Estimation after adaptive allocation

Melfi, Vincent; Page, Connie

doi:10.1016/s0378-3758(99)00198-6

Cited by 60 publications

(37 citation statements)

References 11 publications

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“…So, also the intervals I A i , I B i , I C i will be random and they will change for any i ≤ n. This generates two sequences (δ i ) i , (η i ) i instead of two parameters δ, η, since we need to maintain the parameters of the urn model within the corresponding intervals: δ i ∈ I A i and η i ∈ I C i . From Melfi and Page (2000) we have that the adaptive estimators S 2 R (n) and S 2 W (n) are strongly consistent, since the sequences N R (n) and N W (n) increase to infinity almost surely. Moreover, since ρ(·) and n β ( p, ·) are continuous functions, the consistency of S 2 R (n) and S 2 W (n) implies that n β ( p; ρ(i)) a.s. −→ n β ( p) for any p ∈ (0, 1).…”

Section: Different Response Distributionsmentioning

confidence: 95%

“…However, because of this asymptotic behavior, RRU models are not in the class of designs targeting a proportion in (0, 1), that usually is previously fixed or computed to optimize some suitable criteria. Hence, all the asymptotic properties concerning these procedures presented in literature [see for instance Melfi and Page (2000), Melfi et al (2001)], are not straightforwardly fulfilled by the RRU designs.…”

Section: Introductionmentioning

confidence: 99%

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An urn model to construct an efficient test procedure for response adaptive designs

Ghiglietti

Paganoni

2015

Stat Methods Appl

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We study the statistical performance of different tests for comparing the mean effect of two treatments. Given a reference classical test T 0 , we determine which sample size and proportion allocation guarantee to a test T , based on response-adaptive design, to be better than T 0 , in terms of (a) higher power and (b) fewer subjects assigned to the inferior treatment. The adoption of a response-adaptive design to implement the random allocation procedure is necessary to ensure that both (a) and (b) are satisfied. In particular, we propose to use a Modified Randomly Reinforced Urn design and we show how to perform the model parameters selection for the purpose of this paper. Then, the opportunity of relaxing some assumptions on treatment response distributions is presented. Results of simulation studies on the test performance are reported and a real case study is analyzed.

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Section: Different Response Distributionsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

An urn model to construct an efficient test procedure for response adaptive designs

Ghiglietti

Paganoni

2015

Stat Methods Appl

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“…The first lemma can be proved using the same argument as that used to prove Lemma A.4 of [20] (see also [26]). and…”

Section: A1 Proofs Of the First-order Asymptotic Propertiesmentioning

confidence: 99%

Asymptotic Properties of Multicolor Randomly Reinforced Pólya Urns

Zhang

Cheung

et al. 2014

Adv. Appl. Probab.

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The generalized Pólya urn has been extensively studied and is widely applied in many disciplines. An important application of urn models is in the development of randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed, but, although the model has some intuitively desirable properties, it lacks theoretical justification. In this paper we obtain important asymptotic properties for multicolor reinforced urn models. We derive results for the rate of convergence of the number of patients assigned to each treatment under a set of minimum required conditions and provide the distributions of the limits. Furthermore, we study the asymptotic behavior for the nonhomogeneous case.

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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%

“…However, the asymptotic normality holds now in almost all cases. Another special case (see Example 2.3) is the sequential maximum likelihood procedure mentioned by Melfi and Page [9,10] and Melfi et al [11]. In Section 2, we define the new design and give some examples.…”

Section: Introductionmentioning

confidence: 99%

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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Estimation after adaptive allocation

Cited by 60 publications

References 11 publications

An urn model to construct an efficient test procedure for response adaptive designs

An urn model to construct an efficient test procedure for response adaptive designs

Asymptotic Properties of Multicolor Randomly Reinforced Pólya Urns

Asymptotic results on a class of adaptive multi-treatment designs

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