On Selecting Among Treatments with Binomial Outcomes

Buzaianu, Elena M.; Chen, Pinyuen

doi:10.1081/sta-200060706

Cited by 9 publications

(11 citation statements)

References 2 publications

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“…We now apply Lemma 1.2.1 from Buzaianu and Chen (2005) and obtain that, dS dθ k is positive, that is, S(θ ) is increasing with respect to θ k . Thus P(CS|(n i j ), θ) is an increasing function in θ k .…”

Section: As Before For Fixedmentioning

confidence: 95%

“…They used the normal approximation to express their P(CS) and used the normal approximation to show that the LFC of their hybrid procedure is slippage. Buzaianu and Chen (2005) were the first to express the P(CS) of the hybrid procedure in terms of exact Bernoulli random variables and use that exact expression to derive the LFC. This article proposes two Bernoulli selection procedures for two different goals, respectively, in rice inspection applications.…”

Section: Concluding Remarks and Directions For Further Researchmentioning

confidence: 99%

“…, θ k ) that minimizes P (CS) under the corresponding preference zone. Our derivations are exact, making use of the binomial distribution only, and are based on certain results by Buzaianu and Chen (2005).…”

Section: Introductionmentioning

confidence: 99%

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Selection Among Bernoulli Populations with Uniformly Distributed Sample Sizes

Buzaianu

Chen

2014

American Journal of Mathematical and Management Sciences

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SYNOPTIC ABSTRACTIn this article we study the problem of selecting among k independent Bernoulli populations whose success probabilities are unknown, and the sample size for each population is assumed to follow a discrete uniform distribution with known range. We consider two goals and propose procedures for each goal: (1) selecting the best and (2) selecting the best in comparison with a standard. The "best" is defined as that having the highest success probability. We derive the probability of a correct selection and the least favorable configuration for each procedure by using the exact binomial distribution, without any approximation. Simulations and examples are provided to illustrate our procedures.

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Section: As Before For Fixedmentioning

confidence: 95%

Section: Concluding Remarks and Directions For Further Researchmentioning

confidence: 99%

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Selection Among Bernoulli Populations with Uniformly Distributed Sample Sizes

Buzaianu

Chen

2014

American Journal of Mathematical and Management Sciences

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“…In Section 2, we state the non-curtailment procedure proposed by Thall et al (1988) and its refinement from Buzaianu and Chen (2005). In Section 3, we use strong curtailment to define a hybrid selection and testing procedure for Bernoulli populations, having as a reference point Buzaianu and Buzaianu and Chen's (2005) procedure . In Section 4, we show that our curtailment procedure reaches the same probability of a correct selection as the original procedure, uniformly in .…”

Section: Purposementioning

confidence: 99%

A Hybrid Selection and Testing Procedure with Curtailment for Comparative Clinical Trials

Buzaianu

Chen

2009

Sequential Analysis

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In this paper we use the idea of strong curtailment to define a hybrid selection and testing procedure for finding the best among several experimental Bernoulli populations, provided that it is better than a control Bernoulli population. Our curtailment procedure is based on the fixed-sample-size selection and testing procedure proposed by Thall et al. (1988). Our curtailment procedure reaches the same probability of a correct selection as the original procedure, but requires fewer observations.

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“…This paper addresses the problem of selecting the most (or least) integrated population using the Bechhofer type selection procedure (Bechhofer, 1954) that depends on the indifference zone approach. For the latest literature refer to Mulekar and Matejcik (2006), Mukhopadhyay (2005), and Buzaianu and Chen (2005). A brief review of Bechhofer-type procedures is given by Panchapakesan (2005).…”

Section: Introductionmentioning

confidence: 99%

Selection Using Overlap Coefficients

Mulekar

Mishra

2009

American Journal of Mathematical and Management Sciences

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SYNOPTIC ABSTRACTSelection of population with the largest (smallest) amount of overlap is applicable in many socio-economic, ecological as well as geological situations.From the available k(k ~ 2) populations, the goal is to select the population corresponding to the largest (smallest) amount of overlap between two mutually exclusive subgroups of each population. A Bechhofer style selection procedure is proposed, which is carried out based on a random sample of size n taken independently from each subgroup. The relation between the Mahalanobis distance and the overlap coefficient is used to develop the selection procedure required to achieve a pre-specified probability of correct selection. The least favorable configuration and the expressions for the infimum of the probability of correct selection are given under two scenarios, namely (a) the population variances are known and (b) the population variances are unknown. A table of constants is provided for determining the optimal sample sizes needed from each population to meet the specifications. One application of this procedure to the hospitalization data for newborn babies is discussed.

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On Selecting Among Treatments with Binomial Outcomes

Cited by 9 publications

References 2 publications

Selection Among Bernoulli Populations with Uniformly Distributed Sample Sizes

Selection Among Bernoulli Populations with Uniformly Distributed Sample Sizes

A Hybrid Selection and Testing Procedure with Curtailment for Comparative Clinical Trials

Selection Using Overlap Coefficients

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