# On an asymptotic optimality property of play-the-winner and vector-at-a-time sampling.

• Volume: 35, Issue: 1, page 92-103
• ISSN: 0041-0241

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## Abstract

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Simon and Weiss (1975) consider the formulation of the clinical trial as a selection procedure (Bechhofer, Kiefer and Sobel, 1968). The object of the trial is to choose the better treatment with probability ≥ P*, where P* is assigned, when the difference in success probabilities is ≥ Δ*, Δ* also being assigned. They consider a family of single step allocation methods for the reduction of the number of patients given the poorer treatment. Using numerical results, Simon and Weiss conclude that if the stopping rule is based on the difference in successes then either alternating allocation or play-the-winner allocation appears to be optimal (Robbins, 1956; Sobel, Weiss, 1970). We make precise the above statement and then in our main theorem prove it to be true for all Δ* sufficiently small and P* → 1.

## How to cite

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Nebenzahl, Elliott. "On an asymptotic optimality property of play-the-winner and vector-at-a-time sampling.." Trabajos de Estadística e Investigación Operativa 35.1 (1984): 92-103. <http://eudml.org/doc/40755>.

@article{Nebenzahl1984,
abstract = {Simon and Weiss (1975) consider the formulation of the clinical trial as a selection procedure (Bechhofer, Kiefer and Sobel, 1968). The object of the trial is to choose the better treatment with probability ≥ P*, where P* is assigned, when the difference in success probabilities is ≥ Δ*, Δ* also being assigned. They consider a family of single step allocation methods for the reduction of the number of patients given the poorer treatment. Using numerical results, Simon and Weiss conclude that if the stopping rule is based on the difference in successes then either alternating allocation or play-the-winner allocation appears to be optimal (Robbins, 1956; Sobel, Weiss, 1970). We make precise the above statement and then in our main theorem prove it to be true for all Δ* sufficiently small and P* → 1.},
author = {Nebenzahl, Elliott},
journal = {Trabajos de Estadística e Investigación Operativa},
keywords = {Ensayo clínico; Métodos de ensayo; Estadística médica; Probabilidades; Optimización; Prueba secuencial truncada; clinical trial; selection procedure; single step allocation methods; alternating allocation; play-the-winner allocation},
language = {eng},
number = {1},
pages = {92-103},
title = {On an asymptotic optimality property of play-the-winner and vector-at-a-time sampling.},
url = {http://eudml.org/doc/40755},
volume = {35},
year = {1984},
}

TY - JOUR
AU - Nebenzahl, Elliott
TI - On an asymptotic optimality property of play-the-winner and vector-at-a-time sampling.
JO - Trabajos de Estadística e Investigación Operativa
PY - 1984
VL - 35
IS - 1
SP - 92
EP - 103
AB - Simon and Weiss (1975) consider the formulation of the clinical trial as a selection procedure (Bechhofer, Kiefer and Sobel, 1968). The object of the trial is to choose the better treatment with probability ≥ P*, where P* is assigned, when the difference in success probabilities is ≥ Δ*, Δ* also being assigned. They consider a family of single step allocation methods for the reduction of the number of patients given the poorer treatment. Using numerical results, Simon and Weiss conclude that if the stopping rule is based on the difference in successes then either alternating allocation or play-the-winner allocation appears to be optimal (Robbins, 1956; Sobel, Weiss, 1970). We make precise the above statement and then in our main theorem prove it to be true for all Δ* sufficiently small and P* → 1.
LA - eng
KW - Ensayo clínico; Métodos de ensayo; Estadística médica; Probabilidades; Optimización; Prueba secuencial truncada; clinical trial; selection procedure; single step allocation methods; alternating allocation; play-the-winner allocation
UR - http://eudml.org/doc/40755
ER -

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