: whether participants had full health care benefits through CVS Caremark and whether their annual household income was at least $60,000 (the CVS Caremark workforce median) or less than $60,000. We developed an adaptive randomization algorithm [23][24][25][26] that updated the assignment probabilities to the five groups after every third enrolled participant. Updated probabilities reflected the inverse of the proportion of participants assigned to that group who accepted the intervention, relative to total acceptance across groups.…”

Higher Order Response-Adaptive Urn Designs for Clinical Trials with Highly Successful Treatments

“…In this section we compare the new urn designs with the doubly adaptive biased coin design (Hu and Zhang, 2004) and the efficient randomized adaptive design (Hu, Zhang and He, 2009). …”

“…This can result in observing more failures in the trial than under equal allocation, therefore defeating the purpose of a response adaptive design to reduce the average number of failures in the trial. Other response adaptive designs such as doubly adaptive biased coin designs (Eisele, 1994; Hu and Zhang, 2004), and the efficient randomized adaptive design (ERADE) (Hu, Zhang and He, 2009) can target any desired allocation including the allocation that maximizes power.…”

“…The variability of the allocation proportion depends on the type of allocation procedure as well as on the allocation that the design targets and the amount of randomness it provides. The urn design of Ivanova (2003) yields the lowest variability as it achieves the lower bound of the asymptotic variance of the allocation proportion (Rosenberger and Hu, 2003; Hu, Rosenberger and Zhang, 2006), so does the ERADE (Hu, Zhang and He, 2009). The doubly adaptive coin design achieves the lower bound only when the procedure is deterministic (Rosenberger and Hu, 2003).…”

A new family of covariate-adjusted response adaptive designs and their properties

“…A response-adaptive design that attains this lower bound will be said to be first order efficient. More recently, Hu, Zhang and He [9] proposed a new family of efficient randomized adaptive designs that can adapt to any desired allocation proportion. But all these studies are limited to the designs that do not incorporate covariates.…”