Implementing Optimal Allocation in Sequential Binary Response Experiments

Tymofyeyev, Yevgen; Rosenberger, William F.; Hu, Feifang

doi:10.1198/016214506000000906

Cited by 108 publications

(118 citation statements)

References 15 publications

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“…Similarly, we substitute g ⋆ i (1) to g s i (1) and allow γ to vary in [δ ,1−δ ] only in (12), yielding another adaptive CAR treatment mechanism g a n (where the superscript a stands for aggressive). The same kind of δ -thresholding, which makes perfect sense from an applied point of view too, was already suggested in (Tymofyeyev et al, 2007).…”

Section: Strategymentioning

confidence: 81%

“…But we emphasize that there is nothing special about targeting the Neyman allocation, the whole methodology applying equally well to any choice of targeted treatment mechanism. To be more specific, we could also have chosen to target that treatment mechanism which minimizes the expected number of treatment failures subject to power constraint (the optimal allocation proposed by Rosenberger, Stallard, Ivanova, Harper, and Ricks (2001)), or any other treatment mechanism of interest (see for instance (Hu and Rosenberger, 2006, Chapter 2) or (Tymofyeyev, Rosenberger, and Hu, 2007)). Quoting James Hung of the FDA (about design adaptation in general-see (Hung, 2006)), our adaptive design meets clearly stated objectives, it is certainly a "more careful planning, not sloppy planning".…”

Section: The Notion Of Adaptive Group Sequential Designsmentioning

confidence: 99%

See 1 more Smart Citation

Targeting the Optimal Design in Randomized Clinical Trials with Binary Outcomes and No Covariate: Theoretical Study

Chambaz

Laan²

2011

The International Journal of Biostatistics

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This article is devoted to the asymptotic study of adaptive group sequential designs in the case of randomized clinical trials (RCTs) with binary treatment, binary outcome and no covariate. By adaptive design, we mean in this setting a RCT design that allows the investigator to dynamically modify its course through data-driven adjustment of the randomization probability based on data accrued so far, without negatively impacting on the statistical integrity of the trial. By adaptive group sequential design, we refer to the fact that group sequential testing methods can be equally well applied on top of adaptive designs. We obtain that, theoretically, the adaptive design converges almost surely to the targeted unknown randomization scheme. In the estimation framework, we obtain that our maximum likelihood estimator of the parameter of interest is a strongly consistent estimator, and it satisfies a central limit theorem. We can estimate its asymptotic variance, which is the same as that it would feature had we known in advance the targeted randomization scheme and independently sampled from it. Consequently, inference can be carried out as if we had resorted to independent and identically distributed (iid) sampling. In the testing framework, we obtain that the multidimensional t-statistic that we would use under iid sampling still converges to the same canonical distribution under adaptive sampling. Consequently, the same group sequential testing can be carried out as if we had resorted to iid sampling.Furthermore, a comprehensive simulation study that we undertake in a companion article validates the theory.A three-sentence take-home message is "Adaptive designs do learn the targeted optimal design and inference, and testing can be carried out under adaptive sampling as they would under the targeted optimal randomization probability iid sampling. In particular, adaptive designs achieve the same efficiency as the fixed oracle design. This is confirmed by a simulation study, at least for moderate or large sample sizes, across a large collection of targeted randomization probabilities.'"

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Section: Strategymentioning

confidence: 81%

Section: The Notion Of Adaptive Group Sequential Designsmentioning

confidence: 99%

Targeting the Optimal Design in Randomized Clinical Trials with Binary Outcomes and No Covariate: Theoretical Study

Chambaz

Laan²

2011

The International Journal of Biostatistics

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“…Examples for the choice of target functions are discussed by Zhang, et al [21] , Rosenberger, et al [13] , Rosenberger, Vidyashankar and Agarwal [14] and Hu and Rosenberger [5] . Recently, Tymofyeyev, Rosenberger and Hu [18] developed a general framework to obtain optimal allocation proportion for K-treatment clinical trials. However, when P(ξ = x) = 0, for example, in the continuous covariate case, the "conditional" allocation proportion N n,k|x /N n (x) is not welldefined because both the numerator and denominator are zeros almost surely.…”

Section: Cara Designs With a Targetmentioning

confidence: 99%

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

Zhang

2009

Appl. Math. J. Chin. Univ.

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It is often important to incorporate covariate information in the design of clinical trials. In literature there are many designs of using stratification and covariate-adaptive randomization to balance certain known covariate. Recently, some covariate-adjusted response-adaptive (CARA) designs have been proposed and their asymptotic properties have been studied (Ann.Statist. 2007). However, these CARA designs usually have high variabilities. In this paper, a new family of covariate-adjusted response-adaptive (CARA) designs is presented. It is shown that the new designs have less variables and therefore are more efficient. §1 Introduction Response-adaptive designs for clinical trials incorporate sequentially accruing response data into future allocation probabilities. A major objective of response-adaptive designs in clinical trials is to minimize the number of patients that is assigned to the inferior treatment to a degree that still generates useful statistical inferences. The preliminary idea of response adaptive randomization can be traced back to Thompson [17] and Robbins [11] . A lot of responseadaptive designs has already been proposed in literature (e.g., Rosenberger and Lachin [12] , Hu and Rosenberger [5] ). Much recent work has focused on proposing better randomized adaptive designs. The three main components for evaluating a response-adaptive design are allocation proportion, efficiency (power), and variability. The issue of efficiency or power was discussed by Hu and Rosenberger [4] , who showed that the efficiency is a decreasing function of the variability induced by the randomization procedure for any given allocation proportion. Hu, Rosenberger and Zhang [6] showed that there is an asymptotic lower bound on the variability of responseadaptive designs. 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.

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“…Biswas and Mandal (2007) provided a three treatment optimal response-adaptive design for binary treatment responses with arbitrary Ψ . In the sequel, for binary responses, Tymofyeyev, Rosenberger, and Hu (2007) derived a multi-treatment analogue of Neyman allocation. However, they failed to provide the optimal proportion for general Ψ .…”

Section: Background and Introductionmentioning

confidence: 99%

Multi-treatment optimal response-adaptive designs for phase III clinical trials

Biswas

Mandal

Bhattacharya

2011

Journal of the Korean Statistical Society

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a b s t r a c tResponse-adaptive designs are used in phase III clinical trials to allocate a larger number of patients to the better treatment. Optimal response-adaptive designs have become popular in recent days for this purpose, where the design is derived from some optimal viewpoints, mostly by optimizing some objective function subject to some constraint(s). However, most of the optimal designs are derived with two treatments and only a few works are available for several treatments. The present paper provides a generalized framework to derive multi-treatment optimal response-adaptive designs. A detailed performance study is provided for three treatment trials minimising failures. The applicability is also judged by redesigning some real clinical trials.

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Implementing Optimal Allocation in Sequential Binary Response Experiments

Cited by 108 publications

References 15 publications

Targeting the Optimal Design in Randomized Clinical Trials with Binary Outcomes and No Covariate: Theoretical Study

Targeting the Optimal Design in Randomized Clinical Trials with Binary Outcomes and No Covariate: Theoretical Study

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

Multi-treatment optimal response-adaptive designs for phase III clinical trials

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