Randomized group up and down experiments

An up and down (U&D) procedure is a sequential experiment used in binary response trials for identifying the treatment corresponding to a prespecified probability of positive response. Recently, a group version of U&D procedures has been proposed whereby at each stage a group of units is tre...

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Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics Vol. 60; no. 1; pp. 45 - 59
Main Authors: Antognini, Alessandro Baldi, Bortot, Paola, Giovagnoli, Alessandra
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.03.2008
Springer Nature B.V
Subjects:
Algorithms
Clinical trials
Economics
Experiments
Finance
Insurance
Management
Markov analysis
Mathematics
Mathematics and Statistics
Probability
Random variables
Random walk theory
Statistics
Statistics for Business
Stochastic models
Studies
Toxicity
Markov chain
Phase I clinical trials
Dose-response problems
Random walk
Stochastic ordering
Sequential experiments
Stationary distribution
ISSN:0020-3157, 1572-9052
Online Access:Get full text
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Summary:An up and down (U&D) procedure is a sequential experiment used in binary response trials for identifying the treatment corresponding to a prespecified probability of positive response. Recently, a group version of U&D procedures has been proposed whereby at each stage a group of units is treated at the same level and the number of observed positive responses determines the treatment assigned to the next group. The deterministic nature of this algorithm leads to some limitations that in this paper we propose to overcome by introducing a randomization mechanism. A broad class of randomized group U&D’s is presented, giving the conditions for targeting the treatment level of interest. In addition, we study how the properties of the design change as we vary the method of randomization within this general class and find randomization schemes which guarantee desirable results in terms of the asymptotic behavior of the experiment.
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ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-006-0081-5