Asymptotic properties of doubly adaptive biased coin designs for multitreatment clinical trials

Abstract

A general doubly adaptive biased coin design is proposed for the allocation of subjects to K treatments in a clinical trial. This design follows the same spirit as Efron's biased coin design and applies to the cases where the desired allocation proportions are unknown, but estimated sequentially. Strong consistency, a law of the iterated logarithm and asymptotic normality of this design are obtained under some widely satisfied conditions. For two treatments, a new family of designs is proposed and shown to be less variable than both the randomized play-the-winner rule and the adaptive randomized design. Also the proposed design tends toward a randomization scheme (with a fixed target proportion) as the size of the experiment increases.

Response-adaptive treatment allocation for clinical studies with ordinal responses

“…Among the various classes of response-adaptive design, DBCD, which was first proposed by Eisele, 28 is considered to be superior to many other procedures. 19,29,30 Desirable optimal criteria can be incorporated into the DBCD, and treatment allocations converge to the pre-specified targets. The mechanism to implement treatment randomization with DBCD is given in the following subsection.…”

“…Using the treatment allocation procedure in Hu and Zhang, 19 the allocation function for treatment 1 in the second step is where τ≥0 is a tuning parameter that has a negative association with the level of randomness of the treatment allocation process, with a maximum degree of randomness when τ = 0. The recommended range for τ is between 2 and 4, striking a balance between too much variability (τ<2), which slows the speed for the allocation proportion to converge to the desire allocation target, and too little variability (τ>4), which increases predictability, which could in turn induce an undesirable selection bias.…”

“…Asymptotic variance of allocation proportion for the latent Weibull model Let the variance of the allocation proportion of treatment 1 be σn1/n 2. According to Hu and Zhang, 19 asymptotically, where σρ^ 2 is the variance of ρ^. Let ω=(ω1',ω2')'.…”

“…The primary objective of this paper is to introduce a response-adaptive treatment allocation scheme that can be applied to compare treatments with ordinal responses. Of the various types of available response-adaptive designs, the doubly adaptive biased coin design (DBCD) proposed by Hu and Zhang 19 has two important features. First, it enables the inclusion of pre-specified targets, such as the treatment of fewer patients with the inferior treatment.…”

Maximizing power and minimizing treatment failures in clinical trials

“…However, the choice of an appropriate distance function has not been clear. Hu and Zhang [13] developed an appropriate function, which we now describe.…”