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Journal ArticleDOI

Sequential nonparametric tests based on randomized play-the-winner rule for restricted bivariate alternatives

01 Jun 1999-Journal of Statistical Planning and Inference (North-Holland)-Vol. 79, Iss: 1, pp 45-57
Abstract: For comparing two treatment effects in a clinical trial under a univariate set-up, a sampling design called randomized play-the-winner (RPW) rule was used by different authors (see, e.g., Wei, 1979 Wei, 1988 ; Wei and Durham, 1978 ). The objective of using such a rule was to allocate more patients to the better treatment. The present work suggests a bivariate version of the RPW rule. The rule is used to propose some sequential-type nonparametric tests for the equivalence of two bivariate treatment effects against a class of restricted alternatives. Some exact and asymptotic results associated with the tests are studied and examined. The limiting proportions of allocations to the two treatments are also obtained.

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Topics: Bivariate analysis (52%)
Citations
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Journal ArticleDOI
William F. Rosenberger1Institutions (1)
TL;DR: This paper traces the historical development of randomized urn models, their applications in sequential design, and research into properties of randomized _urn models and associated designs.

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Abstract: Researchers in sequential design have drawn extensively from the probabilistic literature on randomized urn models. This paper traces the historical development of randomized urn models, their applications in sequential design, and research into properties of randomized urn models and associated designs.

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59 citations


Cites background or methods from "Sequential nonparametric tests base..."

  • ...Coad and Rosenberger (1999) perform a simulation comparison of the randomized play-the-winner rule with fixed sample size and the triangular sequential test with equal allocation....

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  • ...In Bandyopadhyay and Biswas (1999a), they introduce heterogeneity in patient characteristics through a discrete ordinal covariate with levels 0, . . . , G, where G is the most favorable condition....

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  • ...Bandyopadhyay and Biswas (1997, 1999b) employ a decision-theoretic approach to establish a stopping rule and derive exact and asymptotic characteristics of the sequential test procedure....

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  • ...Coad and Rosenberger (1999) perform a simulation comparison of the randomized play-the-winner rule with fixed sample size and the triangular sequential test with equal allocation. Stallard and Rosenberger (2002) compute the exact distribution of a test statistic (using a networking algorithm) when randomized play-the-winner allocation is used in conjunction with a group-sequential monitoring procedure....

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Journal ArticleDOI
Taoufik Zoubeidi1, Mustapha AbaneInstitutions (1)
Abstract: Consider a longitudinal experiment where subjects are allocated to one of two treatment arms and are subjected to repeated measurements over time. Two non-parametric group sequential procedures, based on the Wilcoxon rank sum test and fitted with asymptotically efficient allocation rules, are derived to test the equality of the rates of change over time of the two treatments, when the distribution of responses is unknown. The procedures are designed to allow for early stopping to reject the null hypothesis while allocating less subjects to the inferior treatment. Simulations – based on the normal, the logistic and the exponential distributions – showed that the proposed allocation rules substantially reduce allocations to the inferior treatment, but at the expense of a relatively small increase in the total sample size and a moderate decrease in power as compared to the pairwise allocation rule.

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1 citations


Cites methods from "Sequential nonparametric tests base..."

  • ...In a non-parametric context, Rosenberger [9] and Bandyopadhyay and Biswas [10,11] proposed procedures based on urn models....

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References
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Journal ArticleDOI

1,763 citations


Book
01 Jan 1967-
Abstract: Introduction and Coverage. Preliminaries. Elementary Theory of Rank Tests. Selected Rank Tests. Computation of Null Exact Distributions. Limiting Null Distributions. Limiting Non-Null Distributions. Asymptotic Optimality and Efficiency. Rank Estimates and Asymptotic Linearity.

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1,636 citations


Journal ArticleDOI
M. Zelen1Institutions (1)
TL;DR: Investigation of the conduct of a clinical trial where the “Play the Winner Rule” (PWR) is used to assign patients to the different therapies shows that over a wide range of situations this rule leads to near optimum results when used in a two-stage manner.

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Abstract: Consider a clinical trial to compare two treatments where response is dichotomous and patients enter the trial sequentially. This paper investigates the conduct of such a trial where the “Play the Winner Rule” (PWR) is used to assign patients to the different therapies. The implementation of the PWR in a clinical trial tends to place more patients on the better treatment. Both theoretical and numerical investigations show that over a wide range of situations this rule leads to near optimum results when used in a two-stage manner. Furthermore, these results are insensitive to optimum sample size requirements.

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422 citations


Journal ArticleDOI
Abstract: In comparing $K(\geqslant 2)$ treatments in a medical trial, suppose that the response of the patient to treatment is dichotomous. We propose and analyze a class of simple and nondeterministic treatment assignment schemes which tend to put more patients on better treatments. These schemes are also applicable when we have delayed responses from patients.

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147 citations


Journal ArticleDOI
L. J. Wei1Institutions (1)
01 Sep 1988-Biometrika
Abstract: In comparing two treatments in a clinical trial, the randomized play-the-winner rule tends to assign more study subjects to the better treatment. It is applicable when patients have delayed responses to treatments. It is not deterministic and is less vulnerable to experimental bias than other adaptive designs. In this paper, an efficient algorithm is provided to construct exact permutation tests for testing the equality of the two treatments with the randomized play-the-winner rule. The test procedure is illustrated with a real-life example. The example shows that the design used in the trial should not be ignored in the analysis.

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80 citations


Performance
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No. of citations received by the Paper in previous years
YearCitations
20091
20021