Variability in Adaptive Designs for Estimation of Success Probabilities

Melfi, Vincent; Page, Connie

doi:10.1214/lnms/1215456190

Cited by 28 publications

(33 citation statements)

References 11 publications

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“…3.28 in [20] starting from the result of Th. 3.22 there, we get exactly the same expressions (when a = 1) for E(V V ) and E( V V ) as I,12 and I, 22 ; if we prove (ii) using Corollary 3.16 [20], the results match those in Th. 3.28 [20], however the expressions for these asymptotic covariances are more involved, so we use the version here.…”

Section: Theoremsupporting

confidence: 70%

Optimal adaptive generalized Pólya urn design for multi-arm clinical trials

Yuan

Chai

2008

Journal of Multivariate Analysis

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A class of optimal adaptive multi-arm clinical trial designs is proposed based on an extended generalized Pólya urn (GPU) model. The design is applicable to both the qualitative and quantitative responses and achieves, asymptotically, some pre-specified optimality criterion. Such criterion is specified by a functional of the response distributions and is implemented through the relationship between the design matrix and its first eigenvector. The asymptotic properties of the design are studied using the existing methods on GPU. Some examples for commonly used clinical designs are given as illustration.

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Section: Theoremsupporting

confidence: 70%

Optimal adaptive generalized Pólya urn design for multi-arm clinical trials

Yuan

Chai

2008

Journal of Multivariate Analysis

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“…At the mth stage, no matter what the response of the mth patient is, we assign the (m + 1)th patient to treatment j with probabilityq m−1,ĵ q m−1,1 +q m−1,2 , j = 1, 2. This is the sequential maximum likelihood procedure proposed by Melfi and Page [9,10] and Melfi et al [11]. If 0 < p 1 , p 2 < 1, then…”

Section: Many Maximum Likelihood Estimators and Moment Estimators Satmentioning

confidence: 99%

“…The variability of allocation may have a strong effect on the power. This has been demonstrated by the simulation studies of Melfi and Page [9] as well as Rosenberger et al [12], and Hu and Rosenberger [8]. Due to the unknown distribution and high variability, the designs in which we use urn models become less applicable when the treatments have high cure rates, in sense that it is difficult to test whether or not a design truly assign more patients to better treatments or the design fit the desirable goals.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic results on a class of adaptive multi-treatment designs

Zhang

2006

Journal of Multivariate Analysis

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The play-the-winner (PW) rule is an important method in clinical trials where patients can be assigned to one of the two treatments. In the PW rule, the probability of the next patient to be assigned to a particular treatment only depends on the response of the current patient. In this paper, we consider a general kind of PW rule for multi-treatment adaptive designs, in which the probability that a treatment is assigned to the next patient depends upon both the response of the previous patient and an estimated parameter, e.g., the observed success rate. Using this kind of adaptive designs, more information of previous stages are used to update the model at each stage, and more patients may be assigned to better treatments. The strong consistency and the asymptotic normality are established for the allocation proportions.

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“…The concept applies to both few-stage and fully sequential designs in which optimal 1-stage allocations can be derived as long as certain parameters are specified. (See for example Melfi and Page (1998) and Robbins, Simons and Starr (1967).) The idea is simply to determine the optimal 1-stage allocation using estimators of the unknown parameters, updating the estimators before each new allocation decision is made.…”

Section: -Stage Estimation With Ethical Costmentioning

confidence: 99%

Optimal few-stage designs

Hardwick¹,

Stout²

2002

Journal of Statistical Planning and Inference

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Optimal designs are presented for experiments in which sampling is carried out in stages. There are two Bernoulli populations and it is assumed that the outcomes of the previous stage are available before the sampling design for the next stage is determined. At each stage, the design specifies the number of observations to be taken and the relative proportion to be sampled from each population. Of particular interest are 2-and 3-stage designs.To illustrate that the designs can be used for experiments of useful sample sizes, they are applied to estimation and optimization problems. Results indicate that, for problems of moderate size, published asymptotic analyses do not always represent the true behavior of the optimal stage sizes, and efficiency may be lost if the analytical results are used instead of the true optimal allocation.The exactly optimal few stage designs discussed here are generated computationally, and the examples presented indicate the ease with which this approach can be used to solve problems that present analytical difficulties. The algorithms described are flexible and provide for the accurate representation of important characteristics of the problem.

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Variability in Adaptive Designs for Estimation of Success Probabilities

Cited by 28 publications

References 11 publications

Optimal adaptive generalized Pólya urn design for multi-arm clinical trials

Optimal adaptive generalized Pólya urn design for multi-arm clinical trials

Asymptotic results on a class of adaptive multi-treatment designs

Optimal few-stage designs

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